Computational Models of Neural Circuitry in the Macaque Monkey Primary Visual Cortex

Der Technischen Fakultat¨ der Universitat¨ Bielefeld

vorgelegt von

Ute Bauer

zur Erlangung des akademischen Grades Doktor der Naturwissenschaften

Oktober 1998

Acknowledgements

The interdisciplinary scope of this thesis is an example of how the collaboration between experimental and theoretical disciplines contributes to the understanding of the functional structure of the brain. In the first place I want to thank my supervisors Prof. Klaus Obermayer, Prof. Jennifer S. Lund and Prof. Helge Ritter for introducing me to the field of ’Computational Neuro- science’. The work would not have been possible without the generous support of Prof. Jennifer S. Lund and her group, especially Dr. Jonathan B. Levitt, who introduced me to the anatomy and physiology of the macaque primary visual cortex. The close collaboration with these excellent experimenters was one of the major benefits of my work. I am very grateful to Prof. Klaus Obermayer for his guiding and careful advice which was the important foundation of my work. His continuous encouragement gave strong impetus and major benefits for my research. I appreciated the creative support of Prof. Helge Ritter who always had an open mind for my interdisciplinary work done in the Neu- roinformatics research group at the University of Bielefeld headed by him. I would also like to thank Dr. Michael Scholz who introduced me to my project and accompanied my work all the time with helpful discussions and critical comments not only in scientific respects. Since the ’team’ was distributed all over Germany (Bielefeld, Berlin) and Europe (London, U. K.) I am grateful to everyone for the excellent long-distance cooperation. During my work I was member of the Graduiertenkolleg ”Strukturbildungsprozesse” at the Forschungsschwerpunkt Mathematisierung headed by Prof. Andreas Dress and I want to thank him and the other members of the program for providing a pleasant working atmosphere. This work was made possible by a grant of the German Science Foundation. Additional thanks go to Péter Adorján who was a stimulating colleague and many of our discussions have been fruitful for my work. Michael Scholz, Jonathan B. Levitt, Jörg Ontrup and Tim Nattkemper read all or parts of the manuscript and gave me valuable feedback. I want to express very special thanks to Heiko who accompanied my work during the last months with outstanding patience and whose help goes far beyond reading and com- menting on this manuscript. Finally I want to dedicate this work to my grandparents and parents, especially to my grandfather who always supported me on my way.

iii

Abstract

The manuscript in hand is concerned with the functional architecture of the primary visual cortex (visual area V1, striate cortex) of the macaque monkey which serves as an excellent animal model for the human visual system. The first part of the thesis reviews the relevant anatomical and physiological findings. The early stages of visual processing in primates are characterized by two physiologically distinct pathways: the magnocellular (M) channel characterized by large receptive fields and high contrast sensitivity and the parvocellular (P) channel characterized by small receptive fields and low contrast sensitiv-

ity. Both channels originate in the retina and relay via the lateral geniculate nucleus (LGN) to the and subdivision of layer 4C in the primary visual cortex. The physiologically distinct LGN-P and LGN-M inputs to layer 4C are transformed into three partially overlapping output channels shown to emerge from neurons at different depths of the layer. Physiological ﬁndings from more

than one laboratory indicate that receptive field size and achromatic contrast sensitivity of cells in the upper () and lower ( ) half of layer 4C reflect the properties of the LGN-M and LGN-P afferents, however, there is a nonlinear gradient in these properties from top to bottom of the layer. It is the gradient in receptive field size and achromatic contrast sensitivity in depth of layer 4C that should be replicated by the modelling work presented in this thesis. In the second part of the manuscript computational models are developed which address the transformation of the afferent parvo- and magnocellular relays and the local excitatory and inhibitory circuitry of layer 4C. The models are calibrated as far as possible by known anatomical and physiological data. Characteristic to the modelling approach are realistic dendritic and axonal arbor spread and constant synaptic loads used to establish the connectivities between the connectionist model neurons. The first model of LGN input to layer 4C has been used to test the functional hypothesis that feedforward convergence of P and M inputs onto layer 4C spiny stellate cells is sufficient to explain the observed gradual change in receptive field size and contrast sensitivity with rise in depth of the layer. Overlap of dendrites of postsynaptic neurons between M and P input zones proved to be sufficient to explain changes through the lower two-thirds of layer 4C, while the more rapid change in upper 4C was matched by proposing two different M inputs with

partial overlap in the upper 4C. The second model of local intralaminar circuitry of layer 4C has been used to test the functional hypothesis that differences in the overall balance between recurrent excitation and lateral inhibition from two different neuron types cause the rapid increase of

receptive ﬁeld size and contrast sensitivity in upper 4C. The numerical simulations show that the lateral excitatory inputs which are known to come from an increasingly wider range within the retinotopic map with rise in depth of the layer have to become substantially more effective towards

the top of the layer to account for the increased receptive ﬁeld size in upper 4C. The lateral so-

matic inhibition which also arises from a wider range in upper 4C has to have a higher threshold and gain to result in a rapid increase of contrast sensitivity at the top of the layer. Both hypotheses are consistent with the available anatomical and physiological data. Based on the numerical simulation results, new experimental tests are proposed which may conﬁrm, refute, or distinguish between the different functional hypotheses. The numerical simulation of brain functions known as ”Computational Neuroscience” plays an increasingly important role in revealing the basic principles of neural information processing. This thesis is a ﬁrst step to systematically develop a ”transfer function” of layer 4C in the macaque striate cortex.

Contents

Acknowledgements i

Abstract iii

Table of Contents 1

1 Introduction 5 1.1 ScopeandGoals ...... 5 1.2 PlanoftheManuscript ...... 7

2 Neurobiological Background 9 2.1 Principles of Neural Information Processing ...... 9 2.2 SingleNeuronModels ...... 13 2.3 The Visual System of Primates: An Overview ...... 18 2.4 Early Stages of Visual Information Processing ...... 25 2.4.1 TheRetina ...... 25 2.4.2 The Lateral Geniculate Nucleus ...... 29 2.4.3 ThePrimaryVisualCortex ...... 33 2.5 Summary ...... 41

3 The Depth-Dependence of Basic Response Properties of Cells in Layer 4C 43 3.1 Afferent and Efferent Connections of Layer 4C ...... 43 3.2 Functional Gradient in Depth of Layer 4C ...... 45 3.2.1 Physiological Properties of LGN-P and LGN-M Cells ...... 45 3.2.2 Basic Response Properties of Cells in Layer 4C ...... 49 3.3 Summary ...... 52

4 Anatomical and Physiological Findings: Thalamic Feedforward Connections 53 4.1 Overview of Relevant Anatomical Findings ...... 53 4.1.1 ThalamicAxons ...... 53 4.1.2 Local Spiny Stellate Cells ...... 56 4.2 Overview of Relevant Physiological Findings ...... 57 4.2.1 Three Functional Groups of LGN Cells ...... 58 4.2.2 Response Latencies of Cells in Layer 4C ...... 60 4.3 Extrapolations from Comparison of Anatomical and Physiological Findings . . . 60 2 CONTENTS

5 A Feedforward Model for the Depth-Dependence of Basic Response Properties in Layer 4C 63 5.1 Anatomical and Physiological Parameters ...... 63 5.1.1 Anatomical Parameters ...... 64 5.1.2 Physiological Parameters of LGN cells ...... 66 5.1.3 Overview of the Parameter Space ...... 68 5.2 Methods...... 70 5.2.1 Neural Network Architecture ...... 70 5.2.2 Connectionist Model Neuron ...... 72 5.2.3 VisualStimulation ...... 72 5.2.4 LGNNeurons...... 74 5.2.5 CorticalNeurons ...... 77 5.2.6 Implementation...... 82

6 Results of the Feedforward Model 83 6.1 Results Model I: One LGN-M population ...... 83 6.1.1 Percentage of P- vs. M-inputs as a Function of Depth ...... 84 6.1.2 Threshold Dependence of Response Properties ...... 85 6.1.3 Transfer Functions of Geniculate P-cells ...... 86 6.1.4 Dendritic Arbor Size of Layer 4C Spiny Stellate Neurons...... 88 6.1.5 BestPredictions ...... 89 6.1.6 Summary ...... 90 6.2 Results Model II: Two LGN-M populations ...... 91 6.2.1 Physiological Properties of M2 and M1 Subpopulations ...... 91 6.2.2 Percentage of M1- vs. M2-inputs as a Function of Depth ...... 95 6.2.3 Effects of Receptive Field Size of M2 and M1 Neurons ...... 96 6.2.4 Effects of Contrast Sensitivity of M2 and M1 Neurons ...... 97 6.2.5 BestPredictions ...... 98 6.2.6 Summary ...... 99 6.3 Discussion...... 101

7 Anatomical and Physiological Findings: Intracortical Lateral Connections 107 7.1 Overview of Relevant Anatomical Findings ...... 107 7.1.1 Lateral Connections of Spiny Stellate Cells ...... 110 7.1.2 Strategy of Local Inhibition ...... 112 7.2 Overview of Relevant Physiological Findings ...... 113 7.2.1 The Functional Role of Recurrent Excitation and Inhibition ...... 113 7.2.2 Intrinsic Physiological Properties of Inhibitory and Excitatory Cells . . . 114 7.2.3 Spatial Summation Properties of Cells in Layer 4C ...... 115 7.3 Extrapolation from Anatomical and Physiological Findings...... 118

8 An Intracortical Model for the Depth-Dependence of Basic Response Properties in Layer 4C 119 8.1 Anatomical and Physiological Parameters ...... 120 8.1.1 Anatomical Parameters ...... 120 8.1.2 Physiological Parameters ...... 122 8.2 Methods...... 125 CONTENTS 3

8.2.1 Neural Network Architecture ...... 125 8.2.2 Connectionist Model Neuron ...... 125 8.2.3 VisualStimulation ...... 127 8.2.4 LGNNeurons...... 127 8.2.5 TheCorticalLayers...... 129 8.2.6 Implementation...... 136

9 Results of the Intracortical Model 139 9.1 Results Model I: One LGN-M population ...... 139 9.1.1 Efﬁcacy of the Lateral Stepped Connections ...... 139 9.1.2 Physiological Properties of Inhibitors: Parameter Regimes ...... 141

9.1.3 Intrinsic Physiological Properties of the -6 Neuron ...... 144 9.1.4 Geniculocortical and Intracortical Contributions ...... 145 9.1.5 Contrast- and Threshold-Dependence of Response Properties ...... 146 9.1.6 BestPredictions ...... 147 9.1.7 Summary ...... 148 9.2 Results Model II: Two LGN-M populations ...... 149 9.2.1 General Remarks and Results ...... 149 9.2.2 Efﬁcacy of the Lateral Stepped Connections ...... 153

9.2.3 Intrinsic Physiological Properties of the -6 Neuron ...... 154 9.2.4 Effects of Physiological Properties of M2 and M1 Cells ...... 155 9.2.5 Geniculocortical and Intracortical Contributions ...... 156 9.2.6 BestPredictions ...... 157 9.2.7 Summary ...... 159 9.3 Discussion...... 160

10 Conclusions and Outlook 167

A The Feedforward Model 173 A.1 The Parameter-Interface of the Simulation Tool ...... 173 A.2 Results for the Data Set of Spear et al...... 178 A.2.1 Results Model I: One LGN-M population ...... 178 A.2.2 Results Model II: Two LGN-M populations ...... 181 A.3 Statistical Signiﬁcance of Best Predictions ...... 185

B The Intracortical Model 189 B.1 The Graphical User Interface of the Simulation Tool ...... 189 B.1.1 ParameterWindows ...... 189 B.1.2 Online Visualization ...... 192 B.2 TheStochasticUpdate ...... 195 B.3 Intracortical Model II: Summary of Results ...... 197

Bibliography 203 4 CONTENTS Chapter 1

Introduction

1.1 Scope and Goals

One of the most fascinating structures in biology is the brain of mammals which enables them to interact with their environment in many sophisticated ways. The basis of all kinds of neural information processing is the incredibly large number of single nerve cells which form a network of enormous computational capacity. Despite the simplicity of the basic units the complexity of behaviour is achieved by concerted signalling of the enormous number of neurons that are functionally grouped together. Specific tasks e.g. visual perception or motor control are localized in different areas of the brain which are interconnected by many neural pathways. Although a great deal is known about the principle task of many subcortical and cortical areas and the functional principles of the single nerve cell, surprisingly less is known about the functional logic of cortical microcircuits. The cortical microcircuits which are restricted assemblies of interconnected neurons constitute the elementary functional units of the cerebral cortex. Thus, to understand the processing strategy of the cortex, it is of great importance to understand the algorithmic principles of the cortical microcircuits. Macaque monkeys are frequently used as a model system to study the primate cerebral cortex. If brain volume dedicated to a specific task is by any means related to the importance and difficulty of the problem it has to deal with, then by far the biggest problem primates have is interpreting their visual world. Although the visual cortex seems to be one of the most complex sensory systems, models of visual information processing have always been a prominent field of research in neuroscience. The pioneering work of Hubel and Wiesel in the early 1960s was followed by a proliferation of investigation, and new pictures began to emerge about the organisation of the primary visual cortex. New ideas about the anatomical structure, perceptual theory, psychophysical mechanisms and nerve network interactions came up within the following decades. Most central to these ideas were physiological studies of receptive field structure and the origins of stimulus selectivities. Today there exist huge amounts of experimental data and a dramatic number of models have been published which try to explain these data. One of the most serious problems neuroscience has to face today is that there is no unifying systematical approach and there exist discrepancies between experimental data from different laboratories and, as a consequence, between the corresponding models. Experimental neuroscience tries to approach the visual system by more and more sophisticated experiments, but there exist methodological problems and limitations. While neuroanatomists are concerned with neural composition, connectivity structure and morphological identification of 6 Introduction

cortical nervous tissue, neurophysiologists try to record extra- and intracellular signals from single nerve cells. Because functional hypotheses get increasingly complex and the experimental eval- uation is in many cases difficult or impossible, the field of computational neuroscience becomes more and more important in revealing the principles of neural information processing systems. The focus of this thesis is to develop neural network models of functional microcircuits of the macaque monkey primary visual cortex. The aim of the modelling work is to develop and test functional hypotheses about cortical circuits where details of the actual circuitry are difficult to explore experimentally. Therefore the models are to be constrained as far as possible by real anatomical and physiological data, and are designed to help us understand the functional architecture of the region. There is a wealth of detailed anatomical knowledge, available from the literature, that addresses the neuronal circuitry of area V1 in the macaque monkey (for reviews, see Peters & Rockland, 1994; Levitt et al., 1996); there is also a large body of physiological studies on the same region which helps to assign reasonable response properties to the model neurons. There has been a great deal of interest in exploring how cortical orientation and direction selectivity could arise from direct thalamic fiber convergence (reviewed by Das, 1996), but the emergence of more basic response properties – like receptive field size and achromatic contrast sensitivity – on which other response properties depend have been surprisingly little investigated. This thesis is a first attempt to fill this gap. The models presented here wish to determine how the basic response properties of layer 4C – the primary input zone of thalamic fibres into area V1– are generated. More specifically I will address the following questions:

To what degree can the basic response properties of the thalamic recipient spiny stellate neurons of layer 4C be explained on the basis of convergent feedforward excitation from the lateral geniculate nucleus?

How do the intracortical recurrent connections of excitatory and inhibitory neurons inside layer 4C affect the basic response properties of cells in the layer?

This knowledge about the generation of basic response properties can be used as a sound base to address realistic neural circuitry for generating other prominent response properties of cortical neurons. The ﬁrst step towards an adequate model of visual information processing in the primary visual cortex is to determine the function which is carried out by a subsystem. The subsystem in turn will require certain properties of local circuits and single cells within it. For each of these hypothesized functions, there may be several different mechanisms by which they can be achieved. Thus for each functional hypothesis there will be several models which have to be tested and only a small number of these models will be able to provide plausible explanations. According to Rose (1985) a canonical procedure to be carried out for building and testing models under a functional hypothesis is as follows:

1. Identify and specify all the aspects of the system which are considered essential or in some degree relevant to its function and make explicit, which of the system parameters are most important and critical.

2. Simplify the representation of each parameter by reducing the number of possible values to a minimum of discrete states, i.e. extreme or opposite conditions. This step helps to reduce the parameter space and enables subsequent testing to discover the best model as rapidly as possible. 1.2 Plan of the Manuscript 7

3. Combine all the relevant parameter states so that principle models are formed and considered in the analysis.

4. Test and asses the different models according to pre-speciﬁed criteria e.g. simplicity, com- pleteness and predictions compared to experimental evidence. Each test should be designed to decide between two alternative states and reduce uncertainty by identifying the most sig- niﬁcant model parameters.

5. Subsequently models can be ranked according to the plausibility of parameter state and empirical evidence can help to distinguish between different hypothesis or parameters states.

6. If the general classes of model which work best have been identiﬁed then for each class of models (and for each parameter) the possibility can be explored if intermediate cases may exist along a continuum between the extremes.

Thus the testing of different functional models generally involves the use of reasoning and argu- ment, mathematics, computer simulation, and experiments, but no single method can provide an absolute deﬁnitive solution.

1.2 Plan of the Manuscript

In my thesis I attempt to demonstrate how functional hypotheses of the macaque primary visual cortex can be tested via computational models which help to understand the functional architecture of the region. The modelling process requires several canonical steps. First of all the biological background and all relevant experimental findings have to be reviewed and the functional hypothesis has to be formulated. In a second step the important anatomical and physiological findings have to be transformed into an adequate mathematical description which is subsequently implemented on a computer system. Since the goal of the theoretical modelling work is to explore functional aspects that can not be tested experimentally it is important to explore the model parameters which are not constrained by experimental findings in order to refute or confirm the hypothesis. Ideally the parameter explorations lead to theoretical predictions which are in good agreement with the available anatomical and physiological data. More important, however, is to suggest new experimental tests which either confirm or refute the functional hypothesis. After a short outline of scope and goals in the first chapter, the second chapter provides the neurobiological background of the macaque visual system. I will briefly describe the relevant properties of single nerve cells and review the most common neuron models which range from very abstract to highly complex descriptions of the single nerve cell. This is followed by an overview of the primate visual system and a more detailed review of the early stages of visual information processing which captures the anatomical, physiological and functional organisation of the retino-cortical pathway and the primary visual cortex. The third chapter focuses on the afferent and efferent relays and the physiological organisation of layer 4C of the primary visual cortex. The aim is to motivate and formulate the basic questions which are addressed by the modelling work. Since layer 4C is known as the principle thalamic input zone, the re-organisation of the afferent parvocellular (P) and magnocellular (M) information channels assumes a particular significance. Therefore the second part of the chapter summarizes the physiological properties of the parvocellular and magnocellular information channels and provides the physiological evidence for the depth-dependence of the basic response 8 Introduction

properties in layer 4C. It is the functional gradient of basic response properties in depth of the layer – across the anatomically segregated termination zones of the subcortical information channels – that I am seeking to replicate by the modelling work. Chapter 4 provides the detailed anatomical organisation of the geniculocortical projections. The second part of the chapter summarizes the relevant physiological data which is available for the existence of physiological distinct LGN-M groups. The extrapolation of the anatomical and physiological findings results in the formulation of the feedforward hypothesis which address the geniculocortical information transfer. The mathematical model which is used to test the feedforward hypothesis for the depth-dependence of the basic response properties in layer 4C is summarized in Chapter 5. The first part of the chapter provides an overview of anatomical and physiological parameters which are used to constrain the model. The detailed network architecture, the mathematical description of the model neurons and the algorithms which were used to establish realistic connectivity and reasonable transfer functions for the model neurons are provided in the second part of the chapter. Chapter 6 presents the simulation results of the feedforward model. In order to test how realistic geniculocortical information transfer can account for the pattern of basic response properties in depth of layer 4C, I explore the parameter space of the model. The numerical simulation results and the model predictions are followed by a discussion of the likelihood of the feedforward circuitry in the context of anatomical and physiological evidence and new experiments will be suggested that confirm or refute the predictions of the feedforward model. Since it is important to ask if other, or additional, factors may contribute to the gradual change of basic response properties in depth of layer 4C, Chapter 7 reviews the relevant anatomical organisation of local excitatory connections and inhibitory circuitry of the region and the physiological findings which is available on the role of recurrent feedback in layer 4C. The extrapolation of the anatomical and physiological result in the formulation of an alternative intracortical hypothesis which is based on changes in lateral excitation and inhibition in layer 4C. The mathematical model which is used to test the intracortical hypothesis for the depth-dependence of the basic response properties in layer 4C is described in Chapter 8. Again the first part summarizes the anatomical and physiological date used to constrain the model parameters. The network architecture, the mathematical formulation of the model neurons, and the algorithms which are used to establish realistic connectivity, reasonable transfer functions, and recurrent network dynamics are described in the second part. Chapter 9 presents the simulation results of the intracortical modelling. The parameters of the model which cannot be derived from the experimental data have been explored by numerical simulations. The systematic exploration of the parameter space is followed by a discussion of the likelihood of the intracortical versus the thalamic feedforward circuitry and suggestions are made for new experiments that may confirm, refute or distinguish between the different hypotheses. The concluding Chapter 10 discusses the general results of the work which is presented in this thesis and gives an outlook for future modelling directions. Chapter 2

Neurobiological Background

This chapter provides the general biological background of the modelling work presented later on in the manuscript. The first section summarizes important properties of single nerve cells and introduces the basic anatomical and physiological definitions which are used throughout the manuscript. The biological description of the nerve cell is followed by a brief review of the most common mathematical neuron models. Because it is impossible to describe the functional architecture of the primary visual cortex without discussing its relationship to other visual areas of the cortex, a short overview of the primate visual system is given before subcortical and cortical organisation is described in more detail. The functional hypotheses which are considered in my thesis address the early convergence of two major subcortical information channels in the visual pathway. Since the anatomical and physiological segregation into magno- (M) and parvocellular (P) information channels is unique to the primate visual system, a great deal of the literature concentrates on the functional role and interaction of the subcortical information channels within subsequent cortical processing stages. Part of the section is therefore devoted to a review of the most prominent view points of visual perception in respect to magno- and parvocellular information channels. The second part of the chapter summarizes the early stages of visual information processing. I concentrate in more detail on the preprocessing of the retinal image, the properties of the magno- and parvocellular cell systems, and the organisation of the lateral geniculate nucleus which is known as the thalamic relay station of the visual system. The last part of the chapter deals with the first cortical processing stages. The entry of thalamic information channels, the anatomical organisation and the most prominent response properties of neurons in the primary visual cortex are briefly discussed in the context of columnar organisation and functional architecture of the region.

2.1 Principles of Neural Information Processing

The basic functional element of the nervous system is the nerve cell or neuron. In the mammalian brain many millions of these neurons are connected to form neural network of considerable complexity. To consider some of the basic principles of neural information processing it is convenient to use the highly schematic model of a vertebrate nerve cell shown in Figure 2.1. The cell body or soma is by deﬁnition the part of the neuron that contains the nucleus. Different types of processes arises from the cell body. The axon hillock is that part of the neuron from which the axon arise and the long single nerve process that extends from the axon hillock is deﬁned as the axon. If the axon becomes myelinated the axon initial segment (AIS) is the unmyelinated part 10 Neurobiological Background

Terminals

Axon hillock and Axonal branches initial segment (AIS) Axon

Synaptic Presynaptic vesicles terminal Synapse Soma Synaptic Cleft

Postsynaptic membran

Dendrites

Figure 2.1: A schematic model of a typical (multipolar) vertebrate neuron. The neuron consists of three compartments: axon, soma, and the dendrites. Neurons in the central nervous system (CNS) are usually connected via chemical synapses. For details see text.

at the beginning of the axon just beyond the axon hillock. Axons characteristically have branches that distribute the signals travelling in them to more than to one destination. During a long distant course, axons may give off relatively large branches so-called collaterals which may be either lateral or recurrent if they turn backwards. After dividing into smaller branches, the axon ends in terminals1 which contact the postsynaptic cells. Dendrites are generally deﬁned as a process which does not originate from the axon hillock. Each dendrite has an initial stout trunk which splits into branches deﬁning a tree-like structure. In the central nervous system (CNS) the transmission of information between an axon terminal and the postsynaptic cell typically occurs via chemical synapses. A transmitter substance accumulated in the synaptic vesicles is released into the synaptic cleft (Fig. 2.1). The release of transmitter results in a conductance change of the postsynaptic membrane directly under the axon terminal (Fig. 2.2a). If the change in membrane conductance causes a depolarization of the membrane potential, the synaptic response is termed excitatory postsynaptic potential (EPSP). If the change in membrane conductance results in a hyperpolarization of the postsynaptic membrane, the response of the synapse is called inhibitory postsynaptic potential (IPSP). The strength of a single EPSP and IPSP depends on the amount of transmitter substance released at the presynaptic site and the effects of the transmitter release on the postsynaptic membrane. A good indication for the postsynaptic effect is the type of the synapse. There are two common types of chemical synapses in the central nervous system: type I2 or asymmetric synapses which are usually excitatory and type II or symmetric synapses which are usually inhibitory. 3 Two prominent transmitter substances in the vertebrate nervous system are frequently associated with

1also called boutons,buttons, or end-feet 2 also called Gray type I and II 3The morphological type of a synapse is identiﬁed in the ultrastructure (electron microscopy level) by several criteria, e.g. the accumulation of dense material either next to the postsynaptic membrane (asymmetric) or symmetrically on both pre- and postsynaptic sides. 2.1 Principles of Neural Information Processing 11

a) Axon

V [mv] EPSP Spike generation zone b) (AIS) V V [mv] rest V IPSP treshold

Synapse V 0 10 rest t [msec]

0 2 t [sec]

Figure 2.2: Typical response recorded at different sites of the neuron: a) postsynaptic membrane, b) AIS, and c) axon. (a) Transmitter release in the presynaptic terminal results in a hyperpolarization (IPSP) or depolarization of the postsynaptic membrane (EPSP). The time course of the EPSP and IPSP depends on the time constant of the postsynaptic membrane. (b) EPSPs and IPSPs travel through the dendrite and integrate at the AIS. Spatial and temporal summation of excitatory and inhibitory inputs result in ﬂuctuations of the membrane potential at the AIS. Each time the membrane potential exceeds a certain threshold a spike is generated. (c) The regenerative spikes travel in the axon over a long distance; the individual spike train can be recorded at each point of the axon.

type I and type II synapse. GABA (Gamma-amino-butyric acid) which is an inhibitory transmitter and Glutamate which is an excitatory transmitter. Neurons releasing GABA and Glutamate are called GABAergic and glutaminergic, respectively. It is largely the interaction of excitatory and inhibitory synaptic input which determines the output of the neuron. The competing inputs accumulate in the postsynaptic neuron by a process called neural integration. The EPSPs and IPSPs from different parts of the neuron spread passively through the dendrites and the soma, where they finally arrive at the common integration or spike generation zone of the AIS. Because the dendritic membrane has certain time and length constants the signals progressively decrease while travelling through the neuron. The complex tree-like structure of the dendrites with its different sites of synaptic input results in a spatial and temporal summation4 of EPSPs and IPSPs. This leads to a membrane potential at the initial trigger zone which fluctuates over time and reflects the integrated synaptic input to the neuron (Fig. 2.2b). If the membrane potential at the integrative component has reached a certain threshold the neuron starts to produce single events, so-called spikes or action potentials, which are carried by an active, regenerative process over a long distance along the axon to the terminals where they finally cause a transmitter release (Fig. 2.2c). The action potentials are all-or-none events almost indistinguishable from each other. Thus the information accumulated in the gradual changes of the membrane potential is transformed into a so-called spike train. The information is not coded by the magnitude or duration of the single spike, but the frequency or rate at which events occur5.

4not necessary linear in nature 5However, there are alternative view points; one is that information is not coded by rate, but additional structure in the interspike intervals 12 Neurobiological Background

Axon

Axon initial segment (AIS) axo-axonic

Soma axosomatic

Dendritic Shaft + + axodendritic + - - - Spine + a) Dendrite b)

Figure 2.3: (a) Synaptic contacts can occur on all three regions of the cell body. Therefore synapses are categorized as axodendritic, axosomatic and axo-axonic. Axodendritic synapses are either made on the main shaft of a dendritic branch or on spines which represent distinct bio- chemical compartments of the dendrite. For details see text. (b) Some key principles of neural connectivity. Top: Divergence (left) of information ﬂow occurs if a single neuron branches many times and terminates on many target cells. Neuronal convergence (right) allows a target cell to integrate diverse information from many sources. Bottom: Possible connections between excitatory and inhibitory neurons. If an excitatory or inhibitory neuron connects to a neuron which does not feed back to the source cell, one speaks of feed-forward excitation or inhibition respectively (left and right). If an excitatory cell contacts an inhibitory or excitatory cell which in turn feeds back into the source neuron it is called feedback inhibition or excitation respectively (left). If an inhibitory cell contacts an inhibitory cell which in turn feeds into a target neuron the effect is called disinhibition (right), because the source cell becomes excited.

The relative contribution of the input at an individual excitatory or inhibitory synapse depends on several factors e.g. location, size, type, and the proximity of other synergistic or antagonistic synapses. In particular, the location of a synapse has a great inﬂuence on the outcome at the trigger zone. Figure 2.3a summarizes the most common types of contacts with respect to their location on the neuron. In principle there exist three regions of the cell which can be receptive sites for a synaptic contact: the axon, the dendrite and the soma. Therefore synapses are categorized as axodendritic, axosomatic and axo-axonic synapses. Each dendritic branch in turn has two major sites for synaptic input: the spine and the main shaft6. The spine is a highly specialized input zone which receives at least one synapse on its surface. The synapses made on spines and dendritic shafts are frequently excitatory (type I) (Kandel & Schwartz, 1991). By contrast, most synapses on the soma or the axon initial segment are inhibitory (type II) synapses (Kandel & Schwartz, 1991). The location of inhibitory and excitatory synapses plays a critical role for their functional effectiveness. Excitatory input from the dendrites must pass through the soma as it moves to the

6For smooth neurons which lack spines the major site are the dendritic shafts. 2.2 Single Neuron Models 13

AIS. Simultaneous inhibition on the cell body or on the AIS (even more effective) by shunting will reduce much of the depolarization provided by distal excitatory inputs. Thus the proximity of a synapse to the trigger zone of the postsynaptic cell is obviously important in determining the effectiveness of a synapse and it is a general rule, that important inhibitory input often occurs on the cell body, while the major site of excitation and selective inhibitory inputs are on dendritic shafts and spines. There are a few general aspects of neural information processing which should be emphasized. The nervous system of higher vertebrates is made up of atomic nerve cells, which integrate the EPSPs and IPSPs in space and time. The majority of nerve cells uses electrical impulses to carry information often over a considerable distance to many other neurons. Therefore, the structure in the connectivity patterns, i.e. selective presynaptic inputs and postsynaptic targets, are an important foundation for the almost unlimited richness and reliability of function within the central nervous system. One key strategy in the nervous system is subdivision and localization of function. This is accomplished by two key principles of neural connectivity, divergence and convergence, illustrated in Figure 2.3b. A good example for neuronal divergence are afferent neurons7 which provide input to many subcortical and cortical areas. An example for convergence in the nervous system are neurons of different afferent pathways which provide input to the same cortical region. Although different in nature, convergence and divergence exist in parallel in almost all neural networks. Another important point is that nerve cells do not connect indiscriminately to one another to form a random network. Rather each cell makes speciﬁc connections at precise points of synaptic contacts with some postsynaptic target cells but not with other. Moreover, many neurons in the central nervous system are so-called local interneurons which receive and also make contacts only with neurons in a close neighbourhood. If one further considers that the microcircuits are build of excitatory and inhibitory neurons, a considerable complex behaviour can result from only a few elements (compare Fig. 2.3b). All the connectivity schemes which are shown in Figure 2.3b are mono- and disynaptic 8. The connectivity structure becomes even more complicated for multisynaptic connections with speciﬁc connections. The goal of computational neuroscience is to help understanding the organisation principles of biological neural networks at different levels of detail and time scales. For example the aim of functional models on the network level is to reveal the nature of convergence and divergence which are present almost everywhere in the nervous system as well as to explore the principles of the local connectivity structure in small neural circuits which are the elementary building blocks of the whole network called brain. To approach these questions it is necessary to account for anatomical details such as sites of synaptic inputs, neural composition, postsynaptic targets, and shape of processes9.

2.2 Single Neuron Models

While the last section has summarized the neurobiological basis of a single nerve cell, this section brieﬂy summarizes the most prominent mathematical descriptions of a neuron. The different classes of models can be distinguished by their level of description ranging from rather simple to

7The term afferent (carried toward the nervous system) applies to all information reaching the central nervous system from the periphery. Afferent neurons carry sensory information to the central nervous system. 8Information ﬂow occurs within one or two synapses 9e.g. spread of dendritic and axonal ﬁelds 14 Neurobiological Background

more realistic and highly complex models of a single nerve cell. It is important to emphasize that the more realistic models require detailed knowledge about the biophysical properties of a neuron while becoming compuational very expensive. To develope functional models of brain functions it is important to choose an adequate neuron model.

The Continuous-valued McCulloch-Pitts Neuron McCulloch & W.Pitts (1943) proposed a simple model of a neuron – a binary threshold unit.

This class of model neurons computes a weighted sum of its inputs I from other neurons. The output of the neuron is either binary e.g. one or zero, indicating whether the neuron is ﬁring or not. Since many neurons are often not even approximately threshold devices, the original model has been generalized to respond in a continuous or graded way (Figure 2.4a). In mathematical

terms the continuous-valued neuron can be formulated in the following way:

w I t O t f j

ij (2.1)

j w

The weight ij represents the strength of the synapse connecting a presynaptic neuron j and the

postsynaptic neuron i. The weights can be positive or negative corresponding to an excitatory or w

inhibitory synapse respectively. If ij is zero there exist no synapses between neuron i and j. The

nonlinear function f is called the activation, gain or simply transfer function of the neuron. O

The continuous output i is called the activation or state of the neuron and can be interpreted as

the cell’s average spike rate. Time t is taken discrete with one time step elapsing per processing step. Although this simple neuron model omits many complications of the real neurons it is computationally a powerful device and it still serves as a mathematical models for exploring the dynamical behaviour of very large interconnected neural networks.

The Integrate-and-Fire Neuron This type of model employs a simple mechanism of spike generation and dendritic integration. In particular the focus is on the nonlinear dynamics of the membrane potential which is continuous in time. The model, however, does not account for the precise form of the action potentials and the

axonal transmission process. The integrate-and-ﬁre model can be interpreted as a simple electric R

circuit consisting of a capacity C that is parallel to a resistance (Figure 2.4b). The capacity

I V

is charged by a current which may be the sum of all postsynaptic currents and the voltage m

changes according to

V dV

m m

C (2.2)

dt R C

If the membrane potential m has reached a certain threshold , an action potential is generated. Although the integrate-and-ﬁre model is more realistic in terms of synaptic integration in time and spike generation, it is rather phenomenologic and does not account for realistic channel based biophysical aspects. The integrate-and-ﬁre model is an approximation of the channel-based Hodgkin-Huxley model in the limit case that the membrane loading time is the dominant time scale of the neural dynamics. Therefore it is a good compromise if large scale neural networks of spiking neurons have to be 2.2 Single Neuron Models 15

j V R C w m ij F(x)

a) b)

Figure 2.4: (a) Schematic diagram of a simple continuous-valued connectionist neuron. The neuron integrates the synaptic inputs by summing up the weighted synaptic input which is subsequently mapped be a continuous-valued transfer function to the cell’s output firing rate. (b) The integrate-and fire model is based on the electrical circuit model of a small patch of passive membrane. The resistor represents the conductivity of the transmembrane channels through which specific ion currents flow across the membrane. The capacitor correspond to the membrane which lacks ion channels and which separates the charges on each side of the model.

simulated and details about biophysical parameters are rare (e.g. Somers et al., 1995).

The Hodgkin-Huxley Model The ﬁrst quantitative channel-based description of neural spiking goes back to Hodgkin &

Huxley (1952) who introduced the following ansatz:

3 4

I g m hV V g n V V g V V C

m N a K m K L m L

N a (2.3)

V m V m

m m m m

V n V n

n m n m

V h V h

m m

h h

V m n h

The set of four differential equations in the variables m , , and describes the conservation

C V

of an electric charge on a piece of membrane of capacity under the inﬂuence of a voltage m ,

the external driving current I and the sum of ionic currents through the channels of the cell membrane. The channels are two voltage-and-time-dependent ion channels (sodium and potassium)

and a passive ”leakage” channel. The parameters of the ion channels are given by the experi-

g g g V V V

K L N a K L

mentally observed conductances N a , , and and the equilibrium potential , and

respectively. The ’s and ’s are functions of m which are essential to characterize the dynamical behaviour of the system of differential equations. For biologists this class of models is particular attractive because it is based on directly measur- able biophysical entities. By systematically varying the many model parameters one can predict 16 Neurobiological Background

Figure 2.5: In a compartmental model the spatial structure of the dendritic tree is discretized into a set of simple R-C compartments i.e. an isopotential patch of membrane (Figure 2.5b) and the compartments are connected via axial cytoplasmatic membrane (after Segev, 1992).

the possible repertoire of electrical activity of a neuron having a particular array of channels. Though certain phenomena e.g. exact time course of a single spike can be understood on physical grounds by channel based modelling approaches they are computationally quite demanding due to the numerical complexity of the model and complicated for mathematical analysis. Therefore this type of models which is rich in biophysical meaningful parameters is useful for the simulation of relatively small cell ensembles (e.g. Rinzel et al., 1998).

Cable Theory and Compartmental Models The models described so far are morpho-less because they neglect the morphological details and physiological signiﬁcance of the dendrites. In other words, they do not consider how the different synaptic inputs are integrated in a complex dendritic tree. In the 1950’s Rall developed an approach to study the physiological signiﬁcance of dendritic

trees. The continuous cable equation is a second order partial differential equation for a passively

V t x

spreading voltage m in time at location . The partial differential equation can be solved with boundary conditions imposed by an morphological complex dendritic tree. One can analytically compute the voltage response at any point in a tree to a current injected at any other point. Thus the time-course and the amplitude of the EPSPs and IPSPs can be estimated at any location in a putatively passive dendritic tree. In a cable model the dendritic tree is decomposed into branched cylindrical segments. The electrical properties of the membrane and the cytoplasm can be assigned to the model by directly ﬁtting the experimental results to the predictions using cable theory. Rall (1964) has also developed a complementary compartmental model which has become one of the most popular modelling approaches at the single cell level and at the level of neural networks. In this modelling approach the continuous cable representation of the modelled tree becomes discrete and the dendritic segments are assumed to be isopotential. Thus each segment can be modelled by single R-C membrane compartments (or a complex channel based approach). Single compartments are connected to each other via resistivities according to the tree structure 2.2 Single Neuron Models 17

(Fig. 2.5). Hence, the compartmental model replaces the cable equation by a set of ordinary differential equations which can be solved by numerical methods. In the limiting case, if the dendritic tree is divided into sufﬁciently small compartments, the compartmental approach which is discrete in space converges to the solution of the continuous cable equation. This type of model allows an arbitrarily detailed modelling of the morphological and physiological properties of a single neuron (e.g. Douglas & Martin, 1990).

Summary: The different classes of single neuron models which are mentioned above differ by their level of description which ranges from rather simpliﬁed to more realistic, but highly complex models of a single nerve cell i.e. models may consist of thousands of compartments and different types of channels. Although the theoretical framework exists it is often impossible to constrain the model parameters of more realistic neuron models due to the lack of suitable experimental data. Therefore, if one aims at building models of brain function, it is important to carefully choose the level of abstraction in the neuron model and to be aware of the trade-off between biologically realistic and computational complexity. The particlar choice depends on many factors e.g. the particular question which is addressed by the modelling work or the data which is available to constrain the particular model parameters. 18 Neurobiological Background

2.3 The Visual System of Primates: An Overview

Most primates are highly visual creatures, capable of different tasks which are carried out in a complex visual environment (Van Essen et al., 1991). The visual performance of a macaque monkey and the organization of the primate visual system closely resembles the visual system of humans (De Valois et al., 1974). Therefore the visual system of primates has received close attention from many different disciplines ranging from molecular biology to cognitive psychology and computational neuroscience (Douglas et al., 1993) and especially neuroanatomists and neurophysiologists are using primates as a valuable model system to study human vision. The evidence reported in the following sections refers exclusively to the primate visual system and in general the data are drawn from macaque monkeys. The visual system of primates can be divided into three principle stages: a peripheral and subcortical level which captures the retinocortical pathway and a cortical processing stage which consists of many areas within the cerebral cortex.

Basic Definitions A general feature of the visual system is that spatial relationship in the peripheral surface i.e. the retina of the eye are preserved through the central visual pathways. An orderly topographic map of the visual field (visotopic map) is retained in the brain, because neighbouring groups of cells at each successive level of the visual system project to neighbouring cells in the target region. The classical receptive field of a neuron in the visual system is defined as the area of the retina where stimulation of the photoreceptors with light causes either an increase or decrease of the cell’s firing rate. The size of the receptive field strongly depends on the measurement technique10. Within its receptive field a neuron exhibits selectivity to specific stimulus modalities e.g. colour, orientation and length of edges, direction and velocity of movements and so forth. The selective responses to specific features of the stimulus are called response properties of the cells. The response of neurons in the visual cortex to stimuli presented in the classical receptive field can be modulated by stimuli presented in surrounding regions that do not themselves evoke responses. In this case one speaks of contextual effects. Cells in the visual system report principally on stimulus contrast in the visual input. Thus one of the basic response properties of cells in the visual system is the sensitivity to luminance contrast. In addition to other response properties, receptive field size and contrast sensitivity are the most basic response properties of cells in the visual system.

Peripheral and Subcortical Pathways Figure 2.6 summarizes the overall layout of the peripheral and subcortical visual pathways in the primate visual system. The visual image falling onto the photoreceptor sheet of the retina is already pre-processed by retinal nerve cells11. The retinal output is relayed via the optic chiasma and the optic tract to three subcortical centers located in the midbrain and the thalamus. The pretectum uses input from retinal ganglion cells to produce pupillary reﬂexes whereas the superior colliculus integrates visual inputs together with somatic and auditory inputs to generate saccadic eye movements (Manson & Kandel, 1991). Both subcortical centers are involved in optokinetic reﬂexes

10e.g. a small spot of light which is systematically moved across the visual field is frequently used to define the so-called minimum response field which is usually very small 11note that the retina is a proper part of the brain and belongs to the central nervous system 2.3 The Visual System of Primates: An Overview 19

visual field

thalamus occipital lobe

optic radiations optic tract

optic chiasm

optic primary nerve visual retina cortex midbrain optic nerv

thalamus optic tract optic chiasm

LGN

lateral geniculate nucleus parvocellular

magnocellular optic radiation primary visual cortex

pretectum superior colliculus midbrain

Figure 2.6: Overview of the peripheral and subcortical pathways in the primate visual system. Retinal projections relay to three subcortical centers located in the midbrain (pretectum, superior colliculus) and the thalamus. Only visual information relayed via the magnocellular and parvocellular subdivisions of the lateral geniculate nucleus (LGN) results in visual perception. Almost all LGN cells terminate within the primary visual cortex. The optic nerves partially cross at the optic chiasma. Visual information originating from the left and right visual field are processed in right and left cortical hemisphere. (left figure adapted from Manson & Kandel, 1991; right figure after Hubel & Wiesel, 1977).

which are responsible for stabilizing the visual image on the retina (for review see Douglas et al., 1993). Only the lateral geniculate nucleus (LGN) relays visual information that results in visual perception. Two major information channels provided by the retina terminate in the magnocellular (M) and parvocellular (P) subdivisions of the LGN. Almost all LGN cells in turn project via the optic radiations to the occipital lobe of the cerebral hemispheres where they terminate within the primary visual cortex12.

The Visual Cortex is Part of the Cerebral Cortex The cerebral cortex13 is a folded sheet of cells which is about 2mm thick in the macaque (Fig. 2.7, left). The cerebral sheet consist of six distinct layers which are numbered sequentially from the

12synonyms are visual area 1, V1, striate cortex, (Brodman’s) area 17 13The visible part of the external surface of the brain is also called the neocortex since this part is the most recently acquired in evolution. 20 Neurobiological Background

Pia 1

2-3 2mm

4A 4B

4C α

4C β

White 500µ m matter

Figure 2.7: Sections of the cerebral cortex at low (left) and high (right) power resolution. Both section were stained for Nissl substance contained in cell bodies. The left section shows part of the the primary visual cortex and adjacent regions. The folded structure but also part of the layered organization of the cerebral cortex is clearly visible. The arrows mark the border between two cortical areas i.e. the primary visual cortex and area V2. The layered structure which is characteristic for the cerebral cortex can be seen in more detail in the section of the primary visual cortex (right). The layers which are characterized by different cell densities are numbered

sequentially from the pia surface to the white matter. Some of the layers, particular layer 4 of the primary visual cortex, can be further subdivided into sublayers 4A, 4B, 4C and 4C . (adapted from Hubel & Wiesel, 1977, left, and Blasdel & Lund, 1983, right).

surface next to the pia matter to the white matter underlying the cortex (Fig. 2.7, right). Individual layers of the cerebral cortex vary in thickness, cell density and neural composition. The layers of the cerebral cortex contain two main types of neurons, pyramidal and nonpyramidal neurons (see Fig. 2.8). The large pyramidal cells have an apical dendrite that runs towards the pia surface and several basal dendrites that project laterally within the layer containing the cell body. The main trunk of the axon enters the white matter and terminates in other cortical regions or subcortical areas. Pyramids also may have some axon collaterals near the cell body and in layers through which they pass. The small nonpyramidal cells, also called stellate cells or granule cells, have dendrites that are mostly conﬁned to the layer where the cell body lies. The axon of nonpyramidal cells branches profusely in the region near the soma but may have an axon that projects to other layers within the same area. While the pyramidal neurons are regarded as projecting neurons, the small stellate cells are considered as local interneurons. In particular the proportion of pyramidal and nonpyramidal cells is an indication of the putative functional role of each layer. Layer 4 which is generally rich in nonpyramidal cells receives most of the afferent (thalamic) input. Superﬁcial14 layers 2-3 which consist mostly of pyramidal cells

14 because layer 4 contains granule cells, superﬁcial and deep layers are often called supergranule and supragranule layers 2.3 The Visual System of Primates: An Overview 21

apical 2-3 dendrite

axon

nonpyramidal neuron 4

dendrite

pyramidal basal neuron 5 dendrite

axon 6

To other cortical or subcortical areas

Figure 2.8: The cerebral cortex contains two types of neurons. Pyramidal neurons which derive their name from the shape of the cell body and nonpyramidal neurons which are called stellate cells because their cell body is rather stellate shaped. The pyramids are known as the output or projecting neurons of the cortex since the main trunk of the axon leaves through the white matter to terminate in other cortical or subcortical regions. They are characterized by an apical dendrite that runs vertically towards the pia surface. The nonpyramidal cells have dendrites that are largely conﬁned to the layer where the cell body lies. The axon of nonpyramidal cells terminate in other layers but stay within the same cortical region. Therefore the stellate cells are considered as local or intrinsic neurons.

provide efferent relays to other cortical areas. Deep layers 5 and 6 also contain mainly pyramids but project back to subcortical structures (Kelly, 1991). Although the six-layered structure is a unique organization principle of the cerebral sheet, it is subdivided into different areas which are concerned with processing of different tasks and sensory modalities. Figure 2.9 shows a two-dimensional map of the macaque cerebral cortex which indicates the location and size of different cortical areas. More than 50% of the cerebral cortex of Old World monkeys like the macaque is involved in visual information processing. In comparison, 10% of the cortex are implicated in somatosensory and less than 5% are involved in auditory processing. Based on anatomical, physiological and/or behavioural studies the view has emerged that the visual cortex of the macaque monkey can be further subdivided in 32 visual areas15 (Felleman & Van Essen, 1991). The visual areas occupy almost the whole occipital lobe and considerable parts of the parietal and temporal lobes as well as some areas in the prefrontal

15of which 25 are predominantly or exclusively involved in vision and 7 are visual associated areas 22 Neurobiological Background

medial prefrontal posterior parietal

V4 Parietal Frontal

Occipital motor lateral prefrontal V1 somatosensory V2 Temporal V3 auditory orbito- MT frontal V4 V1

inferior temporal V2

1 cm

Figure 2.9: Two-dimensional unfolded map of the macaque cerebral cortex. The ﬂattened cortical map shows the entire right hemisphere. The inset gives a lateral view of the same region. The cerebral cortex falls into four major divisions, the occipital, temporal, parietal and frontal lobe. Regions shown in grey are associated with visual information processing. The largest visual areas, V1 and V2, which are located in the occipital lobe are associated with early stages of cortical processing. Areas V4 and MT among many others belong to an intermediate stage of visual information processing and higher visual areas are accumulated in inferior temporal (IT) and posterior parietal (PP) cortex (adapted from Van Essen et al., 1991).

cortex. Within the visual system the early stages of visual information processing i.e. the primary and secondary visual areas, V1 and V2, are largest and each of them occupying roughly 10% each of the total neocortex.

Hierarchical and Concurrent Processing in the Visual Cortex

The different visual areas are heavily interconnected by at least 305 pathways (Felleman & Van Essen, 1991). A general principle seems to dominate the organization of these connections: the vast majority of the cortico-cortical pathways are reciprocal with pronounced asymmetries in laminar organization. The feedforward or ascending pathway originates from cells in the superﬁcial and deep layers and terminates predominantly in layer 4 of the target area. By contrast, the feedback or descending pathway preferentially avoids layer 4 of the target area and originates in the deep or superﬁcial layers. Based on the anatomical termination patterns the various areas can 2.3 The Visual System of Primates: An Overview 23

Posterior Inferior Higher visual areas Parietal Temporal

MT V4

Intermediate visual

V3 areas

Thick Inter Thin M-D P-I P-B V2

Early visual areas 4BInter Blob M-D P-I P-B V1

M P LGN Subcortical and

α β Retina Peripheral

Figure 2.10: Hierarchy of early and intermediate stages of visual information processing in the macaque monkey. The hierarchy is deﬁned by the anisotropic connection patterns between different areas. Visual cortical areas lying at an early stage are subdivided in functional compartments (see text). At higher levels the various visual areas are summarized by an inferior temporal (IT) complex and a collection of areas in the posterior parietal (PP) cortex (after DeYoe & Van Essen, 1988).

be arranged in a hierarchical relationship and the visual cortex can be viewed as a distributed hierarchical system (Van Essen et al., 1991). Part of the complex hierarchical connection scheme is shown in Figure 2.10. In brief, the diagram suggests that there are at least three parallel processing streams within the early stages of visual information processing (area V1 and V2) which segregate at an intermediate level (area MT and V4) to form a posterior parietal and an inferior temporal processing stream. The dichotomy between parvo- and magnocellular streams which is established in the retina and preserved in the LGN is rearranged into three concurrent streams running through different compartments of area V1 and V2. The functional compartments i.e. blob and interblob regions of area V1 (Horton & Hubel, 1981) and thin, thick and (pale) interstripes of area V2 (Hubel & Livingstone, 1987), respectively, have been revealed by staining for the metabolic enzyme cytochrome oxidase which is known to mark functional pathways in the visual cortex. The magno-dominated (MD) stream 24 Neurobiological Background

which is named after the major source of subcortical input relays via the thick stripes of area V2 to the middle temporal area MT16 and feeds into a collection of areas located in the posterior parietal cortex. The processing streams associated with blob (P-B) and interblob (P-I) regions which are dominated by subcortical parvocellular input relay via thin stripes and interstripes of area V2 to area V4 and another group of areas in the inferior temporal cortex. It should be emphasized that a clearcut into separate visual pathways is tendentious since there is extensive crosstalk between visual areas at all levels of cortical processing.

The Functional Logic of Visual Information Processing Concerning the functional organization of visual information processing different views have emerged. The differences between the three hypothesis are conceptually reﬂecting the different methodology from which they have emerged.

The ﬁrst concept arranges visual areas in an orderly hierarchy with area V1 forming the base of an inverted pyramid of visual areas (Van Essen, Felleman, DeYoe, & Knierim 1991). Each level of the hierarchy is concerned with progressively more speciﬁc processing of various visual attributes of colour, form, motion, depth and so forth. The hierarchical view is motivated entirely by anatomical connectivity patterns between visual areas (see Fig. 2.10 and text above).

Another view is based on physiological recording related to intrinsic connectivity patterns of layers and compartments but originates from subcortical parvo- and magnocellular processing streams (Livingstone & Hubel, 1987). Based on physiological recordings from LGN cells it is suggested that the parvocellular-dominated pathway which relays via V4 to IT carries high acuity information about colour, form and texture deﬁned by high contrast, whereas the magnocellular dominated pathway which relays via MT to PP is thought to carry low acuity information about low contrast, motion and depth.

The third view which is based on behavioural studies of animals and patients with localized cortical lesions suggests the existence of two general visual tasks (Mishkin et al., 1983; Ungerleider & Mishkin, 1982). One task is to decide where the object is and the other is to decide what the object is. These tasks are thought to be reﬂected in two processing streams; one which runs through MT to the parietal cortex answering the question where the object is, and the other one which runs via V4 to the inferotemporal cortex ﬁnding out what the object is.

To summarize the overall baseline of these hypotheses: It is generally accepted that different characteristic image primitives which are carried by the anatomically and physiological segregated LGN-P and LGN-M channels are transformed within area V1 into three partially segregated information channels associated with motion/depth, form and colour. These pathways can be followed up for several stages of visual information processing either in terms of anatomical connectivity and physiological response properties or in terms of speciﬁc perceptual tasks. The segregation into concurrent processing streams is by no means complete and there are various levels of divergence and convergence between them.

16also called area V5 2.4 Early Stages of Visual Information Processing 25

2.4 Early Stages of Visual Information Processing

The visual system of primates, particular the early stages of visual information processing, have become one of the most intensively studied regions of the brain and a wealth of data has been published concerning the anatomical and physiological organization of this area. This chapter gives an overview of the early stages of visual information processing. It is brieﬂy considered how the visual world is mapped onto the retina and in which way the retinal image is pre-processed by the network of retinal nerve cells. The retina provides two major information channels which become segregated anatomically in the lateral geniculate nucleus. The LGN is considered as a relay station which provides input to the primary visual cortex. Finally the chapter addresses the anatomical organization and functional architecture of the ﬁrst cortical processing stage.

2.4.1 The Retina The eye is an optic device and it contains the retina which is the sensory part of the visual system. On the other hand the retinal neuronal network is a proper, although peripheral, part of the brain and the retinal neurons carry out the initial analysis of the visual information.

The Retinal Image The optics of the eye can be compared to the optics of a camera. Figure 2.11 shows how the visual world is mapped on the retina of both eyes. The left and right visual hemifield are mapped on the nasal and temporal hemiretina of both eyes. The fibres of retinal nerve cells leave the retina through the optic disc, a region which contains no photoreceptors. The region of the visual field which is mapped on the optic disc is called the blind spot. The blind spot which is a monocular region within the binocular zone of the visual field is covered by the fact, that in binocular vision there is no single point within the binocular zone that is mapped onto both optic discs simultaneously.

The Retinal Network Compared to the cerebral cortex the primate retina is a considerably simple neural network. The retina consists of three principle layers containing the photoreceptors, different types of specialized interneurons and the retinal ganglion cells (Fig 2.12). For a comprehensive review of the anatomical organization see Rodieck (1988); for details about physiological organisation see Ka- plan et al. (1990) for example. The photoreceptors fall into four classes: the rods and three types of cones. The rods are very sensitive to low light intensities and specialized for night vision. The rod system has low spatial resolution which results from heavy convergence onto postsynaptic retinal interneurons. Rods are absent from the central fovea which is very densely packed with cones. The cone system is less sensitive to changes in absolute light intensity and mediates normal trichromatic daylight vision. Cones can be categorized into three classes based on their wavelength sensitivity. S- or B-

cones respond best to blue light of short wavelength (420 m) M- or G- cones have a maximum

sensitivity to green light of medium wavelength (531m) and L- or R- cones respond best to red

light of long wavelength (558 m). The photoreceptors provide direct input to different types of retinal nerve cells: the bipolar cells, the horizontal cells, and the amacrine cells. The bipolar cells are the main route for photoreceptors to reach the ganglion cells. In the fovea some bipolar cells are activated by only one 26 Neurobiological Background

visual field

left visual right visual hemifield hemifield binocular zone

fixation point

left monocular zone

temporal nasal hemiretina hemiretinas

fovea optic disc

optic chiasma optic nerv

optic tract

retina

photorecptors superior

fovea

lens optic disk

inferior

optic nerve

Figure 2.11: The visual world is projected on the retina of both eyes. The visual field is the view seen by the fixated eyes without movement of the head. Due to the camera optics of the eye the retinal image is an inverse of the real visual scene. The superior half of the visual field is projected onto inferior half of the retina and vice versa. The left visual hemifield is mapped on the temporal hemiretina of the right eye and the nasal hemiretina of the left eye. The right visual hemifield is mapped on the nasal hemiretina of the right eye and the temporal hemiretina of the left eye. The fixation point is mapped onto the fovea which is the region of highest visual acuity and least optic distortion. In the central region of the visual field where the light from one point enters both eyes binocular images are recorded. The binocular zone is flanked by two monocular regions. 2.4 Early Stages of Visual Information Processing 27

Light

Figure 2.12: The retina contains five major classes of neurons: rods and cones (photoreceptors), amacrine, horizontal and bipolar cells and the retinal ganglion cells. Information flows vertically from photoreceptors to bipolar to ganglion cells. The lateral information flow is mediated by bipolar and amacrine cells; note that the light which falls on the retina has to pass through the nuclear layers before it reach the photoreceptors. (adapted from Tessier-Lavigne, 1991).

photoreceptor. The horizontal cells spread visual signals laterally across the retina and there is evidence that the horizontal cells are responsible for the surround antagonism of the receptive ﬁelds of retinal ganglion cells (Naka, 1977). Amacrine cells are a diverse class of interneurons and their function is not well understood. A reasonable assumption, however, is that some types of the amacrine cells help to sharpen the time course of the ganglion cells response (Kaplan et al., 1990).

The retinal interneurons are non-spiking cells and only the ganglion cells which carry the signal out of the retina produce spikes. Thus it is the ﬁring pattern of retinal ganglion cells in which the whole visual scene is encoded. 28 Neurobiological Background

ON-center OFF-center

ON region OFF region

OFF region ON region

0.5 1.0 1.5

Figure 2.13: Receptive field organization of retinal ganglion cells (after Kuffler, 1953). The receptive field of ganglion cells consists of a circular center and an antagonistic surround region. The recorded action potentials are shown next to each stimulus condition. The duration of the stimulus is indicated by the bar above the recording. Diffuse illumination of the whole receptive field has no effect (bottom row). ON-center cells are excited (increase in spike rate) if stimulated in the center and inhibited (decrease in spike rate) when light falls in the surround (left). OFF-center cells behave vice versa (right). Therefore ganglion cells are sensitive to contrast in their receptive fields.

Center-surround Receptive Fields of Retinal Ganglion Cells

The specific connectivity and the physiological properties of the interneurons are responsible for the contrast-enhancing center-surround organisation of the receptive fields of retinal ganglion cells (Kuffler, 1953; Fig. 2.13). There are two principle types of center-surround organisation in the retinal ganglion cells. ON cells show an increase in spike activity or excitatory ON response, if light falls on the center region and a discharge in spike rate or inhibitory OFF response, if light falls on the surround region; OFF cells behave vice versa. The key interneuron of the retina is the bipolar cell which also exhibits antagonistic center-surround receptive fields of ON or OFF type. Depending on the type of the bipolar cell, the activation of photoreceptors in the center either produce an ON or OFF response in the bipolar cell which in turn results in an ON or OFF response of the postsynaptic ganglion cells. In addition to the ON and OFF channel, the retinal ganglion cells fall into two major cell

systems: the magnocellular (M) ganglion cells, also called or parasol ganglion cells and the

parvocellular (P) ganglion cells, also called or midget ganglion cells (Perry & Cowey, 1981; Leventhal et al., 1981; Rodieck et al., 1985). The P ganglion cells comprise nearly 80% of the 2.4 Early Stages of Visual Information Processing 29 ganglion cells, while 10% account for the M ganglion cells17. In physiological respect both P and M cell types differ along several low level stimulus dimensions; for details about the physiological properties of P and M retinal ganglion cells see Section 2.4.2. The remaining 10% of the ganglion cells project to the superior colliculus and the pretectum; their physiological properties are different from those of the P and M population (Schiller & Malpeli, 1977).

The Retinogeniculate Projections After leaving the retina, the axons of the ganglion cells become myelinated and form the optic nerve which travels towards the optic chiasma. In the optic chiasma both optic nerves partially cross; slightly more than half of the fibres – those originating from the nasal half of the retina – cross to the opposite side joining the fibres of the the temporal hemiretina (Fig. 2.11). This results in the segregation of the left and right visual hemifield in the right and left optic tract. The information of the left and right visual hemifield is independently relayed via the right and left lateral geniculate nucleus to the primary visual cortex in the contralateral cerebral hemisphere (compare Fig. 2.6).

2.4.2 The Lateral Geniculate Nucleus The lateral geniculate nucleus (LGN) is located in the thalamus. It is the major thalamic relay stage in the central visual pathway of primates. The LGN receives its principal afferent input from retinal ganglion cells through the optic nerve and optic tract. The major projection site of thalamic neurons is the primary visual cortex.

Anatomical Organization and Topographic Representation In anatomical respect the LGN consists of six coaxially arranged layers of cell bodies which are intervened by layers of axons and dendrites (Fig 2.14). Each layer is innervated by ganglion cells originating from either the temporal hemiretina of the ipsilateral eye or the nasal hemiretina of the contralateral eye (Kaas et al., 1972; Kaas et al., 1978). The most ventral magnocellular layers 1 and 2 contain relatively large cell bodies and are innervated by M retinal ganglion cells; the dorsal parvocellular layers which are characterized by small cell bodies are innervated by retinal P ganglion cells (Leventhal et al., 1981; Perry & Cowey, 1981). There are 1.3 million LGN cells (Connolly & Van Essen, 1984) which are roughly as many as afferent retinal ganglion cells. At least in the fovea and parafoveal regions of the visual field, receptive field structure of retinal and geniculate P and M cells suggests a 1:1 projection (Schein & de Monasterio, 1987). On the other hand only 10 to 20% of the presynaptic connections onto geniculate relay cells are from retinal ganglion cells (Manson & Kandel, 1991). The majority of connections are from other subcortical regions or from the primary visual cortex18. The putative role of this connections is to control the flow of visual information from the retina to the cortex. Most of the cells in the LGN are relay cells which apparently send an axon to the visual cortex (Hámari et al., 1983). There is a third population of LGN cells which is located in the interlaminar regions (intercalated layers) between and ventral to the main layers of the LGN. The retinal input

171.2 million P ganglion cells and 0.15 million M ganglion cells 18especially layer 6 pyramidal neurons establish a prominent feedback loop 30 Neurobiological Background

Horizontal Section

LGN

1 2 3 4 5 6

dorsal

1 Contra M Layers medial 2 Ipsi } 3 Ipsi 4 Contra anterior P Layers 5 Ipsi 6 Contra }

Figure 2.14: Left: An anterior-lateral view of a model LGN adapted from Connolly & Van Essen (1984). Right: A horizontal section through the LGN indicates six anatomically segregated layers adapted from Schiller & Malpeli (1978). Each layer is innervated by either the contra- or ipsilateral eye. The magnocellular layers correspond to the most ventral layers 1 and 2 which are innervated by magnocellular ganglion cells. The parvocellular layers correspond to the dorsal layers 3 through 6. They are are innervated by parvocellular ganglion cells.

to the interlaminar cells and their physiological characterisation is unknown, although these interlaminar cells are as numerous as the cells of the magnocellular subdivision (Hendry & Yoshioka, 1994). The termination pattern of retinal ganglion cells in each layer is organized in a topographic way (Connolly & Van Essen, 1984) i.e. neighbouring LGN cells have receptive fields nearby in the visual field. Thus each layer in the LGN contains a representation of the contralateral visual hemifield. Because the layers are stacked on top of each other in precise vertical register (Kaas et al., 1972; Kaas et al., 1978), an orthogonal electrode penetration through all layers would mark a single location in visual space. The layers which receive input from the nasal hemiretina of the contralateral eye contain a complete representation of the contralateral visual hemifield. The layers innervated by the ipsilateral eye lack the representation of the monocular crescent (compare Fig. 2.11). The surface of the retina is not represented isometrically in the LGN. The fovea which is the 2.4 Early Stages of Visual Information Processing 31

vertical meridian

fovea

horizontal meridian

a) b)

Figure 2.15: Anisometric representation of the visual field in the LGN. (a) The left visual hemifield is divided by a grid of isoeccentricity (circles) and isopolar (rays) lines into regions that are approximately square. The perimeter of the visual field is given by the dark line. (b) Two- dimensional map of LGN layer 6 overlaid with the same gridwork as in a). The central 5% of the visual field has been stippled in both representations. (adapted from Connolly & Van Essen, 1984). region of highest visual acuity has the highest density of retinal ganglion cells. Therefore the fovea and the region just around it (parafoveal) have much larger representation compared to the peripheral part of the visual field (Figure 2.15; Connolly & Van Essen, 1984). The anisometric mapping of foveal versus peripheral vision is a general principle not only found in the LGN but also seen in the primary visual cortex and higher visual areas. The reason for the anisotropic mapping is obvious: The ganglion cells in and near the fovea are most densely packed. In the LGN where the retinal surface is first mapped on a two-dimensional visuotopic map, packing density is replaced by surface representation which allows for a constant cell density per unit area.

Physiological Organization Besides the parcellation of ipsi- and contralateral and the segregation into parvo- and magnocellular layers, the LGN is considered as a relay station. Wiesel & Hubel (1966) report that the receptive ﬁelds of LGN neurons are similar to those of the retina i.e. organized in circular center and surround regions. There are no striking differences in the response properties of P and M retinal ganglion cells and their geniculate counterparts in the P and M layers of the LGN – particular in terms of spatial and spectral organization. The characteristic physiological properties of P and M cells are summarized in Table 2.1. For a comprehensive review see Kaplan et al. (1990) and Shapley (1990). Annectotically: originally, the retinal ganglion cells were grouped into M and P cells because 32 Neurobiological Background

Property P cells M cells Contrast Sensitivity lower higher Receptive ﬁeld size smaller higher Temporal resolution lower higher Conduction velocity lower higher Response to luminance contrast tonic (sustained) phasic (transient) Spectral selectivity yes no

Table 2.1: Physiological properties of P and M cells. Note that many of the properties are compared in relative, not absolute terms which indicates that there is considerable overlap between the P and M cell population. The P and M cells are often referred to as colour-opponent versus broad-band or tonic versus phasic cells which refers to a single property of the cells.

they terminate in the magno- and parvocellular layers of the LGN, which is rather an anatomical designation (Perry & Cowey, 1981). Subsequently Lee et al. (1983) measured pre- and postsynaptic potentials of cells in the LGN. The measurements revealed that a LGN cell receives about twice as many spikes from a retinal ganglion cell as it produces but in other respect the pre- and postsynaptic potentials show a simple linear relationship. P cells provide information at high spatial resolution (De Monasterio & Gouras, 1975; Der- rington & Lennie, 1984; Hicks et al., 1983), while M cells are more sensitive to small changes in luminance contrast (Kaplan & Shapley 1982; Kaplan & Shapley 1986). In the temporal domain P cells convey information mainly about stimuli that are static or slowly moving while M cells emphasize more rapid motion or high temporal frequencies in luminance contrast (Purpura et al., 1988). This is particular reflected in the more transient or phasic, short burst response of M cells to onset or offset of light, compared to the sustained discharge or tonic response of P cells (Gouras, 1968). Gouras, 1969 also reports shorter conduction velocities for phasic than for tonic retinal ganglion cells while Kaplan & Shapley (1982) demonstrate that magnocellular LGN cells had shorter latency of response to electrical stimulation of the optic chiasma. The most intriguing although highly controversary difference is that only P cells convey information about colour (Wiesel & Hubel, 1966; De Monasterio, 1978). While the center and surround of M cells respond best to luminance contrast of achromatic (broad-band) stimuli, center and surround of P cells exhibit chromatic selectivity in the center as well as in the surround. The single colour-opponent receptive fields of the P cells are characterized as follows: light of a certain wavelength in the center and antagonistic surround – preferentially red and green, less frequently blue-excitation opposed by some combination of red and green inhibition – produce maximal response. The neural mechanism underling the physiological colour-opponent versa broad-band receptive fields of P and M cells is not yet known. Although chromatic stimuli are best suited for P cells, they also respond to small white spots in the center. This implies that P cells do not only code for colour but also for low spatial frequency of broad-band (achromatic) stimuli. Therefore there is ambiguity in the response of P cells between luminance contrast at low spatial frequency and colour coding and it remains still unclear, if and to what degree the P channel codes for spectral information (e.g. discussed in Kaplan et al., 1990). The separation into P and M pathways discussed above is independent of ON- and OFF- pathways; within each pathway there is a population of ON and OFF cells. In order to cover the visual field equally well, the P- and M-, ON- and OFF-pathways must be spatially intermingled in 2.4 Early Stages of Visual Information Processing 33 the retina, before they become anatomically separated.

Functional Organization The function of the elaborate lamination has not been conclusively determined, but various suggestions regarding laminar specialization have been made. For example it was reported that there is mild bias towards ON centre cells within the parvocellular laminae 5 and 6 (Kaplan & Shapley, 1982; Derrington & Lennie, 1984) while cells getting input from blue-sensitive S cones are more likely to be found in the lower pair of parvocellular layer 3 and 4 (Schiller & Malpeli, 1978). Since the LGN is the only relay in the flow of visual information where P and M channels are expressed in different layers, lesion studies have been carried out. One of the most intriguing outcome was, that, if P layers are destroyed, no colour vision was found (Schiller et al., 1990). The authors further report that the P channel is essential for the processing of texture and fine pattern while lesions in the M layers of the LGN seriously damage the perception of fast flicker and motion stimuli. The current understanding of independent functional pathways is, that the M channel is concerned with initial analysis of movement and the P pathway carries out analysis of fine structure and colour vision. The cells in the magno- and parvocellular layer of the LGN relay via the optic radiation towards the primary visual cortex where they terminate in the thalamic input zones of layer 4.

2.4.3 The Primary Visual Cortex The first relay point in visual information processing where receptive fields significantly change, is the primary visual cortex. The first section reviews the overall anatomical organization of the primary visual cortex. It will be further described how the complexity of the intrinsic circuits affects the response properties of cortical cells and how the cells having different response properties are distributed within the primary visual cortex.

Anatomical Organization The primary visual cortex consists of six principle layers 1-6 between the pia surface and the underlying white matter. Some of the layers can be further subdivided into sublayers; especially layer 4 consists of three prominent sublaminae 4A, 4B and 4C (see Figure 2.16, compare also Fig. 2.7); sublayers 4A and 4C, but also layer 6, are clearly seen in cortical tissue stained for

the metabolic enzyme cytochrome oxidase which is known to indicate zones of thalamic input. The axons of thalamic P and M cells project very precisely to sublaminae 4C and 4C (Hubel

& Wiesel, 1972; Blasdel & Lund, 1983). Almost all LGN-M cells terminate within layer 4C and many of them give off collaterals in layer 6. The majority of LGN-P cells terminate in layer

4C and the remaining P cells terminate within layer 4A. No single P axon was reported which

terminates in both sublaminae, 4C and 4A. The layer speciﬁc arborisation of single LGN-P cells might be an indication of two functional different LGN-P subpopulations. The CO-rich blobs are innervated by the third group of thalamic afferents, the so-called interlaminar cells (Fitzpatrick et al., 1983). For details see Figure 2.16. The different layers are identiﬁed by different cell densities and neural composition. For exam-

ple, layer 4C contains 50-100 times more neurons than the LGN (Chow et al., 1950; Peters et al., 1994) and there is gradual increase in cell density from top, 4C, to bottom, 4C , of the layer (Fig 2.16). The number ratio suggest that a thalamic neuron provides input to many postsynaptic 34 Neurobiological Background

Pia Blob Blob 1

2-3

4A 4B

4Cα

4Cβ

White 500 µm matter } LGN I M P

Figure 2.16: Left: Section of the primary visual cortex stained for the metabolic enzyme cytochrome oxidase which is known to indicate zones of thalamic input. Laminae 4C, 4A, lower parts of layer 6 and CO-rich blobs in layer 2-3 (arrows) which are prominent thalamic input zones occur as dark regions; adapted from Blasdel & Lund (1983). Right: Schematic diagram of the layer structure. In the vertical domain the thalamic afferents terminate in distinct layers. Afferent

ﬁbres from the magnocellular (M) LGN laminae terminate in layer 4C and lower part of layer

6. The majority of afferent ﬁbres from the parvocellular (P) LGN laminae terminate in layer 4C . A smaller population of LGN-P cells projects to layer 4A. Afferent ﬁbres from the interlaminar (I) LGN layers innervate the blob regions of layer 2-3. Layer 4C contains approximately 50-100

times more neurons than the LGN. A gradual increase in cell density is observed from 4C to

4C .

cells in layer 4C. Based on the sampling density of the visual field by retinal neurons, Barlow suggests a simple but precise interpolation mechanism by which the visual image is reconstructed from the sparse coded information provided by the retina, and thus can explain the psychophysical phenomenon of hyperacuity; for details see Barlow (1981). There are several types of resident neurons that make up the primary visual cortex (Fig. 2.17a). Excitatory spiny stellate cells which are concentrated in the input layer 4C, and pyramidal neurons which are prominent in the superficial layers 2-3, 4B and deep layers 5 and 6. The anatomical organisation of the primary visual cortex suggests that once information from the LGN has entered layer 4, it is distributed in a systematic way through different layers until the readily processed information leaves the area via efferent relays of the pyramidal neurons. A simplified working

paradigm of the rich circuitry is summarized in Figure 2.17b:

LGN-M and LGN-P cells project to the and subdivision of 4C respectively. The blob regions of layer 2-3 receive direct input from the interlaminar LGN cells. 2.4 Early Stages of Visual Information Processing 35

1 To other cortical 2 areas pyramidal 2-3 V2,V3,V4 3 MT

4A 4A 4B 4B

smooth 4Cα α spiny stellate 4C stellate

4Cβ pyramidal 4Cβ 5 5 To subcortical areas 6 6

200µ m I M P P a) To other cortical areas To subcortical areas b) From LGN

Figure 2.17: Anatomical organization of the primary visual cortex (after Manson & Kandel, 1991). (a) Neural composition of different layers in the primary visual cortex. Layer 4C contains excitatory spiny stellate cells. Layer 4B, deep layers 5, 6 and superﬁcial layers 2-3 contain mainly pyramidal cells which project to the white matter. The majority of cells in the primary visual cortex are excitatory spiny stellate cells and pyramidal cells; a smaller population of resident cells are smooth (inhibitory) stellate cells. One example of a smooth stellate cell is shown in layer 4C (b) The diagram summarizes the intrinsic relays of area V1 in relation to thalamic inputs and effer-

ent projections. Afferent cell populations project to different laminae and speciﬁc compartments: LGN-P and LGN-M cells project to layer 4A, 4C and 4C ; the interlaminar (I) LGN cells project to the blobs of layer 2-3. Populations of efferent neurons are located in superﬁcial layers and layer 4B; these layers project to other visual areas. Efferent projections of deep layers 5 and 6 terminate in subcortical areas. For details see text.

Layer 4C provides different output channels which are staggered in depth of the layer 4C Spiny stellate cells in upper 4C projects to layer 4B cells in lower 4C relay via layer 4A to layers 2-3 (e.g. (Yoshioka et al., 1994)).

While a population of neurons in 4B provides efferent projections to area MT (Shipp & Zeki, 1989), another population of 4B cells project to layer 2-3 (Lund & Boothe, 1975).

The blob and interblob regions of layer 2-3 contain distinct sets of efferent neuron populations which project to different compartments in visual areas V2 (thin, thick, and inter stripes) and to other higher visual areas.

Deep layer 5 gets input from layer 2-3 pyramids via axon collaterals and layer 5 pyramidal neurons send recurrent axon collaterals to layer 2-3 (Lund, 1973; Lund & Boothe, 1975). Layer 5 pyramids also project to layer 6 pyramidal cells.

Finally layer 6 pyramidals establish recurrent projection with layer 4C (Lund, 1973; Lund

& Boothe, 1975; Wiser & Callaway, 1996). The layer 6 pyramids exhibit clear sublaminar speciﬁcation of their recurrent axons and apical dendrites for and subdivision (e.g. 36 Neurobiological Background

(Lund & Boothe, 1975; Wiser & Callaway, 1996)). The main trunk of the layer 6 pyramidal neurons projects back to the LGN (Fitzpatrick et al., 1987).

Pyramidal neurons in layers 2-3 make widespreading intralaminar axonal projections of considerable lateral spread (e.g. Blasdel et al., 1985; Yoshioka et al., 1996). The laterally spreading axons

form roughly circular terminal patches with a diameter of approximately 250m. The patches are offset from one another forming a lattice-like terminal field. The terminal field of a local cluster of pyramidal neurons occupies an elongated region of about 2-3mm (compare scale bar of Fig. 2.17). The postsynaptic targets of these terminals are mainly dendrites of other pyramidal neurons. The functional role of these lattice-like connections which replicate across the cortical sheet remains unclear, but it was suggested that they connect together neurons that share common receptive field property and thus help sharpening the tuning of response properties (Yoshioka et al., 1996). In- deed, the response of neurons in the primary visual cortex is not completely invariant and depends on the context in which a stimulus is embedded (Levitt & Lund, 1997a). Lateral connections of considerable spread are already found in the principal input layer 4C (Yoshioka et al., 1994) and more clearly in layer 4B (Asi et al., 1998). These lateral connections

first occur in mid 4C where they are of moderate lateral extent. In upper 4C and layer 4B the terminal fields are about the same size as in layer 2-3, but the shape of a single patch is rather bar- or stripe-like. The functional role of the bar-like connections is unknown but since the stripe-like connections of layer 4B have somewhat different properties than the patch-like connection in layer 2-3, their functional role may be also different (Asi et al., 1998). Besides rich excitatory circuitry there are several varieties of smooth19 stellate cells (see Fig. 2.17a). Many of the smooth or sparsely spined local interneurons contain GABA. It is believed that these cells are inhibitory (Houser et al., 1994) and predominantly fulfill modulatory functions. The inhibitory circuitry of area V1 is complex but highly ordered; the morphological types of local smooth or sparsely spined neurons associated with different layers of the macaque striate cortex are described in detail in (Lund & Wu, 1997; Lund & Yoshioka, 1991; Lund, 1987; Lund et al., 1988). The current understanding of the anatomical organization of the striate cortex is summarized as follows:

The spiny stellate cells in layer 4C integrate properties among the incoming M and P inputs. The reorganized visual information is distributed via output channels to layer 4B, 4A and the superﬁcial layers 2-3.

The pyramidal cells of the deep and superﬁcial layers feed axons up and downward to inte-

grate activity within the layers of area V1; There is integration in 4C , 4B and layers 2-3 via widespreading lattice connections running laterally from any single point of neurons.

Intralaminar and interlaminar information processing is assisted by the a rich circuitry of local inhibitory interneurons.

Anatomically segregated information channels are apparent in the afferent thalamic input and the initial cortical relays, as well as in the speciﬁcity of efferent pathways of the deep and superﬁcial layers.

19because they bear no spines 2.4 Early Stages of Visual Information Processing 37

120

100

60 No. of spikes 40

0 0 30 60 90 120 150 180 -150 -120 -90-60 -30

Stimulus orientation [degree]

Figure 2.18: Orientation tuning curve of an orientation selective cell in the primary visual cortex

(upper 4C). The x-axis shows different orientations (stepsize 30 deg) of a bar moving in the directions perpendicular to the axis of orientation (indicated by the arrow). The y-axis show the

response of the cell. The optimal stimulus for the cell is a horizontal bar (90 degree) (size 1.2 x 1 0.4 deg moving at velocity 4.0 deg sec ). Since the peak response is lower for the bar moving in one (90 degree) than the other direction (-90 degree) the cell is also direction selective. Note that for bars which are missoriented by more than 20 degree the response drops dramatically (adapted from Sato et al., 1996).

For more comprehensive reviews of the anatomical organisation and functional interpretation refer to Lund (1973), Lund (1990), and Levitt et al. (1996).

Physiological Organization No particular re-organisation of receptive field properties occurs within the retinocortical pathway – neither convergence of ON- and OFF- pathway nor convergence of input from the ipsi- and contralateral eye. Retinal ganglion cells and geniculate cells respond best to a roughly circular spot of light. The optimal size of the spot varies from cell to cell, and for any one cell the spot must be presented at a particular part of the visual field. The first change of response properties occurs in the primary visual cortex. Cortical cells in V1 exhibit substantially more complex and selective responses to a particular stimulus. Since most of the response properties of the cortical neurons are not seen in the cells of the lateral geniculate nucleus, they must be generated either by specific geniculo-cortical projections or by the rich intracortical circuitry. Orientation and direction selectivity: The most prominent response properties of cells in the monkey striate cortex are orientation and direction selectivity first described by (Hubel & Wiesel, 1968). A cell is classified as orientation selective, if the stimulus which evokes consistent strong response is a specifically oriented straight line segment i.e. a slit or bar-shaped stimulus. The stationary or moving straight line has to be presented within a restricted receptive field. A vigorous response is evoked by a bar of particular orientation and usually the response of the cell 38 Neurobiological Background

declines rapidly if the bar becomes missoriented. An orientation tuning-curve which emphasizes the characteristic response profile of a orientation-selective cortical cell is shown in Fig.2.18. Moving stimuli are in general very powerful in evoking a response in a cortical cell. In many cortical cells movement of a slit in one direction evokes a much more vigorous response than movement in the reverse direction (Fig. 2.18). In many cells movement in one of two directions evokes no response at all. In the first case the cell is at least directional biased while in the latter case the cell is called direction selective. Simple and complex cells: The receptive field of a simple cell is rectangular in shape with a specific axis of orientation and it falls into discrete inhibitory (OFF) and excitatory (ON) zones. Thus a simple cell responds to an optimally oriented bar of optimal size in some narrowly defined position in the visual field. Even a slight misplacement in position without changing the orientation renders the bar ineffective. In contrast, a complex cell is just as specific in its orientation requirements as a simple cell, but less sensitive to the exact positioning of the stimulus. A complex cell which also has a rectangular receptive field – usually bigger than that of a simple cell – will respond wherever an optimal oriented line is projected within the receptive field. Monocular and binocular cells: Most of the cells in cortex are driven by input from both eyes. The receptive fields in respect to the left and right eye lie in the same place. A so-called binocular cell is usually dominated by input from either left or right eye, i.e. the response of the cell is stronger in the case of stimulating the dominant eye versus the non-dominant eye. There are various degrees of ocular dominance and there are also cells exclusively responding to the right and left eye, so-called monocular cells.

Functional Architecture The distribution within the cortex of cells having different receptive field properties is known as functional architecture. If the physiological properties of cells in the primary cortex are examined layer by layer, it emerges, that there is a correlation between complexity and layers. Figure 2.19 shows part of the functional architecture of the striate cortex in relation to afferent thalamic inputs and extrastriate projections. Cells in the LGN have nonoriented receptive fields. M cells have larger receptive fields and higher achromatic contrast sensitivity than P-cells. Only cells in parvocellular subdivisions of the LGN are selective to wavelength. The least-complicated cells are found in layer 4C which gets the majority of LGN input.

Cells in 4C have small circular receptive ﬁelds and low contrast sensitivity (Blasdel & Fitz- patrick, 1984). Not many of cells in layer 4C show clear colour-opponency though 4C is the

termination zone of the geniculate P cells. Cells in upper 4C and layer 4B are characterized by large receptive ﬁelds and high contrast sensitivity, but they respond only to broad-band stimuli (Blasdel & Fitzpatrick, 1984). While many cells in layer 4C lack orientation selectivity the ﬁrst step in the generation of this property occurs within layer 4C. Blasdel & Fitzpatrick (1984) and

Hawken & Parker (1984) report that the proportion of orientation selective cells increases as cells are recorded higher within the layer i.e. from 4C to 4C . The principal population of direction selective cells lies in layer 4B but there is a small popula-

tion of direction selective cells in upper 4C (Hawken et al., 1988). Note that direction selective

cells are only found in upper 4C and layer 4B which provides direct relays to the ’motion’ area MT and the thick stripes of area V2. Orientation selective cells are prominent in all layers above and below layer 4C except the blob regions of layer 2-3 (Hubel & Wiesel, 1977). While many orientation selective cells in layer 4B are of simple type, layers 2-3 also contain populations of 2.4 Early Stages of Visual Information Processing 39

MT V2 Thick Stripes Interstripes Thin Stripes

Interblob Blob Orientation 2-3 Direction

4B, Wavelength 4C α Spatial Frequency

High 4A, 4C β Low

V1 Contrast Sensitivity

High

LGN Low

M P

Figure 2.19: Functional architecture of the primary visual cortex. The figure shows the anatomically identified connections between the subcortical information channels, the principal input layer 4 and the superficial layers of the primary visual cortex The prominent efferent relays to extrastriate areas V2 and MT are also included. The response properties associated with different laminae and compartments are indicated by different symbols depicted on the right side. Please note that receptive field size and achromatic contrast sensitivity are the essential response properties of the geniculate P and M channel. For further details see text.

complex cells. The blobs of layer 2-3 which get direct thalamic input from the interlaminar LGN cells are characterized by cells with large non-oriented receptive ﬁelds and high contrast sensitivities. The blob cells are markedly color-speciﬁc cells. Blobs project in turn to the thin stripes of area V2 (Livingstone & Hubel, 1987). Another fact about lamination is binocular convergence. Cells in

layer 4C are almost exclusively monocular while cells in upper 4C and layer 4B are predominantly binocular. Cells in the other layers have binocular receptive ﬁelds with some preference to one or the other eye (Hubel & Wiesel, 1977).

Columnar Organization

One of the most fundamental observations was that the primary visual cortex is organized into vertical columns (see Fig. 2.20, for review see Hubel & Wiesel, 1977). The distribution of cells 40 Neurobiological Background

Ocular dominance Blobs Layers columns ipsi 1

contra 2-3

4A 4B

4C α

4C β

Orientation columns

LGN

Layer 6&4 5&3 2 1 C I IC P layers M layers

Figure 2.20: Model of a hypercolumn in the monkey primary visual cortex. A single hypercolumn represents the nerve tissue necessary to analyze a discrete region of the visual ﬁeld. A hypercol-

umn contains a complete set of orientation columns representing 360o , a set of left and right ocular dominance columns and several blobs which are the domains of non-oriented, colour speciﬁc cells. A hypercolumn corresponds to an area of about 1 mm. Note that cells in layer 4C are monocular

and most of the cells in lower 4C and mid-4C are non-oriented. The full range of orientation

selectivity is ﬁrst seen in upper 4C (dotted lines). Each ocular dominance column receives input from either the contra- (C) or ipsilateral (I) eye via projections from cells in individual layers of

the LGN; cells from the magnocellular layers 1&2 project to layer 4C and the parvocellular LGN

layers 3-6 project to layer 4C and 4A (projections to 4A are not shown); to Manson & Kandel (1991). 2.5 Summary 41 preferring either the same eye or the same stimulus orientation is by no means random. While making horizontal electrode penetrations Hubel & Wiesel (1968) found that cells sitting side by side have the same ocular dominance. While traversing systematically several millimetres tangential through the striate cortex they found that ocular dominance shifts between the left and right eye occur in more or less regular intervals. The conclusion of many studies - including single cell recordings, anatomical techniques like radioactive tracers and optical recording techniques – was that the striate cortex is subdivided into regions of about 0.4 mm width devoted to either the right or the left eye. Regions sharing the same eye preference are known as ocular dominance columns20. Not only ocular dominance but also receptive ﬁeld orientation is laid out in a columnar fashion. Making a tangential electrode penetration through the striate cortex reveals that neighbouring cells prefer the same orientation. If the electrode advances, one sees a gradual shift of preferred orientation in the recorded cells e.g. in counterclockwise fashion. Again the conclusion of many studies

was that the axis of preferred orientation changes regular across the cortical sheet and approxi- 0 mately every 50m a shift of about 10 in preferred orientation is encountered. If one quantiﬁes the gradual shift in orientation across the cortex one ends up with a map of so-called orientation columns. Thus to cover the visual ﬁeld either by the full 1800 , or the both eyes, requires roughly 1mm of the cortical sheet. The term hypercolumn is used to refer to a set of columns which are responsive to all orientations from a particular region in space with both eyes. A model of the columnar organisation in relation to thalamic inputs to layer 4C and blob/interblob regions in layer 2-3 is shown in Figure 2.20.

2.5 Summary

This chapter has reviewed important aspects of neural information processing in the primate visual system. Convergence and divergence of parallel information channels and recurrent connections are general organisation principles of the brain. It is, however, the specific connectivity structure between cortical neurons which brings about the complexity of visual informations processing. As visual information is transfered from photoreceptors to retinal ganglion cells, it segregates into parallel on- and off-center pathways. Ganglion cells and their geniculate counterparts have nonoriented circular receptive fields which are sensitive to the luminance contrast in the visual field. The retina provides two major information channels each specialized for somewhat different aspects of the visual image: the magnocellular system which is concerned with the processing of low contrast stimuli of high spatial frequency and the parvocellular system which provides information about fine spatial detail of high contrast stimuli. The understanding of the visual cortex is based on the relationship between cortical circuitry, functional architecture and receptive field structure of single neurons. The connections in the

central visual pathway are very speciﬁc. The M and P ganglion cells terminate in anatomically segregated layers of the lateral geniculate nucleus which in turn project to the and subdivision of layer 4C. The cortical cells in different layers of V1 have their own stereotyped pattern of intralaminar, interlaminar and efferent connections with other, extrastriate and subcortical, areas. The cells in the primary visual cortex are arranged functionally into columnar systems: orientation speciﬁc columns, ocular dominance columns and blobs. Neurons within the columnar systems are

20The word column implies that they run perpendicular to the cortical surface; on the other hand the word column is misleading since the ocular dominance regions are stripes running parallel to one another 42 Neurobiological Background

linked by horizontal connections. Thus information ﬂows between different layers in the axis perpendicular to the pial surface and laterally through each layer. The visual system is the largest sensory system in primates and consists of dozens of different areas. Area V1 forms the basis of a hierarchy of progressively more specialized areas. In area V1 the two input channels –LGN-P and LGN-M – are rearranged into three distinct output channels

– the magno-dominated stream which is associated with the direction selective layers, upper 4C and layer 4B, and two parvocellular dominated channels which are associated with the color- speciﬁc blob and orientation selective interblob regions of layer 2-3. At higher visual areas the magno-dominated channel runs through area MT to the collection of areas in the inferior temporal cortex which are associated with motion and depth processing. The parvo-dominated channels project via area V4 to the posterior parietal complex which is associated with the processing of color and form. It has become clear that visual information processing involves parallel pathways, each with its own function; integration of visual information, however, is achieved by interactions between the different pathways already early in visual information processing. One of the fundamental questions which immediately arises is: where and particularly how do the parvo- and magnocellular information channels interact in the primary visual cortex, V1. This question of parvo- and magnocellular convergence in area V1 is still an unsettled question and a topic of current investigations; see for example Sawatari & Callaway, 1996; Vidyasagar et al., 1998. Chapter 3

The Depth-Dependence of Basic Response Properties of Cells in Layer 4C

Although layer 4C is part of the primary visual cortex, most of the cells in layer 4C do not exhibit

the orientation selective responses and binocularity normally associated with striate cortical neurons. On the other hand, sublaminae 4C and 4C receive the vast majority of thalamic afferent input from the M and P division of the LGN. This arrangement ensures that most of the visual information passes through this lamina before becoming available to other cortical cells. Therefore, layer 4C might be seen as the gateway of visual information to the visual cortex. Visual information diverges and converges during its pass through layer 4C and, in this process, becomes reorganized. Due to the location of this reorganization – at the interface between the LGN and the striate cortex – the transformations that occur assume a particular signiﬁcance. Especially the non-overlapping but adjacent terminal zones might form the basis of a ﬁrst integration of parvo- and magnocellular information channels at the step of cortical entry. It is also known that at least three spatially separate sets of efferent neurons in V1 project to area V2 which differ from one another in important physiological characteristics. The question of how each of the incoming channels of thalamic P- and M-input contributes to building the response properties of each of the efferent neuron groups remains uncertain, but it is a crucial issue in terms of understanding the origins of different visual channels.

3.1 Afferent and Efferent Connections of Layer 4C

Layer 4C is of particular importance since it is the principal recipient zone of two major channels of information, provided by the (or M) and (or P) ganglion cells of the retina (Leventhal et al., 1981). These channels relay through the magnocellular (M) and parvocellular (P) layers

respectively of the LGN to cortical area V1; the M ﬁbers terminate in the upper () division of

4C and the P ﬁbers terminate in the lower ( ) half of the layer (Hubel & Wiesel, 1972; Blasdel & Lund, 1983) – see Figure 3.1. The major postsynaptic target of the thalamic axons are spiny

stellate cells which make up the population of excitatory cells in layer 4C. Laminae 4C and 4C differ in their pattern of projections to the superﬁcial layers of the

primary visual cortex. Axons from neurons in lamina 4C ascend through lamina 4B without

giving off collaterals and terminate in lamina 4A. By contrast, axons from lamina 4C terminate 44 The Depth-Dependence of Basic Response Properties of Cells in Layer 4C

Primary Visual Cortex Blob Inter Pia

1-3

4A 4B

4C α

4C β

6 White

LGN M P Lateral Geniculate Nucleus

α β Retinal Ganglioncells

Figure 3.1: Summary diagram of afferent and efferent connections of layer 4C in the macaque monkey striate cortex. The retino-cortical relays terminate in laminae 4C and 4C which are known as the fully segregated termination zones of thalamic P and M axons. Interlaminar axon

projections provide outputs from the layer which form three separate relays staggered in depth of the layer – upper 4C, mid-4C and lower 4C . The relays pass to layer 4B, to layer 3B and layer 4A respectively which contain key sets of efferent neurons projecting to other visual areas. 3.2 Functional Gradient in Depth of Layer 4C 45

40 Rc 30 Kc M 30 20

10 20 K c G e Sensitivity

0 10 Response [impulses/second] Ks e R K 10 s s 0 60 100 3 2 10 1 2 3 0 C50 40 80 (a) [degree] (b) Contrast [%]

Figure 3.2: Quantitative models of the physiological response properties of LGN cells. (a) Gaus-

sian functions representing the center and surround mechanism of the receptive ﬁeld. The pa-

K K s

rameters c and give the peak sensitivity of the center and surround. The points where peak

K e K e R R

s c s sensitivity declines to c and deﬁne the radius of the center and surround, and .

(b) Michaelis-Menten function which is frequently used to describe the response of a LGN cell

M C

to changes in stimulus contrast. The parameters and 50 correspond the maximum spike rate

M G M C

and the contrast at which the response is . The initial slope of 5 is a reasonable measure of the cell’s contrast gain. in lamina 4B (Fitzpatrick et al., 1985). Later Yoshioka et al. (1994) found that interblob, but

probably not blobs, receive relays from mid 4C neurons. Blobs, however, get inputs from layer

4B and 4A which in turn get input from upper 4C and lower 4C . Thus three separate relays with cells of origin staggered in depth of the layer – lower 4C , mid-4C and upper 4C , pass from layer 4C to different strata in the more superﬁcial cortex, each stratum containing key sets

of efferent neurons (see Figure 3.1). If one assumes that mid 4C neurons receive convergent P and M inputs from the initial thalamic relays while upper 4C and lower 4C emphasize M and P characteristics respectively, the ﬁrst merging of thalamocortical channels takes place in layer 4C (Levitt et al., 1996; Bauer et al., 1998a; Scholz et al., 1997). One can summarize that the two subcortical input channels that terminate in fully segregated subdivisions of layer 4C are transformed in three partially overlapping output channels staggered in depth of layer 4C.

3.2 Functional Gradient in Depth of Layer 4C

Receptive ﬁelds of many cells in layer 4C lack the prominent orientation selectivity normally asociated with simple cells. However, the transformation of visual information that occurs between the LGN and the thalamo-recipient layer 4C, entails some degree of rearrangement.

3.2.1 Physiological Properties of LGN-P and LGN-M Cells Physiological studies of the macaque monkey show the P and M cells in the LGN at any given eccentricity to differ in their mean receptive field size, contrast sensitivity and maximum firing rate. As first shown by Kaplan & Shapley (1982), M cells’ firing rates typically exceed those of P 46 The Depth-Dependence of Basic Response Properties of Cells in Layer 4C

100 LGN-M

10 LGN-P Contrast sensitivity

1 0.1 1 10 100 Spatial frequency [cycles/deg] (a) 100 LGN-M

LGN-P 1

0.1 Response amplitude [impulses/sec] 0.01 0.1 1 (b) Contrast

Figure 3.3: (a) Contrast sensitivity vs. spatial frequency curves for a typical LGN-M cell and a typical LGN-P cell; also adapted from Derrington & Lennie (1984). Smooth curves drawn through the points are best-fitting solution of a difference-of-gaussians function (eq. 3.2; e.g. Rodieck, 1965). (b) Response vs. contrast curves for a typical LGN-M cell and a typical LGN- P cell; adapted from Derrington & Lennie (1984). Smooth curves drawn through the points are best-fitting solutions of a Michaelis-Menten function (eq. 3.4; Naka & Rushton, 1966). Reflected in this data is the fact that P and M neurons have different mean response characteristics in terms of maximum firing rate and contrast sensitivity – if defined as the reciprocal of the contrast level which would elicit a criterion response. 3.2 Functional Gradient in Depth of Layer 4C 47 cells at each contrast level of stimulation (see Figure 3.3b). The figure also shows that the contrast sensitivity for P cells is lower than that of M cells, where contrast sensitivity is typically defined as the reciprocal of the contrast level which can elicit criterion responses in the cells. The quantitative terms the receptive field organisation of LGN cells is typically described by a Difference-of-Gaussians (DoG) model (Rodieck, 1965; Enroth-Cugell & Robson, 1966; Linsen-

meier et al., 1982):

xR xR

s c

K e f x K e s c (3.1)

The Gaussian weighting functions of the DoG-model are assumed to describe the sensitivity of the

K K c

center and surround summation region respectively (Figure 3.2a). The parameters s and are

R R s the maximal sensitivity values for the center and the surround mechanism; c and are the radii

of the center and surround mechanisms at the point at which sensitivity is 1/e of maximum.

If sine-wave gratings of different spatial frequency v are used to stimulate the LGN cell and contrast sensitivity is deﬁned as reciprocal contrast threshold 1, the contrast-sensitivity (CS) func-

tion in the spatial-frequency domain is given by:

2 2

2 ( R v ) 2 ( R v )

s c

K R e e CS v K R s

c (3.2)

s c

This particular description, derived by (Enroth-Cugell & Robson, 1966), is the difference of two

Gaussian spectra and results from the convolution of sine-wave gratings with the DoG proﬁle

v f sinv eq. (3.1) in Fourier space, CS . Further Croner & Kaplan (1995) argue, that if the threshold at which contrast sensitivity is measured is within the range of contrast to which the cell responds linearly, then the contrast sensitivity curve scales linearly with the responsivity

of the cell.

K K R R

s c s The parameters c , , , and are typically derived by minimizing the residual sum of

square errors RSS deﬁned as

log CS v log S v

RSS (3.3)

v v where S is the experimentally observed value of contrast sensitivity at spatial frequency . Figure 3.3a shows the contrast sensitivity vs. spatial frequency tuning curves for a typical M cell and a typical P cell in the LGN together with the best fit solution of eq. (3.2). As the M cell has a lower peak spatial frequency, it can be inferred that the receptive field centre size of the M cell is larger than that of the P cell centre. The receptive field size of M cells is on average 2-3 times larger than that of P cells at any particular eccentricity across the visual field representation, although there is considerable variation as well as overlap in the receptive field sizes of both populations (Derrington & Lennie, 1984; Hicks et al., 1983; Spear et al., 1994). Similar results using various measurement techniques have also been obtained by many other investigators (e.g., Shapley, 1990). Naka & Rushton (1966) introduced the Michaelis-Menten equation2 as a suitable model to visual neuroscience and it has become a common model to describe the response to changes in

contrast. The Michaelis-Menten relationship can be written as:

c M

R (3.4)

C c 50

c = (l l )(l + l ) l l

max min max min max The contrast of a sinusiodal grating is usually deﬁned as min were and are the minimum and maximum luminance of the grating. Contrast threshold is deﬁned as contrast at which the stimulus elicit a criterion response. 2originally used to describe saturating enzyme kinetics 48 The Depth-Dependence of Basic Response Properties of Cells in Layer 4C

(a) (b)

Figure 3.4: Measurement of receptive field size and contrast sensitivity as described in the study of Blasdel & Fitzpatrick, 1984. (a) To determine the minimum response field of a non-oriented cell, a small bar of low contrast was systematically moved orthogonally to the edge of the limit under consideration. If the cell stops responding i.e. the response of the cell falls below a critical threshold, the limit of the minimum response field was defined. Eight separate determinations, set at the edge of an imaginary octagon, are used to define the receptive field limits. (b) Contrast threshold was determined against a broad-band background luminance. The luminance contrast of a spot whose dimension coincides with those of the minimum response field was systematically increased until the response of the cell has reached a criterion threshold.

where R is the response of the cell, c is the contrast in percent, M is the maximum response, and C

semi-saturation contrast 50 is the contrast at which the cell has reached 50% of the maximum

M C

response (Figure 3.2b). The parameters and 50 are determined by the best ﬁt of Michaelis- Menten relation to the response vs. contrast curve of the cell’s response.

A suitable measure of the contrast gain G which is deﬁned as the change in response of a

1 1 neuron per unit change in contrast [spikes sec %contrast ] is the initial slope of the best-

ﬁtting Michaelis-Menten relations, given by

dR c

lim

G (3.5)

lim M C C c

50 50

MC 50

Figure 3.3b shows the response vs. contrast function tuning curves for a typical M cell and a typical P cell in the LGN together with the best best-fitting solution of eq. (3.4). The response vs. contrast function are typically determined at the optimal spatial frequency (peak spatial frequency). As the M cell has higher maximum firing rate and and lower semi-saturation contrast it can be inferred that the LGN-M cell has a higher contrast gain than the P-cell (eq. 3.5). This is a general finding at any particular eccentricity across the visual field representation, although there is considerable variation as well as overlap in the contrast gain and maximum spike rate of both populations (Derrington & Lennie, 1984; Hicks et al., 1983; Shapley, 1990; Spear et al., 1994). 3.2 Functional Gradient in Depth of Layer 4C 49

(a)

0.4

0.3 Size [degree] 0.2

0.1

(b) 0.0

0.8

0.6 Contrast 0.4

0.2

4C α 4Cβ

Figure 3.5: (a) Section of the striate cortex stained for Nissl substance. During the course of a single tangential electrode penetration, several lesions (dark spots) were made which are used to reconstruct the location of the recorded units. The dotted lines delimit the part of the penetration which was made in layer 4C. Receptive field size (31 single cells measures) (b) and contrast threshold (31 single cells measures) (c) of non-oriented units recorded along the track through layer 4C, respectively. The minimum response fields of units recorded at the beginning of the traverse through layer 4C were larger than those of units recorded towards the end of the traverse. The luminance contrast threshold of units recoded at successively greater depths in layer 4C increases in a fashion reciprocal to receptive field size. Note that contrast sensitivity is usually defined as reciprocal contrast threshold. Thus the largest receptive field size and highest achromatic contrast

sensitivity are recorded in upper 4C. (adapted from Blasdel & Fitzpatrick, 1984; their Figure 4).

3.2.2 Basic Response Properties of Cells in Layer 4C

There are only two physiological studies which systematically address the response properties of cells in depth of layer 4C across the and subdivision – the discrete termination zones of thalamic LGN-P and LGN-M cells. Blasdel & Fitzpatrick (1984) and Hawken & Parker (1984) recorded from cells in layer 4C while making tangential electrode penetrations through the depth of V1. Blasdel & Fitzpatrick measured both receptive field size and achromatic contrast sensitivity for a population of non- oriented cells; they used small slit or spot stimuli of low contrast to determine a minimum response field for each cell. The cell’s contrast threshold was then measured by using stimuli fitted to the cell’s receptive field center and by gradually changing the contrast of the stimuli. The method used by Blasdel & Fitzpatrick is shown in Figure 3.4. Figure 3.5 shows the original data from one electrode penetration of (Blasdel & Fitzpatrick, 1984). By contrast, Hawken & Parker used drifting sine-wave gratings of optimal spatial frequency and orientation to measure achromatic contrast sensitivity for a group of cells most of them classified as being orientation selective or orientation-biased. To determine achromatic contrast sensitivity the luminance contrast of the sine 50 The Depth-Dependence of Basic Response Properties of Cells in Layer 4C

100 12 Blasdel/Fitzpatrick Fig.4 Hawken/Parker Blasdel/Fitzpatrick Fig.5 10 80

8 60

6 40 4 20 2 Contrast Sensitivity [1/contrast] Contrast Sensitivity [1/contrast]

0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 3.6: Contrast sensitivity of cells in layer 4C as a function of anatomical depth in the layer. Left: Contrast sensitivity values of 58 non-oriented cells from two tangential electrode penetrations adapted from Blasdel & Fitzpatrick (1984), their Figure 4 and 5. The original data given as threshold contrast (Fig. 3.5) was readily converted to the reciprocal contrast representation (1/contrast). Right: Contrast sensitivity of 23 units adapted from Hawken & Parker (1984), their Figure 2c. Many of the cells were classiﬁed as orientation-biased or orientation-selective. One cell from the sample was not included in the plot since it was classiﬁed as an ’outlier’. This unit which was

located at the border of layer 4C and layer 5 had extremely high contrast sensitivity probably located in layer 5A. Note that the absolute values of contrast sensitivity as measured in the two studies differ though the changing trends as a function of depth in layer 4C are compatible.

wave grating was systematically increased until the cell response exceeds a criterion threshold. Due to the different measurement techniques the contrast sensitivity reported in the two studies differs in the absolute value3. Nevertheless, the changing trend in contrast sensitivity as a function of depth in layer 4C is comparable (see Fig. 3.6). Since both sets of data show similar trends, they can be combined in one representation. First, the data of Blasdel & Fitzpatrick were readily converted to the reciprocal contrast representation used by Hawken & Parker. Since the absolute sensitivity values of both studies were not comparable the single cell measures were divided by the mean value of each sample thus obtaining normalized contrast sensitivities. The re-analysed contrast sensitivities are shown in Figure 3.7a. The receptive ﬁeld sizes which are shown in Figure 3.7b are exclusively from the data of Blasdel & Fitzpatrick (1984) since Hawken & Parker (1984) did not report them. Two noticeable features are that there is a gradual decrease in receptive ﬁeld size and contrast sensitivity in the cells recorded from top to bottom of layer 4C, and that the rate of decrease is much

more rapid through the upper half of layer 4C than through the rest of layer 4C, particularly for contrast sensitivity. More precisely, the data can be interpreted as exponential looking gradients for ﬁeld size and contrast sensitivity through depth of layer 4C. In both plots of Figure 3.7 I have divided the depth of layer 4C into 8 equally sized intervals and calculated the mean value and standard deviation of the single unit measures falling in each depth interval. Since there is considerable scatter in the experimental data I use the statistical representations i.e the mean values in Figure 3.7 as a suitable description of basic response properties at different depths of

3As stated by Blasdel & Fitzpatrick their measurement technique produces contrast thresholds that were approximately three times higher than those produced with drifting sine wave gratings 3.2 Functional Gradient in Depth of Layer 4C 51

5 Blasdel/Fitzpatrick Fig.4 Blasdel/Fitzpatrick Fig.5 4 Hawken/Parker

1 Normalized Contrast Sensitivity 0 (a) 4C alpha 4C beta 0.5 0.45 Blasdel/Fitzpatrick Fig.4 Blasdel/Fitzpatrick Fig.5 0.4 0.35 0.3 0.25 0.2 0.15 0.1

Receptive Field Size [degree] 0.05 0 (b) 4C alpha 4C beta

Figure 3.7: Basic response properties of layer 4C spiny stellate neurons. The solid lines in each

panel intersect mean values ( standard deviations) at eight equally sized depth intervals through layer 4C. (a) Normalized contrast sensitivity of layer 4C spiny stellates (see text); plots are combined for the results of Blasdel & Fitzpatrick (1984) and Hawken & Parker (1984). (b) Minimum response ﬁeld (diameter) of layer 4C spiny stellate neurons as reported in the study of Blasdel & Fitzpatrick (1984). Since there are only two receptive ﬁeld size measures falling in the interval at

the top of layer 4C, it is impossible to give a reliable expectation in this region. 52 The Depth-Dependence of Basic Response Properties of Cells in Layer 4C

layer 4C. Please note that there is considerable scatter throughout the whole depth of the layer. How-

ever, the standard deviations are largest in upper 4C. From straightforward extrapolation of the anatomical data one would rather expect variances to be larger across the / border in mid-4C.

3.3 Summary

This chapter has emphasized the importance of layer 4C known as the principle thalamic input

zone of the primary visual cortex. The relays of the LGN-P and LGN-M cells terminate in anatom-

ical segregated but neighbouring subdivisions, and , of layer 4C. Three partially overlapping output channels – lower 4C , mid-4C and upper 4C are shown to relay via different routes to layer 4A, 4B and the superficial layers of area V1. These findings suggest some significant reorganization of afferent parvo- and magnocellular relays in depth of the layer. In physiological respect parvo- and magnocellular cells differ in receptive field size, achromatic contrast sensitivity and maximum firing rate. Physiological studies, from more than one laboratory, which have looked for the depth-dependence of basic response properties – receptive

ﬁeld size and achromatic contrast sensitivity – in layer 4C, report a continuous gradual change of basic response in depth of the layer, rather than a discontinuous abrupt change at the / border as to be expected from the sharp anatomical segregation of LGN-P and LGN-M termination zones. One can interpret the basic response properties of the neurons of layer 4C from top to bottom of the layer, as observed in the studies of Blasdel & Fitzpatrick (1984) and Hawken & Parker (1984), as a gradient in achromatic contrast sensitivity and receptive ﬁeld size between M and P properties. Moreover, the gradient in achromatic contrast sensitivity shows more rapid decrease in

upper 4C than in the lower 2/3 of the layer. It is the functional gradient in basic response properties in depth of layer 4C that I am seeking to replicate by the modelling work presented in the following chapters. Different alternative hypthoseses will be tested how the gradient can emerge from the initial entry of thalamic information channels in two non-overlapping territories. The combination of sets of physiologically distinct inputs to create a vertical functional gradient is of considerable importance to understanding the properties of the relays shown anatomically to emerge from layer 4C and which feed information to different sets on neurons providing extrinsic relays from the region. Chapter 4

Anatomical and Physiological Findings: Thalamic Feedforward Connections

The first functional hypothesis which I want to test is based on the anatomical organisation of feedforward geniculocortical projections. Therefore this chapter reviews the anatomical and physiological findings which are relevant to a feedforward model for the depth-dependence of basic response properties in layer 4C of macaque primary visual cortex. The first part of the chapter provides the detailed anatomical organisation of LGN-P and LGN- M input and thalamic recipient spiny stellate cells of layer 4C. The anatomical data suggests the existence of two subpopulations of LGN-M cells. Therefore the second part of the chapter summarizes the relevant physiological data which is available for the existence of two physiological distinct LGN-M groups. The functional hypotheses which result from the experimental observation and the extrapolation of the relevant anatomical and physiological findings are summarized at the end of the chapter.

4.1 Overview of Relevant Anatomical Findings

The cartoon of Figure 4.1 summarises the anatomical observations of layer 4C which are important to the feedforward model. The figures shows the detailed anatomical organisation of the geniculocortical connection. Three types of thalamic axons have been identified by their specific arborization pattern in depth of the layer. These thalamic relay cells target the the spiny stellate cells which are prominent in the layer.

4.1.1 Thalamic Axons Studies of the terminal ﬁelds of single thalamic axons (Blasdel & Lund, 1983) show that the axon

terminals of single LGN-P cells are restricted to 4C (i.e. lower half of the depth of layer 4C);

each P axon terminal ﬁeld has an approximately circular axon spreading in the lateral dimension no more than 200m but spanning the whole depth of 4C (see Figure 4.2a). Single LGN-M axons

terminating in layer 4C have ﬁelds that can spread up to 1.5 mm along an ocular dominance

stripe and up to three ocular dominance stripes (each approximately 400m wide) in the other dimension (see Figure 4.2b); thereby the axonal arbor of a M cells innervates only one set of ocular dominance columns and systematically gaps the other set of ocular dominance columns ((Blasdel & Lund, 1983)). The ratio of mean ﬁeld width of single P to M axon arbors is about 1:3 (Blasdel 54 Anatomical and Physiological Findings: Thalamic Feedforward Connections

4A 4B

M1 4Cα M2

P 4Cβ

LGN

M P Retinal Ganglion Cells

Figure 4.1: Anatomical organization of LGN inputs into layer 4C of macaque monkey primary visual cortex in comparison with the dendritic organisation and axon projections of the postsynaptic spiny stellate neurons within the layer (modiﬁed from Lund, 1990). The LGN afferents entering layer 4C in V1 can be divided into three sets: P ﬁbers from the parvocellular LGN layers, and

two sub-groups of ﬁbers, M1 and M2, from the LGN-M layers: P axons terminate only in layer 4C , M2 axons cover the whole depth of layer 4C , and M1 axons occupy only the top half of

layer 4C. See text for further discussion. Within layer 4C, spiny stellate neurons are the major postsynaptic targets of LGN axon terminals. Through the depth of layer 4C, these spiny stellate

cells have dendritic overlap over one another. Particularly, cells in the mid layer 4C have dendritic intrusion into both 4C and 4C regions. Outputs from the layer form three sets from top to bottom of the layer: to layer 4B from cells in upper 4C, to layer 3B from cells in middle depth and to layer 4A from the deepest part of the layer. 4.1 Overview of Relevant Anatomical Findings 55

4Cα

4Cβ

100 µm (a)

4C α

4C β

White Matter

100 µ m

(b)

Figure 4.2: (a) Drawing of an afferent LGN-P axon (left). The axons of LGN-P cells typically

arborize in layer 4C forming a tight terminal cluster of boutons. The width of the axon arbor is approximately 200m and spans the whole depth of the sublaminae. The afferent axon arbor can be compared to the drawing of a spiny stellate cell (right) which is located in mid-4C. The dendritic arbor of the spiny stellate cell is of the same size as the afferent LGN-P axon arbor. The spiny stellate cell has a local axonal arbor within layer 4C of roughly the same size as its dendritic ﬁeld; a raising axon trunk projects to layer 3. (b) Drawing of an afferent LGN-M axon. The axon

has a terminal arborization which spans the whole depth of layer 4C and extends laterally about

800m; The LGN-P and LGN-M axons were ﬁlled with horseradish peroxidase (HRP) from a white matter injection. The spiny stellate cell was Golgi-impregnated. (adapted from Blasdel & Lund, 1983). 56 Anatomical and Physiological Findings: Thalamic Feedforward Connections

& Lund, 1983). Most single M axon terminal ﬁelds occupy almost the whole depth of 4C though

terminals may become sparse in upper-most 4C. Here they are termed M2 axons. Rare, large

arbor M axons can be restricted in their terminal field to the top half of 4C overlapping the upper half of the M2 fiber distribution (Blasdel & Lund, 1983, their Fig. 7; Freund et al., 1989, see their Fig. 1A). In the following these axons are called M1 axons. Note that the existence of two M fiber groups is supported by both anatomical studies which have examined M axon morphologies

by intracellular ﬁlling techniques: Blasdel & Lund (1983); Freund et al. (1989). Upper 4C is characterized by a band of heavily myelinated, horizontally oriented, large diameter ﬁbers which may partially correspond to these largest thalamic axons (Lund, 1973).

4.1.2 Local Spiny Stellate Cells

Within layer 4C, excitatory spiny stellate neurons constitute approximately 80% of the total cell

population in the layer and are the major post-synaptic targets of LGN axon terminals. There is

a gradual increase in cell density from 4C to 4C ; the ratio of total number of 4C cells to

that of 4C cells is about 3:5 (O’Kusky & Colonnier, 1982b) which is invariant with eccentricity (Livingstone & Hubel, 1988). Cortical cells in layer 4C are about 50-100 times more numerous than LGN cells (Chow et al., 1950; Peters et al., 1994). While the model creates realistic lateral overlap factors in cortical space for thalamic fiber arbors which are essential to the model, it does not attempt to realistically replicate the cortical cell density. The dendrites of single spiny stellate neurons are of much the same length and richness for single cells through the depth of the layer; an example of a typical cell located in mid-4C is shown in the Figure 4.2. Although the dendritic fields of the spiny stellate cells are highly uniform, the overall orientation of the dendritic field of single neurons changes through the layer from a slight

emphasis on vertical extent for neurons in the division to an emphasis on horizontal stratiﬁcation in upper 4C. The lateral spread of the dendritic arbor is however close to 200 m for single cells at any depth in layer 4C (Lund, 1980). A related important observation is that the total number of excitatory spine synapses per spiny stellate neuron is approximately constant through the depth of layer 4C (Lund & Holbach, 1991; Peters et al., 1994) and each spine receives a single synapse (Mates & Lund, 1983). Since spines are a major sites of excitatory input to these cells, the constant spine number can be interpreted as a constant excitatory load to individual cells through depth of the layer although excitation derives from different sources. Geniculocortical synapses account for only about 5-19% of total excitatory synapses on spiny stellate neurons in layer 4C (Peters et al., 1994; Anderson et al., 1994; Latawiec et al., 1997). The rest of the excitatory terminals are derived from recurrent axon collaterals of layer 6 pyramidal neurons (Anderson et al., 1994), intralaminar local projections from other layer 4C spiny stellate neurons (Fitzpatrick et al., 1985) and a light subcortical input from the claustrum (Carey et al., 1980; LeVay & Sherk, 1981). While geniculocortical synapses account for only a small proportion of the total number of excitatory synapses, they do appear to provide a reliable and potent drive to these cells. Recently Stratford et al. (1996) showed that EPSPs evoked by geniculocortical inputs are unusually large and invariant compared to EPSPs evoked by intracortical synapses. The conclusion of this study1 was that the basic structure of receptive ﬁelds are established by the pattern of thalamic innervation while the more numerous synaptic connections from adjacent neurons act to amplify the initial thalamic excitation.

1done in cat slices 4.2 Overview of Relevant Physiological Findings 57

Parvo-X Magno-X Magno-Y Spatial summation Linear 75% Linear 25% Non-linear Chiasma Latency Long Short Short Spatial Resolution High Medium to high Low (Fundamental) Spatial Resolution – – Medium to high (2nd Harmonic) Contrast Sensitivity Low High High

Table 4.1: Major results reported in Kaplan & Shapley (1982). Almost all LGN-P cells are classified as X-like. A quarter of the LGN-M cells was classified as non-linear (Y-Like). Spatial resolution is defined as that spatial frequency of a drifting sine wave grating at which the response at the fundamental modulation frequency of the cell disappears into the noise. The spatial resolution (2nd Harmonic) of the non-linear response of Y cells is defined with respect to the second harmonic of the modulation frequency. Latencies distribution to electric stimulation of the optic chiasma are shown in Figure 4.3

Throughout the depth of the layer, the spiny stellate cells have their dendrites heavily overlap-

ping one another (Figure 4.1). While P axon terminals occupy only 4C , cells in the lower part of

4C have dendritic intrusion into the 4C division. This suggest that LGN-P axons would therefore also contribute inputs to these lower 4C cells. Similar, neurons in upper 4C have dendrites extending into M axon territory, and therefore these neurons should also receive some LGN-M

inputs. The axons of the LGN-M and P cell populations are heavily overlapped laterally within their respective and territories of layer 4C; this suggests that any single postsynaptic spiny stellate cell has a dendritic ﬁeld receiving input from many laterally overlapped axon ﬁelds. Despite the presence of other inputs, one can make the assumption (important to the model) that the total number of geniculocortical synapses per spiny stellate neuron is constant throughout the depth of layer 4C. Taking this assumption together with the fact that dendritic overlap of spiny stellate neurons occurs through the depth of layer 4C, one can postulate that layer 4C cells receive different numerical proportions of synapses from the LGN-M and P afferent sets to make up a constant proportion of LGN inputs. The proportion of M to P terminals depends on the position of the cell in depth of the layer.

4.2 Overview of Relevant Physiological Findings

Part of the relevant physiological data has already been reviewed in section ’Functional Gradient in Depth of Layer 4C’ of Chapter 3 which concentrates on the physiological properties of LGN-P and LGN-M cells and the gradual change in basic response properties of the postsynaptic spiny stellate cells in depth of layer 4C. The review of relevant anatomical data provides evidence for two sub-groups of geniculate M cells. Here I want to discuss further physiological data which might correspond to the anatomically classiﬁed M2 and M1 cells. 58 Anatomical and Physiological Findings: Thalamic Feedforward Connections

10 LGN-P

6 Number of cells 4 LGN-M (X-like) 2

4 LGN-M (Y-like) 2

0 0 12 3 4 5 Latency [ms]

Figure 4.3: Latency distribution in a population of LGN-P and LGN-M cells to brief electrical

stimulation of the optic chiasm by repetitive constant current pulses of 50s duration (average of three to ﬁve trials). Latency was measured from the start of the stimulus pulse to the peak of the nerve impulse. The average latency for each population is indicated by the arrow below the distributions. LGN-M cells have a mean latency below 2 ms while LGN-P cells have a mean latency close to 3 ms. Note that there is considerable overlap between cell populations and that magnocellular X cells have a slightly longer latency than Y cells though this is not signiﬁcant. (adapted from Kaplan & Shapley (1982)) .

4.2.1 Three Functional Groups of LGN Cells

Kaplan & Shapley (1982) investigated the properties of parvocellular and magnocellular X and Y cells in respect to several response characteristics (see Table 4.1). A quarter of the M cells show nonlinear (Y-like) summation across the receptive ﬁelds, while the majority of M and all P cells exhibit linear (X-like) summation (Kaplan & Shapley, 1982). Blakemore & Vital-Durand (1981) however report a slightly lower percentage of 15% Y cells in the magnocellular layers. The response of an X cell to grating contrast reversal strongly depends on the spatial phase of the grating and is best described by a linear model (Enroth-Cugell & Robson, 1966). By contrast, the response of Y cells to grating contrast reversal shows an additional nonlinear component which is insensitive to the spatial phase of the grating. At high spatial frequency the response of the Y cells is dominated by a frequency-doubled, second harmonic component of the temporal modulation frequency. Kaplan & Shapley (1982) suggest that an array of many ’non-linear subunits’ are arranged in parallel with a conventional, linear receptive ﬁeld center and surround. This model explains why the Y cells appear most non-linear in response 4.2 Overview of Relevant Physiological Findings 59

-0.8

-0.4

0.0 } 4Cα 4Cβ

Cortical Depth } 0.4

0.8 0 10 2030 40 50 60 Latency [ms]

Figure 4.4: Scatterplot of latency as a function of depth in striate cortex. The plot was adapted from Maunsell & Gibson (1992) (their ﬁgure 12; plot of all units). The data shows multiunit latencies recorded in depth of area V1 in alert monkey. Zero depth was physiological determined layer 4C and negative values are towards pia surface. By comparison to proportional depth measures compared to CO stained V1 J. S. Lund believes that layer 4C lies between -0.1 to +0.3 as indicated on the right (personal communication; J. S. Lund). Note that shortest latencies occur in the upper

part of layer 4C which corresponds to the termination zone of anatomically classified M1 cells. to gratings of high spatial frequency, gratings which are to fine to be resolved by the Y cells large linear center but which are still resolvable by the cell’s non-linear subunits. Therefore the magnocellular Y cells form a second functional group with properties distinctly different from the magnocellular X cells. However, as reported in Linsenmeier et al. (1982), the assumption of linear Gaussian sensitivity distributions is adequate for X- and Y-type cells. The reason is that Y-cells respond at double frequency to alternating stationary gratings, but this nonlinearity is not seen when drifting gratings are used (Enroth-Cugell & Robson, 1966). Hochstein & Shapley (1976) have demonstrated that this second harmonic nonlinearity in response to stationary gratings is due to a component of the receptive field separate from the center and surround. Therefore, by stimulating with drifting gartings, and by measuring only the fundamental component of the response modulation (around the mean firing rate) a Gaussian sensitivity distribution can also be applied to the Y cells (Enroth-Cugell & Robson, 1966). A particularly important observation is that Y cells in the magnocellular layers have lower fundamental spatial resolution than the magno-X cells which might indicate a large receptive field center size. Unfortunately, only one of two contrast sensitivity tuning curves of magno-Y cells shown in Kaplan & Shapley (1982) (their Figure 9) exhibits an extremely low peak spatial frequency. A way to study parallel processing in the visual pathway is to measure the speed of impulse conduction velocities in different cell populations. Kaplan & Shapley (1982) demonstrate that 60 Anatomical and Physiological Findings: Thalamic Feedforward Connections

magnocellular cells have shorter latency of response to electric stimulation of the optic chiasma than the parvocellular X cells (see Fig. 4.3). Furthermore magnocellular X cells have a slightly longer latency than the magnocellular Y cells on average. The difference in X and Y type latencies is however not signiﬁcant because of the large variance in the population of X LGN-M cells.

4.2.2 Response Latencies of Cells in Layer 4C

The anatomical data suggests, that the LGN-M cells are anatomically classiﬁed into two subgroups (M1 and M2). Possible physiological counterparts of the M1 axons, tentatively identiﬁed

anatomically as terminating in the upper part of layer 4C, are the data reported by Bullier & Henry (1980). At the time the study of Bullier & Henry was published, the technique of using cytochrome oxidase staining to reveal sharp boundary positions of layers within V1 of the monkey

was not yet developed. It’s now accepted that the Nissl boundaries overemphasize the depth of layer 4B. Therefore their boundary positions for layers 4B, 4C, and 4C have to be corrected to conform with CO staining (compare their Nissl stained cytoarchitecture boundaries with the CO boundaries of Blasdel & Lund, 1983; or Fitzpatrick et al., 1985). With corrected boundaries,

the units they report as having shortest latency input lie in upper 4C (not in layer 4B), medium latency input occurs to cells of middle depth in 4C, and slowest latency is seen in the lower half

of 4C . Nowak et al. (1995) used the same cytoarchitectural boundaries as Bullier & Henry and

so it is very likely that their fast thalamic inputs lie in layer 4C rather than in 4B as reported but they do not provide a precise plot of latency in cortical depth. Maunsell & Gibson (1992) recorded multiunit latencies in depth of V1 in alert monkeys and their data is shown in Figure 4.4; In summary, the data on response latencies in depth of layer 4C emphasize the rapid change of

response properties in upper 4C and a gradual change from P to M properties with rise in depth of the layer.

4.3 Extrapolations from Comparison of Anatomical and Physiologi- cal Findings

The model hypothesis is that the functional gradient for contrast sensitivity and field size in layer 4C, as observed in the studies of Blasdel & Fitzpatrick (1984) and (Hawken & Parker, 1984) (Section 3.2) is derived from a changing ratio of M versus P inputs on spiny stellate neurons at different depths in the 4C layer. As the position of spiny stellate neurons in layer 4C shifts from the very top of the layer to its base, they change the degree of their dendritic overlap into the terminal zones of M and P axons, and therefore one can suggest that the relative weights of these thalamic inputs change accordingly. The section has reviewed the physiological data of three physiologically identified functional groups of LGN cells – parvo-X, magno-X and magno-Y. On the other hand three anatomically classified LGN populations exist – LGN-P, LGN-M2 and LGN-M1. One might speculate that the anatomical identified LGN-M1 cells correspond to the magno-Y cells which are identified by physiological criteria. However, this is not an assumption of the modelling work. The particular issue is discussed in more detail in Section 6.3. I do not attempt to model the non-linear spatial summation of Y-like cells. The most compelling reason is the lack of sufficient experimental data to constrain a model of the nonlinear part of the response which only becomes apparent for high spatial frequency. On the other hand there is a 4.3 Extrapolations from Comparison of Anatomical and Physiological Findings 61 lack of any suitable data for the spiny stellate cells in depth of layer 4C which indicate particular nonlinear parts that might correlate to these inputs. The difference in response latencies in depth of layer 4C which has been observed by more than one study provides a strong additional link to the experimental data on receptive field size and achromatic contrast sensitivity. Because the largest receptive field size, highest achromatic contrast sensitivity and shortest response latencies (i.e. largest diameter axons) occur in upper

4C, the LGN-M1 cells which selectively project to this region may be the anatomical substrate for the physiological data. 62 Anatomical and Physiological Findings: Thalamic Feedforward Connections Chapter 5

A Feedforward Model for the Depth-Dependence of Basic Response Properties in Layer 4C

The aim of the modelling work presented in this chapter is to determine how the neuron response properties of layer 4C are generated – speciﬁcally, to what degree the response properties of the thalamic recipient spiny stellate neurons of layer 4C can be explained simply on the basis of feedforward excitation from the lateral geniculate nucleus (LGN). The model (Bauer et al., 1998a; Bauer et al., 1997; Scholz et al., 1997) attempts to establish how the thalamic afferent terminals from different thalamic cell populations distribute their effective weights on the postsynaptic excitatory neurons of layer 4C to produce the pattern of physiological response properties recorded in depth of the layer; for relevant experimental observations see Chapter 3 and 4. The model is based on purely monocular ON input from the LGN and considers thalamic input channels, M and P, with biologically appropriate anatomical and physiological properties. On purpose I have neglected all sources of intracortical input to layer 4C since I want to address the functional aspects of purely feedforward convergence of the thalamic information channels. The physiological properties of LGN neurons in M and P layers, accurate arbor size and degree of overlap of thalamic axon arbors and appropriate vertical spread of spiny stellate neuron dendritic arbors are fundamental to the model. Therefore, the ﬁrst part of the chapter summarizes the relevant anatomical and physiological properties used to constrain the model. The detailed network architecture, the mathematical description of the model neurons and the algorithms which were used to establish realistic connectivity and reasonable transfer functions for the model neurons follow this summary.

5.1 Anatomical and Physiological Parameters

Because the model is calibrated by realistic anatomical and physiological data, all parameters which are important to the model are summarized and explained in detail in this section. Most of the data are taken from adult macaque monkeys from a region in the visual ﬁeld at eccentricity 5o to 8o . 64 A Feedforward Model for the Depth-Dependence of Basic Response Properties in Layer 4C

Property Value Source

Linear Magniﬁcation

LGN magniﬁcation factor 300 m / degree Connolly & Van Essen, 1984

cortical magniﬁcation factor 1500 m / degree Van Essen et al., 1984

Relative Cell Densities

LGN-P to LGN-M cells 6:1 Livingstone & Hubel, 1988

LGN to layer 4C cells 1:100 Chow et al., 1950 4C to 4C cells 3:5 O’Kusky & Colonnier, 1982a

LGN Axonal Arbor Spread

1 12

LGN-P axonal arbor 200 m (n=32) Blasdel & Lund, 1983

2 Freund et al., 1989 1

LGN-M2 axonal arbor 600 m (n=10) 2

LGN-M1 axonal arbor 1100 m (n=3)

4C Spiny Stellate Cells

dendritic arbor spread 200 m (n=25) Lund, 1980 number of spines per cell constant Lund & Holbach, 1991 geniculate synapses per cell approx. 10% Peters et al., 1994; Latawiec et al., 1997

Table 5.1: Anatomical ﬁndings and magniﬁcation data used in this study. All parameters are taken o from adult macaque monkeys and correspond to 5o - 8 eccentricity. The ratio of LGN-M2 to

LGN-M1 cells was taken to be 8:1, if not mentioned otherwise. The numbers n given in brackets

indicate the sample size on which axonal and dendritic arbor sizes are based. 1 from Blasdel &

Lund; 2 from both Blasdel & Lund and Freund et al.

5.1.1 Anatomical Parameters Table 5.1 summarises the known anatomical data on which the modelling study is based including its sources. Some of the data is reviewed in Chapter 4, other parameter choice need some further explanations.

Geniculate and Cortical Magniﬁcation The visual ﬁeld is not represented isometrically in subcortical and cortical areas (see Section

2.4.2). The standard approach to account for anisotropies between foveal and peripheral vision 2 is to determine areal magnification factors in mm2 /deg . Fig. 5.1 shows the areal magnification of the LGN layers (Connolly & Van Essen, 1984) and the striate cortex (Van Essen et al., 1984) as a function of eccentricity in visual space. Connolly & Van Essen (1984) report only the magnification for the most dorsal and ventral layers of the LGN. Therefore I used a linear interpolation to 5.1 Anatomical and Physiological Parameters 65 ] ] 2 2 14 0.4 /deg /deg 12 2 2 10 0.3

[mm Layer 6 [mm Striate Cortex 8 0.2 6 4 0.1 Layer 1 2 0 0 3 4 5 6 7 8 9 Areal Magnification Areal Magnification 3 4 5 6 7 8 9 Eccentricity [deg] Eccentricity [deg]

Figure 5.1: Left: Areal magniﬁcation in the most dorsal LGN layer 1 and most ventral LGN layer 6. To calculate the average magniﬁcation factor for all LGN layers a linear approximation has been

used. The arrows indicate the average areal magniﬁcation for LGN layer 1 and 6 corresponding

o 2 2 to 5o -8 degree eccentricity respectively. The resulting areal magnification (0.09 mm /deg ) for all LGN layers is given by the mean value of the most ’extreme’ LGN layers 1 and 6. Right: Areal magnification in the striate cortex. To calculate the average magnification factor of the

striate cortex the same linear approximation has been applied. The arrow indicate the average

o 2 2

areal magnification corresponding to 5o -8 degree eccentricity which is (2.25 mm /deg ). o calculate an overall magnification factor of the LGN layers for 5o -8 degree eccentricity (see Fig. 5.1). Although there are differences in the magnification along the horizontal and vertical meridian as well as representation of the inferior and superior visual field these details are neglected due to the lack of suitable experimental data. From the experimental data I inferred a linear magnification

of 300 m per degree of visual space for the LGN layers and an average magniﬁcation factor of

1500 m per degree of visual space for layer 4C in the striate cortex.

Relative Cell Densities

Connolly & Van Essen (1984) claimed that in the LGN the ratio of cell number in the magnocellular system to the number in the parvocellular system representing the same area of visual ﬁeld does change 20-fold with eccentricity. This observation was not conﬁrmed in a later study by (Living- stone & Hubel, 1988) who reported an average parvo-to-magno ratio of 6:1 which is independent of eccentricity. Although cortical cells in layer 4C are much more numerous than cells in the LGN the model does not attempt to replicate realistic cell density neither in the LGN nor in layer 4C of the striate cortex because it does not bear on the results of this particular model. Therefore absolute cell densities are neglected in the model. However, cell ratios in the LGN and in layer 4C

are modelled in accordance with the experimental data i.e. cell ratio of LGN-P to LGN-M 6:1 and 4C to 4C cells 3:5. One particular problem in this respect is to choose a realistic number ratio of LGN-M2 cells to LGN-M1 cells. Note that the sample of identiﬁed LGN-M2 and LGN-M1 (see below and Table 5.1) suggests a ratio of roughly 3:1. The sample size is too small to estimate reliable cell densities. In the model the ratio of LGN-M2 cells to LGN-M1 cells was taken to be 8:1 if not mentioned otherwise. This a priori estimate is based on the assumption that the M1 cells should sample the 66 A Feedforward Model for the Depth-Dependence of Basic Response Properties in Layer 4C

visual image with a reasonable density i.e. the M1 coverage factor1 is at least 1.0, or slightly higher.

LGN Axonal Arbors There are only two studies which investigate the precise arborisation pattern of single LGN-P and LGN-M axons. Blasdel & Lund (1983) provides a sample of 21 intracellular LGN-P axons with

a highly stereotyped appearance and 11 LGN-M axons. One of their M cells showed a stratiﬁed C arborisation restricted to upper which is typical for the postulated M1 class neurons. Two

other examples of LGN-M1 cells are published in (Freund et al., 1989); note that in the study of Freund et al. the boundary between 4C and 4C is placed too high in their Figure 1A (see Blasdel & Lund, 1983, for laminar boundary positions, which are best deﬁned by cytochrome oxidase – CO – staining); this particular observation was conﬁrmed by personal communication with T. Freund.

Layer 4C Spiny Stellate Cells The dendritic ﬁelds of spiny stellate cells in layer 4C are highly uniform in appearance. The lateral

spread of the dendritic ﬁeld is 200m – an estimation based on the reconstruction of 25 single cells (Lund, 1990). The number of spines on a 4C spiny stellate cell is constant. Although estimates of the proportion of asymmetric synapses formed by relay cells from the LGN vary between 5-19% it is reasonable to assume a constant 10% of geniculocortical synapses on a single spiny stellate cell.

5.1.2 Physiological Parameters of LGN cells At the moment there are two studies in the literature which provide an analysis of the receptive field organisation for a sufficiently large population of P and M cells in the macaque monkey. Ta- ble 5.2 shows the corresponding physiological data reported in Croner & Kaplan (1995) and Spear et al. (1994); for details about quantitative models of receptive field organisation and character-

istic physiological parameters see Section 3.2.1. The physiological properties give the center and

R R s

surround radius, c and , of the sensitivity proﬁle according to the DoG model, the maximum G spike rate M and contrast gain of the corresponding LGN population.

The Different Data Sets The data set by Spear et al. (1994) was taken from macaque LGN P- and M-layers but the aim of this study was to reveal the effects of aging on the primate visual system. Therefore the study includes data from a group of young adult and old macaque monkeys. Because the majority of anatomical and physiological studies are done in young adult monkeys only the data corresponding to this group is used to constrain the model parameters. Spear et al. report mostly mean values

and standard deviations which were averaged over different animals using each animal as a single o datum; their data corresponds to a range of eccentricities from 0o and 10 . The data set by Croner & Kaplan (1995) provides a large sample of cells, but the data were collected from retinal P and M ganglion cells rather than their geniculate counterparts. The data were recorded in the LGN in form of excitatory postsynaptic potentials (short: S-potentials) which

defined as ratio of number of M1 cells M1 receptive field center size to the total visual field size 5.1 Anatomical and Physiological Parameters 67

Physiological Croner & Kaplan Spear et al.

Parameters

LGN-P Center Radius c 0.05 0.03 0.087 0.046

Surround Radius s 0.43 0.28 0.53 0.39 Integrated Surround- –

Center Sensitivity K 0.547 0.181 Contrast Gain G 0.963 0.483 0.66 0.32

Max. ﬁring rate M – 31.11 11.32

LGN-M Center Radius c 0.10 0.02 0.103 0.021

Surround Radius s 0.72 0.23 1.16 0.48 Integrated Surround- –

Center Sensitivity K 0.546 0.120 Contrast Gain G 5.896 2.161 1.43 0.87

Max. ﬁring rate M - 45.05 24.45

Table 5.2: Physiological parameters of P and M cells. The table provides median interquar-

tile range for the Croner & Kaplan (1995) data and mean values standard deviations for the

data of Spear et al. (1994). Radii are given in degrees of visual ﬁeld, contrast gains are given in

1 1 b 1 [spikes sec %contrast ] , and neural responses are given in [spikes second ]. Although the Croner & Kaplan data are from retinal ganglion cells, it is reasonable to assume that the organization of receptive ﬁelds found in the LGN does not differ much from those of retinal ganglion cells,

especially at eccentricities near the fovea (personal communication L. Croner). The integrated

2 2

K K R K R

s c c surround / center sensitivity is defined as s . As reported in Croner & Kaplan the average ratio of surround/center sensitivity is constant across the visual field and equal for P and M cells (see also text). Since Croner & Kaplan do not report maximum firing rates of P and M cells I have used the values given in the study of Spear et al. Note that the contrast gain of LGN-M cells differ by a factor of four between the two data sets, while the other measures are within the

same range. For further details see text.

L L c = (L L )L

0 p 0 0

The contrast of an object with luminance p seen on a background , can be deﬁned as: (Weber

c = 100(L L )(L + L ) L L

max min max min max contrast) or min (Rayleigh-Michelson Contrast) where and are the lowest and highest luminance of the pattern. is a method routinely used to monitor retinal afferent activity in the LGN (Kaplan et al., 1990). As Lisa Croner conﬁrmed by personal communication the difference in the physiological prop-

erties between retinal and geniculate populations is small. Their data corresponds to a range of o eccentricities from 5o and 10 .

The integrated sensitivity of a receptive field region is the product of the peak sensitivity and 2 the collecting area, K R . It represents the ”volume” of the receptive field region’s sensitivity en- velope or its total sensitivity. Croner & Kaplan view receptive field regions as ”domes” of roughly constant volume but variable shape which depends on retinal location and cell type. Croner &

Kaplan demonstrate, that the mean ratio of integrated surround sensitivity to integrated center sen-

2 2

K R K K R c

sitivity, s , is roughly constant and independent of cell type. In general, the

c s surround of the cell is less sensitive to contrast than the center and the ratio of sensitivities is such

that the surround can reduce the center’s response by about 55% (K 0.55). Contrast gain is a measure of how much the cell’s response changes with a change in suprathreshold contrast of the stimulus. The contrast gain of a cell is typically measured as the response to 68 A Feedforward Model for the Depth-Dependence of Basic Response Properties in Layer 4C

(drifting) sinusoidal gratings of different contrast where the spatial frequency of the grating is taken to be optimal. The optimal spatial frequency which can be analytically derived from eq. 3.2

is given by

l nK R

opt (5.1)

2 2

R R R

c s

To be sure to isolate the center mechanism of the receptive ﬁeld Croner & Kaplan used center- isolating spatial frequencies which were slightly higher than the optimal spatial frequency deﬁned

above. Spear et al. deﬁned optimal spatial frequencies by the experimentally observed maximum v

response rather than the analytically derived frequency opt of the best-fit solution of the DoG model. Croner & Kaplan defined the contrast gain G as the initial slope of the best-fitting Michaelis- Menten relations (see eq. 3.4, 3.5). Spear et al. did not use a Michaelis-Menten representation of the contrast response function. Instead they defined contrast gain as the slope of a linear regression which best fits to the initial linear rising phase of the response vs. contrast function. Note, however, that, both measures of contrast gain refer to the slope of the initial rising phase of the contrast response function and therefore represent comparable descriptions. Only Spear et al. (1994) report the distribution of maximum firing rates for LGN-P and LGN-M cells.

Physiological Properties of the LGN-M1 cells None of the studies distinguish between two populations of geniculate M cells, but it is reasonable to assume that M1 cells on average have larger receptive fields than the M2 cells: Sclar et al. (1990) report that increase in field size is accompanied by increase in contrast sensitivity along the visual path from LGN to area MT, thus larger fields imply higher contrast sensitivities. Therefore I assume that LGN-M1 cells correspond to the upper fraction of the LGN-M population with respect to contrast gain, maximum response and receptive field size and I study the effect of varying the ratio between LGN-M1 and LGN-M2 cells in detail in the Results Chapter 9. Note that a biological plausible heuristic is applied to constrain the physiological parameters of LGN-M2 and LGN-M1 cells; in other word, there is evidence that receptive field size, contrast gain and maximum response are covarying parameters (Sclar et al., 1990).

Unsettled Questions

2 2

K R R R K K R

c c s s s Center ( c ), surround ( ) radii, and the ratio of the integrated

surround/center sensitivities as well as contrast gain G and maximum response M of the model LGN cells are drawn independently from one-dimensional normal distributions given by the mean values and standard deviations of Tables 5.2 and 6.1. Though the different receptive ﬁeld parameters may be correlated and the distribution of parameter values may be skewed (see Fig 5.2), there are not sufﬁcient experimental data available to us to estimate the corresponding parameters, e.g. calculate covariance of parameters or infer more complicated distributions.

5.1.3 Overview of the Parameter Space The previous sections provide details about all anatomical and physiological data which are used to constrain the model by realistic parameter values. Some of the parameters given above were 5.1 Anatomical and Physiological Parameters 69

Parameter State Linear Magniﬁcation

LGN magnification factor fixed cortical magnification factor fixed

Relative Cell Densities

ratio LGN-P to LGN-M cells ﬁxed ratio LGN-M2 to LGN-M1 cells explored Section 6.2.1, 6.2.3, 6.2.4

ratio LGN to layer 4C cells ﬁxed ratio layer 4C to layer 4C cells ﬁxed

LGN Axonal Arbor Spread

LGN-P axonal arbor fixed LGN-M2 axonal arbor fixed LGN-M1 axonal arbor fixed Projection territories of LGN Axons fixed

4C Spiny Stellate Cells

dendritic arbor spread explored Section 6.1.4 number of spines per cell ﬁxed geniculate synapses per cell ﬁxed

Dendritic Intrusion of 4C Spiny Stellate Cells

into LGN-P and LGN-M projection territory explored Section 6.1.1

into LGN-M2 and LGN-M1 projection territory explored Section 6.2.2

Physiological Properties of LGN cells

contrast threshold of LGN-P and LGN-M cells explored Section 6.1.3

ﬁeld size and contrast processing explored Section 6.2.1, 6.2.3, 6.2.4 of LGN-M2 and LGN-M1 cells

Table 5.3: Overview of all anatomical and physiological parameters which are used to constrain the model. For each parameter I indicated the corresponding state in the model: many parameters were generally ﬁxed. The remaining parameters of the model have been explored in detail because they are crucial to the hypothesis i.e. cannot be derived from the fragmentary experimental data. The right column indicates the paragraph of the ’Results’ section where the corresponding parameter explorations are shown. 70 A Feedforward Model for the Depth-Dependence of Basic Response Properties in Layer 4C

40 4

30 P cells 3 M cells

20 2 count count

10 1

0 0 0 2 4 6 8 10 0 2 4 6 8 10 Contrast Gain Contrast Gain

Figure 5.2: Histogram of contrast gain for P and M cells adapted from Croner & Kaplan, 1995. The arrows indicate mean value of each cell population. Note that there is a group of M cells that has very high contrast gains. The distribution of contrast gain of the M cells may be skewed though there is not sufﬁcient experimental data available to test this hypothesis.

fixed because they are based on reliable experimental data. Other parameters which are crucial to the functional hypothesis and cannot be entirely fixed on the basis of the experimental findings, are explored by computer simulations. Therefore I have summarized the parameter space of the model in Table 5.3 which indicates the state of each model parameter.

5.2 Methods

The modelling work presented in this section addresses two basic approaches:

(i) model I which is based on a population of LGN-P cells and one homogenous population of LGN-M cells

(ii) model II which is based on an LGN-P and two anatomically and physiologically distinct LGN-M2 and LGN-M1 subgroups.

Most of the methods account for both models equally. If there are differences in the basic model set-up of model I and model II I will separately discuss each of both alternatives.

5.2.1 Neural Network Architecture The model consists of three sets of layers: the visual ﬁeld, the LGN and cortical layer 4C (Figure 5.3a). The visual ﬁeld layer is used to present the grating, bar and spot stimuli (discussed in more detail in the next section). Each geniculate layer corresponds to a different population of geniculate cells, hence there are two layers for the P- and M-, and three layers for the P-, M2- and

M1 populations of the corresponding versions of the network model. Thus model I and model II

fP M g S fP M M g corresponds to the LGN conﬁguration S and respectively. Layer 4C

consists of eight sublayers which correspond to eight different depths D . The upper four sublayers 5.2 Methods 71

Layer 4C Depth of V1 D=8 (20x20) D=7 (21x21) D=6 (22x22) D=5 (23x23) D=4 (24x24) 4C α D=3 (25x25) D=2 (26x26) D=1 (27x27) 4C β LGN 4500 µ m M1 (8x8) M2 (23x23) LGN P (61x61)

M (25x25)

P (61x61) µ 900 m 900 µ m

(90x90) VFLD

(a) 3 o

Total Ratio Layer 4C Depth Grid size (no. of cells) no. of cells 4Cα4C: β

D=8 20 x 20 (400) D=7 21 x 21 (441) 4C α 1854 D=6 22 x 22 (484) D=5 23 x 23 (529) 3:5 D=4 24 x 24 (576) D=3 25 x 25 (625) 2606 4C β D=2 26 x 26 (676) D=1 27 x 27 (729)

Ratio Ratio LGN Grid size (no. of cells) Grid size (no. of cells) P:M M2:M1

LGN-M1 8 x 8 (64) LGN-M 25 x 25 (625) 8:1 6:1 LGN-M2 23 x 23 (529) LGN-P 61 x 61 (3721) LGN-P 61 x 61 (3721)

VFLD Grid size (no. of cells)

90 x 90 (8100) (b)

Figure 5.3: (a) Neural network architecture. The model consists of three sets of layers. The visual

ﬁeld is represented by one, the LGN cell populations by either two (M and P, left) or three (M1,

f g

M2, and P, right) and layer 4C by eight sublayers (eight different depth values, D );

the upper and lower four sublayers correspond to 4C and 4C . The numbers denote grid sizes

LGN LGN 4C 4C

N N N

(N and ) and are - for the geniculate and the cortical layers - proportional

S S D D to the cells’ number densities Magniﬁcation factors and relative cell densities are summarized in

Table 5.1. (b) Summary of grid size and cell ratios of the network architecture shown in (a). Grid

LGN LGN

size (N ) and the corresponding cell numbers are given for the model I, left, and

S S model II, right, conﬁguration of the LGN. Note that the number of LGN-M cells is roughly equal in both models and that the ratio of LGN-P to LGN-M cells is taken 6:1. If the LGN-M population

falls into two subclasses the ratio of LGN-M2 to LGN-M1 cells is taken 8:1 (for details see text). A

4C 4C

N N

ratio of 3:5 for layer 4C to 4C cells is adopted by a linear increase in the grid size ( )

D D from top to bottom of layer 4C.

72 A Feedforward Model for the Depth-Dependence of Basic Response Properties in Layer 4C

f g D f g D represent the subdivision and the lower sublayers correspond

to the divisions, respectively. The cells in each sublayer form quadratic grids of different size. Details about grid size and cell

ratios are summarized in Figure 5.3b. The cells in each sublayer in the LGN lie on quadratic grids

LGN LGN

N S fP M M M g

of size N . Grid sizes are different for each subpopulation ,

S S but note that the number of LGN-M2 plus LGN-M1 cells of model II is roughly equal to the number of LGN-M cells of model I. For computational reasons no realistic total cell numbers –

neither in the LGN layers nor in cortical layer 4C – are used, but the ratio of P to M (M2+M1) cells which is 6:1 and the ratio of 4C to 4C neurons which is 3:5 match the experimental data. The grid size of the LGN-M1 layer is ﬁxed to ensure a receptive-ﬁeld coverage factor of greater than 1. M1 cells are the least frequent cell population and thus provide lowest sampling density of all LGN populations according to the hypothesis. Since the ratio of LGN-M2 to LGN-M1 cells is at least 8:1 an appropriate number of LGN-M2 cells is provided. It is further guaranteed that the grid size of the LGN-P layer is proportional to the densities of the M population i.e. the cells in the P

population scale relative to M cells of model I and M2+M1 cells of model II respectively. The cells

4C 4C

N D f g

in each sublayer of layer 4C lie on quadratic grids of size N , where ;

D D note that grid size of sublayers increases linearly from top to bottom of layer 4C. Since the ratio between the total number of layer 4C cells to the total number of geniculate cells is not critical to the feedforward model; it was much less than 100:1.

5.2.2 Connectionist Model Neuron Layers are connected in a feedforward manner. Lateral and recurrent projections in layer 4C are ignored, because the purpose of this model study is to single out the effect of the feedforward convergence of LGN afferents to spiny stellate neurons in layer 4C. Spiny stellate cells at each depth of layer 4C receive their input from LGN neurons, often from more than two different sublayers, which in turn receive their input from the units of the visual ﬁeld layer. Although sophisticated mathematical theories exist which allow detailed modelling of morphological and biophysical features of single neurons (see Section 2.2), I regard this level of detail unnecessary to test the nature of projections to layer 4C. The most compelling reasons to discard a more sophisticated compartmental model approach are the lack of precise experimental data for the biophysical parameters of the neurons involved and the large numbers of cells that must be

modelled in order to obtain quantitative predictions. O

All neurons are modelled as continuous connectionist neurons, whose output values i ,

w O O f I I

ij j i i

i (5.2)

I j w ij

denote the cells’ ﬁring rates. j is the total input of neuron , the weight of the connection

i f between neurons j and , and is a sigmoid transfer function speciﬁc to each population of cells.

5.2.3 Visual Stimulation

x y x y Stimuli are coded by the activity O of the units at positions in the visual ﬁeld layer.

The different stimuli are deﬁned as follows:

r c x y m

Spots of radius and contrast at position m in the visual ﬁeld:

2 2 2

l c x x y y r

0 m

if m

x y

O (5.3) l

0 otherwise 5.2 Methods 73

d d y x

l r l p p a

l l Activity O(x,y) 0 0 Activity O(x,y)

VFLD VFLD

3 degree 3 degree

l p

l 0 Activity O(x,y)

VFLD

3 degree

v-1

x y x y

Figure 5.4: Activity O of the units at positions in the visual ﬁeld layer for different

r d d a y

stimuli: (a) spots of radius ; (b) bars of size x and orientation ; (c) sine wave gratings of

v c c

0 0 variable spatial frequency and phase . Contrast is deﬁned as l p l l .

d d a c x y

y m m

Bars of size x , orientation , contrast at position in the visual ﬁeld:

j x x cos a y y sin a j d l c

m m x 0

O x y j x x sin a y y cos a j d

m y

and m

0 otherwise (5.4)

v c

Sine wave gratings of variable spatial frequency , contrast and phase deﬁned by

c sin v x O x y 0

l 0 l (5.5)

0 0 p

Stimulus contrast is given by l p l l where l denotes the luminance of the spot, the l

bar or the maximum luminance of the sine wave grating, and 0 is the luminance of the background

l cdm

or the mean luminance (Weber contrast). The background luminance 0 was taken 40 to be the same as in the experiments by Croner & Kaplan (1995). Note that contrast values vary from 0.0 to 1.0. Often it is more convenient to consider contrast values ranging from 0% to 100%

(Rayleigh-Michelson contrast2 ) which can be easily inferred from the Weber contrast deﬁnition. 1

) ( + ) c = 100 (

max min max max min Rayleigh-Michelson contrast is deﬁned as lmin l l l where l and l are the lowest and highest luminance of the pattern respectively. 74 A Feedforward Model for the Depth-Dependence of Basic Response Properties in Layer 4C

R c

LGN-P 2.5 2.5 R LGN-M c

1.5 1.5 R s R

weight w s weight w 0.5 0.5 1/e 1/e

-0.5 -1.5 -1 -0.5 00.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 degree degree

Figure 5.5: One-dimensional receptive ﬁeld proﬁles of a typical model LGN-P and

1 2 2

w R expx R

LGN-M cell given by a DoG function: c

1 2 2

K R expx R R R K

c s

s ; parameters , and correspond to the mean values re-

R R K R R

s c s

ported by Croner & Kaplan i.e. c =0.05, =0.43, = 0.547 for the P cell, =0.1, =0.43, w K =0.546 for the M cell (Table 5.2). Note that weights in the model are calculated via a two-

dimensional DoG function given in eq. (5.6) and that each model cell is parametrized by an

R R K

s i

individual parameter set c , and

i i

It is important to mention, that the Nyquist critical frequency for a sine wave grating is given

by cr it =1/ , where denotes the sampling interval (Press et al., 1992). In other words, the critical sampling frequency of a sine wave grating is two sample points per cycle. The sampling

interval in the model is given by the number of neurons in the visual ﬁeld which is 30 cells per degree ( 0.03). Thus the limiting frequency for sine wave gratings in the model is 15 cycles

per degree which is well above the spatial-frequency resolution of LGN-P cells (mean 7.52 3.44 cycles/degree; Spear et al., 1994).

5.2.4 LGN Neurons

As already mentioned each LGN neuron i is parametrized by ﬁve individual physiological param-

R R s

eter: receptive ﬁeld center and surround radius c and , integrated surround /center sensitivity

i i

K G M

i i i , contrast gain and maximum firing rate which are drawn from the normal distributions given in Table 5.2 and 6.1. These parameters are used to establish realistic receptive field size and transfer functions of the model LGN cells. The parameters of the model transfer functions are fitted to realistic response vs. contrast functions.

Receptive Fields

The response properties of the LGN cells are modelled by a Difference-of-Gaussians (DoG) function (Rodieck, 1965; Enroth-Cugell & Robson, 1966; Linsenmeier et al., 1982) which describes the sensitivity to a light pulse across the visual ﬁeld. The antagonistic center-surround organisation is described by two superimposed Gaussian function. Figure 5.5 shows the (one-dimensional)

receptive ﬁeld proﬁles of a model LGN-P and LGN-M cell .

w j x y

j j The corresponding weights ij between a LGN neuron at position and a visual ﬁeld 5.2 Methods 75

p LGN 1 LGN f f p p 0 0 Type 1 Type 2 p 1 0.5 p0

p + ε 3 ( - ) 0 0

p 0 p

0 2 x 2 x

p p p

1 2

Figure 5.6: Rectiﬁed sigmoid transfer functions of model LGN cells. The parameters 0 , , p

and 3 determine the maximum spike rate, the gain, horizontal and vertical offset. Left: Transfer

p p p

3 0

function of type 1; note that 3 i.e. is a small non-negative number . Right:

p p 0 Transfer function of type 2; note that 3 and that the type 2 transfer function is always positive. The type 2 transfer function is used to account for the high threshold of LGN-P cells to

low contrast stimuli.

i x y i

unit at position i are given by:

1 1

2 2 2 2

[(x x ) +(y y ) ] [(x x ) +(y y ) ]

j i j i j i j i

2 2

2R 2R

c s

i i

w e e

2 2

R R

c s i

i (5.6)

R R K

s i

c and denote the center and surround radii, the integrated surround/center sensitivity and

i i

x y i x y

i j j i the position of the receptive ﬁeld center of the geniculate neuron in visual space.

is the position of a unit j in the visual ﬁeld layer. To save computation time, weights were set to

zero outside a circular region of radius s . i

Transfer Functions

Transfer functions are rectiﬁed sigmoid functions

p (xp )

1 2

LGN

f x max p p 0

3 (5.7)

p (xp )

1 2

p p p

1 2

parametrized by the maximum spike rate 0 , the gain and the horizontal and vertical offsets

p p p p p p

0 1 2 3

and 3 summarized by a parameter vector . In the following I consider transfer

p p p

3 0 functions of type 1 ( 3 ) and transfer functions of type 2 ( ) and if not explicitly mentioned in the text transfer functions of type 1 are used. Because I wish to explain the nonlinearity in the gradient of basic response properties in depth of layer 4C, it was necessary to test whether the difference in low contrast processing between P- and M-cells could affect the shape of the curves. If the low contrast processing of LGN cells is tested, I use type 2 transfer functions for the LGN-P cells. Transfer function of type 1: Given the above parameter constraint, the type 1 transfer function

is deﬁned as

p (xp )

1 2

LGN

x max p f

0 (5.8)

p (xp )

1 2

e 76 A Feedforward Model for the Depth-Dependence of Basic Response Properties in Layer 4C

80 LGN-M (experiment) 80 LGN-M (experiment) LGN-P (experiment) LGN-P (experiment)

LGN-M LGN-M

40 40

LGN-P LGN-P (Type 1) (Type 2) Response [spikes/sec] Response [spikes/sec]

0 50 100 0 50 100 Contrast [%] Contrast [%]

Figure 5.7: The contrast response functions of a model LGN-P and LGN-M cell (solid lines) are compared to the experimentally observed contrast response function adapted from Derrington & Lennie (1984). Left: Type 1 transfer functions are used for both model P and M cells. Right: The

LGN-M cell is again characterised by a type 1 transfer function but the P cell is characterised by c

a type 2 transfer function which was ﬁtted with a contrast threshold min =10%. Note that the the

model LGN-P cell does not respond very well for contrast below 10%.

p p 0 where is small and non-negative, much less than 0 ( ). Contrast response functions are usually described by a Michaelis-Menten relationship (Naka

& Rushton, 1966), c

r c

i (5.9)

r i c i where i is the response of cell , denotes the %contrast of an optimal sine wave grating, M

is the maximum response and Ci is the %contrast at which the response has reached 50% of its maximum (semi-saturation). The contrast gain G of a geniculate cell is deﬁned as the slope of the initial rising phase of the response vs. contrast function (see Croner & Kaplan, 1995; Spear et al.,

1994). It therefore directly follows that the semi-saturation contrast is related to the contrast gain

i i i Gi via C M G . Contrast gain, maximum response and receptive ﬁeld parameters were randomly assigned to each LGN neuron drawn from the normal distributions with parameters given in Tables 5.2 and 6.1. Because the model LGN cells have to be ﬁtted to the contrast vs. response characteristic of

the real LGN cells, the parameters of the transfer function have to be optimized. The parameters

p p p

1 2 0 of the type 1 transfer function were determined via a least squares ﬁt of the model predictions – eqs. (5.2), (5.5) and (5.6) for sine wave gratings of optimal spatial frequency eq. (5.1)

– to the actual response given by eq. (5.9). The parameter optimization of the transfer function of

i x y i

neuron at position i is done by minimizing the quadratic error

LGN

E p I c r c f

i i i k

k (5.10)

I c i i

The values k denote the input of neuron for a sine wave grating of optimal spatial frequency

v c i x i

and contrast k centered in the receptive ﬁeld of neuron at position . To ﬁt the model cell’s opt 5.2 Methods 77

responses twelve different contrast values are used, varying from 0% 100%; contrast sampling

points k are spaced equidistant i.e. 0%, 8.33%, , 91.66%, 100%. The optimization of eq. (5.10) was done with a gradient descending method (Press et al.,

1992). It should be mentioned that the start values p of the local minimization routine are chosen

p M p I c p M I c p

i 2 i 1 i i 2

as follows: 0 , , , and ; For local

p p 0 minima was always less than 10% of the maximum response 0 i.e. much smaller than . Transfer function of type 2: Type 2 transfer functions are used only in one special case and only for model LGN-P cells (see Section 6.1.3) to account for differences in the response of geniculate P- and M-cells to low contrast stimuli (Spear et al., 1994; Livingstone & Hubel, 1987). Spear et al. report mean contrast threshold of 4.3% contrast for LGN-P cells. By contrast, Livingstone & Hubel report a contrast thresholds of 10% which is one of the most extreme values found in the literature. Because I try to explain the nonlinearity in the gradient of basic response properties in depth of layer 4C, it was necessary to test whether the difference in low contrast processing

between P- and M-cells could affect the shape of the curves in a qualitative way. Therefore I

chose one of the most extreme values reported for the ( min 10% taken from Livingstone &

Hubel, 1987).

p p 0

Given the parameter constraint 3 the type 2 transfer function is deﬁned as

p (xp )

1 2

LGN

f x p

0 (5.11)

p (xp )

1 2

p p p p

1 2 The parameters 0 were determined in the same way as described above (see eq. 5.10), but with the following exception: to obtain a realistic ﬁt for low contrast stimuli, the actual

response was given by

c c min

r c

i (5.12)

c c min

c p p p

0 1 2

where min denotes the contrast threshold of the geniculate cell. Parameters are opti-

p M p I c

i 2 i

mized via eq. (5.10) and start values of the local minimization are set 0 ,

p M I c p

i i 2 and 1 ;

5.2.5 Cortical Neurons Accurate arbor size of LGN axons and lateral spread of dendritic ﬁelds of 4C spiny stellate cells are essential to establish the feedforward connections between the geniculate cells and the postsynaptic cortical cells at different depths of layer 4C.

Geniculocortical Connectivity Because the connectivity between the LGN and layer 4C is based on anatomical data, a detailed geometric model is used. Figures 5.8a,b show a schematic drawing of the afferent axon arbors in

comparison with spiny stellate dendritic ﬁelds in layer 4C. P and M (M2) axon arbors project to

the full and sublayers respectively; M1 arbors are restricted to the top of 4C . Width and height of spiny stellate dendritic arbors are assumed to be approximately independent of depth (but see Section 6.1.4). I have made two important assumptions to calculate the geniculocortical connectivity:

the three-dimensional spread of dendritic and axonal ﬁelds is roughly cylindric 78 A Feedforward Model for the Depth-Dependence of Basic Response Properties in Layer 4C

Depth µ D 600

7 M µ 200 4Cα 6 200 µ 5 200 µ 4 200 µ 3 200 µ 2 P 4Cβ 200 µ 1 200 µ

(a) 200 µ 200 µ

Depth µ D 600

8 M1 7 M2 µ 200 4Cα 6 1100 µ 200 µ 5 200 µ 4 200 µ 3 200 µ 2 P 4Cβ 200 µ 1 200 µ

(b) 200 µ 200 µ

Figure 5.8: Schematic drawing of afferent axon arbors in comparison with spiny stellate dendritic ﬁelds. Numbers indicate lateral spread. (a) Situation for model I which is based on afferent projections from a LGN-P and a homogenous LGN-M population. (b) Situation for model II which

is based on afferent projections from a LGN-P, LGN-M2, and LGN-M1 populations. P axon arbors project to the , M (M2) arbors to the sublayers respectively. M1 arbors are restricted to the top

half of 4C. Width and height of spiny stellate dendritic arbors are assumed to be approximately independent of depth (but see Section 6.1.4 for numerical simulations with varying dendritic arbor parameters). 5.2 Methods 79

axonal arbor of LGN-M cell j dendritic field of cortical cell i at depth D M

WLGN-M(D) Depth D LGN-P W (D) P

axonal arbor of M LGN-P cell j a ik a P 200 µ ij

Figure 5.9: The ﬁgure shows the axonal arbors of a LGN-P and LGN-M cell j together with the

SD w

dendritic ﬁeld of a cortical neuron i at depth D of layer 4C. The connection weight between

S fP M g i

a geniculate cell j of population and a cortical cell in depth D of layer 4C is

P M a

calculated via the areal overlap of cylinder bases a and . The vertical overlap of axonal and

ij ij

LGN P LGN M

D LGN D dendritic cylinders is represented by the model parameters W and .

Note that the areal overlap is independent of depth D and it is the vertical overlap in depth which determines the proportional weight from each geniculate population. It is the vertical overlap i.e. the thalamic weight portion which is important to the model and which cannot be derived from the experimental data.

the distribution of thalamic boutons and dendritic spines is uniform within the cylinder volumes.

Under these assumptions the geniculocortical weights are interpreted as the percentage of spines which are occupied by the synapse of a geniculate neuron. In other words, geniculocortical weights

represent the probability that a geniculate synapse derives from a particular geniculate cell.

j S

The weight w of the connection between a geniculate cell of population and a cortical

ij D

cell i in layer scale with the three-dimensional overlap of the corresponding axonal and dendritic

fP M g S fP M M g arbors. The geniculate populations correspond to S for model I and for model II, respectively. The three-dimensional overlap of axonal and dendritic arbors is calculated via a two-dimensional areal overlap of cylinder bases and the vertical overlap of cylinders in

depth (see Figure 5.9). S

The two-dimensional areal overlap a is the circular cross-sections of the corresponding axonal ij

and dendritic arbors and can be derived from the anatomical parameters; for details see Figure 5.8,

SD S

5.9 and Table 5.1. The weight w of a geniculate cell of population also scales with the ij

vertical overlap of cylinders in depth D of layer 4C. This is indicated by the different heights and

locations of cylinders in depth D (see Figures 5.8 and 5.9). Because it is the overlap in depth of layer 4C which is crucial to the model I have introduced

a separate set of parameters. The layer speciﬁcity of afferent termination and dendritic sam-

LGN S

D pling zones is taken into account by the thalamic weight portion W which denotes the probability that a spiny stellate neuron receives a synaptic contact from a cell of the geniculate

80 A Feedforward Model for the Depth-Dependence of Basic Response Properties in Layer 4C D

subpopulation S . Thus the thalamic weight portions for depth of layer 4C satisfy the constraint

LGN S

W (model I) (5.13)

S fP M g

LGN S

W (model II) (5.14)

S fP M 2M 1g

Since the number of spines is fairly constant for each spiny stellate cell i and a constant percentage SD

of spines is occupied by thalamic axon terminals, the synaptic weights w have to be normalized, ij

i.e.

LGN S

W D

w a P

ij (5.15)

fP M g S fP M M g

where S and respectively.

LGN S

D The change of the quantities W with depth must be consistent with the overall anatomical data i.e. there should be a linear transition from P to M-input with rise in depth of layer 4C (see Figure 5.8), but the numerical values cannot be derived from the experimental data. In order to explore the inﬂuence of thalamic weight portions on receptive ﬁeld sizes and contrast sensitivities different thalamic weight distributions have to be tested (see Results section).

Measurement of Receptive Field Size and Contrast Sensitivity Receptive ﬁeld size and contrast sensitivity are calculated as described in Blasdel & Fitzpatrick

(1984) (see Section 3.2.2, Figure 3.4):

o o

d d c y

A small bar of low contrast, eq. (5.4) with x , and 20%, is

systematically moved along each of eight directions l from the

center towards the border of the receptive ﬁeld. The angle a of the bar in eq. (5.4)

was chosen perpendicular to the orientation of movement i.e. a .

r I

The average distance at which the total input i (see eq. (5.2)) of the cortical cell

i t

falls below a given threshold 0 is interpreted as the radius of the receptive ﬁeld. i

Subsequently a spot of radius r is ﬁtted to the individual minimum response ﬁeld, I

and its contrast is increased until the cell’s input i reaches another ﬁxed threshold t

1 . Contrast is increased iteratively by 1%. Contrast sensitivity is then deﬁned as the t

reciprocal threshold contrast for the corresponding total input 1 .

Figure 5.10 and 5.11 show typical receptive field profiles and contrast response functions of cells at different depths of model layer 4C. It is important to emphasize that it is the nonlinear trend in receptive field size and contrast sensitivity in depth of layer 4C that has to be matched by the model simulations. Contrast sensitivity curves as a function of depth are normalized to the average contrast sensitivity of the total sample in order to allow a comparison with data (for details refer to Section 3.2.2 of Chapter 3). Receptive field size and contrast sensitivity are ”threshold properties” i.e. both response properties depend on a predefined critical threshold for the neuron response. Thus in the purely feedforward model considered in this section it is not necessary to to define an elaborate transfer function. This becomes different in the next chapter when I consider recurrent connections in layer 4C. 5.2 Methods 81

1.0 D=8 Input I

0.0 7 8 7 6 degree 6 degree 5

1.0 D=5 Input I

8 7 0.0 8 7 6 degree 6 degree 5

1.0 D=1 Input I

0.0 8 7 7 6 degree 6 degree 5

Figure 5.10: Three examples of simulated receptive ﬁeld proﬁles of model cortical cells living in lower 4C (depth D=1), mid-4C (D=5) and upper 4C (D=8). The cells are located in the center

of each cortical layer. Input was calculated for light pulses (small spots of radius r=0.003 deg r ee and contrast c=100%) which are placed systematically in different locations in the visual ﬁeld layer. Thus each plot shows the sensitivity of the cortical to input from different regions of the visual ﬁeld. Note that the region where the light pulses could elicit a criterion input value is large

in upper 4C, medium size in mid 4C and small in lower 4C . This in turn indicates that receptive ﬁeld size is large in upper 4C (D=8), medium in mid-4C (D=4) and small in lower 4C . 82 A Feedforward Model for the Depth-Dependence of Basic Response Properties in Layer 4C

40 D=8

30 D=5 Input I 20 D=1

10 t 1

0 0c(D=8) c(D=5) c(D=1) 60 80 100 contrast [%]

Figure 5.11: Three examples of simulated contrast-input functions for model cortical cells living in lower 4C (depth D=1), mid-4C (D=5) and upper 4C (D=8). Input was calculated for spots of optimal size (i.e. ﬁtted to the individual minimum response ﬁeld) while the contrast of the

spot was systematically increased by steps of 1% contrast. The contrast at which the input of the t

cortical cell exceeds a certain threshold e.g. 1 =10.0 is taken as threshold contrast c. Contrast

sensitivity is deﬁned as reciprocal threshold contrast 1/c. Note that threshold contrast at different depths decreases i.e. c(D=8) c(D=5) c(D=1) which in turn implies that contrast sensitivity is

highest in upper 4C.

5.2.6 Implementation The model was implemented in C on a standard Unix workstation. For simulations an SGI power challenge computer was used. The average set-up time of the connection weights and the fit of the LGN transfer functions is close to one hour, but depends on the hardware configuration of course. The average amount of computation time to calculate the response properties of a cortical cell is close to one minute. Because the receptive field properties of the geniculate cells are noisy, the geniculate input cannot be calculated in a straightforward way i.e. via the convolution of receptive field profile and the stimulus in Fourier space. Thus there is a trade-off between memory usage – if the connection weights are stored – and computation time – if connection weights are re-calculated each time they are used. In the current implementation of the simulator the connection weights are stored which results in a total memory size of roughly 250 MB for the network configuration

shown in Figure 5.3. The calculation of the areal overlap of cylinder base was performed in mu discretized space using a resolution of 1000 pixels per 4500 m (0.22 pixels/ m). The parameter interface of the simulator is speciﬁed in Appendix A, Section A.1. Chapter 6

Results of the Feedforward Model

This chapter presents the numerical results of the feedforward model introduced in Chapter 5. I systematically explore which are the essential parameters of the feedforward model that are able to induce the functional gradient in basic response properties in depth of the layer (see Chapter 3). The ﬁrst part of the chapter considers feedforward input from the LGN-P population and one homogenous population of LGN-M cells. I explore how the differential convergence of P- and M- cells affects receptive ﬁeld size and achromatic contrast sensitivity of the postsynaptic spiny stellate cells at different depths of the layer. It is further considered how other model parameters, i.e. cortical threshold parameters, differential low contrast processing of LGN-P and LGN-M cells and lateral spread of dendritic arbor affect the basic response properties of cells in model layer 4C. In the second part of the chapter I concentrate on the feedforward model which is based on

two anatomically identiﬁed LGN-M subgroups: LGN-M1 cells which preferentially arborize in upper 4C and LGN-M2 cells which project to the whole depth of 4C . Since neither the number ratio nor the physiological properties of the LGN-M1 cells are constrained by the experimental data, I test how differences in number ratio, receptive ﬁeld size and contrast sensitivity of the two

LGN-M populations affect the basic response properties of model cortical cells in layer 4C. It is further explored how the feedforward projections which emphasize different strata in depth of

layer 4C combine to produce the almost exponential increase in contrast sensitivity in depth of the layer. The parameter explorations are followed by a discussion of the likelihood of the feedforward circuitry in the context of anatomical and physiological evidence. Moreover suggestions for new experiments are made that may conﬁrm or refute the circuitry suggested by the functional model of geniculocortical information transfer.

6.1 Results Model I: One LGN-M population

In the following I consider the feedforward model with one M population (see Figure 5.3 and 5.8) which I call model I. Both data sets, Croner & Kaplan (1995) and Spear et al. (1994), were used to estimate the parameters of geniculate neurons, but numerical simulations lead to virtually identical conclusions. Therefore, in most cases I present only the results for the Croner & Kaplan data. The corresponding simulation results for the Spear et al. data set are summarized in Appendix A, Section A.2. 84 Results of the Feedforward Model

W LGN-P W LGN-PLGN-P W LGN-M W LGN-M 100 100

75 75

50 50

25 25 Thalamic Weight Portion [%] 87 6 5 4 3 2 1 D Thalamic Weight Portion [%] 8 7 6 5 4 3 2 1 D (a) 4C alpha 4C beta (b) 4C alpha 4C beta LGN-P LGN-P W W LGN-M W W LGN-M 100 100

75 75

50 50

25 25

87 6 5 4 3 2 1 D Thalamic Weight Portion [%] 87 6 5 4 3 2 1 D Thalamic Weight Portion [%] (c) 4C alpha 4C beta (d) 4C alpha 4C beta

Figure 6.1: Proportion of P- and M-inputs to spiny stellate cells as a function of depth D in model

LGN P LGN M

D W D layer 4C. Each plot shows the thalamic weight portions W and at eight

discrete depths of layer 4C. (a) Full segregation of P- and M-inputs. (b) Small zone of conver-

gence at the border between layers 4C and layer 4C ( =4,5). (c) Spiny stellate neurons deeper

D in the and divisions (up to sublayer =3,6) are allowed to listen to both types of incoming af-

ferents. (d) Spiny stellate neurons at almost every depth of layer 4C (up to sublayers D =2,7) make intrusions into the termination zones of both pathways. The weight distribution (c) corresponds to the cartoon in Figure 5.3b and thus represents the proportional overlap of dendritic and axonal fields in depth of layer 4C as observed anatomically. It results in the best fit of simulated and real physiological data in depth of layer 4C and it is furthermore the most plausible configuration in terms of anatomical evidence.

6.1.1 Percentage of P- vs. M-inputs as a Function of Depth

LGN P

I performed numerical simulations for the four sets of thalamic weight portions W and

LGN M

D W as shown in Figure 6.1. The predicted receptive field sizes and contrast sensitivities are summarized in Fig. 6.2. The overall shape of the curves changes from a step function for segregated inputs to an almost linear function in the case of heavily convergent thalamic input. As the degree of convergence increases, the curves become smoother and the flat plateaus at the top and bottom of layer 4C which resemble pure LGN-M and LGN-P properties become less significant. Note that none of the

curves shows the dramatic increase of contrast sensitivity in upper 4C seen in the experimental

data. A good match, however, is obtained for lower 4C and mid-4C for the weight distribution of Figure 6.1c, which is the biologically most realistic given the anatomical ﬁndings. This set of weights is used as a baseline for further modelling steps. 6.1 Results Model I: One LGN-M population 85

0.4 4 weights (a) weights (a) 0.35 weights (b) 3.5 weights (b) 0.3 weights (c) 3 weights (c) weights (d) weights (d) 0.25 experiment 2.5 experiment 0.2 2 0.15 1.5 0.1 1

Receptive Field Size [degree] 0.05 0.5 Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 6.2: Parameter exploration of model I (one M pathway). The ﬁgure shows receptive ﬁeld

size (left column) and contrast sensitivity (right column) of layer 4C spiny stellate neurons as a

D function of depth D , . Symbols denote mean values of 20 cells selected at random from each sublayer; plots of the experimental data from Figure 3.7 are added for comparison. Each

curve corresponds to a particular thalamic weight distribution of Figure 6.1. Cortical threshold

t t 1 parameters were 0 and .

6.1.2 Threshold Dependence of Response Properties

0.4 4 t0=1.60 t1=8.00 0.35 t0=2.05 3.5 t1=11.00 0.3 t0=2.45 3 t1=13.75 t0=2.15 t1=15.00 0.25 experiment 2.5 experiment 0.2 2 0.15 1.5 0.1 1 0.05 0.5 Receptive Field Size [degrees] Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 6.3: Parameter exploration of model I (one M pathway). The ﬁgure shows the effect of

t t 1 different values of the threshold parameters 0 and of the cortical transfer function on receptive ﬁeld size (left) and contrast sensitivity (right) of layer 4C spiny stellate neurons. Each curve corresponds to a particular choice of the threshold parameter. The thalamic weight distribution was taken from Figure 6.1c. For other conventions see caption of Figure 6.2. The much smaller

threshold dependence of the contrast sensitivity curves is due to the normalization of the simulated t

data. Changes in absolute contrast sensitivity values with threshold parameter 1 are comparable to the changes in the receptive ﬁeld size curves.

Next I ask how the response properties of the cortical model neurons change with the numerical

t t 1 values of the thresholds 0 and which are free model parameters associated with the response properties of the cortical cells (see Section 5.2.5). Figure 6.3 shows the receptive ﬁeld size and

86 Results of the Feedforward Model

t t 1 contrast sensitivity curves for various thresholds 0 and . The simulation results indicate that a change in threshold parameters affect the absolute values. The response properties increase when thresholds decrease, but no combination of thresholds values can account for the strong increase of contrast sensitivity at the top of 4C. Neither the receptive ﬁeld size curves nor the contrast sensitivity curves show any signiﬁcant changes in shape which depends on the threshold value. The much reduced threshold dependence of the contrast sensitivity curves in Figure 6.3 is due to the normalization of contrast sensitivity values. Note that the normalized curves indicate the deviation from the mean contrast sensitivity. Therefore, the similarity of normalized contrast

sensitivity curves blurs the shift in the mean contrast sensitivity. The absolute contrast sensitivity t

changes with threshold parameter 1 are comparable to those seen in the receptive ﬁeld size data.

t t 1

In summary, the variations of cortical threshold parameters 0 and over a considerable large

t t 1 range ( 0 - and - ) lead to different absolute values of receptive ﬁeld size and contrast sensitivity curves, but leave the shape of both curves unchanged.

6.1.3 Transfer Functions of Geniculate P-cells

0.4 4 type 2 type 2 0.35 type 1 3.5 type 1 0.3 experiment 3 experiment 0.25 2.5 0.2 2 0.15 1.5 0.1 1 0.05 0.5 Receptive Field Size [degrees] Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 6.4: Parameter exploration of model I (one M pathway). The ﬁgure shows the effect of pronounced differences in the low contrast processing of LGN-P and LGN-M cells on receptive ﬁeld size (left) and contrast sensitivity (right) of layer 4C spiny stellate neurons. The simulated

curves correspond to response properties for type 1 vs. type 2 LGN-P transfer functions. The

thalamic weight distribution was taken from Figure 6.1c. Threshold parameters were 0

and 1 . For other conventions see caption of Figure 6.2. The higher normalized contrast

sensitivity at the top of layer 4C in the type 2 vs. the type 1 curve is an artefact of normalization;

the absolute contrast sensitivities at the top of layer 4C are equal for both type 2 and type 1 simulations.

I seek to explain the nonlinear gradients of basic response properties in depth of layer 4C. There- fore, it was necessary to test if differential processing of low contrast stimuli of the P- and M- cells could affect receptive ﬁeld size and contrast sensitivity of cortical cells in a qualitative way, i.e. could induce symmetry breaking in depth of layer 4C. Therefore, for simulation results discussed in this section, a type 2 transfer function was chosen for model P-cells (cf. Section 5.2.4). Figure 6.4b shows the effect of the type 1 and type 2 transfer functions when applied to geniculate P cells. Given the fact, that type 2 transfer functions lead to model P cells which remain basically silent below contrast values of 10%, it is not surprising that the differences in con- 6.1 Results Model I: One LGN-M population 87

Depth µ D 600

250 µ 7 M 4Cα 6 235 µ 5 221 µ 4 207 µ 3 193 µ 2 P 4Cβ 178 µ 1 164 µ

(a) 200 µ 150 µ

W LGN-P LGN-M W

100 75 50 25

Thalamic Weight Portion [%] 8 7 6 5 43 2 1 D (b) 4C alpha 4C beta

Figure 6.5: More realistic model of dendritic arbors size of spiny stellate cells in depth of layer 4C. (a) Cartoon of afferent axon arbors in comparison with changes in dendritic arbor geometry of

spiny stellate cells (compare Figure 5.8a). Numbers indicate lateral spread. The lateral spread of the dendritic ﬁelds changes linearly from 150 m at the bottom to 250 m at the top of layer 4C.

The elongation of dendritic ﬁelds in vertical direction decreases with rise in depth – towards an

LGN P

W D

elongation in lateral direction in upper 4C. (b) Thalamic weight distributions and

LGN M

D W which correspond to the geometric model shown in (a). The vertically elongated

ﬁelds of spiny stellate cells deep in layer 4C (D=2) reach into the input zone of LGN-M cells.

By contrast, the pronounced horizontal elongation of dendritic ﬁelds in upper 4C (D=6,7,8) restricts thalamic input of spiny stellate cells to pure LGN-M input. Note that there are basically no changes of thalamic weights in mid-4C (D=4,5) if compared to thalamic weight distribution based on uniform dendritic ﬁelds (Figure 6.1c).

88 Results of the Feedforward Model trast sensitivity and receptive ﬁeld size between cells in lower 4C and upper 4C become more

pronounced and that the region of strongest increase of receptive ﬁeld size is shifted into 4C .

Without normalization of the simulation data a similar shift into 4C is also apparent for the contrast sensitivity curve. Unfortunately, this observation is obscured by the normalization procedure and thus a shift in the normalized contrast sensitivity curve in Figure 6.4 is not clearly visible. The overall shape of the curves remains sigmoidal, though, and the contrast sensitivity remains

plateau-like in upper 4C. Note that the higher values of the normalized contrast sensitivity at the

top of layer 4C in the type 2 curve is an artefact of normalization. The values of the absolute

contrast sensitivity at the top of layer 4C are equal for both type 2 and type 1 simulations.

6.1.4 Dendritic Arbor Size of Layer 4C Spiny Stellate Neurons

0.4 4 changing geometry changing geometry 0.35 uniform geometry 3.5 uniform geometry 0.3 experiment 3 experiment 0.25 2.5 0.2 2 0.15 1.5 0.1 1 0.05 0.5 Receptive Field Size [degrees] Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 6.6: Parameter exploration of model I (one M pathway). The ﬁgure shows the effect of changes in the dendritic arbor geometry on receptive ﬁeld size (left) and contrast sensitivity (right)

of layer 4C spiny stellate neurons. The lateral spread of the dendritic ﬁelds changed from 150 m

at the bottom to 250 m at the top of layer 4C (see Figure 6.5a). The thalamic weight distribution of Figure 6.1c was adapted to account for the vertical vs. horizontal elongation of the dendritic ﬁelds in lower and upper layer 4C (see Figure 6.5b). The response properties for spiny stellate

cells with uniform dendritic ﬁeld geometry are also shown (compare Figure 6.2 , weights (c)).

t t 1 Threshold parameters were 0 and . For other conventions see caption of Figure 6.2.

So far I have assumed that the lateral and vertical spread of layer 4C spiny stellate neurons are independent of depth but anatomical ﬁndings suggest that spiny stellate dendritic arbors at the bottom of layer 4C are more strongly elongated in the vertical direction while dendrites of neurons at the top of layer 4C show an increased lateral spread (see Section 4.1 ”Overview of Relevant Anatomical Findings”). In order to study the effect of changing dendritic arbor geometry, dendritic ﬁelds of neurons

at the bottom of layer 4C were allowed to reach into the termination zone of the M pathway while dendrites of upper 4C neurons were conﬁned to the 4C subdivision. Also, the lateral

diameter of the dendritic spread was assumed to change linearly from 150m at the bottom of

4C to 250m at the very top (Jennifer S. Lund, personal communication). The simulation results (Figure 6.6) still show curves of receptive ﬁeld size and contrast sensitivity which saturate at the top of layer 4C similar to the other results shown in Figure 6.2. Effects are apparent in upper

6.1 Results Model I: One LGN-M population 89 4C (D=6,7,8) and lower 4C (D=1,2,3) due to changes in the lateral spread and thalamic weight portions. The changes in the geometry of dendritic arbors by an amount that is plausible in terms of anatomical evidence do not affect the shape dramatically due to the marginal changes in the model parameters. Pronounced changes in the geometry of dendritic arbors result in a stronger effects on the simulated curves (not shown), however, the asymmetries in dendritic ﬁeld geometry between the top and the bottom of the layer are biologically unrealistic. Thus a more realistic model of dendritic ﬁeld lateral spread is still not able to explain the exponential increase of contrast

sensitivity at the top of layer 4C.

6.1.5 Best Predictions

0.4 4 simulation (Croner/Kaplan) simulation (Croner/Kaplan) 0.35 simulation (Spear et al.) 3.5 simulation (Spear et al.) experiment experiment 0.3 3 0.25 2.5 0.2 2 0.15 1.5 0.1 1

Receptive Field Size [degree] 0.05 0.5 Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 6.7: Best fits for receptive field size and contrast sensitivity curves for model I (one LGN-M populations) based on the Croner & Kaplan and Spear et al. data set. The figure show mean values

and standard deviations for the eight layers of model-layer 4C Left: Receptive ﬁeld size as a

t t 0 function of depth; threshold parameters were 0 (for Croner & Kaplan) and (for

Spear et al.). Right: Normalized contrast sensitivity as a function of depth; threshold parameter

t t 1 were 1 (for Croner & Kaplan) and (for Spear et al.). The physiological parameters of P, M population are listed in Table 5.2 and the thalamic weight portions are given in Figure 6.1c.

The best predictions of the model were selected according to the following criteria:

1. The overall correspondence of the mean values in the whole depth of layer 4C (D=1,...,8) for simulated receptive ﬁeld size and contrast sensitivity with the experimental data.

2. The plausibility of the parameter regime compared to known experimental data.

Please note that the biological constraints i.e. plausibility of the parameters do not allow to use a simple least squares fit. Figure 6.7 shows the best predictions of model I based on one homogenous population of LGN- M cells, considering the overall correspondence to experimental findings. The proportional overlap of dendritic and axonal fields in depth of the layer corresponds to the most plausible overlap in terms of anatomical evidence (compare Figure 6.1c and 5.8a). Note that standard deviations of the model predictions are without exception smaller than those observed in the experimental data. 90 Results of the Feedforward Model

This is what to be expected, since most sources of anatomical noise e.g. variability in dendritic and axonal arbor sizes were neglected in this particular model. It should be mentioned that the best contrast sensitivity curve adopted for the LGN data set of Spear et al. (1994) appears to provide an overall bad fit to the experimental data. However, the receptive field size curve perfectly fits to the experimental data through the lower two-third of the layer. The small deviations of normalized contrast sensitivity in depth of layer 4C are due to the small differences in contrast gain between LGN-P and LGN-M cells for the data set of Spear et al.. No better fit of the contrast sensitivity curve can be adapted for this data set (compare Appendix A, Section A.2). I have tested the statistical significance of the best fit of model I predictions and the experimental data. The results are summarized in Appendix A, Section A.3. The statistical tests confirm

the conclusion that predicted mean values in upper 4C are signiﬁcantly different from the experimentally observed mean values; the signiﬁcance level is particular high for contrast sensitivity in

upper 4C.

6.1.6 Summary

The results suggest that model I is not able to produce a good ﬁt to the data in upper 4C though it leads to reasonable results for the rest of 4C. The parameter explorations of this section have demonstrated that:

1. Biological realistic convergence of LGN-P and LGN-M input – induced by dendritic overlap of spiny stellate cells across the / border of layer 4C – is an essential mechanism to produce a functional gradient in basic response properties in depth of the layer.

2. The shape of functional gradient is robust against changes in cortical threshold parameters.

3. A more realistic model of low contrast processing of LGN-P cells and dendritic arbor size of spiny stellate cells does not alter the overall sigmoid shape of receptive ﬁeld size and contrast sensitivity curves in depth of layer 4C. 6.2 Results Model II: Two LGN-M populations 91

6.2 Results Model II: Two LGN-M populations

The numerical simulations of the previous section showed that model I is not able to produce

a good ﬁt to the data in upper 4C, though it leads to reasonable results for the rest of 4C. Therefore, in this section I concentrate on the assumption of two LGN-M populations and explore

the parameter space of model II (Figure 5.3 and 5.8b) with focus on the upper 4C region and on the properties of the postulated M1 and M2 afferents. Again, both data sets, Croner & Kaplan (1995) and Spear et al. (1994), were used to estimate the parameters of geniculate neurons, but numerical simulations lead to virtually identical conclusions. Therefore, in most cases I present only the results for the Croner & Kaplan data. The corresponding results for the (Spear et al., 1994) data set are shown in Appendix A, Section A.2.

6.2.1 Physiological Properties of M2 and M1 Subpopulations

Set A LGN-M Set B LGN-M

LGN-M2 LGN-M2

LGN-M1 LGN-M1

0 0

Set C LGN-M Set D LGN-M

LGN-M2 LGN-M2

LGN-M1 LGN-M1 0 0

Figure 6.8: The ﬁgure schematically illustrates how the physiological parameters of the LGN-M population (dashed line) are reanalyzed. According to the criteria given in the text, the physiological parameters of the LGN-M population are split into clusters corresponding either to the LGN-M2 or LGN-M1 population. The clusters are determined by a hypothesized number ratio of LGN-M2 to LGN-M1 cells. Mean values and standard deviations are re-estimated for each of the potential M2 and M1 clusters (grey Gaussian distributions). The number ratios of LGN- M2 to LGN-M1 cells are chosen 59%:41% (Set A), 72%:28% (Set BB), 80%:20% (Set C), and 88%:12% (Set D). The mean value and standard deviation of the whole LGN-M distribution which had been measured experimentally remains constant for each set of LGN-M2 and LGN-M1 parameters. Note that there is considerable overlap between the distribution of LGN-M2 and LGN-M1 cells. The analysis is done for each individual physiological parameter (compare Figure 6.9). The number values corresponding to the four sets of LGN-M2 and LGN-M1 parameters are given in Table 6.1a,b. 92 Results of the Feedforward Model

Three basic assumptions are made to assign reasonable physiological response properties to the LGN-M2 and LGN-M1 populations:

1. LGN-M1 cells are less numerous than LGN-M2 cells. This model assumption is based on the ratio of anatomically identiﬁed M1 to M2 cells which is roughly 1:3 (see Table 5.1). However, the overall sample size of LGN-M cells is small and a sampling bias cannot be excluded. Therefore the number ratio has to be considered carefully hence does not provide a strong constraint for this particular model parameter.

1.2

0.14

1.0 0.10 M M 0.6 0.06 P M2 P M2 Surround Radius [degree] Center Radius [degree] M1 0.2 M1 0.02 (a) Model I Set A Set B Set C Set D Model I Set A Set B Set C Set D

M2 100 M1 8

M 60 4 M

M2 P P M1 20

0 Maximum Response [spikes/sec] (b) Contrast Gain [spike/(sec %contrast)] Model I Set A Set B Set C Set D Model I Set A Set B Set C Set D

Figure 6.9: Re-analyzed physiological parameters of LGN-M2 and LGN-M1 cells. Each plot shows mean values and standard deviations of the physiological response properties which corre-

spond to the four sets of hypothesized number ratios of the M2 and M1 cells. (a) Receptive ﬁeld

R R G s size parameters (center radius c and surround radius ); (b) Contrast gain and maximum

response M . The number values which correspond to the four sets A-D of re-analyzed LGN- M parameters are summarized in Table 6.1a+b. Each plot also shows mean values and standard deviations of the LGN-P and LGN-M population which had been measured experimentally by Croner & Kaplan (Table 5.2). The parameters of LGN-P and LGN-M were used for parameter explorations of model I. Note that the distribution of the whole LGN-M population (M2 plus M1) remains constant for each particular set of physiological parameters and that the distributions of LGN-M2 and LGN-M1 cells partially overlap with one another. Given a number ratio of 88% M2 cells and 12% M1 cells (Set D) the mean value of M1 cells is roughly one standard deviation above the mean value of the classical LGN-M cells. 6.2 Results Model II: Two LGN-M populations 93

2. LGN-M1 cells have larger receptive ﬁelds than LGN-M2 cells. This is also a reasonable assumption because the axonal arbors of LGN-M1 cells have much larger lateral spread compared to the LGN-M2 cells.

3. LGN-M1 cells have higher contrast sensitivity than LGN-M2 cells. This particular assumption is based on the observation by Sclar et al. (1990), that receptive ﬁeld size and contrast sensitivity are strongly correlated response properties along the central visual pathway from the LGN to area MT.

All criteria mentioned above are given in qualitative terms, i.e. provide a trend useful to constrain the model parameters. Thus, the number ratio of LGN-M2 to LGN-M1 cells and the physiological parameters of LGN-M1 vs. LGN-M2 subpopulation are hypothetical and must be explored by computer simulations. An important constraint – not mentioned so far – is that the mean values and standard deviations of the whole LGN-M population – which had been determined experimentally by Croner & Kaplan and Spear et al. – reﬂect the distribution of a more numerous LGN-M2 and a less numerous LGN-M1 subpopulation. In order to explore the parameter space, the unimodal, though partially skewed, distributions of physiological LGN-M parameters are systematically split into four different number ratios of LGN-M2 and LGN-M1 cells. In the following I refer to the four data sets as Set A, B, C and D. The number ratio of M2 to M1 cells ranges from 59%:41% (Set A), up to 88%:12% (Set D). Mean values and standard deviations are re-estimated from the potential M2 and M1 clusters. This is schematically depicted in Figure 6.8. If there are roughly as many M2 as M1 cells (Set A), the mean value and standard deviation of LGN-M2 and LGN-M1 cells are virtually identical. If the number ratio of LGN-M1 cells decreases, mean values and standard deviations of the M2 and M1 cluster diverge but the mean value of the whole LGN-M population (LGN-M2 plus LGN-M1) remains constant. If the LGN-M1 cells make up the uppermost 12% of the LGN-M population (Set D), the mean value of the M1 subpopulation lies roughly one standard deviation above the mean value of the LGN-M cells. Of course there is a range of physiological data that cannot be assigned unequivocal to one or the other population of LGN-M cells; please note that there is natural overlap between the distribution of physiological parameters of the LGN-P and LGN-M population (cf. Figure 6.9, Table 5.2). Therefore, it is reasonable that the distribution of the physiological properties of LGN-M2

and LGN-M1 cells overlap partially with one another. The number values of mean and standard

R R s deviation of receptive ﬁeld size parameters ( c and ) of the LGN-M2 and LGN-M1 subpopula-

tions which correspond to each of the four sets of number ratios are given in Figure 6.9a and Table M 6.1a. The mean values and standard deviation of contrast gain (G) and maximum spike rate ( ) of the LGN-M2 and LGN-M1 subpopulations that correspond to each of the four sets are sum-

marized in Figure 6.9b and Table 6.1b. Since Croner & Kaplan (1995) report, that the integrated K surroundcenter sensitivity is independent of cell population and eccentricity, this particular parameter is not re-analyzed with respect to the LGN-M2 and LGN-M1 subpopulation. In the following the four sets of parameter values listed in Tables 6.1a and 6.1b are considered and I concentrate on convergence of LGN-M1- LGN-M2 first. 94 Results of the Feedforward Model lls for ells used in ontrast gains M population, 0.12); therefore GN-M2 and LGN-M1 d. The mean values and 0.018 0.026 16.76 23.43 1.899 0.988 12% 12% 0.20 0.25 ion (0.55 Set D 0.69 0.98 88% Set D 88% 0.093 0.121 41.65 79.32 5.313 8.806 r all sets. 0.019 0.025 17.82 20.37 1.791 1.383 20% 20% 0.20 0.24 (Croner & Kaplan, 1995), are constant over all sets. Set C 0.094 0.70 0.116 0.93 80% Set C 43.07 70.28 80% 5.472 7.899 ], respectively. The maximum spike rates are taken from the 0.019 0.021 18.46 19.96 1.877 1.811 1 28% 28% 0.21 0.24 s Set B 0.096 0.71 0.110 0.84 72% Set B 43.46 66.06 72% 5.599 6.920 R and iven in the last row. Mean values and standard deviations of c 0.02 0.022 1.974 19.90 1.899 21.14 41% 41% m. The mean values and standard deviations for the total LGN- ] and [spikes sec 0.21 0.21 nd LGN-M1 cells. Note that number ratio of LGN-M2 to LGN-M1 ce Contrast Processing Receptive Field Size 1 ontrast gains and maximum spike rates for LGN-M2 and LGN-M1 c s of center and surround radii are given in degrees visual fiel s of receptive field sizes and number densities (last row) of L (a) (b) ter sensitivity K is independent of the specific cell populat Set A 0.097 0.72 0.103 0.75 59% Set A 5.711 44.58 6.270 56.23 59% c %contrast R s s 1 R R c c M M R R G G (Croner & Kaplan, 1995; Spear et al., 1994), are constant ove Center Radius Surround Radius Center Radius Surround Radius number ratio Contrast Gain Max. firing rate Contrast Gain Max. firing rate number ratio M1 M1 M and LGN-M2 LGN-M1 M2 LGN-M2 LGN-M1 M2 cells used in this study.standard Mean deviations values for and the total standard LGN-M deviation population, K remained constant forthis all study. parameter sets. Number densities (b) of Four LGN-M2 sets and of LGN-M1 c cells are g Note further, that the value of the integrated surround/cen data set of Spear et al. since Croner & Kaplan do not report the Table 6.1: Four sets of physiological parameters of LGN-M2 a G corresponding sets in both tables is identical. (a) Four set and maximum spike rates are given in [spikes sec 6.2 Results Model II: Two LGN-M populations 95

LGN–P LGN-P W W LGN–M2 LGN-M2 W W LGN–M1 W LGN-M1 W 100 100

75 75

50 50

25 25 Thalamic Weight Portion [%] Thalamic Weight Portion [%] 876 5 4 3 2 1 D 8 7 6 54 3 2 1 D (a) 4C alpha 4C beta (b) 4C alpha 4C beta

LGN–P LGN–P W LGN–M2 W LGN–M2 W LGN–M1 W LGN–M1 W W 100 100

75 75

50 50

25 25 Thalamic Weight Portion [%] 87 6 5 43 2 1 D Thalamic Weight Portion [%] 87 6 5 4 3 2 1 D (c) 4C alpha 4C beta (d) 4C alpha 4C beta

Figure 6.10: Proportion of P-, M1- and M2-inputs to spiny stellate cells as a function of depth

LGN P

W D

D =1, ,8 in model layer 4C. Each plot shows the thalamic weight portions ,

LGN M 1 LGN M 2

D W D W and at eight discrete depths of layer 4C. The initial proportion

of P- vs. the total M-input was taken from model I (Figure 6.1c); the LGN-M input to upper 4C and mid-4C is subsequently substituted by input from the LGN-M1 and LGN-M2 subpopulation.

(a) Full segregation of M1- and M2-inputs. LGN-M1 cells provide input only to the topmost frac-

tion of layer 4C. (b) Small zone of convergence of M1- and M2-inputs in upper 4C ( 7,8).

4C sample from both types of LGN-M afferents. Since the sample of anatomically identiﬁed M1 cells is small it is not possible to decide if weight distribution (b) or (c) is the most plausible conﬁguration in terms of anatomical evidence. (see also Section 6.2.5).

6.2.2 Percentage of M1- vs. M2-inputs as a Function of Depth

As mentioned above, it is reasonable to assume that M1 cells have larger receptive ﬁeld size, contrast gain and maximum spike rates than the M2 cells. Based on this biologically plausible assumption the physiological parameters of the LGN-M cells are assigned to the two anatomically identiﬁed M populations. The physiological parameters of model M2 and M1 cells used to study the distribution of thalamic M2 vs. M1 input are given in Tables 6.1a+b (Set D). For details about M2 and M1 physiological parameters see Section 6.2.1.

Because the response properties of spiny stellate cells in lower 4C and mid-4C should not

be affected by LGN-M1 input to upper 4C the distribution of synaptic contacts between the

P- and the M-afferents from Figure 6.1c may be used as a starting point and the weight portion

LGN M LGN M 1 LGN M 2

W W W in layer 4C is just split between the new subpopulations and . Figure 6.10 a-d shows four sets of thalamic weight portions with different degrees of M1-M2 convergence which were explored in numerical simulations. 96 Results of the Feedforward Model

0.45 4 0.4 weights (a) weights (a) weights (b) 3.5 weights (b) 0.35 weights (c) 3 weights (c) weights (d) weights (d) 0.3 experiment 2.5 experiment 0.25 2 0.2 1.5 0.15 0.1 1

Receptive Field Size [degree] 0.05 0.5 Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 6.11: Parameter exploration of model II (two M pathways). The ﬁgure shows receptive

ﬁeld size (left) and contrast sensitivity (right) of layer 4C spiny stellate neurons as a function

D of depth D , . Symbols denote mean values of 20 cells selected at random from each sublayer. Each curve corresponds to a particular choice of model parameters; plots of the experimental data from Figure 3.7 are added for comparison. The simulation results illustrate the effect of changing degrees of convergence between M1- and M2-inputs. Each curve refers to the corresponding thalamic weight distribution of Figure 6.10. LGN parameters were taken

from Table 5.2 (P cells), Table 6.1a and 6.1b (M2+M1 cells; Set D). Threshold parameters were

t t 1 0 and .

Figure 6.11 shows the corresponding predicted curves for receptive ﬁeld size and contrast sen-

sitivity. Both response properties are dramatically increased at the top of layer 4C as soon as M1-input is present. The best match with the experimental data is obtained for the set of weights depicted in Figure 6.10b, which is also consistent with the anatomical ﬁnding that LGN-M1 axon

arbors are restricted to the top of layer 4C with little intrusion of dendrites from cells in the lower

parts of 4C. The optimal set of weights shown in Figure 6.10b will be used for the parameter explorations presented in the next paragraphs.

6.2.3 Effects of Receptive Field Size of M2 and M1 Neurons In order to explore the influence of receptive field parameters on the model predictions this section only considers the four sets of parameter values listed in Table 6.1a. The size of the LGN-M1 fields was increased from set A to set D of Table 6.1a such that the mean values and the standard deviations for the whole LGN-M population (LGN-M1 plus LGN- M2) remain constant (see caption 6.1a). As a consequence, the mean receptive field sizes of the LGN-M2 population slightly decrease from set A to set D but - more important - the ratio of LGN-M1 to LGN-M2 cells also decreases: While LGN-M1 cells form the topmost 41% fraction of the LGN-M population for set A they occupy only the topmost 12% for set D. Contrast gains and maximum spike rates were taken from Table 5.2 and were - for the numerical simulations presented in this section - assumed to be identical for both M populations. Figure 6.12 shows simulated receptive field size and contrast sensitivity curves. The shape of the curves is almost identical for all four sets of parameters given in Table 6.1a, hence the changes in receptive field size of the LGN-M1 cells do not have a strong impact on the gradient 6.2 Results Model II: Two LGN-M populations 97

0.45 4 0.4 set A set A set B 3.5 set B 0.35 set C 3 set C set D set D 0.3 experiment 2.5 experiment 0.25 2 0.2 1.5 0.15 0.1 1

Receptive Field Size [degree] 0.05 0.5 Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 6.12: Parameter exploration of model II (two M pathways). The figure shows receptive field size (left) and contrast sensitivity (right) of layer 4C spiny stellate neurons as a function of depth. Plots of simulated response properties illustrate the effect of different receptive field parameters of the LGN-M1 and LGN-M2 cells. The parameters for the different datasets A to D are listed in Table 6.1a; contrast gains and maximum firing rates were identical for both LGN-M

populations and taken from Table 5.2. The thalamic weight distribution was taken from Figure

t t 1 6.10b. Threshold parameters were 0 and . For other conventions see Figure 6.11. of physiological properties in 4C. The fact that both populations of M-cells are now assigned

similar contrast gain values leads to a drop of the contrast sensitivity in upper 4C and to an

increase in mid 4C when compared to Figure 6.11. This is to be expected, because the sensitivities

1 1 2 (spikes sec %contrast degree ) were increased for the LGN-M2 cells, which dominate mid

4C input, and decreased for the LGN-M1 cells, which dominate the input to upper 4C. Contrast

sensitivity in upper 4C, however, is even less than in mid 4C, although equal values were chosen for the contrast gains of LGN-M1 and LGN-M2 cells. This is also due to the larger receptive ﬁeld

area (in degree2 ) of the M1-cells at similar contrast gain which leads to a lower average sensitivity

1 1 2 (spikes sec %contrast degree ).

The increased values of normalized contrast sensitivity in lower 4C are due to the normalization procedure. The drop of contrast sensitivity in the upper part of the layer results in an overall

decreased mean contrast sensitivity for the whole depth, thus, to smaller deviations in lower 4C from the mean values and increased normalized values in this region.

6.2.4 Effects of Contrast Sensitivity of M2 and M1 Neurons From the results presented in the previous section it becomes clear that contrast sensitivity as well as receptive ﬁeld size must differ between LGN-M1 and LGN-M2. Therefore, contrast gain values and maximum spike rates were now also increased, according to Table 6.1b. The weight distribution was set according to Figure 6.10b; the physiological properties of LGN-P cells were taken from Table 5.2. The results are shown in Figure 6.13. As differences in receptive ﬁeld size and contrast sensitivity between LGN-M1 and LGN-M2 cells increase (Tables 6.1a,b) both response properties

increase for cells in upper 4C and decrease for cells in mid 4C until the curves ﬁnally match the 98 Results of the Feedforward Model

0.45 4 0.4 set A set A set B 3.5 set B 0.35 set C 3 set C set D set D 0.3 experiment 2.5 experiment 0.25 2 0.2 1.5 0.15 0.1 1

Receptive Field Size [degree] 0.05 0.5 Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 6.13: Parameter exploration of model II (two M pathways). The figure shows receptive field size (left) and contrast sensitivity (right) of layer 4C spiny stellate neurons as a function of depth. Simulated response properties show the effect of different receptive field parameters, contrast gains and maximum spike rates of the LGN-M1 and LGN-M2 cells. The parameters for

the different datasets A to D are listed in Tables 6.1a and 6.1b. The thalamic weight distribution

t t 1 was taken from Figure 6.10b. Threshold parameters were 0 and . For other conventions see Figure 6.11.

experimental data. A perfect match is achieved with parameter set D of Tables 6.1a,b for which DoG parameters, contrast gains and maximum spike rates of the M1 cells are roughly one standard deviation above the mean value of the total LGN-M population.

6.2.5 Best Predictions So far only the results of simulations using the Croner & Kaplan data set have been presented, although parameter explorations were also performed for the Spear et al. (1994) data set. To conclude this chapter, the optimal ﬁts of model II to the experimental data for both data sets (Croner & Kaplan, 1995; Spear et al., 1994), including error bars and single cell measures, are summarized in Figure 6.14. Again the best ﬁts of the numerical results and the experimental data were selected according the following criteria:

1. The overall correspondence between mean values in the whole depth of layer 4C (D=1,...,8) of simulated and experimental receptive ﬁeld size and contrast sensitivity.

2. The plausibility of the parameter regimes which are compared to to known anatomical and physiological data.

I have again tested the statistical significance of the best fit of model II predictions. The results are summarized in Appendix A, Section A.3. The statistical tests show that there are no significantly different mean values for simulated and experimental receptive field size and contrast sensitivities at anny depth of layer 4C. Note that this result does not verify model II but lends support to model II compared to model I. While the data of Croner & Kaplan suggest a ratio of M and P contrast gains of 5:1, the ratio for the Spear et al. data is only 3:1 (see Table 5.2). Therefore, the exponential 6.2 Results Model II: Two LGN-M populations 99

change of response properties through depth of layer 4C requires an onset of M1 input deeper in

layer 4C for the Spear et al. than for the Croner & Kaplan data. The model results indicate that M1 input cannot be conﬁned to a sharp border in depth of layer 4C; in fact, intrusion of depth 6

spiny stellate cell dendrites into the upper half of layer 4C , i.e. into M1 axon territory as predicted for the Spear et al. data (compare Table 6.15), is consistent with biological ﬁndings.

6.2.6 Summary The results suggest that model II is able to produce a good ﬁt for the entire depth of layer 4C even

for the rapid increase of contrast sensitivity values in the upper part of layer 4C. The systematic parameter explorations presented in this section have demonstrated that:

The anatomically classiﬁed LGN-M2 and LGN-M1 cells cover the lower and upper range of LGN-M physiological parameters which have been measured experimentally by Croner & Kaplan (1995) and Spear et al. (1994).

Larger receptive ﬁeld size and higher contrast sensitivity on average are characteristic properties of the LGN-M1 population.

Roughly 12% of the LGN-M cells correspond to the subgroup of LGN-M1 cells. The predicted distributions of M2 and M1 synaptic contacts onto 4C spiny stellate cells are consistent with the dendritic overlap into the termination zones of the LGN-M2 and LGN-M1 axonal arbors.

0.5 4 0.45 simulation (Croner/Kaplan) simulation (Croner/Kaplan) simulation (Spear et al.) 3.5 simulation (Spear et al.) 0.4 experiment 3 experiment 0.35 0.3 2.5 0.25 2 0.2 1.5 0.15 1 0.1

Receptive Field Size [degree] 0.5

0.05 Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 6.14: Best ﬁts for receptive ﬁeld size and contrast sensitivity curves for model II (two LGN- M populations) based on the Croner & Kaplan and Spear et al. data sets. The plots show mean

values and standard deviations for the eight layers of model-layer 4C. Left: Receptive ﬁeld size as

t t 0 a function of depth. Threshold parameters were 0 (for Croner & Kaplan) and

(for Spear et al.). Right: Normalized contrast sensitivity as a function of depth. Threshold param-

t t 1 eters were 1 (for Croner & Kaplan) and (for Spear et al.). The physiological parameters of P, M2 and M1 population are listed in Table 5.2, 6.1a and 6.1b and the thalamic weight portions are given in Figure 6.15. For the definition of cortical threshold parameters see Section 5.2.5 100 Results of the Feedforward Model son, at eight D 2 to figure 6.10b M number is specified LGN 1 results shown in Figure (D = 8,7) in case of the LGN–P LGN–M2 LGN–M1 W W W W and 3 D 1 M 4 2 LGN W , 6 5 Layer 4C D subdivision (D = 6). P 7 4C alpha 4C beta 8 D 465% 3 87%35% 100% 13%0% 100% 2 0% 0% 0% 0% 1 0% LGN W

75 50 25

100 Thalamic Weight Portion [%] Portion Weight Thalamic ic P, M2 and M1-inputs for the Croner & Kaplan data. In compari e Spear et al. data. Note that the optimal weights correspond so to neurons deeper in the numbers, and the Spear et al. data, right numbers. If only one spiny stellate cells as a function of depth in layer 4C for the 1 amic weight portions fﬁcient to assign thalamic M1 input to the top of layer 4C LGN–P LGN–M2 LGN–M1 2 Layer 4C W W W 3 4C beta 4 80%25/17% 775/83% 62/50% 0% 38/50% 87/72% 0/18% 65% 13/10% 6 0% 35% 5 5 D 4C alpha Depth D LGN-P LGN-M2 LGN-M1 8 7 6

50 25 75 Thalamic Weight Portion [%] 100 Portion Weight Thalamic ﬁgure summarizes the optimal weight distribution of thalam left ﬁgure shows the optimal thalamic weight distribution for th right 6.14. The the and c respectively. The table gives number values of the thal Figure 6.15: Optimal proportions of P-, M1- and M2-inputs to discrete depths of layer 4C for the Croner & KaplanCroner data, & left Kaplan data, the Spear et al. data suggest M1 input al equal values were obtained for both datasets. While it was su 6.3 Discussion 101

6.3 Discussion

The simulation results suggest that the rapid rate of change in ﬁeld size and contrast sensitivity

values through the upper half of layer 4C cannot be due to purely feedforward excitation from what I have called the classical thalamic input, i.e. single populations of M and P ﬁbers that have individual axon arbors distributed through the depth of the upper and lower halves of layer 4C respectively. Interestingly, however, the simulation provides a good match for the real physiolog-

ical data through the lower half of the layer and just over the border into 4C, suggesting that the concept of dendritic overlap across the / border allowing single neurons to sample both M

and P input is likely to have functional relevance. However, in the upper third of layer 4C the simulated and real physiological data shows statistically signiﬁcant differences. The real physiological data could not be matched using single M and P LGN cell populations.

Subsequently, I introduced two populations of M ﬁbers with partial terminal overlap in upper 4C and with response properties constrained within the known range for LGN M cells. In this case, a very close match to the physiological data from more than one laboratory could be obtained with simple feedforward excitation. In other words, using staggered dendritic overlap of the spiny stellate neurons and changing weight of synaptic input from these three ﬁber sets (P, M1, M2), realistic response properties were achieved. I have earlier reviewed the fragmentary anatomical and physiological data that exists concern-

ing the presence of two M ﬁber groups terminating in layer 4C. The results of this modelling study provide a strong impetus for further examination of the M cells in the LGN and their inputs to the striate cortex. The model shows that certain characteristics are given to the population termed LGN-M1: their larger receptive ﬁeld sizes, higher contrast sensitivity, wider axon arboriza-

tion and restricted termination to the upper half of 4C compared to the LGN-M2 input, may be crucial identiﬁers of this ﬁber population.

Physiological Identiﬁcation of the M2 and M1 cells As mentioned in the review of the literature, physiological data with corrected laminar boundaries

shows the fastest conducting (i.e. largest diameter) M axons to terminate in upper 4C (Bullier & Henry, 1980). In recording in the LGN it has been found that neurons of Y type in the M layers receive the fastest conducting retinal ganglion cell input (Shapley et al., 1981). In addition, cells

in the upper part of layer 4C receive the fastest conducting input including those with the most

transient response (Maunsell & Gibson, 1992). Thus it is possible that the M1 input to upper 4C corresponds to the fastest Y type cells in the magnocellular LGN layers. However, as mentioned in the review of the literature there is no evidence that the Y-type LGN-M cells have larger receptive ﬁeld size or higher contrast sensitivity than X type LGN M cells. From a comparison of the known physiological properties of Y type M cells and the physiological properties attributed to the M1 cells one can tentatively conclude that the population of Y-type cells in the monkey LGN is not the hypothesized M1 type population. Sampling problems in recording from LGN units may, however, have precluded recognition of a distinct M1 population since the model suggests that the M1 population need be no more frequent than 12% of LGN M cells. It is also apparent that there can be some overlap in properties in the two M populations without signiﬁcant loss of the match between model and real physiological data. In support of the hypothesis one may also stress the fact that the physiological properties of the model M1 cells are in the range of physiological properties which have been recorded in the monkey LGN. This is important since recent extensive quantitative characterizations of the 102 Results of the Feedforward Model

macaque LGN (Spear et al., 1994; Levitt et al., 1998) have failed to reveal distinct subclasses of M neurons. Therefore, the model strongly suggests to re-examine the LGN data with respect to the correlation of different response properties, i.e. receptive field radii, contrast gain and maximum response and the presence of functional clusters preferentially in the upper range of physiological properties of LGN-M cells. Note that for example long tails in the distribution of the physiological parameters may be an indication for a second though smaller subpopulation of LGN cells. I suggest that features to search for in new physiological studies aimed at identifying distinct M subpopulations might include investigation of firing rates and patterns of response in LGN M cells; in layer 4C postsynaptic cells at different depths, NMDA and non-NMDA EPSP’s in relation to input conduction velocity might produce useful signatures.1 It is crucial to extrapolate what signatures are expected from the much bigger and longer-lasting NMDA EPSP’s compared to the non-NMDA ones. The on average higher firing rate of the hypothesized LGN-M1 population might cause a higher transmitter release and a higher depolarization in the postynaptic membrane of the cortical cell and thus result in a strong activation of the NMDA receptors in the postsynaptic membrane. This in turn may lead to a large late phase of the EPSPs recorded in the postsynaptic spiny stellate cells. In other words, the timecourse of the synaptic potential produced by NMDA inputs is different, and that might effect other properties like LTP (longterm potentiation) of the particular synapses. However, intracellular recordings must reveal the detailed effects. In both layer 4C and M layers of the LGN an investigation of the most transient cells following 60 Hz refresh rate of the stimulus monitor or having the most transient and fast oscillatory responses (50-100 Hz; Maunsell & Gibson, 1992) could be useful. These might be crucial identifiers for input from the M1 fibre group. A more direct way to assess the physiological properties of the LGN-M1 cells is to intracellu- larely record from LGN-M axons. Subsequently, intracellular filling of the recorded axons could reveal correlations between physiological response properties and antomical signatures (see Blas- del & Lund, 1983). However, a sufficiently large number of LGN-M cells must be identified in respect to morphological features and physiological response properties to extrapolate a reliable characterisation. An experimental test for the convergence of LGN-P and LGN-M cells onto cortical cells in mid-4C could be the examination of the response properties of layer 4C cells to chromatic stimuli. From the finding that LGN-M cells respond best to broad-band stimuli while LGN-P cells have colour-opponent receptive fields (Wiesel & Hubel, 1966; Derrington & Lennie, 1984) one would expect to see differences in the response properties of LGN-P and LGN-M driven cells in depth of the layer; especially cortical cells in mid-4C which are supposed to get input from both thalamic cell populations should exhibit cromatic-selective response to changing degrees. For example Vidyasagar et al. (1998) suggest that chromatic selectivity to isoluminant stimuli, combined with a preference for slow moving bars indicates P inputs. However, the characterisation of LGN-P and LGN-M response properties to chromatic stimuli and therefore the usability of these signatures are highly controversial (e.g. Shapley, 1990, Livingstone & Hubel, 1987). Therefore, it might

1The NMDA (N-methyl-D-aspartate) receptor is activated by the excitatory neurotransmitter glutamate. The associated receptor channel is normally blocked by Mg+ . However, it becomes activated when the postsynaptic cell is adequately depolarized by strong cooperative input from many presynaptic neurons. The more the neuron is depolarized by the activation of the non-NMDA (i.e. other glutamate) receptors, the more NMDA-activated channels are opened, and the more current ﬂows through the NMDA-activated channels. This delayed opening of NMDA-activated channels contributes a characteristic late phase to the normal EPSP’s. There is evidence that the long-lasting NMDA EPSP’s are involved in long term potentiation (LTP) of a synapse. 6.3 Discussion 103 be difﬁcult to design a suitable experiment that uses chromatic selectivity as a test of P inputs in depth of layer 4C (personal communication; J. B. Levitt).

Anatomical Signatures for the Convergence of P and M input in Layer 4C It has never been looked for anatomical data for the convergence of P and M input to single cells. Therefore, one test of the model predictions would be to search for dual inputs to cells in mid-4C. However, it is impossible to distinguish M and P terminals by simple morphology at EM level and it is hard to see how this can be accomplished anatomically by current approaches. In this respect it is worth pointing out that during early postnatal development layer 4C has rich cytochrome

oxidase label only down to mid 4C (Fitzpatrick et al., 1985, their Fig. 22). The bottom half of layer 4C remains pale suggesting that thalamic drive to 4C has not yet developed its full adult

state. By contrast, the heavy CO label in upper part of layer 4C covers the territory of those cells

the model predicts to have dendritic spread into M arbors of lower 4C, a region rich in CO in the early postnatal period. Presumable the early postnatal drive derives from M relays which appear to

develop before the P inputs (Mates & Lund, 1983). This developmental picture provides support for the model prediction that in mid-4C there is dendritic overlap between and , since upper

4C cells are metabolically active at this early postnatal stage. Another factor that might be important for interpreting the model predictions is that contacts from different thalamic cell populations might cluster at different sites on the dendrites of the cortical cell. For example the LGN-M1 cells might preferentially contact spines near the soma and the LGN-M2 cells might prefer the distal spines of the dendrite. This would result in different effects of the excitatory postsynaptic potential on the outcome at the soma. If this is the case this would affect the model predictions in the following way: either there are less M1 cells due to the increased efﬁcacy of the synapses hypothesized to be close to the soma, or, the differences in the physiological properties of M2 and M1 cells are smalller and more M cells belong to the M1 population. However, as already mentioned above, it is impossible to distinguish the thalamic terminals of different cell populations by simple morphology at EM level and it is hard to see how this can be accomplished anatomically by current approaches. Anatomical studies employing biocytin injections in different layers of V1 (Yoshioka et al., 1994) have demonstrated that mid layer 4C neurons project to the inter-blob regions of layer 2-3, the upper part of layer 4C project to layer 4B, and the bottom part of layer 4C project to layer 4A, with staggered partial overlap of cells giving rise to these three different outputs through the depth of layer 4C. These characteristic output channels in turn occupy different segments of the gradient of contrast sensitivity and ﬁeld size through the depth of the layer. It is possible that the particular balance of the three depth-dependent inputs on individual spiny stellate neurons could determine their particular projection patterns within and out of layer 4C during early development.

Other Explanations of the Functional Gradient in Basic Response Properties It is important to ask if factors other than direct excitatory input from the LGN could determine the increasingly rapid change in response properties with rise in depth of layer 4C. One factor that might cause differences in receptive ﬁeld size and contrast sensitivity of neurons at the top of

layer 4C are differences in inhibition to the spiny stellate neurons at different depths in layer 4C. Another factor that could lead to the gradual change in response properties in depth of layer 4C is the presence of lateral excitatory connections known to exist between the spiny stellate neurons. Both possibilities will be explored in the following chapters of the manuscript, hence are discussed 104 Results of the Feedforward Model

in Section 9.3. If increased receptive ﬁeld size and contrast sensitivity are due to intracortical reﬁnement of the local recurrent connections one would expect that in such circumstances the earliest responses

from upper 4C neurons should convey a smaller receptive field than the later parts of the response; or that earlier responding neurons should have smaller receptive fields than later responding neurons (on which the earlier responders – perhaps the purely intrinsically projecting cells – terminate) at the same depth in layer 4C. However, in support of the hypothesis that direct thalamic relays may be the effective deter- minant of the basic properties, I have used (i) data of Blasdel & Fitzpatrick (1984) who recorded from a population of non-oriented cells, which are most likely to be first order cells, and (ii) data of Hawken & Parker (1984) who recorded from a group of orientation specific cells which are more likely to receive lateral recurrent input (in addition to thalamic input) refining or even inducing orientation specific responses (see e.g. Adorján et al., 1998); since both data sets show the same form of progression in contrast sensitivity with depth, the interpretation is that contrast sensitivity can be accounted for by the pattern of direct thalamic input. As well, I have demonstrated that realistic dendritic overlap and feedforward excitation is sufficient to explain neuron properties in the lower two-thirds of layer 4C. In addition, despite their small number relative to intrinsic lateral connections, the thalamic inputs drive spiny stellate neurons (in cat V1 layer 4) with large and reliable EPSP’s whereas the intracortical synaptic connections are individually less reliable than thalamic inputs as a driving force (Stratford et al., 1996).

Concluding Remarks

If the model is correct in predicting two M populations, it is the M1 input that is almost entirely restricted to neurons projecting to layer 4B and perhaps predominating in driving the generation of

direction selectivity that is seen in upper 4C and in layer 4B. The large axons presumed to be M1 axons, provide extensive collateral input to layer 6 which also contains direction selective neurons (Blasdel & Lund, 1983; Hawken et al., 1988; Freund et al., 1989). The M2 population, while

contributing to neurons in upper 4C has a primary role in combining with P input to neurons of mid layer 4C; these neurons project to the superﬁcial layers, particularly to interblob territories of

layer 3B. Pure P input is seen predominantly in neurons of the lower half of 4C and their relays pass on to engage layer 4A, itself the recipient of direct LGN P input. In summary, the modelling work presented in this chapter has proved that purely feedforward excitation is sufﬁcient to produce a good match to the physiologically observed response properties of layer 4C neurons in macaque area V1. The model has used real anatomical and physiological data where it is known and made predictions for anatomy and physiology where there is currently not sufﬁcient information. I think that one of the most important functions of the above model is to

encourage new biological experiments that would test the model predictions. The model predicts:

i that there are two M pathways entering layer 4C with different emphasis of the range of

properties currently assigned to M cells in the LGN,

ii that dendritic overlap in depth of layer 4C allows single cells to receive both M and P inputs,

and

iii that recurrent excitation and inhibition are not essential determinants of the size of the minimum response ﬁeld and contrast sensitivity of layer 4C neurons. 6.3 Discussion 105

These insights in the logic of the geniculocortical information transfer form a good foundation on which other aspects of the organisation of layer 4C local circuitry can be explored. 106 Results of the Feedforward Model Chapter 7

Anatomical and Physiological Findings: Intracortical Lateral Connections

The second functional hypothesis which I consider is based on the organisation of the local lateral connections of layer 4C. Therefore this chapter gives a review of the relevant anatomical and physiological ﬁndings which are relevant to the intracortical recurrent model for the depth-dependence of basic response properties in layer 4C of macaque primary visual cortex. The ﬁrst part of the chapter is concerned with the anatomical organisation of local excitatory feedback connections which are known to exist between the spiny stellate cells; this is followed by relevant anatomical data on local inhibitory circuit neurons. In particular, two varieties of somatic inhibitors will be discussed which are associated with different depths in the layer. There is now a long line of evidence which indicates that intracortical recurrent feedback is essential in the generation and sharpening of cortical response properties. However, the majority of cells in layer 4C of the macaque primary visual cortex have response properties similar to the non-oriented geniculate cells.1 Response properties normally associated with cortical cells

– orientation tuning, direction selectivity and binocular disparity – emerge ﬁrst in upper 4C. Therefore, the second part of the chapter reviews the relevant physiological data about the functional role of recurrent excitation and inhibition in layer 4C, the intrinsic physiological properties of inhibitory interneurons and the spatial summation properties of cells in layer 4C. Finally, the functional hypothesis that results from the extrapolation of the relevant anatomical and physiological ﬁndings will be discussed.

7.1 Overview of Relevant Anatomical Findings

The majority of cells (75-80%) in layer 4C are spiny stellate cells; the rest is made up by different varieties of smooth dendritic interneurons (Lund, 1987). The ratio of excitatory to inhibitory synapses on a single cell is approximately 8:2 (Beaulieu et al., 1992). Only a small portion, roughly 10%, of the constant number of spines of each spiny stellate cell is occupied by thalamic synapses. The rest of the excitatory input comes from local collaterals of other spiny stellate cells within the layer and recurrent collaterals of layer 6 pyramids (Lund & Boothe, 1975), which I do not consider in this study.

1By contrast, in the cat visual system, which lacks the dichotomy of magno- and parvocellular cell classes the majority of cells in layer 4 exhibit clear orientation selective response (see for example Gilbert, 1977). 108 Anatomical and Physiological Findings: Intracortical Lateral Connections

Lateral excitatory connections are known to exist between the spiny stellate neurons in layer 4C (Saint-Marie & Peters, 1985; Kisvarday et al., 1986). Recent estimates in the cat striate cortex suggest that the majority of excitatory input to the spines of layer 4C spiny stellate cells is from other spiny stellate cells in the layer; the excitatory synapses which contact the spines make up 28% of the total number of excitatory synapses (contacts on spines and dendritic shafts); layer 6 pyramidal cells provide 45% of the total excitatory synapses, but they preferentially contact the dendritic shafts (Ahmed et al., 1994). The schematic drawing in Figure 7.1 summarizes the anatomical observations which are important to the intracortical model. Although the retino-cortical projections and the differential convergence of P- and M-inputs onto spiny stellate cells are not the most crucial part of the intracortical hypothesis, the drawing also includes the three types of LGN inputs into layer 4C. Please

remember, that the almost exponential gradient of the basic response properties in upper 4C led us to predict higher contrast sensitivity and ﬁeld size for the anatomically identiﬁed M1 cells

which preferentially project to upper 4C. In the following sections I review the anatomical evidence for other potential sources of strongly

increased contrast sensitivity and field size in upper 4C: differences in the local circuitry of recurrent excitation of spiny stellate cells in depth of layer 4C and a change in inhibitory strategy in upper layer 4C. 7.1 Overview of Relevant Anatomical Findings 109 α β 3B 4A 4B 4C 4C he layer where it is LGN-P and LGN-M stellate neurons in lower iny stellate cells, however, er 4C of macaque primary ed by a dense dendritic and id-4C form narrow terminal clutch α−6 Local Interneurons project lateral over a wide range and form at iny stellate cell has a local axonal field (not shown) which orization. all basket neuron is apparently absent in the upper third of t Spiny Stellate Neurons art of the figure shows the projection territory of a thalamic tsynaptic target of the intralayer connections are other sp tatory collaterals. The ”clutch” cell which is characteriz s of spiny stellate cells and inhibitory interneurons in lay ls at different depths of the layer (compare Fig. 4.1). Spiny spiny stellate cells at the top of layer 4C (black). The local axon collaterals of excitatory cells in m M1 Retinal Ganglion Cells differ in their lateral connection patterns (grey). Each sp LGN M2 P P -6 basket cell which has larger and more stratified axonal arb M , mid-4C and upper 4C Figure 7.1: Anatomical organization of lateral connection visual cortex (modified from (Baueraxon et together with al., the 1998a)) efferent The relays left of p spiny stellateis cel slightly larger in lateralclusters spread lateral from than their the somata. dendriticleast The field two axon terminal collaterals zones of within thethe same local depth. interneurons The may major also pos axonal get field input is from prominent the inreplaced local by the exci the lower 2/3 of the layer. This sm 4C 110 Anatomical and Physiological Findings: Intracortical Lateral Connections

7.1.1 Lateral Connections of Spiny Stellate Cells Each spiny stellate cell provides axon collaterals to neurons in a close neighbourhood. The spread

of this ’very local’ axonal ﬁeld is slightly larger than the dendritic ﬁeld and extends 250 m in diameter (cf. Fig. 4.2 and 7.2a). Using HRP2 and biocytin based neuroanatomical tracing techniques several studies revealed that the intralaminar connections increase in lateral spread in

a stepwise fashion from the lower third, to mid third, to upper third of layer 4C being widest in upper 4C (Fitzpatrick et al., 1985; Yoshioka et al., 1994). Spiny stellate cells in the lower 4C

apparently lack the lateral connections which emerge ﬁrst in the middle depth of layer 4C . The cells in mid-4C provide lateral projection to narrowly focused terminal zones within the same

middle depth stratum offset by 300-500 m to either one or both sides. Spiny stellate cells in

the upper part of layer 4C project widely within the same layer forming at least two narrowly focused terminal clusters at 500 m and 1100 m lateral from their cell bodies (Figure 7.2a,b).

Using the anterograde tracer biocytin, Asi et al. (1998) demonstrate that the cells in upper 4C and layer 4B appear to innervate a series of stripe- or bar-like terminal regions surrounding the injection point (see Fig 7.2b). Using a retrograde tracer3 this study further indicates reciprocity of connections between bars and the injection point. However, the correlation of three different

anatomical label patterns in layer 4B and upper 4C with optically imaged maps of orientation and ocular dominance columns provides no obvious relation of lateral projection patterns and functional columns. Single bars generally cover amounts of right and left eye and there is no direct relationship between topography of ocular dominance stripes and the bar-like label zones. Moreover, single bars cover a wide range of orientations, thus they do not appear to favour regions of the same orientation as the injection site. In summary, these observations suggest that the bar-

like connections in layer 4C do not link regions sharing the same response properties than the injection site – as for example do the lateral patch-like connections of the superficial layers 2-3 (Malach et al., 1993). From the anatomical organisation I suggest that each neuron in layer 4C gets a constant proportion of excitatory synapses from other spiny stellate cells within the layer. Cells in the lower third of layer 4C get input from local neighbouring cells via ’very local’ axon collaterals. Cells in the upper two third of layer 4C, i.e. the region where lateral side-step connections are present, receive inputs from laterally displaced neurons in a roughly circular region which corresponds to the average stepsize and width of the bar-like connections. There is evidence from a few intracellularly filled cells (Anderson et al., 1993) that individual layer 4C cells either project laterally within the layer (i.e. lack rising efferent axons collaterals) or project outside layer 4C (in this case lack lateral collateral projections within the layer). Although there is support for two classes of spiny stellate cells – purely intrinsic lateral projectors and those which provide efferent relays to superficial layers – this particular finding does not bear on a model of purely intralaminar circuitry. Another observation which is important to the model is that the density of terminals per unit area of layer 4C produced by similar sized injections appears to be the same at different depths

within layer 4C (personal communication J. S. Lund). However, there are much more cells in 4C /mid-4C than in upper 4C and more cells should take up the label in mid-4C than in upper-

4C. Because the density in labelled terminals is constant, the observation suggests that either a smaller number of cells make lateral projections in mid-4C, if the lateral terminal clusters of a single cell are of the same richness at any depth (see below), or, the number of terminals contributed

2Horseradish peroxidase 3Cholera Toxin 7.1 Overview of Relevant Anatomical Findings 111

4α

4β

100 µ m

(a)

400µm (b)

Figure 7.2: (a) Drawing of an intracellular filled spiny stellate neuron in layer 4C of macaque striate cortex. The cell has a small dendritic field (thick lines) and wide projecting axon collaterals forming terminal clusters lateral from the cell body (adapted from Anderson et al., 1993). (b) Two examples of tangential maps of patterns of terminal fields established by lateral projections

of spiny stellate neurons in upper 4C and layer 4B (adapted from Asi et al., 1998). The circles indicate the injection site of the tracer. The axonal ﬁbres which leave the injection sites form

extended bar or stripe shaped regions of terminals in upper 4C and layer 4B. From a sample of

nine biocytin injections, Asi et al. (1998) inferred a mean center-to-center bar gap of 400m, an

average bar width of 175 m, and a mean bar length of 990 m. The total area of the stripe-like

connections is on average 2750 m 1450 m. 112 Anatomical and Physiological Findings: Intracortical Lateral Connections

by a single cell is lower in mid-4C. On the other hand, the same density of labeled terminals per unit area suggests that a single postsynatic cell should receive more terminals from lateral

side-step connections in upper 4C than a cell in mid-4C, since the number of cells per unit area increases from top to bottom of the layer. However, more data is needed to clarify this particular issue because there are technical problems, e.g. uptake of label, to interprete the data in this way. In addition, the number of laterally offset cell bodies (one or multiple side-steps away) that are retrogradely labeled by equivalent sized injections at different depths in layer 4C increase in number as the injection site rises in depth of the layer. In other words, the lateral projectors make up an increasing proportion of the excitatory cell population at each level and the actual numbers of lateral projecting cells are increasing with rising position in the layer (personal communication J. S. Lund).

7.1.2 Strategy of Local Inhibition The organization of neurons in layer 4C with smooth and sparsely spined dendrites has been studied in detail by Lund (1987) using Golgi preparations. Inhibitory circuitry within the layer

is complex but highly precise; altogether more than a dozen different local circuit neurons have been identified within layer 4C and layer 4C . Each type of local interneuron is characterized by a specific pattern of dendritic arborization and axonal projections within and outside of layer 4C. Interestingly, the dendritic arborization and the local axonal projections of different groups are restricted to different divisions of layer 4C suggesting different strategies of inhibition in depth of the layer. While details about the morphological organization of local inhibitory circuitry are well known, less data is available concerning cell densities, presynaptic inputs and postsynaptic targets of different anatomically identified inhibitors. Unpublished electron microscopy studies from the laboratory of Jennifer Lund show that there is no significant difference in the number of type 2 (GABAergic) synapses per unit area of cell soma surface through the depth of the layer. Because the cell bodies gradually increase in size toward top of the layer and the absolute number of type 2 synapses increases in step with this I suggest that the amount of somatic inhibition is constant in depth of the layer. There are at least two candidates at different depths of layer 4C which are known to provide synapses to the cell bodies of spiny stellate neurons (see Fig. 7.1). In particular, there is one

variety of interneuron – apparently absent from the upper half of layer 4C – that is known to

contact the cell bodies and the dendrites of spiny stellate cells deeper in the layer. The so-called 4C and 4C type 1 neuron (Lund, 1987; Mates & Lund, 1983) or clutch cell (Kisvarday et al., 1986) has richly branched, very localized arbors and is closely associated with the layers that

are directly innervated from the LGN. The dendritic ﬁeld of the clutch cell is close to 200m in

diameter while the dense axon plexus is conﬁned to a region of 150 m in diameter. Original arguments that the clutch cell might selectively ’veto’ excitation by geniculocortical synapses at the level of dendritic spines were discarded by Dehay et al. (1991). Recent evidence from layer 4 in cat striate cortex suggests that 84% of the inhibitory contacts on a spiny stellate cells are provided by the clutch cell (Ahmed et al., 1994). Kisvarday et al. (1986) report that the clutch cell also contacts other inhibitory cells, though GABAergic cells are rare targets of this particular interneuron. The presynaptic input of the GABA-positive clutch cell are unknown, but it may receive input from both sources of excitatory input to layer 4C which I consider in my model: (1) In cat layer 4 it has been demonstrated that the clutch cell gets monosynaptic input from the LGN (Martin et al., 1983). Unfortunately, Kisvarday et al. (1986) failed to conﬁrm 7.2 Overview of Relevant Physiological Findings 113

this observation in monkey. However, Freund et al. (1989) reports that up to 10% of the postsynaptic targets of LGN-P and LGN-M cells are GABA-positive which suggest that LGN afferents target the local inhibitors.

(2) While the major postsynaptic targets of the local collaterals of the spiny stellate cells are spines, they may also provide input to the clutch cell (Kisvarday et al., 1986; Saint-Marie & Peters, 1985).

Because the data on presynaptic inputs are fragmentary I assume that the clutch cell receives a small portion of thalamic synapses but the majority of the excitatory input derives from the local spiny stellate cells. In addition, the clutch cell might also get inhibitory (type 2) synapses from

other GABAergic cells. In upper 4C the clutch cell is replaced by an -6 wide arbor basket cell (Lund 1987). The cell

has rather horizontal spreading dendrites (diameter close to 200m) which are mostly conﬁned to

the top of layer 4C. Their stout axon trunks spread laterally away from the neuron for very long distance up to 700 m to either side of the neuron in upper 4C (or in layer 4B). The presynaptic

input and the targets of the -6 cell are unknown but its ”basket” morphology suggests it may also contact the somata of the local spiny stellate cells (Somogyi et al., 1983; Martin, 1988).

7.2 Overview of Relevant Physiological Findings

Since I wish to explain the more basic response properties of cells in layer 4C by differences in recurrent excitation and inhibition, it is important to review the data which is available for the role of recurrent intracortical feedback in layer 4C. In addition, I review evidence which suggests that cells in the primary input layer 4C already integrate information from stimuli far beyond their classical receptive ﬁeld.

7.2.1 The Functional Role of Recurrent Excitation and Inhibition The functional role of recurrent excitation and inhibition is frequently discussed in the context of orientation and direction selectivity. Therefore, the knowledge about the role of recurrent excitation and inhibition in layer 4C of macaque striate cortex is mostly restricted to studies that investigate the mechanisms underlying these ’second order’ properties. Layer 4C in macaque striate cortex is characterized by a small proportion of orientation selective cells which increases with rise in depth of the layer but many cells in this layer lack orientation selective response (Blasdel & Fitzpatrick, 1984; Hawken & Parker, 1984)4. The uppermost region

of layer 4C also has a small population of direction selective cells – though the principle population of neurons with this property lies in layer 4B and 6 (Hawken et al., 1988). Ringach et al. (1997) who investigated the temporal dynamics of orientation tuning in macaque striate cortex found that the dynamics of cells within and outside layer 4C are different in several respects. All cells outside layer 4C have an early excitatory component followed by a delayed inhibitory or suppressive component with similar preferred orientation (multimodal dynamics). By contrast, all cells in layer 4C lack a delayed iso-oriented suppressive component (unimodal

4Please remember, that the data on receptive ﬁeld size and achromatic contrast sensitivity in layer 4C reported by Blasdel & Fitzpatrick (1984) are taken from a population of non-oriented cells; by contrast, the achromatic contrast sensitivities reported by (Hawken & Parker, 1984) reﬂect data of a population of orientation selective and orientation biased cells in layer 4C. 114 Anatomical and Physiological Findings: Intracortical Lateral Connections

dynamics); moreover a number of cells in layer 4C respond to non-optimal orientations with a probability signiﬁcantly larger than zero. The broadly tuned unimodal dynamic which is unique to layer 4C is consistent with the assumption that most of the local inhibition in layer 4C works independent of the orientation scheme. By blocking intracortical inhibition5 in layer 4C of macaque striate cortex, Sato et al. demonstrated that:

– The response of cells in layer 4C which had overall poor tuning to stimulus orientation were generally facilitated without bias to particular orientations, suggesting the presence of orientation-insensitive excitatory and inhibitory inputs; the ﬁring activity of cells in layer

4C which exhibit clear orientation selectivity was overall increased and the response was facilitated to all stimulus orientations fairly evenly also suggesting the operation of poorly

oriented inhibitory inputs to these cells (Sato et al., 1995). – The response of cells in layer 4C and 4C which were poorly sensitive to the direction of stimulus motion are facilitated under the blocking of inhibition which suggests an operation of intracortical inhibition on neural activity of even non-directional (the majority 6 of) cells; however, the overall direction selectivity index of cells in upper 4C decreased signiﬁcantly during blockade of intracortical inhibition (Sato et al., 1996).

These experimental observations suggest that intracortical inhibition certainly operates in layer 4C but it rather operates unspeciﬁc to orientation and motion direction of the visual stimuli. Therefore it is likely that at least the clutch cell, the most frequently observed inhibitory interneuron in the lower two third of layer 4C, acts to detect overall excitation in this region, and through unspeciﬁc inhibition raises the threshold of their target cells.

I further suggest that the -6 circuitry neurons which are found in the uppermost stratum of layer 4C are excellent candidates for providing the feedforward inhibition to excitatory spiny cells which putatively underly direction selectivity (e.g. Barlow & Levick, 1965). The apparent lack of

the ’clutch’ cell inhibition and the hypothesised input from the fast conducting LGN-M1 axons may allow the spiny stellate neurons and -6 basket cells in upper 4C to respond with minimum delay to incoming information, a potential useful property for a pathway concerned with the detec-

tion of motion. In addition to detailed temporal timing of excitation and inhibition in upper 4C,

the emergence of direction selective response from feedforward inhibition would require powerful inhibition provided by the -6 cell. The strong inhibition of the -6 could either result from high discharge rate to presynaptic inputs or from strong postsynaptic effects.

7.2.2 Intrinsic Physiological Properties of Inhibitory and Excitatory Cells Despite their prevalence and essential role in cortical function only a few studies have examined the physiological properties of GABAergic inhibitory interneurons. Recently Azouz et al. (1997) evaluated the intrinsic properties of inhibitory interneurons in cat striate cortex by in vivo intracellular recordings. In particular, this study reports that many inhibitory interneurons display a steep linear relation between depolarizing current input and the action potential discharge, with relatively little spike frequency adaptation. Furthermore (McCormick et al., 1985) have demonstrated in vitro that the slope of the primary frequency current relationship of excitatory cells is on

by microionotophoretic administration of the GABAA antagonist bicuculline methiodide (BMI)

1 (R R ) R R

p p np The direction selectivity index (DSI) was deﬁned as DSI= np where and represents the response elicited by a stimulus moving in the preferred direction and the non-preferred direction respectively. 7.2 Overview of Relevant Physiological Findings 115

4 J. B. Levitt 2.5 3.5

3 2

2.5 1.5 2 1 1.5

1 0.5 0.5

Receptive Field Size [degree] 0 0 0 0.5 1 1.5 2 2.5

4C alpha 4C beta Pk size from area summation [degree] MRF size (sqrt area) [degree]

Figure 7.3: Left: Mean value and standard deviation of minimum receptive ﬁeld size of cells

in layer 4C (derived from unpublished data with the permission of Jonathan B. Levitt). Single cells are categorized as lying in layer 4C, mid-4C and layer 4C . The ﬁgure also includes two

samples of cells which could not be unequivocal classified as lying in layer 4C. These cells are located near the border of layers 4B/4C and layers 4C /5. Field size was measured by small patches of high contrast optimal grating stimuli (patch size 0.3-0.4 degree; contrast 75%) which were placed at different locations of the visual field. The measures give the square root of the area in which the stimulus can elicit criterion response. Right: Correlation of MRF size and peak size from area summation functions of cells in layer 4C (unpublished data from Jonathan B. Levitt). Peak size is defined as the diameter of a patch of optimal grating stimulus centered in the receptive field which evokes peak response of the cell (cf. Figure 7.4). Note that the peak response was on average elicited by stimuli similar in size to the MRF size, though some of the neurons gave optimal response to stimuli smaller or larger than the MRF.

average lower than that of the fast spiking inhibitory cells. However, the excitatory cells exhibit strong spike frequency adaption.

7.2.3 Spatial Summation Properties of Cells in Layer 4C Levitt & Lund (1997b) have studied the extent of visual space from which a neuron in the monkey striate cortex can be driven or response can be modified. First of all the authors determined the minimum response field (MRF) of cells in layer 4C by using small patches of high contrast optimal grating stimuli (see Fig. 7.3). The asymptotic diameter of the receptive field was then measured by increasing the diameter of a stimulus patch centered over the MRF until the response no longer decreased. From the comparison of the MRF size with the asymptotic diameter it can be inferred that the stimulus size at which the response asymptotes was in some cases much larger than the MRF, often extending 10 degrees in diameter, even in layer 4C. In some cases optimal response was elicited when a small central region of the receptive field was blanked out, indicating strong inhibition arising from within the receptive field. The area summation functions which were measured by isotropically increasing the diameter of optimal stimuli centered over the cell’s receptive field indicate that the peak summation areas of cells in layer 4C are on average of similar size as the MRF (see Figures 7.3 and 7.4). However, some of the cells gave optimal response to stimuli smaller or several degrees larger than the MRF. The spatial extent of modulatory surrounds of neurons in striate cortex was on average 3 degrees 116 Anatomical and Physiological Findings: Intracortical Lateral Connections

4Cβ

mid-4C

4C α

Stimulus Diameter [degree] Figure 7.4: Area summation functions of a cell in layer 4C , mid-4C, and 4C (unpublished data from Jonathan B. Levitt). The size of a patch of optimal grating stimulus centered in the receptive ﬁeld was systematically increased from below 1 degree to 13 degrees in diameter. Peak size from summation area is deﬁned as the diameter that elicit peak response. All three cells respond over a

large range of stimulus size; note that response of the cell in upper 4C falls below spontaneous activity (dashed line) for large stimulus diameter. 7.2 Overview of Relevant Physiological Findings 117

3 Blasdel/Fitzpatrick 2.5

1.5

0.5 Normalized Receptive Field Size 0 4C alpha 4C beta

Figure 7.5: Normalized receptive ﬁeld size of layer 4C cells. The original data of Blasdel & Fitz- patrick (1984) was normalized to the average MRF size in layer 4C (see also text). The solid line

in each panel connect mean values ( standard deviations) at seven equally sized depth intervals through layer 4C. Since there are only three receptive ﬁeld size measures falling in the interval at

the top of layer 4C, it is impossible to give a reliable expectation in this region.

in diameter from the edge of the minimum response ﬁeld, but could extend up to 13 degrees in total diameter (Levitt & Lund, 1997b). The results of Levitt & Lund suggest that many neurons in the striate cortex – even in the input

layer 4C – integrate visual signals over a distance commensurated with the spread of lateral connectivity (i.e. 6-8 mm in the superﬁcial layers; 3 mm in upper 4C ). A substantial proportion, however, cannot be accounted for by monosynaptic spread of intrinsic horizontal connections. In

particular, the spread of lateral connections in layer 4C which extend up to 1000m in mid-4C

and cover a mean area of 2750m 1450 m in the uppermost part of the layer (Asi et al., 1998) cannot account for the spatial summation properties observed in this layer. Therefore, I suggest that the monosynaptic input of layer 4C lateral connections contributes to the classical receptive field, and thus affects field size and achromatic contrast sensitivity of cells at different depths of layer 4C. The data on MRF size of Blasdel & Fitzpatrick (1984) and J. B. Levitt (personal communication) which are shown in Figure 3.7b and 7.3 differ considerably in their mean value by a factor of 2-3 which reflects the different measurement techniques used by the experimenters. While Blasdel & Fitzpatrick used small slit stimuli of low contrast which where systematically moved towards the edges of the receptive field, Levitt & Lund used small patches of optimal grating stimuli of high contrast which were placed at different locations in the receptive field. Hawken & Parker do not report receptive field size, but they used drifting sine wave gratings to explore the response properties of cells in layer 4C. To become independent of stimulus conditions and measurement techniques I have divided the single cell measures of Blasdel & Fitzpatrick by the mean value of the whole sample thus obtain normalized receptive field sizes (Figure 7.5). Subsequently the normalized MRF data was binned to eight equally sized depth intervals and mean value and standard 118 Anatomical and Physiological Findings: Intracortical Lateral Connections

deviation of the field size were determined for each depth interval. In the intracortical modelling study I use the normalized receptive field size data shown in Figure 7.3 instead of the absolute receptive field size values reported by Blasdel & Fitzpatrick. Moreover, the strong correlation of MRF size and peak size of area summation in the data of J. B. Levitt (Figure 7.3) indicates that both measures, minimum response field and peak size of area summation, are in most cases equivalent. Therefore, peak size of summation area will be used as a suitable measure of receptive field size in the intracortical modelling study.

7.3 Extrapolation from Anatomical and Physiological Findings

The model hypothesis is that the functional gradient of receptive field size and contrast sensitivity as observed in the studies of Blasdel & Fitzpatrick (1984) and Hawken & Parker (1984) reflects differences in the anatomical organisation in depth of layer 4C. The different width of the lateral projections of spiny stellate cells and the different types of somatic inhibitors which are associated with the anatomically segregated termination zones of LGN-P and LGN-M cells provide the potential anatomical substrates for the functional gradient of basic response properties in depth of layer 4C. However, the previously studied feedforward model has demonstrated, that purely feedforward convergence of LGN-P and LGN-M cells onto spiny stellate cells whose dendritic arbors intrude into both termination zones is sufficient to account for the gradual change of basic response properties in lower part of the layer. This suggests that part of the gradient is initially induced by the afferent projections from LGN-P and LGN-M cells, but the almost exponential in-

crease of basic response properties at the top of the layer 4C cannot be due to purely feedforward excitation from a homogenous LGN-M population. The recurrent excitation comprised by a region within the monosynaptic spread of the intrinsic lateral connections may form the anatomical substrate of gradually increased field size with rise in depth of the layer. Multi-synaptic lateral integration might contribute to modulatory effects from regions far beyond the classical receptive field. On the other hand, changes in recurrent inhibition which operates rather unspecific to orientation and direction selectivity in the lower part of the layer could be responsible for the almost exponential increase of contrast sensitivity in the upper part of the layer. Interestingly, the substitution of small somatic inhibitors in the upper part of layer

4C by cells that have large diameter axon trunks coincides with emergence of new physiological response properties. A small population of direction selective neurons is ﬁrst seen in the upper

part of layer 4C, the region that provides direct relays to layer 4B which contains the principle

population of direction selective cells. The strategic position of the -6 cell and the stratiﬁed

arborization in stratum of layer 4C are essential properties to participate in the generation of direction selectivity via strong feedforward inhibition. If the feedforward hypothesis is right and the LGN-M cells fall into anatomical identiﬁed M2 and M1 classes, each class emphasizing somewhat different response properties within the range of physiological observed LGN-M properties, it is crucial to see how the afferent input from the LGN-M2 and LGN-M1 cells combine with realistic intracortical circuitry. In this circumstances

the different strata of thalamic inputs and the different extent of the lateral connections in depth of the layer perfectly match the three output channels – lower 4C , mid-4C and upper 4C , each of them known to project to different strata in the superﬁcial layers containing key sets of efferent relays to other cortical areas. Chapter 8

An Intracortical Model for the Depth-Dependence of Basic Response Properties in Layer 4C

The aim of the modelling work presented in this chapter is to determine how the intrinsic neural circuitry affects the basic response properties of cells in layer 4C – sepciﬁcally to what degree the gradient of basic response properties of cells in layer 4C depends on the local intracortical feedback via lateral connections. The model (Bauer et al., 1998a; Bauer et al., 1998b; Bauer et al., 1998b) of realistic intralaminar circuitry is based on the feedforward model presented in Chapter 5. The feedforward model provides the sound base for how the thalamic LGN-P and LGN-M afferents distribute on postsynaptic excitatory neurons of layer 4C to set up an initial gradient of physiological response properties in the middle stratum of the layer. It is the rapid increase of

the functional gradient in upper 4C that I am seeking to replicate in the intracortical model and how it emerges from the lateral stepped connections and the changes in inhibitory strategy at the top of the layer. In particular, I wish to identify the essential mechanisms of how changes in the intracortical circuitry in depth of layer 4C induce the almost exponential increase of receptive ﬁeld

size and achromatic contrast sensitivity in upper 4C.

The anatomical and physiological data on thalamic feedforward connections provides strong support for the existence of two anatomically and physiologically distinct LGN-M populations. Therefore a second version of the intracortical recurrent model considers feedforward excitation from the LGN-M2 and LGN-M1 populations together with realistic intracortical connectivity.

The recurrent model sets aside ON-OFF segregation and binocular fusion. Thalamic channels with biologically appropriate anatomical and physiological properties constitute the realistic afferent input to the model cortical cells. Accurate lateral spread and arbor size of the excitatory spiny stellate cells and selected types of local inhibitory interneurons are fundamental to the intracortical model. Therefore, the ﬁrst part of the chapter summarizes the anatomical and physiological data used to constrain the model of intralaminar circuitry. The network architecture, the mathematical formulation of the model neurons, and the algorithms which are used to establish realistic connectivity, reasonable transfer functions, and recurrent network dynamics follow this summary. 120 An Intracortical Model for the Depth-Dependence of Basic Response Properties in Layer 4C

8.1 Anatomical and Physiological Parameters

The model of intralaminar circuitry is calibrated as far as possible by realistic anatomical and

physiological data. If possible, the data are taken from adult macaque monkeys from a region in o the visual ﬁeld at eccentricity 5o to 8 . The purely feedforward model provides the sound base for the geniculocortical information transfer. All parameters concerning linear and cellular magniﬁcation, LGN axonal arbor spread, afferent connections and physiological properties of geniculate cell populations are discussed in detail in the Section 5.1.

8.1.1 Anatomical Parameters Table 8.1 summarizes the known anatomical data on which the modelling study is based, together with its sources. However, some of the model parameters can not be derived directly from the anatomical data thus need some further explanations.

Synaptic Inputs and Postsynaptic Targets of Cells in Layer 4C

The data on synaptic input and postsynaptic targets of cells in layer 4C is fragmentary, especially for the population of local circuit neurons. The anatomical evidence indicates that each spiny stellate cell has a constant number of spines1 and a constant number of somatic inhibitory contacts per unit area of the cell soma. Thus, I assume that each spiny stellate cell gets a constant excitatory load of the presynaptic elements that preferentially contact the dendritic spines, and a constant inhibitory load that arises from local somatic inhibitors. Presynaptic elements which are known to contact the spines are other spiny stellate cells within the layer and axon terminals of the afferent LGN cells. Because geniculate synapses occupy roughly 10% of the spines, it is reasonable to assume that the other 90% of the spines are occupied by synapses from the local spiny stellate cells. However, the model neglects all excitatory input from layer 6 pyramidal cells which are known to preferentially contact the dendritic shafts of layer 4C spiny stellate cells (Ahmed et al., 1994).

The somatic inhibitory contacts are provided by the clutch cell and the -6 neuron. The major postsynaptic target of the clutch cell are the soma and proximal dendrites of the spiny stellate

cells in the lower 2/3 of layer 4C; however the corresponding assumption is speculative, though reasonable, in the case of the -6 basket cell which dominates upper 4C . The synaptic input of the local circuit neurons are basically unknown (for details see Section 7.1 ’Relevant Anatomical Findings’). Therefore, I assume that a small portion (10%) of their excitatory input derives from geniculate cells while the rest of the excitation comes from the local spiny stellate cells. In addition I make the assumption that each inhibitory cell gets a small proportion of contacts from other inhibitory cells. The distribution of synaptic inputs to the inhibitory cells is hypothetical, though it seems to be reasonable at least for the clutch cell. The total number of excitatory and inhibitory synapses per cell is assumed constant and the ratio of the number of excitatory to inhibitory synapses is set 8:2 for each cell in layer 4C. Figure 8.1 summarizes the proportion of synaptic contacts from the principle sources of synaptic input that are used throughout the intracortical modelling study.

1each spine receives one excitatory synapse 8.1 Anatomical and Physiological Parameters 121

Property Value Source Linear Magniﬁcation

LGN magniﬁcation factor 300 m / degree Connolly & Van Essen, 1984

cortical magniﬁcation factor 1500 m / degree Van Essen et al., 1984 Relative Cell Densities LGN-P to LGN-M cells 6:1 Livingstone & Hubel, 1988 LGN-M2 to LGN-M1 cells unknown

LGN to layer 4C cells 1:100 Chow et al., 1950 4C to 4C cells 3:5 O’Kusky & Colonnier, 1982a 4C excitatory to inhibitory cells 8:2 Lund, 1987 LGN Axonal Arbor Spread

LGN-P axonal arbor 200 m Blasdel & Lund, 1983 Freund et al., 1989

LGN-M2 axonal arbor 600 m –”–

LGN-M1 axonal arbor 1100 m –”–

ratio of geniculate synapses terminating 9:1 Freund et al., 1989 on excitatory and inhibitory cells 4C Spiny Stellate Cells

dendritic arbor spread 200 m Lund, 1980

dendritic intrusion into see Section 6.1.1 LGN-P and LGN-M termination zone

dendritic intrusion into see Section 6.2.2 LGN-M2 and LGN-M1 termination zone

number of spines per cell constant Lund & Holbach, 1991 geniculate synapses per cell approx. 10% Peters et al., 1994 Latawiec et al., 1997 excitatory synapses per cell approx. 90% Ahmed et al., 1994 (from other cells within the layer)

somatic inhibitory synapses per cell constant Jennifer S. Lund (personal communication) ratio of excitatory to inhibitory synapse 8:2 Beaulieu et al., 1992 Local Axonal Arbors of 4C Spiny Stellate Cells

axonal arbor spread (at any depth) 250 m lateral stepped connections

spread from the soma in mid-4C 300 – 500 m Yoshioka et al., 1994 spread from the soma in upper 4C 400 m (1. step) Fitzpatrick et al., 1985

900 m (2. step) Anderson et al., 1993 Asi et al., 1998

width of terminal region (bar width) 200 m Local Circuit Neurons

dendritic arbor spread (clutch cell) 200m Kisvarday et al., 1986

axonal arbor spread (clutch cell) 150m Lund, 1987

dendritic arbor spread (-6 cell) 200 m axonal arbor spread (-6 cell) 1000 –1400 m

contact region of the somatic inhibitors 30m Jennifer S. Lund around the soma of the target cell (personal communication)

Table 8.1: Anatomical ﬁndings used in the intracortical recurrent study. 122 An Intracortical Model for the Depth-Dependence of Basic Response Properties in Layer 4C

W e i 72% 72% exc. inh. 20% cell cell W 20% e e W i i 8% 8% W i e W W aff aff

Figure 8.1: Proportion of synapses that arise from the different sources of synaptic input: spiny

stellate cells (exc.) and local circuit neurons (inh.). The ﬁgure schematically depicts the constant

W W W

af f

fieg efeig

proportion of afferent ( =0.08), inhibitory ( i =0.2), and excitatory ( =0.72) synapses of a cell in layer 4C. Note that the percentage of excitatory i.e. afferent and recurrent inputs make up 80% of the total synaptic input; the remaining 20% derive from the population of inhibitory cells. The 80% excitatory synapses fall into 10% thalamic synapses and 90% intracortical synapses. Because the anatomical data are fragmentary the numeric values are partially hypothetical. For details see text.

Convergence of Thalamic Input onto Layer 4C Spiny Stellate Cells

One prediction of the purely feedforward model was that the distribution of thalamic inputs onto postsynaptic spiny stellate cells reﬂects the intrusion of the dendritic ﬁelds into the termination zones of the LGN-P and LGN-M (LGN-M2 and LGN-M1) cells. Therefore, it is reasonable to assume that the constant percentage of thalamic input which constitutes only 10% of the total excitatory input to a cell in layer 4C is made up by a changing proportion of P and M (M2+M1) input with rise in depth of layer 4C. The distributions of thalamic weights in depth of layer 4C which correspond to the most plausible weight distributions in terms of anatomical evidence are summarized in Figure 8.2.

8.1.2 Physiological Parameters Physiological Parameters of LGN Cells

I have previously summarized the results of two studies that have quantitatively analyzed the receptive ﬁeld properties of P- and M- retinal ganglion cells and their geniculate counterparts (see Table 5.2). Since both data sets (Croner & Kaplan, 1995; Spear et al., 1994) led to virtually identical results for the feedforward model, it is reasonable to select one of the data sets for further parameter explorations. I have chosen the data set of Spear et al. (1994) which more directly assesses the response properties of LGN-P and LGN-M cells to constrain the response properties of model LGN cells in the intracortical recurrent model. Since the focus of the modelling work presented in the following sections is to test how the intralaminar connectivity of layer 4C affects the response properties of the cortical cells, only the mean values of the physiological P- and M- properties are considered. The feedforward model 8.1 Anatomical and Physiological Parameters 123

LGN-P W LGN–P LGN-M W LGN–M2 W W LGN–M1 100 W 100 75 75

50 50

25 25

87 6 5 4 3 2 1 D Thalamic Weight Portion [%] 87 6 5 43 2 1 D Thalamic Weight Portion [%] (a) 4C alpha 4C beta (b) 4C alpha 4C beta

Figure 8.2: (a) Proportion of feedforward thalamic LGN-P and LGN-M input at different depths of layer 4C (cf. Section 6.1.1). (b) Proportion of feedforward thalamic LGN-P, LGN-M2 and

LGN-M1 input at different depths D of layer 4C (cf. Section 6.2.2). Please note that the thalamic

LGN P LGN M LGN M 2 LGN M 1

W W W

weight portions W and refer to the constant portion W

of thalamic synapses ( af f =8%) of the cells in layer 4C (see Fig. 8.1).

Physiological Parameters LGN-P LGN-M R

Center Radius c [degree] 0.087 0.103 R

Surround Radius s [degree] 0.53 1.16 Integrated Surround- 0.547 0.546

Center Sensitivity K

1 1

Contrast Gain G [spikes sec %contrast ] 0.66 1.43 1

Max. ﬁring rate M [spikes sec ] 31.11 45.05 c

Contrast Threshold min [%contrast] 4.31 1.74

Table 8.2: Physiological parameters of LGN-P and LGN-M cells. The table gives the mean values

for the data set reported by Spear et al. (1994). For details compare Table 5.2. The integrated

2 2

K K R K R

s c c surround / center sensitivity is defined as s and taken from the study of Croner & Kaplan (1995), since Spear et al. (1994) do not report this particular parameter. has demonstrated that the gradient in basic response properties in depth of the layer, especially the nonlinear increase of contrast sensitivity, is not induced by the overlap in the physiological parameters of the LGN-P and LGN-M cells. In addition, it is hard to draw any statistical significance from the sparse experimental data on response properties of cells in layer 4C. Therefore, it is reasonable to neglect the scatter in the physiological data and to concentrate on the mean values of LGN-P and LGN-M cells. The population of model LGN-P and LGN-M cells are described by on average realistic response properties and – by contrast to the feedforward model – all sorts of statistical variability of the P- and M- cells (standard deviations) are neglected. Table 8.2 summarizes the physiological parameters of the LGN-P and LGN-M cells; please note that a realistic contrast threshold below which the cells do not respond has now been assigned to the LGN-P and LGN-M population. The model either considers feedforward thalamic input of one homogenous population of LGN- M cells that are described by the parameters in Table 8.2, or of two anatomically identified LGN- M subgroups, so-called M2 and M1 cells (Table 9.1). In the feedforward model, I have explored 124 An Intracortical Model for the Depth-Dependence of Basic Response Properties in Layer 4C

the statistical distribution of the LGN-M2 and LGN-M1 response properties, since the number ratio and physiological parameters of individual subgroups are unknown. For details about the re-estimation of M2 and M1 parameters based on a biological plausible assumption see Section 6.2.1. 8.2 Methods 125

8.2 Methods

The model presented in this section address the functional role of the intracortical recurrent connectivity which is given by realistic anatomical and physiological data summarized in Tables 8.1, 8.2 and 9.1.

8.2.1 Neural Network Architecture The model consists of three sets of layers, which correspond to the visual ﬁeld, the LGN and cortical layer 4C (Figure 8.3a). The visual ﬁeld layer is used to present the visual stimuli. Each layer in the LGN corresponds to a different population of geniculate cells, hence there are two layers for the P- and M-, and three layers for the P-, M2- and M1 populations, respectively. Again

two version of the model LGN are considered model I which corresponds to the LGN conﬁguration

fP M g S fP M M g S and model II which corresponds to the LGN conﬁguration .

Layer 4C consists of eight sublayers which correspond to eight different depths D . The upper

D four sublayers D represent the subdivision and the lower sublayers

correspond to the divisions, respectively. Each cortical sublayer consists of a population of

excitatory spiny stellate cells and a population of inhibitory cells. The population of inhibitory

f g

cells either corresponds to the clutch cell in the lower part of the layer, D 1, ,6 , or to the

D f g -6 cell in the upper part of the layer, 7,8 . Cells are placed at random locations in each sublayer and the corresponding cell densities are summarized in Figure 8.3b. The cell ratio of LGN-M2 and LGN-M1 cells are unknown, thus has to be tested by parameter explorations. The total number of LGN-M2 plus LGN-M1 cells of model II is, however, equal to the total number of LGN-M cells in the model I configuration. The model does not provide realistic cell densities neither in the LGN nor in layer 4C, but the ratio of LGN-P and LGN-M cells are chosen according to the experimental findings. Because each model cortical cell receives a constant percentage of synaptic load (see Figure 8.1), i.e. the sum of weights from each source of synaptic input are normalized to a constant numerical value, the particular cell ratios of excitatory and inhibitory cells do not bear on the outcome of the model. It is, however, more important to ensure that cortical cell densities used in the model result in a sufficiently dense intracortical connectivity. This is of particular importance, because the absolute number of model cortical cells is far below the cell density in the real cortex.

8.2.2 Connectionist Model Neuron The neurons in different layers are connected in a topographic fashion. The LGN layers are connected in a feedforward manner to the different sublayers of layer 4C. The cortical cells at each depth of layer 4C receive their input from LGN neurons which in turn receive their input from the visual ﬁeld layer. Because the purpose of this model study is to single out the effect of the intracortical recurrent excitation and inhibition at different depths of layer 4C, the excitatory and

inhibitory cells in each sublayer of layer 4C are connected via lateral connections.

The neurons are modelled as continuous-valued connectionist units. The output O of a cell

u u u 2

at position 1

X X

O u f I u I u I u w u x O x dx

k k

k (8.1)

k k

u u is interpreted as the cell’s ﬁring rate. I is the total input of the neuron at position which is a sum of inputs from different cell populations within the same cortical sublayer and from the 126 An Intracortical Model for the Depth-Dependence of Basic Response Properties in Layer 4C

Layer 4C Depth of V1 D=8 D=7 D=6 D=5 D=4 4C α D=3 D=2 D=1 4C β LGN 4500 µ m M1 M2 P LGN M P µ 900 m 900 µ m

VFLD

(a) 3 o

No. of Total Ratio Layer 4C Depth exc. cells inh. cells no. of cells 4Cα4C: β

D=8 2000 2000 D=7 2000 2000 4C α 16 000 D=6 2000 2000 D=5 2000 2000 1:1

D=4 2000 2000 D=3 2000 2000 16 000 4C β D=2 2000 2000 D=1 2000 2000

Ratio Ratio LGN No. of cells No. of cells P:M M2:M1

LGN-M1 LGN-M 625 625 ? 6:1 LGN-M2 } LGN-P 3721 LGN-P 3721 (b)

Figure 8.3: (a) Neural network architecture. The model consists of three sets of layers: the visual ﬁeld layer (VFLD), the different LGN populations represented by either two (M and P, left)

or three (M1, M2, and P, right) layers and layer 4C which consists of eight sublayers that corre-

f g

spond to different depth values, D ); the upper and lower four sublayers correspond to 4C and 4C , respectively. Each sublayer of model layer 4C consists of a population of exci-

tatory and inhibitory cells; inhibitory cells correspond to the clutch cell (D=1,..,6) and the -6 cell (D=7,8), respectively; The LGN and cortical cells are placed at random locations in each sheet. (b) Summary of cell densities for the network architecture shown in (a).

8.2 Methods 127

w u x

LGN layer. k is a weight kernel which gives the connection weight between two neurons

x f at position u and ; is a suitable transfer function which maps the cell’s input to the output ﬁring rate.

I have chosen the concept of weight kernels to denote the connection weights between two x neurons located at position u and because it leads to a more compact notation of the connectivity

structure. In most cases the connection weights do not depend on the exact positions of two

u xj

neurons but on the distance j between them which results in circular symmetric weight

ju xj kernels w .

8.2.3 Visual Stimulation

Visual stimuli are either stationary blobs or gratings which are presented in the visual ﬁeld layer.

Lx x x x 2 The different stimuli are coded as luminance values where 1 denotes the position

within the visual field. The luminance profiles of the stimuli are defined as follows:

r c y y y 2

Blobs of radius and contrast centered at position 1 in the visual ﬁeld:

2 2

(x y ) (x y )

1 1 2 2

2 2

r r

L x c e e

b (8.2)

c c l l l l

0 0 p

The contrast is deﬁned as p where is the maximum luminance of

the blob and 0 is the luminance of the background.

v c

Sinusoidal gratings of spatial frequency and contrast :

L x c cos v x 1

g (8.3)

c l l l l l

min max min max

The contrast is deﬁned as max where is the maximum l

luminance and min is the minimum luminance of the grating.

8.2.4 LGN Neurons

The receptive ﬁeld proﬁle D of a geniculate cell is given by a Difference-of-Gaussians model

1 1

2 2 2 2

[x +x ] [x +x ]

2 2

1 2 1 2

2R 2R

c s

e e x

D (8.4)

2 2

R R

c s

R R s The physiological parameters i.e. center and surround radii ( c and ) and integrated surround/center sensitivity K of the LGN-P and LGN-M populations are given in Table 8.2 and Table 9.1.

The Input Activity

LGN S

I S f g S f g u u u 2

The input , P, M or P, M2, M1 , of a geniculate cell at position 1

L x

g bg is calculated by convolving the luminance values f of a grating or blob stimulus, eq. (8.3)

and (8.2), in the visual ﬁeld layer with the DoG proﬁle D

LGN S

I u D L D x L u xdx

bg g

f (8.5)

fbg g

2 128 An Intracortical Model for the Depth-Dependence of Basic Response Properties in Layer 4C

40 100

30 LGN-M LGN-M LGN-P 20 10

10 LGN-P Response [spikes/sec] Response [spikes/sec]

0 1 0 0.2 0.4 0.6 0.8 1 0.1 1 10 Contrast c Spatial Frequency [cycles/degree]

Figure 8.4: Response Properties of a model LGN-P and LGN-M cell. Left: Contrast vs. response function for a stationary grating stimulus of optimal spatial frequency. Right: Response as a

function of spatial frequency at contrast c=20%.

Thus one obtains for a blob/grating centered at y

2 2

( v R ) LGN S ( v R )

s c

K e I u K c cos v u e

1 and (8.6)

2 2 2 2

(u +u ) (u +u )

1 2 1 2

2 2

LGN S

(R +r ) (R +r )

c s

e e u K c r

I (8.7)

2 2 2 2

R R r r

c s

u v r opt for a grating or blob stimulus centered at . The optimal spatial frequency opt and radius of

a geniculate cell results from

LGN S

u d I

and (8.8)

dv dr

with u respectively.

The Transfer Function

LGN S LGN S

f I

The output O of a geniculate cell is calculated via the transfer function

x X

if min

f (8.9)

X (xX )

min M

otherwise

X +(xX )

50 min

The parameters of the transfer function are determined via a ﬁt of f to the experimental contrast-

X X M

response functions of the geniculate P- and M-cells. In more detail, the parameters min , X

and 50 where determined as follows:

LGN S

X I

1. The threshold min is set equal to the input which a geniculate cell receives for

fv r g

opt opt

v r opt

a grating stimulus of optimal spatial frequency opt or a blob stimulus of optimal radius c

at contrast threshold min (Table 8.2 and 9.1)

LGN S

X K c I min

min (8.10)

fr v g

opt opt 8.2 Methods 129

where

2 2

( v R ) ( v R ) LGN S

opt s opt c

K e e

I for a grating and (8.11)

opt

2 LGN S

r I

for a blob (8.12)

opt r

opt

2 2

R R r r

c s

opt opt

respectively. c

2. With eq. (8.10) the transfer function f can be rewritten as a function of stimulus contrast

c c

if min

f c

X (cc ) min

M (8.13)

LGN otherwise 1

) +(cc ) X (I

min

fr v g

opt opt

Note that the equation only holds for a grating whose positive half is centered in the cell’s receptive ﬁeld or a blob which is centered in the receptive ﬁeld of the cell.

3. The contrast vs. response function of a geniculate cell is given by a Michaelis-Menten

R c M c c MG c c min function min where M corresponds to the maximum

response and G to the contrast gain which are given in Table 8.2 and 9.1

X X R c f c 50 Therefore the parameters M and can be easily inferred via the relation

and one obtains

1 LGN

X M X M G I 50

M and (8.14)

fr v g

opt opt

The response properties of model LGN-P and LGN-M cells which are determined by the above equations are shown in Figure 8.4.

8.2.5 The Cortical Layers

The populations of excitatory and inhibitory cells within each sublayer of model layer 4C are

connected via lateral recurrent connections. Each cortical neuron at position u at depth D is char-

u D t acterized by a time-dependent ”membrane potential” m where t is the time in arbitrary

units. The dynamics of m is given by

P P P P

u t D m u t D I u t D I u D

m (8.15)

l at af f

fe ig I u t D

where P is the cell type i.e. excitatory or inhibitory, is the lateral recurrent

l at

u D

input and I is a stationary afferent input. The output of the cortical cells is calculated af f via a rectiﬁed sigmoid transfer function which is different for excitatory and inhibitory cells. The above dynamics describes cortical nervous tissue of excitatory and inhibitory cell populations which are homogeneously distributed in a planar sheet interacting by way of recurrent lateral connections (Wilson & Cowan, 1973). Note that eq. (8.15) deﬁnes a system of non-linear differential equations. 130 An Intracortical Model for the Depth-Dependence of Basic Response Properties in Layer 4C

Geniculocortical Connectivity

The connectivity between the LGN and layer 4C is calculated according to Section 5.2.5. The W

proportion of afferent synapses af f , however, makes up only a small proportion of the total i synaptic weights of an excitatory (e) and inhibitory ( ) cortical cell at depth D of model layer 4C.

The proportion of the afferent synapses which are occupied by different sources of thalamic input

LGN S

D S fP M g

are given by the depth-dependent thalamic weight portion W where and

S fP M M g W

respectively. For details about the particular choice of parameter values af f

LGN S

and W see Figures 8.1 and 8.2.

fe ig u D Thus the afferent input to a cortical cell of type P at location and depth is given

LGN S

LGN S P LGN S

W D I u D x w ju xj O x

d (8.16)

af f

LGN S

ju xj

where w are normalized circular symmetric weight kernels which are proportional P

to the areal overlap between the afferent axonal arbor of type LGN-S at position x and the dendritic

fe ig u

ﬁeld of a cortical cell of type P at position . The kernels are normalized to satisfy

LGN S

dx w ju xj W

af f P

The Lateral Connectivity i

The excitatory (e) and inhibitory ( ) cells within each sublayer of model layer 4C are connected

e e i i e i i

via lateral excitatory (e , ) and inhibitory ( , ) connections. The lateral

fe ig u

recurrent input to a cortical cell of type P at position in depth D is given by

P P P

dx w ju xj D O I u t D m x t D

P (8.17)

l at

P feig

P P

x t D m w ju xj D O

where P denote normalized symmetric weight kernels and is

x W W

P iP

the output of a cortical cell at position at depth D. The normalization constants e and

fe ig represent the total excitatory and inhibitory synaptic load of a cortical cell of type P (for

number values see Figure 8.1):

P fe ig dx w ju xj D W

P P P

P with

Because the spatial extent of axonal and dendritic ﬁelds as well as neural composition are

P depth-dependent, individual weight kernels P are chosen for each depth D of layer 4C.

Lateral Excitatory Connections

w P fe ig

P The lateral excitatory connections e are established via the geometric models

shown in Figure 8.5. The stepped connections of spiny stellate cells in upper 4C form bar like terminal fields. Since the functional specificity of the stepped connections is unknown, I assume that a cell gets monosynaptic excitatory input from local neighbours and from one or two concentric annuli which correspond to input via the first and second side-step connections. The geometric constraints are given by the spread of the dendritic arbor of the target cell and axonal projection 8.2 Methods 131

200µ 800µ m Depth D

D=8 D=7 α 4C D=6

D=5

D=4

D=3 4Cβ D=2

250µ m D=1

(a) 200µ 300µ m ~ W step-1 ~ 100 Wstep-2 ~ Wlocal 75

25 Initial Proportion of Lateral Excitatory Weights [%] 8 7 6 5 43 2 1 D (b) 4C alpha 4C beta

Figure 8.5: (a) Cartoon of lateral axonal connections of spiny stellate cells at different depths of

model layer 4C. Spiny stellate cells in lower 4C only project to very local neighbours. Cells in mid-4C project make one additional lateral side-step connections while cells at the top of layer

4C have at least two side-steps within the same depth. Numbers indicate lateral spread in the retinotopic map. (b) Initial proportion of lateral excitatory weights from different spatial origin as

a function of depth in model layer 4C. The proportion corresponds to an initial probability to get

W W

step1

a synapse from ’very local’ neighbours ( l ocal ), from spiny stellate cells one ( ) and two

2 side-step ( step ) away, respectively. However the balance between lateral excitation from the

stepped connection (step-1 plus step-2) and lateral excitation from very local neighbours can not W

be derived from the experimental data and is controlled via the ’synaptic efﬁcacy’ s (for details see text and Section 9.1.1). 132 An Intracortical Model for the Depth-Dependence of Basic Response Properties in Layer 4C

pattern of the spiny stellate cell which is depicted in Figure 8.5a. Since I do not consider the functional specificity of the stepped connection connectivity it is reasonable to model the stepped connections as circular concentric annuli around the soma. The terminals of the excitatory spiny stellate cells which originate from different spatial origin within the retinotopic map of layer 4C compete for the constant load of excitatory input to each cortical cell. Therefore the connection probability of a spiny stellate cell and a target cell scales with the areal overlap of the dendritic field of the target cell of type P and the lateral axonal projections shown in Figure 8.5a. The proportional areal overlap of the dendritic field with the

’very local’ axonal ﬁeld, the ﬁrst and the second step projection are given by normalized circular

step1 step2

l ocal

w w

symmetric weight kernels w and which are independent of depth D (cf. eq.

eP eP (8.19)). The lateral spread of the dendritic fields of the excitatory spiny stellate cells and inhibitory interneurons is given in Table 8.2. I further assume that with rise in depth of the layer an increasingly higher proportion of spines is occupied by terminals that originate from lateral stepped connections. In addition, the probability to get a synapse from the lateral stepped connections increases linearly with rise in depth of layer 4C; at the top of layer 4C where spiny stellate cells make two side-steps in addition to the very local projections, the synapses that are from the very local and the stepped connections are divided into equal portions. This reflects the particular finding that the actual number of the lateral projectors increases with rising position in depth of the layer. Thus, it is reasonable to assume that an increasing proportion of excitatory contacts originates from the lateral stepped connections. In other words, the terminals from the stepped connections compete together with the terminals from

the very local neighbours for the constant number of spines on a single excitatory cell.

W D W D

step1

The initial depth-dependent lateral excitatory weight portions l ocal , and

W D

2 step that arise from the ’very local’ axonal ﬁelds, and from the ﬁrst and second lateral side-steps are summarized in Figure 8.5b. Please note that the total number of excitatory synapses

from different spatial origin, i.e.

W D W D W D

step1 step2 l ocal (8.18)

is constant in depth of layer 4C. However, the balance in the number ratio of the excitatory synapses that arise from stepped connections (step-1 plus step-2) and the local neighbouring cells can not be derived from the

experimental data. The particular balance between the lateral stepped connection and the local W

recurrent excitation is controlled by a so-called synaptic efﬁcacy s of the stepped connections (compare Figure 8.5b).

Since the excitatory connections derive from different spatial origin the excitatory weight ker-

nels e at different depths D fall into three sub-kernels that are associated with connections

ju xj

from local neighbours, the ﬁrst and second sidesteps, respectively. Let d denote the

fe ig u distance between a cortical cell of type P at location and a spiny stellate cell at location

x. Hence, the excitatory weights at different depths D are given by

stepj

l ocal

w d D d W d W D W D w W D w

eP s 0 stepj

l ocal

=12 j (8.19)

with

Z Z

stepj

l ocal

ju xj j x w ju xj dx w

d and

2 2 (8.20)

8.2 Methods 133

stepj

0 w

The normalized circular symmetric weight kernels w , and scale with the areal over-

lap of the dendritic ﬁeld with the ’very local’ axonal arbors and the j th stepped axonal projections of the excitatory cell population. The proportion of excitatory synaptic weights of differ-

ent spatial origin corresponds to the proportion of lateral excitatory synapses of different spa-

tial origin in depth D of layer 4C multiplied with the ’synaptic efﬁcacies’ s and

W D W W

0 s

s . Please note that the ’synaptic efﬁcacy’ controls the ratio of the

W (D ) local excitatory load of the stepped connections relative to the excitatory weights from very local neighbours. Since it is the balance in lateral excitatory weights of different retinotopic origin which is crucial to the model I have introduced a separate parameter set. The lateral excitatory weight

portions of different spatial origin are given by

W D W D W D W D W W D j

0 stepj s stepj l ocal l ocal and (8.21)

with

W D W D W D

step1 step2

l ocal W

but note that their values are controlled by the efﬁcacy s . In order to explore how the balance W

controlled by s affects receptive ﬁeld size and contrast sensitivity different synaptic efﬁcacies, i.e. lateral excitatory weight portions have been tested (see Results Chapter 9).

Lateral Inhibitory Connections

w P fe ig

P The lateral inhibitory connections i are based on the anatomically realistic model shown in Figure 8.6a. The geometric model considers two different types of inhibitory cells which are associated with different depths D of model layer 4C. The clutch cell, which has

a small, roughly circular axonal ﬁeld is staggered in the lower depth of the the layer. The - 6 cell has a stratiﬁed arbor restricted to the top of the layer. Moreover, both interneurons are somatic inhibitors, i.e. they contact the soma and the proximal dendrites of the postsynaptic cell

to make up a constant inhibitory load. Thus the connection weight between a clutch cell (- 6 cell) and a cortical cell scales with the areal overlap of the corresponding axonal arbor and a small region which circumscribes the somatic contact region of the postsynaptic cell (small cylinders in Fig. 8.6a). Since there is a small stratum in depth of the layer (D=7) where the axonal arbors of both types of inhibitory interneurons partially overlap, it is reasonable to assume that cells at this particular depth receive the constant number of somatic contacts from both inhibitory

cell types. To account for the change in inhibitory strategy in upper 4C, I introduced a set of

W D W D

6 parameters cl utch and . The parameter values given in Figure 8.6b correspond to

the proportion of lateral inhibition provided by the clutch cells and the -6 cells at different depths D of layer 4C.

Since inhibitory connections derive from different inhibitory cell types (clutch and -6) which

partially overlap in upper 4C the inhibitory weight kernels i fall into two cell-type speciﬁc

ju xj u components. Let d denote the distance between a cortical cell at location and an

inhibitory cell at location x. Thus the inhibitory weights at different depths D of layer 4C are

given by

cl utch 6

w d D W D w d W D w d

iP 6

cl utch (8.22)

iP 134 An Intracortical Model for the Depth-Dependence of Basic Response Properties in Layer 4C

Depth 1400 µ m D

8 α−6 30µ 7 4Cα 6 30µ

5 30µ µ 4 30

30µ 3 30µ 2 4Cβ

30µ 1 clutch

30µ (a) 150µ m

100 Wα−6

Wclutch 75

Proportion of 25

Lateral Inhibitory Weights [%] 8 7 6 5 4 3 2 1 D (b) 4C alpha 4C beta

Figure 8.6: (a) Cartoon of the axonal arbors of the clutch cell (light grey cylinders on the right at depth D=1, ,6) and the -6 cell (dark grey cylinders at depth D=7,8) in comparison to the

contact region, i.e. soma and proximal dendrites of the postsynaptic cell (small white cylinders at depth D=1, ,8). The numbers indicate lateral spread. Note that the clutch cell and the -6 cell are somatic inhibitors which only contact the soma and proximal dendrites of the postsynaptic cell. (b) Proportion of lateral inhibitory weights from different types of inhibitory interneurons

as a function of depth in model layer 4C. The proportions correspond to the probability to get

W W

a synapse from the -6 cell ( and from the clutch cell ( cl utch ) as a function of depth D. Because the axonal arbors of the -6 and the clutch may overlap in a small stratum in layer 4C (D=7), it is reasonable to assume that the constant somatic inhibition comes from both inhibitory cell types in this sublayer. 8.2 Methods 135

with

Z Z

cl utch

ju xj x w ju xj dx w

d and

2 2

cl utch w

The normalized weight kernel w and scale with the areal overlap of the somatic contact

region of a cortical cell with the axonal arbor of the clutch and -6 cell respectively. The depth-

W W W D W D

6 6 cl utch dependent weight portions cl utch and fulﬁl =1 for each depth D of model layer 4C.

Cortical Transfer Functions The output spike rate of a cortical cell is calculated by applying a rectifying, piecewise linear

transfer function

x T

if p

g x

P (8.23)

a x T P

P otherwise

u t D to the membrane potential m given in eq. (8.15). Please note that the transfer function does not saturate. The excitatory and inhibitory cell populations have different intrinsic physiological properties. Therefore, different parameter values are chosen for the transfer functions of the excitatory spiny

stellate cells and the inhibitory interneurons. The threshold and gain of the excitatory cells are set

T a e to e and . These parameters remain constant for all parameter explorations.

It is the change in inhibitory strategy in upper 4C which is crucial to the model. Therefore, I

assume that the clutch cell and the -6 cell differ in their physiological properties. The threshold

T a cl utch

and gain of the clutch cell are set to cl utch , , if not mentioned otherwise. Because upper 4C is characterized by a population of direction selective cell and the -6 cell

is an excellent candidate to provide the putatively powerful inhibition, the gain of the -6 cell is assumed to be higher than that of the clutch cell. However, the onset and the strength of lateral

inhibition in upper 4C cannot be derived from the experimental data. Therefore, I have explored

T a

6 6 how changes in the physiological properties, , of the -6 cell affect receptive ﬁeld size

and achromatic contrast sensitivity of cells in upper 4C (see Results).

Measurement of Receptive Field Size and Contrast Sensitivity Receptive ﬁeld size is determined as the peak summation area of a model cortical cell. The area summation functions are calculated by a blob stimulus of low contrast (c=20%, if not mentioned otherwise) which is centered in the receptive ﬁeld of the cortical cell. In all cases a cell is selected

which lies in the center of the cortical layer. The radius r of the blob is systematically increased

by steps of 0.01 degree from 0.1 to 1.5 degree. For each radius r the steady state response of the

cortical cell is calculated. The steady state response of a cortical cell at position u at depth D is

given by the steady state condition of the membrane potential

u t D

m (8.24)

dt r

The radius peak at which the steady state response of the cortical cell has reached its peak response r

was taken as a suitable measure of receptive ﬁeld size. The radius peak is a suitable measure of 136 An Intracortical Model for the Depth-Dependence of Basic Response Properties in Layer 4C

1.2 3

0.8 2

0.4 t1 Steady State Response Steady State Response

0 0 0.1r 1 peak 0 c 40 60 80 100 Radius [degree] Contrast [%]

Figure 8.7: Measurement of receptive ﬁeld size and contrast sensitivity. Left: Steady state re-

sponse as a function of blob radius r for a cortical cell (c=20%). Receptive ﬁeld size is deﬁned as r

blob radius peak which corresponds to the peak response of the area summation function. Right: r

Steady state response as a function of contrast for a blob of radius peak for the same cortical cell

as in (a). Contrast sensitivity is deﬁned as the reciprocal threshold contrast c at which the steady t

state response has reached the threshold 1 .

peak size of summation area. This measurement does not reﬂect the method used to study the MRF as described in Blasdel & Fitzpatrick (1984) but the strong correlation of MRF size and peak size of area summation in the data set of J. B. Levitt indicates that both measures, minimum response ﬁeld and peak size of area summation, are equivalent in almost all cells of layer 4C (see Section 7.2.3, Figure 7.3). Therefore, peak size of summation area will be used as an adequate

measure of receptive ﬁeld size in the intracortical modelling study. r

The achromatic contrast sensitivity is determined by a blob of optimal radius peak which is centered in the receptive ﬁeld of the cortical cell. The contrast of the blob is systematically

increased by steps of 1%contrast from 0% to 100% contrast. The contrast at which the steady t

state response of the cortical cell (eq. 8.24) has reached a certain threshold 1 is taken as the threshold contrast c. Contrast sensitivity is defined as the reciprocal threshold contrast 1/c. An example of the measurement of receptive field size and contrast sensitivity is shown in Figure 8.7. Simulated receptive field size and contrast sensitivities at different depths D of layer model layer 4C are normalized in order to allow the comparison with the experimental data of Blasdel & Fitzpatrick (1984) and Hawken & Parker (1984).

8.2.6 Implementation The model was implemented in C++ on a standard Unix environment. The graphical user interface of the simulation tool is described in Appendix B, Section B.1. For simulations a PC (dual- processor Pentium II 300MHz) was used. The average set-up time of the cortical connections in one sublayer of model layer 4C takes up to 20 minutes. The average amount of computation time to calculate the basic response properties of a cortical cell is roughly 5 minutes. The computation times are average values since they depend on the conﬁguration of the computer system and scale with the number of lateral connections. Due to the large number of cortical cells and the wide spreading lateral connections at depth D=7,8 the total amount of memory is up to 160 MB for one cortical network layer. 8.2 Methods 137

The calculation of the areal overlap of axonal and dendritic ﬁelds is performed in discretized space using a resolution of 1000 pixels per 4500 m (0.22 pixels/ m). Since in most cases I was only interested in ﬁnding the steady state of the differential equations given by eq. (8.15), I used a rapid asynchronous update algorithm which is described in Section B.2 of Appendix B. The goal of the stochastic update is to obtain the steady state without an explicit integration of the whole trajectories. If the time course of the membrane potentials was needed, eq. (8.15) was integrated by the Euler method (Press et al., 1992) with a time step of 0.1. For the simulations results shown in the next section both methods converge to the same steady state. 138 An Intracortical Model for the Depth-Dependence of Basic Response Properties in Layer 4C Chapter 9

Results of the Intracortical Model

This chapter presents the numerical results of the intracortical model introduced in Chapter 8. In order to test how realistic intralaminar circuitry affects receptive field size and achromatic contrast sensitivity of spiny stellate cells at different depths of layer 4C, I have systematically explored the parameter space of the intracortical recurrent model based on afferent thalamic input of one and two LGN-M populations, respectively. To see, how the lateral excitatory inputs and the change in inhibitory strategy does build a new cumulative spatial extend to the receptive field and a new contrast sensitivity of each individual cell, I have systemically changed the ’efficacy’ of stepped

connections and the physiological properties of the -6 cell. Since cells at different depths of layer 4C get different proportion of afferent thalamic input from LGN-P and LGN-M cells it is important to ask what are the contributions of the feedforward thalamic inputs and which effects are due to intracortical recurrent ampliﬁcation. In the second part of this chapter, I explore how feedforward input from two anatomically identiﬁed LGN-M populations, LGN-M2 and LGN-M1, combine with the excitatory stepped connections and the change in inhibitory strategy in upper

4C. The theoretical predictions are followed by a discussion of the likelihood of the intracortical versus the thalamic feedforward circuitry and suggestions are made for new experiments that may conﬁrm, refute or distinguish between the different hypotheses.

9.1 Results Model I: One LGN-M population

First I consider the neural network architecture which is based on afferent thalamic input from one homogenous LGN-M population and which was called model I (Figure 8.3). The thalamic weight distribution and the physiological properties of the LGN-P and LGN-M population are given in Figure 8.2a and Table 8.2.

9.1.1 Efﬁcacy of the Lateral Stepped Connections W

Numerical simulations are performed for four different ’synaptic efﬁcacies’ s . The corresponding distributions of excitatory weights of different spatial origin within the retinotopic map of layer 4C are shown in Figure 9.1. The predicted receptive ﬁeld size and contrast sensitivity curves are

summarized in Fig. 9.2. W

The overall shape of receptive ﬁeld size curves change signiﬁcantly for different values of s .

If there is no lateral input from the stepped connections (weights (i), s ) the receptive 140 Results of the Intracortical Model

Wstep-1 Wstep-1 100 100 Wstep-2 Wstep-2

Wlocal Wlocal 75 75

50 50 Proportion of Proportion of 25 25 Lateral Excitatory Weights [%] Lateral Excitatory Weights [%] 8 7 6 5 43 2 1 D 8 7 6 5 43 2 1 D (i) 4C alpha 4C beta (ii) 4C alpha 4C beta

Wstep-1 Wstep-1 100 100 Wstep-2 Wstep-2

Wlocal Wlocal 75 75

50 50 Proportion of Proportion of 25 25 Lateral Excitatory Weights [%] Lateral Excitatory Weights [%] 8 7 6 5 43 2 1 D 8 7 6 5 43 2 1 D (iii) 4C alpha 4C beta (iv) 4C alpha 4C beta

Figure 9.1: Lateral excitatory weight portions from different spatial origin within the retinotopic

map as a function of depth in model layer 4C. Each plot shows the proportion of lateral excitatory

W D W D W D

step step

weights given by l ocal , , and (see eq. 8.21) which correspond to a

1 2 W

particular synaptic efﬁcacy s at eight discrete depths D. (i) No excitation from lateral stepped W

connections ( s =0.0) (ii) Only a small proportion of recurrent excitation is made up by the lat- W

eral excitation of the stepped connections ( s =0.33). (iii) Cortical neurons in mid-4 and upper

4C receive stronger excitation from lateral stepped connections ( s =0.66). (iv) Cells at the top

of layer 4C (D=8) get equal proportions of lateral excitatory weights from all three sources of W

recurrent excitation ( s =1.00).

ﬁeld size curve shows only moderate increase with rise in depth of layer 4C. Receptive ﬁeld size

1 saturates or even decreases in upper 4C which is due to strong inhibition from the -6 cell .

Please note, that in the absence of lateral input from the stepped connections in upper 4C the

inhibition of the -6 cell comes from a much wider range within the retinotopic map than the

lateral excitation which only covers a small local neighbourhood.

If the efﬁcacy of lateral stepped connections is gradually increased (weights (ii) and (iii), s

and s ) receptive ﬁeld size curves become steeper until the curve ﬁnally shows an

almost exponential increase in upper 4C (weights (iv), s ). However, if the efﬁcacy of lateral stepped connection is increased, contrast sensitivity decreases slightly in mid-4C but more

rapidly in upper 4C. The reason for a reduction in contrast sensitivity is a the re-distribution of the excitatory weights to regions within the retinotopic map which are driven by a lower ﬁring rate of the presynaptic LGN cells. In summary, the lateral excitation which is known to come from an increasingly wider range with rise in depth of the layer can explain the gradual increase in receptive ﬁeld size in mid-4C

1The experimental data on receptive field size at the top of layer 4C is sparse and rather indicates a decrease in field size at the top of the layer (cf. Section 3.2, Figure 3.7a). Therefore it is worth noting that the simulated receptive field size and contrast sensitivity curves which are computed in the absence of input from the lateral stepped connections account for an almost exponential increase in contrast sensitivity and a decrease in receptive field size at the top of layer 4C. 9.1 Results Model I: One LGN-M population 141

1.4 weights (i) 10 weights (ii) weights (i) 1.2 weights (ii) weights (iii) 8 weights (iv) weights (iii) 1 weights (iv) 0.8 6

0.6 4 0.4 2

Receptive Field Size [degree] 0.2 Contrast Sensitivity [1/contrast]

0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 9.2: Parameter exploration of the intracortical model I (one M pathway). The ﬁgure shows

receptive ﬁeld size (left) and contrast sensitivity (right) of a layer 4C spiny stellate neuron as

a function of depth D , . Each curve corresponds to a particular to a particular W

distribution of lateral excitatory weights i.e. a particular synaptic efﬁcacy s of Figure 9.1(i)-(iv).

The cortical threshold parameter was 1 = 2.0. The parameters of the -6 transfer function were

T a

6 6 = 2.4 and = 3.0.

and upper 4C, but it effectively reduces the contrast sensitivity within the same depth. The optimal balance of lateral excitatory weights of different spatial origin within the retinotopic map correspond to Figure 9.1(iv).

9.1.2 Physiological Properties of Inhibitors: Parameter Regimes In order to test how the physiological properties of the inhibitory interneurons affect receptive

ﬁeld size and contrast sensitivity in depth of layer 4C, I systematically varied the parameters of

g g

6 the inhibitory transfer functions, cl utch and . Since it is the change in inhibitory strategy

in upper 4C which is crucial to the intracortical hypothesis, the explorations are restricted to

lower 4C (D=1) and upper 4C (D=8). Lower 4C is dominated by inhibition from the small clutch cell, local recurrent excitation from a narrow range within the topographic map (no lateral

side-steps) and afferent input from LGN-P cells. By contrast, upper 4C is characterized by the

wide arbor -6 cell, wide spreading lateral excitatory connections and afferent input from LGN-M cells. Receptive ﬁeld size and contrast sensitivities as a function of the threshold and gain of the

inhibitory transfer functions are shown in Figure 9.3. The overall shape of the surface plots in Figure 9.3 is similar for lower 4C and upper 4C ,

however the absolute values differ. The similar trend of simulated response properties in lower 4C and upper 4C with respect to changes in threshold and gain is due to the overall identical connectivity proﬁles. At both depths, lateral inhibition comes from a smaller range within the

retinotopic map than the lateral excitatory input, although the absolute scale of lateral spread differs considerably in lower 4C and upper 4C .

The contour plots of Figure 9.3 indicate that there are at least three different parameter regimes

T a P fcl utch g P which depend on the particular choice of threshold P and gain , of the inhibitory transfer function: 142 Results of the Intracortical Model

Lower 4C beta (D=1)

8 0.48 6

0.44 4

2 4.5 0.40 4.5 4 4 3 3.5 3.5 0 2.5 0 3 0.5 1 2 0.5 1 2 2.5 1.5 1.5 Gain

Contrast Sensitivity [1/contrast] 2 Receptive Field Size [degree] 1.5 2.5 1 2 1.5 Gain 3 2.5 3 1 Threshold a clutch Threshold a clutch T clutch T clutch

0.41 0.39 6 4.5 5 4 4.5 7 3.5 4 0 3 0.40 0.43 3.5 0.5 1 2.5 0.42 3 1.5 2 Gain 0 0.5 2.5 2 2.5 1.5 1 2 3 1 a 1.5 2 1.5 Gain Threshold clutch 2.5 1 3 a clutch Threshold T clutch

T clutch

Upper 4C alpha (D=8)

15 1.4 12

1 9 6 0.6 3 6 6 5 5 0.5 4 0.5 1 4 1 1.5 2 Receptive Field Size [degree] 1.5 2 2.5 2.5 3 3 3.5 3 Gain 3 3.5 2 Contrast Sensitivity [1/contrast] 2 4 4.5 Gain Threshold 4 4.5 a α−6 Threshold a α−6 T α−6 T α−6

0.4 0.6 5 11 6 8 5 1 6 1.3 5 0.5 1 4 1.4 1.5 2 0.5 1 1.5 4 2.5 3 3 Gain 2 2.5 3 3 Gain 3.5 4 4.5 2 3.5 4 2 Threshold a α−6 Threshold 4.5 a α−6 T α−6 T α−6

Figure 9.3: Receptive ﬁeld size and contrast sensitivity of a spiny stellate cell in lower 4C (top)

and upper 4C (bottom) as a function of threshold and gain of the inhibitory transfer functions,

g g

6 cl utch and respectively. The upper plot in each panel shows the surface representation while

the lower plot gives the corresponding contour representation of the simulated data. Synaptic W

efﬁcacy was set to s =1.00 which corresponds to the distribution of lateral excitation shown t

in Figure 9.1(iv). Note, however, that cortical contrast threshold was 1 =1.0. The arrows mark

T T a a

6 6 cl utch the threshold ( cl utch =0.5, =2.4) and gain ( =2.5, =3.0) of the inhibitory transfer functions which led to the best prediction of receptive ﬁeld size and contrast sensitivity in depth of layer 4C. For details see text. 9.1 Results Model I: One LGN-M population 143

Regime 1 – Low Threshold + High Gain: Receptive ﬁeld size and contrast sensitivity are low, because strong recurrent inhibition sets on early and leads to effective suppression of the lateral recurrent excitation.

Regime 2 – Low to Medium Threshold + Low to Medium Gain: Basic response properties depend on both parameters, threshold and gain, of the inhibitory transfer function. However, the plots of Figure 9.3 suggest a stronger dependence on the threshold than on the gain which is an artefact due to the range of treshold and gain which are plotted. There is a regime where the basic response properties depend equally on both

parameters which is most clearly seen in the receptive ﬁeld size plot in upper 4C of Figure 9.3. Because the lateral inhibition sets on later, this allows for an initial ampliﬁcation of the afferent input by the recurrent excitatory connection and it is the balance of threshold and gain of the inhibitory transfer function which controls steady state response, thus controls the basic response properties of the cortical cells.

Regime 3 – High Threshold: The basic response properties depend on the threshold of the inhibitory transfer function and ﬁnally saturate.

Receptive field size in lower 4C saturates early due to late onset of recurrent inhibition by the clutch cell which influences a smaller region in the retinotopic map than the lateral excitation. Only neurons in the center of the receptive field are influenced by the recurrent inhibition. Inhibitory neurons in the peripheral part become not active any longer and thus do not influence the peak summation area which is determined by the excitatory input from the peripheral part of the cumulative receptive field.

Receptive ﬁeld size in upper 4C does not saturate for high treshold of the inhibitor. The saturation is due to the model setup, since the radius of the blob stimuli are not chosen larger than 1.5 degrees to avoid boundary artefacts. In other words, I stopped simulations at a radius of 1.5 degrees and assigned this as the peak summation area (cf. Section 8.2.5).

Therefore the constant plateau in the receptive ﬁeld size in upper 4C has to be interpreted as greater than 1.5. The reason for the saturation in contrast sensitivity at high threshold values is 1. due to late onset or even absence of inhibition for high inhibitory threshold values at low contrast values and 2. due to the saturation in receptive ﬁeld size. Please note, that saturation in

receptive ﬁeld size implies the same afferent input to a cortical cell and the same contrast.

1 1 2 In other words, contrast sensitivity which is deﬁned as [spikes sec %contrast degree ] saturates due to the saturation in the afferent input. In summary, contrast sensitivity does not depend on the intracortical connections in this particular parameter regime and is determined by the contrast sensitivity in the afferent input. The network is not in the marginal phase in the sense of Ben-Yishai et al. (1995).

These parameter regimes generally apply for all other depths D in layer 4C, since the lateral connectivity proﬁles do not qualitatively change in depth of the layer, i.e. the constant inhibitory load always originates from a smaller region within the retino-topic map than the lateral excitatory inputs. However, the ratio in lateral spread of recurrent excitation and inhibition changes in mid- 4C where side-steps start to emerge but inhibition from the clutch cell remains the same. This 144 Results of the Intracortical Model

difference in mid-4C affects the transition between parameter regimes, i.e. at which thresholds and gains of the inhibitory transfer function they occur, but it does not affect the overall characteristics. Please note, that differences in absolute contrast sensitivity and receptive ﬁeld size also result from differences in the stationary afferent input which change in depth of the layer.

9.1.3 Intrinsic Physiological Properties of the -6 Neuron

exc. cell exc. cell exc. cell Output O(x) clutch cell clutch cell

clutch cell Output O(x) 2 2 Output O(x) 2 α−6 cell α−6 cell α−6 cell x x x 2 2 2

Tα−6 =0.5 aα−6 =2.5 Tα−6 =1.0 aα−6 =2.6 Tα−6 =1.5 aα−6 =2.7 (a) (b) (c)

exc. cell exc. cell clutch cell clutch cell Output O(x) 2 Output O(x) α−6 cell 2 α−6 cell x x 2 2 a (d) Tα−6 =2.0 aα−6 =2.8 (e) Tα−6 =2.4 α−6 =3.0

Figure 9.4: Five different parameter sets of the physiological properties of the -6 cell. Each

plot shows the cortical transfer function of the excitatory spiny stellate cells, inhibitory clutch

T a e

cells and -6 cells. The physiological parameters of the excitatory cells ( e =0.1, =1.0) and the

T a cl utch

clutch cell ( cl utch =0.5, =2.5) remain constant (grey curves). (a) The -6 cell has the same

T T

6 6

physiological properties as the clutch cell ( =0.5, =2.5). (b) The -6 cell has slightly

T T

6 6

higher threshold and gain than the clutch cell ( =1.0, =2.6) (c), (d) Threshold and gain

of the -6 cell are gradually increased (e) The -6 cell which dominates inhibition in upper 4C

T T

6 6 has considerably higher threshold and gain ( =2.4, =3.0) than the clutch cell in the lower two third of the layer. The parameter constellation shown in (e) corresponds to the physiological properties of inhibitory interneurons which are marked in Figure 9.3.

To test how differences in the physiological properties of the somatic inhibitors help to sharpen

the rapid increase of basic response properties in upper 4C, I have systematically changed the threshold and gain of the -6 cell which selectively arborize at the top of layer 4C . The cor-

responding parameters of the -6 transfer function are summarized in Figure 9.4. The predicted receptive ﬁeld size and contrast sensitivity as a function of anatomical depth in model layer 4C are shown in Figure 9.5

If the -6 cell has the same physiological properties as the clutch cell, the contrast sensitiv-

ity curve saturate at the top of layer 4C and receptive ﬁeld size curve show moderate increase

(parameters (a)). While threshold and gain of the -6 cell gradually increase (parameters (b) to

(e)) contrast sensitivity values in upper 4C strongly increase. Receptive ﬁeld size values show the same trend. However, the changes are smaller. The simulation results indicated that increased

threshold and gain of the -6 transfer function results in a strong increase of contrast sensitivities 9.1 Results Model I: One LGN-M population 145

8 1.4 parameters (a) parameters (a) parameters (b) parameters (b) 1.2 parameters (c) 6 parameters (c) parameters (d) 1 parameters (d) parameters (e) parameters (e) 0.8 4 0.6

0.4 2

Receptive Field Size [degree] 0.2 Contrast Sensitivity [1/contrast] 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 9.5: Parameter exploration of the intracortical model I (one M pathway). Each curve

corresponds to a particular parameter choice of physiological properties of the -6 cell shown in t

Figure 9.4 (a)-(e). The cortical threshold parameter was 1 = 2.0 and the synaptic efﬁcacy was W

s =1.0 (Figure 9.1 iv). For other conventions see Figure 9.2 at the top of layer 4C (D=7,8). By contrast, the corresponding changes in receptive ﬁeld size at

the same depth are smaller thus, do not dramatically affect the ﬁeld size in upper 4C.

The physiological properties of the -6 cell which result in a rapid increase of contrast sensitiv-

ity at the top of layer 4C are given by parameters (e) of Figure 9.4. The corresponding parameters

T T a a

6 6 cl utch of the inhibitory transfer function ( =2.4, cl utch =0.5 and =3.0, =2.5) are indicated in the contour plots of Figure 9.3. From the comparison of the different parameter regimes

with the ’optimal’ parameters of the -6 transfer function it becomes evident that the increased

contrast sensitivity in upper 4C results from maximal recurrent ampliﬁcation of the afferent input

(regime 3). However, a stronger increase of the -6 gain would result in a decrease of receptive ﬁeld size at the top of layer 4C (regime 2).

9.1.4 Geniculocortical and Intracortical Contributions Because the cortical cells at different depths of layer 4C get different proportions of afferent input from LGN-P and LGN-M it is important to ask which part of the nonlinear gradient of the basic response properties in depth of the layer is due to convergent afferent input from the LGN population and which part is due to differences in lateral excitation and inhibition. Figure 9.6 shows the change of basic response properties in depth of layer 4C which result from simulations with and without intracortical connections. Since the total afferent input makes up only a small proportion of the total excitatory input to a cortical cell, the contrast sensitivity

values which are based on the purely afferent input are smaller than those which are based on the t

cortical output ampliﬁed by recurrent connections. Note that the same cortical threshold value 1 is used for the afferent and the lateral recurrent curves. Receptive ﬁeld sizes which are based on purely feedforward input are also smaller than those which results from additional lateral (stepped) connections. In the lower part of layer 4C there is an overall linear relation between the afferent and lateral gradient. However, the afferent and lateral recurrent curves already diverge in mid-4C (D=3,4) as soon as spiny stellate cells get input from lateral stepped connections. The trend gets stronger 146 Results of the Intracortical Model

8 1.4 lateral lateral afferent afferent 1.2 6 1

0.8 4 0.6

0.4 2 Receptive Field Size [degree]

0.2 Contrast Sensitivity [1/contrast]

0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 9.6: Parameter exploration of the intracortical model I (one M pathway). The ﬁgure shows

receptive ﬁeld size (left) and contrast sensitivity (right) of a layer 4C spiny stellate neuron as a

function of depth D . In order to calculate the gradient in basic response properties P

which is due to the depth-dependent afferent input the lateral recurrent input I of eq. (8.15) was

l at

g I u D

set to zero. Hence the steady state response is given by e , and receptive ﬁeld size af f and contrast sensitivity are calculated as described in Section 8.2.5. The gradient which results

from the model with lateral recurrent connections is calculated as usual. The synaptic efﬁcacy was

W T a

6 6

s =1.00 (weights (iv), Fig. 9.1) and parameters of the -6 cell were =2.4 and =3.0. t

The cortical threshold parameter was 1 = 2.0.

with rise in depth of layer 4C where the lateral excitatory connections become more effective and

inhibitory strategy changes. Both curves diverge strongly in upper 4C. While the afferent curves saturate in the upper part of the layer, receptive ﬁeld size and contrast sensitivity of the lateral recurrent simulation rapidly increase. The results demonstrate that part of the simulated gradient in receptive ﬁeld and contrast sensitivity of the lateral recurrent model is induced by the feedforward convergence of LGN-P and

LGN-M input in mid-4C. However, the rapid increase of the properties in upper layer 4C reﬂects the lateral excitatory inputs of the stepped connections and the change in inhibitory strategy at the top of the layer.

9.1.5 Contrast- and Threshold-Dependence of Response Properties

Next I ask how receptive ﬁeld size curves depend on contrast c of the blob stimulus and how t

contrast sensitivity curves change with the cortical threshold parameter 1 which is a free model parameter associated with the contrast sensitivity measurement of the cortical cells (see Section

8.2.5). Figure 9.7 shows the receptive ﬁeld size and contrast sensitivity curves for various contrasts t

c and thresholds values 1 . The simulation results indicate that a change in stimulus contrast has basically no effect on the

radius of the peak summation area, i.e. receptive ﬁeld size in lower 4C and mid-4C. However,

receptive ﬁeld size in upper 4C (D=7) slightly decreases for high stimulus contrast due to stronger

inhibition from the -6 inhibitor. By contrast, the absolute contrast sensitivity values increase when thresholds decrease, but the shape of contrast sensitivity curves remains the same. Thus, the variation of stimulus contrast leads to moderate changes in receptive ﬁeld size. Vari- 9.1 Results Model I: One LGN-M population 147

1.4 c=20% t1=0.5 20 c=50% t1=0.75 1.2 c=75% t1=1.0 c=100% t1=1.5 1 15 t1=2.0 t1=2.25 0.8 10 0.6

0.4 5 Receptive Field Size [degree]

0.2 Contrast Sensitivity [1/contrast] 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 9.7: Parameter exploration of the intracortical model I (one M pathway). The ﬁgure shows

how the receptive ﬁeld size curves (left) change for different contrast c of the blob stimulus and t

how the particular choice of the cortical threshold parameter 1 affect the contrast sensitivity curves

(right). Each curve corresponds to a particular choice of stimulus contrast c and contrast threshold

t W s

1 respectively. The synaptic efﬁcacy was =1.0 (Figure 9.1(iv)) and the parameters of the -6

T a

6 6

transfer function are chosen =2.4 and =3.0. For other conventions see Figure 9.2. t

ation of the cortical threshold parameters 1 over a large range results in different absolute values of contrast sensitivity but the rapid increase of contrast sensitivity at the top of the layer remains unchanged.

9.1.6 Best Predictions

Figure 9.8 shows the best predictions of the intracortical recurrent model which is based on afferent input from one homogenous population of LGN-M cells. The best predictions are chosen according to overall correspondence of simulated receptive ﬁeld size and contrast sensitivity to the experimental data in depth of layer 4C together with the plausibility of the parameter regime compared to known anatomical data and within physiological realistic properties. Please note that the model has a large number of free parameters and the parameter space could not be searched entirely. The optimal proportions of lateral excitation and optimal constellation of intrinsic physiological properties of the excitatory spiny stellate cells and the inhibitory interneurons are shown in Figure 9.9. The optimal proportions of lateral excitation indicate that the relative contribution of the lateral

stepped connections becomes larger towards the top of the layer. In upper 4C, equal proportions

of intralaminar excitation originate from local neighbours, the ﬁrst and second stepped connections

W D W D W D

step step

of the spiny stellate cells. Since the model parameters l ocal , and give

1 2 the numerical weight portions of lateral excitation, they need some interpretation. If one assumes that each synapse formed by a spiny stellate cell in layer 4C has the same postsynaptic effect then the weight portions can be interpreted as the number of synapses which originate from the different sources of lateral input. Therefore, the model predicts that lateral excitatory input from the stepped connections becomes more ’effective’ or, in other words, more numerous with rise in depth of the layer. 148 Results of the Intracortical Model

3 4 simulation simulation 3.5 2.5 experiment experiment 3 2 2.5

1.5 2 1.5 1 1 0.5

Normalized Contrast Sensitivity 0.5 Normalized Receptive Field Size 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 9.8: Best ﬁts for normalized receptive ﬁeld size (left) and contrast sensitivity curves (right) for the intracortical recurrent model based on one LGN-M population. Each plot shows the mean values and standard deviations of the experimental data of Blasdel & Fitzpatrick (1984) and Hawken & Parker (1984) together with simulated response properties at eight discrete depths

of model layer 4C. The optimal parameter values are summarized in Figure 9.9. The cortical t

threshold was 1 =2.0. The physiological properties of the P, M population are listed in Table 8.2 and the thalamic weight portions are given in Figure 8.2a.

The model further predicts that the -6 cell has not only a higher threshold but also a higher gain than the clutch cell. Hence, the change in inhibitory strategy that has been observed anatomically goes along with a change in the intrinsic physiological properties of the inhibitory interneurons.

9.1.7 Summary

The results suggest that the intracortical recurrent model based on one LGN-M population is able to produce a good ﬁt to the experimental data for the entire depth of layer 4C, especially for the

rapid increase of the response properties in upper 4C. Simulated contrast sensitivities at depth

D are slightly larger than the mean values but still within the standard deviation of the experimental data. The parameter explorations of this section have demonstrated that:

1. The input from the lateral stepped connections results in increased receptive ﬁeld size in

mid-4C and upper 4C though the balance of excitatory synapse from different spatial origin changes in depth of the layer. This result suggests that lateral input via stepped connections is an essential mechanism to produce a new cumulative receptive ﬁeld and a functional gradient in receptive ﬁeld size in depth of the layer.

2. Larger cumulative receptive ﬁelds result in a drop of contrast sensitivity. However, the

decrease in contrast sensitivity in upper 4C can be balanced by the intrinsic physiological properties of the -6 cell, i.e. higher threshold and gain of the -6 transfer function. This allows for strong recurrent ampliﬁcation of the afferent LGN-M input and is essential to

generate the almost exponential increase of contrast sensitivity in upper 4C. 9.2 Results Model II: Two LGN-M populations 149

Wstep-1 100 Wstep-2

Wlocal 75 exc. cell 50 clutch cell Output O(x) 2 Proportion of α−6 cell 25 x 2 Lateral Excitatory Weights [%] 8 7 6 5 43 2 1 D

4C alpha 4C beta Tα−6 =2.4 aα−6 =3.0 Layer 4C Layer 4C Depth D 8 7 6 5 4 3 2 1 local 33% 50% 70% 80% 90% 95% 100% 100% 1. step 33% 35% 30% 20% 10% 5% 0% 0% 2. step 33% 15% 0% 0% 0% 0% 0% 0%

Figure 9.9: Optimal proportion of lateral excitation from different retinotopic origin as a function

of depth in layer 4C together with the optimal physiological properties of the -6 cell. The left ﬁgure shows the proportion of lateral excitation derived from local neighbours and spiny stellate

cells one and two sides-steps away, respectively (cf. weights (iv) of Fig. 9.1); the values of the

W D W D W D

step step

corresponding model parameters l ocal , and are given in the table.

1 2

The right ﬁgure summarizes the optimal parameter constellation of the -6 transfer function in

comparison to the transfer function of the excitatory spiny stellate cells and the clutch cell (cf.

T a T a

e e cl utch parameters (e) of Fig. 9.4; =0.1, =1.0 and cl utch =0.5, =2.5)

3. Part of the functional gradient is due to the afferent convergence of LGN-P and LGN-M input onto postsynaptic spiny stellate cells in mid-4C. Finally, it should be emphasized that the purely feedforward model based on one homogenous LGN-M population was not able to account for the rapid increase of contrast sensitivity and ﬁeld

size in upper 4C.

9.2 Results Model II: Two LGN-M populations

The previous section has summarized the parameter explorations of the intracortical model based on one LGN-M population. Now I want to explore how afferent input from the anatomically identiﬁed LGN-M2 and LGN-M1 populations (model II conﬁguration) combines with the model of intracortical recurrent connectivity.

9.2.1 General Remarks and Results The modelling work presented in Section 6.2 and the previous section has demonstrated that:

The differential convergence of LGN-P and LGN-M inputs onto spiny stellate cells whose dendritic arbors intrude into both termination zones may form the anatomical substrate of 150 Results of the Intracortical Model

Set A Set B Set C Set D R

LGN-M2 Center Radius c 0.101 0.098 0.097 0.095 R

Surround Radius s 1.14 1.10 1.07 1.05

Contrast Gain G 1.41 1.37 1.33 1.31

Max. ﬁring rate M 44.33 43.62 42.91 41.55 c

Contrast threshold min 1.8 1.9 2.1 2.2 R

LGN-M1 Center Radius c 0.108 0.114 0.117 0.125 R

Surround Radius s 1.19 1.24 1.29 1.36

Contrast Gain G 1.83 2.20 2.59 3.01

Max. ﬁring rate M 56.75 65.05 71.28 79.92 c

Contrast threshold min 1.5 1.2 1.0 0.7

M2 M1 number ratio 59% 41% 72% 28% 80% 20% 88% 12%

Table 9.1: Four sets of physiological parameters of LGN-M2 and LGN-M1 cells. The numbers give mean values which are re-estimated from the LGN-M data set of Spear et al. (1994). For details see Section 6.2.1 and Table A.1. The corresponding number densities of LGN-M2 and

LGN-M1 cells are given in the last row. The center and surround radii are given in [degrees] and

R R s the mean value for the total LGN-M population, c and , are roughly constant

over all sets. Mean values of contrast gains, maximum spike rates and contrast thresholds are given

1 1 1

in [spikes sec %contrast ], [spikes sec ], and [%contrast] respectively, and the mean values

G M c

for the total LGN-M population, , , min , are roughly constant over all sets. The value of the integrated surround/center sensitivity K is independent of the speciﬁc cell population (mean 0.55); therefore K remained constant for all parameter sets. The integrated surround/center sensitivity K is taken from the data set of Croner & Kaplan, since Spear et al. do not report them.

the gradual change of basic response properties in depth of layer 4C. To account for the almost exponential increase of basic response properties at the top of the layer it was necessary to assign higher contrast sensitivity and ﬁeld size to a small population of so-called

LGN-M1 cells which have been shown to preferentially arborize in upper 4C. The prediction of the purely feedforward model is that 12% percent of the LGN-M cells correspond to the anatomically identiﬁed LGN-M1 cells. In this case the LGN-M1 cells are characterized by physiological parameters which are roughly one standard deviation above the experimentally observed mean value of LGN-M properties.

The differences in local circuitry in depth of layer 4C, i.e. the different width of local lateral projections of spiny stellate cells and the change in inhibitory strategy may be another potential source of increased sensitivity and receptive ﬁeld size at the top of the layer. The almost exponential increase of receptive ﬁeld size at the top of the layer led me to predict an increasingly higher proportion of lateral excitation to come from the lateral stepped connections. To account for the almost exponential increase in contrast sensitivity it was necessary

to assign higher threshold and gain to the -6 inhibitors which preferentially arborize in up-

per 4C. The ﬁrst prediction of the intracortical model based on one LGN-M population is that the lateral excitatory synapses from the stepped connections becomes more numerous with rise in depth of the layer. At the top of the layer the constant lateral excitatory input splits into equal proportions that arise from the very local neighbours and the ﬁrst and the 9.2 Results Model II: Two LGN-M populations 151

second step of other spiny stellate cells within the same depth. The second prediction is that

the threshold of the -6 transfer function is roughly ﬁve times higher than that of the clutch

cell while the gains of the transfer function differ only moderately, i.e. clutch cell 2.5, -6 cell 3.0.

So far I have assessed the principle hypothesis which are able to explain the experimentally observed gradient in basic response properties in depth of layer 4C. Both models – the purely feedforward model II and intracortical model I – are consistent with the anatomical and physiological data. Now the possibility should be tested if intermediate cases, i.e. a combination of the most plausible feedforward and lateral recurrent model based one LGN-M population exists along the continuum between the two extremes. A canonical procedure to do so is to explore for all essential parameters of both models all possible intermediate cases or values. The crucial parameters of the feedforward model which cannot be derived from the experimental data are the number ratio and physiological properties of LGN-M2 and LGN-M1 cells. Earlier in the manuscript it was described in detail how the physiological properties of the LGN-M2 and LGN-M1 population can be derived from the experimentally observed response properties of the ’classical’ LGN-M cells: based on a hypothetical number ratio of M2 and M1 cells, the homogenous population of LGN-M cells is divided into two clusters and new mean values (and standard deviations) are estimated for the re-analyzed data; for details see Section 6.2.1. Table 9.1 summarizes the four sets of physiological parameters which are used to specify the response properties of LGN-M2 and LGN-M1 in the following parameter exploration. By contrast to the purely feedforward model II where the mean values and standard deviation of two LGN data sets (Croner & Kaplan, 1995; Spear et al., 1994) are used, the parameter explorations of the combined model are restricted to the LGN data set reported by Spear et al. (1994) and only mean values are considered (see also Section 8.1.2). Note that the M2- and M1-parameters of Table 9.1 correspond to the mean values given in Table A.1. The physiological parameters of the LGN-P cells are given in Table 8.2. The most important parameters of the lateral recurrent model are the ’efﬁcacy’ of the stepped

connections and the intrinsic physiological properties of the -6 cell. As in the lateral recurrent W

model I, four different efﬁcacies ( s =0.00, 0.33, 0.66 and 1.00) of the stepped connections are considered which correspond to a distribution of lateral excitatory weights shown in Figure 9.1(i)-

(iv). Because the intrinsic physiological properties of the -6 cell are unknown, the threshold and

gain of the -6 transfer function is varied systematically and the corresponding parameters are summarized in Figure 9.4a-e. Thus, one ends up with four sets of physiological parameters of LGN-M2 and LGN-M1 cells,

four distributions of lateral excitatory weights and ﬁve parameter constellations of the -6 neuron which have to be tested by computer simulations. All possible parameter combinations of the intracortical model II are summarized in Figure 9.10. The simulation results for all parameter combinations are summarized in Section B.3 of Appendix B. To discuss the results of the intracortical model II, I have selected a subset of ’typical’ parameter explorations. Those parameter explorations which are considered in detail in the following sections are indicated in Figure 9.10. 152 Results of the Intracortical Model best = 2.5, (b) (e) 6 a (d) f parameters which respond to synaptic N-M2 and LGN-M1 = 0.5, (c) 6 weights (iv) nation which led to the (b) T (a) -6 cell correspond to parameters (a) to (e) = 3.0. The parameter explorations which 6 (d) a summarized in Section B.3 of Appendix B. * (c) = 2.4, 6 parameters parameters -6 transfer function are (a) (b) α−6 Effects of Physiological Properties of M2 and M1 cells T (a) (e) eters of the = 2.8, and (e) (d) 6 a (c) Neuron l excitatory weights (i) to (iv) shown in Figure 9.1 which cor d. There are four sets A to D of physiological properties of LG α−6 parameters = 2.0, (b) based on two LGN-M populations. All possible combinations o Efficacy of stepped connections Physiological Properties of the neuron 6 ed by different patterns. The star marks the parameter combi Physiological Properties of the T (a) =1.00, respectively. The physiological properties of the (e) s W =2.7, (d) 6 (d) a . The simulation results for all parameter combinations are intracortical model II (c) =0.66, and = 1.5, s parameters 6 (b) weights (i) weights (ii) weights (iii) W Efficacy of Lateral Stepped Connections T (a) =0.33, s W = 2.6, (c) intracortical model II Set A Set B Set C Set D 6

=0.00,

s LGN-M2 and LGN-M1 cells LGN-M1 and LGN-M2 a -6 transfer function which are shown in Figure 9.4. The param

of the

W Physiological Parameters of Parameters Physiological = 1.0, 6 cannot be derived from thewhich experimental data are have given been teste inefﬁcacies Table 9.1 and four distributions of latera prediction (e) of the are discussed in Sections 9.2.2, 9.2.3 and 9.2.4 are indicat Figure 9.10: Parameter space of the T 9.2 Results Model II: Two LGN-M populations 153

9.2.2 Efﬁcacy of the Lateral Stepped Connections

weights (i) weights (i) 1.4 10 weights (ii) weights (ii) 1.2 weights (iii) weights (iii) weights (iv) 8 weights (iv) 1

0.8 6

0.6 4 0.4 2

0.2 Contrast Sensitivity [1/contrast] Receptive Field Size [degree]

0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 9.11: Parameter exploration of the intracortical model II (two M pathways). The ﬁgure

shows receptive ﬁeld size (left) and contrast sensitivity (right) of a layer 4C spiny stellate cell as

a function of depth D . Each curve corresponds to a particular distribution of lateral W

excitatory weights i.e. synaptic efﬁcacy s shown in Figure 9.1 (i)-(iv). The number ratio of LGN-M1 and LGN-M2 cells is taken 80% : 20% and the physiological properties of the LGN- M1 and LGN-M2 cells correspond to set C of Table 9.1. The physiological properties of the

LGN-P cells are taken from Table 8.2. The parameters of the -6 transfer function correspond to

T a

6 6

parameters (c), i.e. = 1.5 and = 2.7. The transfer function of the excitatory cells and the

T a T a

e e e

inhibitory clutch cells are given by e = 0.1, = 1.0 and = 0.5, = 2.5. The cortical threshold t

parameter was 1 = 2.0.

To test how the afferent input from the two different LGN-M populations combines with different W

’synaptic efﬁcacies’ s numerical simulations are performed. The corresponding distributions of excitatory weights of different spatial origin within the retinotopic map of layer 4C are shown in Figure 9.1(i)-(iv) and the number ratio and physiological properties of the LGN-M2 and LGN- M1 population correspond to set C of Table 9.1. The predicted receptive ﬁeld size and contrast sensitivity curves are summarized in Fig. 9.11.

The shape of receptive ﬁeld size curves change in upper 4C for the different distributions W

of the lateral excitatory weights, i.e. different numerical values of s . If there is no or weak

W W s lateral input from the stepped connections (weights (i),(ii), s =0.00 and =0.33) the receptive

ﬁeld size curve shows only moderate increase with rise in depth of layer 4C. Receptive ﬁeld size however decreases in the upper 4C which is due to strong inhibition from the the -6 cell; please

note that compared to the intracortical model I the threshold of the inhibition in upper 4C is taken

6 much lower, i.e. =1.5. Therefore, the absent or weak lateral excitatory inputs of the stepped

connections are not strong enough to balance the inhibition from the -6 cell. If the efﬁcacy

of lateral stepped connections is increased (weights (iii), s ) receptive ﬁeld size curves

become steeper and the curve shows an almost exponential increase in upper 4C. If the efﬁcacy

of the lateral stepped connections is further increased (weights (iv), s ), receptive ﬁeld

size shows only weak increase at the top of layer 4C (D=8) indicating a ’non-optimal’ balance of lateral excitation and inhibition. While receptive ﬁeld size increases due to increasingly more effective lateral input via stepped connections, the overall contrast sensitivity decreases slightly in mid-4C and more rapidly in up- 154 Results of the Intracortical Model

per 4C. The reason for reduced contrast sensitivity is a re-distribution of the constant lateral excitatory weights to regions within the retinotopic map which are driven by lower ﬁring rates of the presynaptic LGN cells. In summary, the changing efﬁcacy of lateral excitation from different spatial origin within the retinotopic map has the same overall effect as for the intracortical model I which is based on one LGN-M population. The input from the physiological distinct LGN-M2 and LGN-M1 cells which

provide afferent input to mid-4C and upper 4C respectively result in a moderate decrease of basic

response properties in mid-4C and an increase in upper 4C (see also Section 9.2.2) – compared to

the same parameter sets of the intracortical model I. Therefore, the optimal efﬁcacy of the stepped W

connections in the intracortical model II corresponds to the weight distribution (iii) ( s =0.66).

9.2.3 Intrinsic Physiological Properties of the -6 Neuron

1.4 parameters (a) 10 parameters (a) parameters (b) parameters (b) 1.2 parameters (c) parameters (c) 8 parameters (d) parameters (d) 1 parameters (e) parameters (e) 0.8 6

0.6 4 0.4 2

Receptive Field Size [degree] 0.2 Contrast Sensitivity [1/contrast]

0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 9.12: Parameter exploration of the intracortical model II (two M pathways). Each curve

corresponds to a particular parameter choice of the -6 transfer function which are shown in W

Figure 9.4(a) to (e). The distributions of lateral excitation correspond to weights (iii) ( s =0.66) of Figure 9.1. The number ratio of LGN-M1 and LGN-M2 cells is taken 80% : 20% and the

physiological properties of the LGN-M1 and LGN-M2 cells correspond to set C of Table 9.1. The t

cortical threshold parameter was 1 = 2.0. For other parameter settings see caption of Figure 9.11

To see how differences in the physiological properties of the -6 cell and the afferent input of the LGN-M1 cells affect the basic response properties in upper 4C, the threshold and gain of the -6

cell was systematically increased. The corresponding parameters of the -6 transfer function are summarized in Figure 9.4 (a)-(e). The simulated receptive ﬁeld size and contrast sensitivity values as a function of anatomical depth in model layer 4C are shown in Figure 9.12.

If the -6 cell has the same physiological properties as the clutch cell (parameters (a)), contrast

sensitivity values show already a moderate increase at top of layer 4C due to the afferent input

from the LGN-M1 cells to this region. While threshold and gain of the -6 cell gradually increase

(parameters (b) to (e)) contrast sensitivity curves increase rapidly in upper 4C. Receptive ﬁeld size curves show the same trend however the overall changes are small. As for the intracortical model I, the simulation results indicated that increased threshold and

gain of the -6 transfer function results in increased contrast sensitivities at the top of model layer 4C (D=7,8), but even for low thresholds an increase is present. The reasons are the lower contrast threshold, higher contrast gain and maximum spike rate of the LGN-M1 cells (cf. Set D, Table 9.2 Results Model II: Two LGN-M populations 155

9.1) which provide the afferent input to upper 4C. Therefore, the physiological properties of the

-6 cell which result in a sufﬁciently rapid increase of contrast sensitivity are given by parameters

T a

6 6 (c) of Figure 9.4 ( =1.5 =2.7).

9.2.4 Effects of Physiological Properties of M2 and M1 Cells

Set A 1.4 Set A 10 Set B Set B 1.2 Set C Set C Set D 8 Set D 1

0.8 6

0.6 4 0.4 2

Receptive Field Size [degree] 0.2 Contrast Sensitivity [1/contrast]

0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 9.13: Parameter exploration of the intracortical model II (two M pathways). Each curve corresponds to a particular set of number ratio and physiological parameters of LGN-M2 and

LGN-M1 cells which are summarized in Table 9.1. The parameters of the -6 transfer function

T a

6 6

are chosen =1.5 and =2.7 (parameters(c)). The distribution of lateral excitation cor- t

responds to weights (iii) of Figure 9.1. The cortical threshold parameter was 1 = 2.0. For other conventions refer to the caption of Figure 9.11.

In order to demonstrate how the afferent input of the LGN-M1 and LGN-M2 subpopulations affect the basic response properties of cells in layer 4C, I have tested different sets of physiological properties which are based on different number ratios of LGN-M2 and LGN-M1 cells (see Table 9.1). The simulated receptive ﬁeld size and contrast sensitivity values as a function of anatomical depth in model layer 4C are shown in Figure 9.13. The different sets of physiological properties of the M2 and M1 cells have only small effects on the receptive ﬁeld size curves. This suggest that in this parameter regime (lateral excitatory

given by weights (iii) and -6 transfer function given by parameters (c)) the receptive ﬁeld size of cortical cells is basically determined by the lateral recurrent excitation from different spatial

origin within the retinotopic map of layer 4C. The results indicate that receptive field sizes in 4C which is the region of M2 and M1 afferent input does not depend on the anisotropy of the input i.e. differences in the physiological properties of M2 and M1 cells. For this particular parameter regime the receptive field size is determined by the balance of intracortical (excitatory) connections of different spatial origin rather than by differences in the physiological properties of the afferent input; for other parameter regimes please refer to Section B.3 in Appendix B. While receptive field size and more important contrast threshold, contrast gain and maximum spike rate of the LGN-M1 cells are increased from Set A to D (cf. Table 9.1) contrast sensitivity of

the postsynaptic cells in upper 4C (D=7,8) also increases. At the same time, however, receptive ﬁeld size and contrast sensitivity of the LGN-M2 cells decrease from Set A to D (cf. Table 9.1) although the changes in the M2 properties are smaller. The change in the physiological properties 156 Results of the Intracortical Model

of LGN-M2 cells results in a moderate decrease of contrast sensitivity of the cortical cells in mid- 4C which get a changing proportion of afferent input from LGN-M2 cells. This indicates that differences in the afferent input affect the contrast sensitivity of the cortical cells, thus, contrast sensitivity does not exclusively depend on the intracortical recurrent connections. These results are consistent with the feedforward model II which also considers afferent input from two LGN-M subpopulations. With additional intralaminar recurrent connections, however, the ratio of M2 to M1 cells and the corresponding physiological properties which led to a good

ﬁt of receptive ﬁeld size and contrast sensitivity in mid-4C and upper 4C correspond to Set C of Table 9.1. In other words, the intracortical model II predicts that more or less 20% of the LGN-M correspond to the LGN-M1 cells while the rest makes up the ’classical’ LGN-M2 population.

9.2.5 Geniculocortical and Intracortical Contributions

10 1.4 lateral lateral

1.2 afferent 8 afferent 1 6 0.8

0.6 4

0.4 2 Receptive Field Size [degree] 0.2 Contrast Sensitivity [1/contrast]

0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 9.14: Parameter exploration of the intracortical model II (two M pathways). In order to

calculate the gradient in basic response properties which is due to the depth-dependent afferent P

input of the LGN-P, LGN-M2 and LGN-M1 cells, the lateral recurrent input I of eq. (8.15) was

l at

g I u D

set to zero. The steady state response is then given by e , and receptive ﬁeld size and af f contrast sensitivity are calculated as described in Section 8.2.5. The gradient which results from the model with additional lateral recurrent connections is calculated as usual. The number ratio

and response properties of the LGN-M2 and LGN-M1 cells are chosen according to Set C of Table

9.1. The synaptic efﬁcacy was s =0.66 (weights (iii)) and parameters of the -6 cell are taken

T a t

6 6 1 =1.5 and =2.75. The cortical threshold parameter was = 2.0.

The cortical cells at different depths of layer 4C get changing proportions of afferent input from LGN-P, LGN-M2 and LGN-M1 (Fig. 8.2b). Therefore, part of the gradient is due to the initial convergence of afferent thalamic inputs in depth of the layer. Figure 9.14 shows the change of basic response properties in depth of layer 4C which result from simulations with and without intracortical connections. The results indicate that the nonlinear gradients in receptive ﬁeld size and contrast sensitivity

in depth of the layer is partially set up by the differential convergence of the afferent inputs from LGN-P, LGN-M2 and LGN-M1 cells to lower 4C , mid-4C and upper 4C . The basic response properties which are based on purely feedforward input are smaller than those which result from additional lateral recurrent connections. In the lower part of layer 4C there is an overall linear 9.2 Results Model II: Two LGN-M populations 157 relation between the gradients of the purely afferent and lateral recurrent simulations. The affer-

ent and the lateral recurrent curves, however, diverge in mid-4C and upper 4C a soon as spiny stellate cells get input from lateral stepped connections, and the small clutch cell is substituted by

the -6 cell. The trend gets stronger with rise in depth of layer 4C where the lateral excitatory connections become wider and more effective and inhibitory strategy changes. Because upper

4C is dominated by input from the LGN-M1 cells which have larger receptive ﬁelds and higher contrast sensitivity than the LGN-M2 cells, the afferent curves do not saturate at the top of the

layer. Afferent and lateral recurrent curves, however, diverge in upper 4C due to the recurrent ampliﬁcation. The results demonstrate that part of the rapid increase of receptive ﬁeld size and contrast sensi-

tivity in upper 4C is due to the feedforward convergence of LGN-M2 and LGN-M1 cells in upper

4C. But the lateral excitatory inputs of the stepped connections and the change in inhibitory strat-

egy contribute a considerable part to the rapid increase of response properties in upper 4C. In comparison to the intracortical model I which is based on afferent input from only one LGN- M population (cf. Section 9.1.4) less effective input via lateral stepped connections and a lower

threshold and gain of the -6 cell are needed to account for the rapid increase of basic response

properties at the top of upper 4C.

9.2.6 Best Predictions

3 4 simulation simulation 3.5 2.5 experiment experiment 3 2 2.5

1.5 2 1.5 1 1 0.5 0.5 Normalized Contrast Sensitivity Normalized Receptive Field Size 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure 9.15: Best ﬁts for normalized receptive ﬁeld size (left) and contrast sensitivity curves (right) for the intracortical model II based on two LGN-M populations. Each plot shows the mean values and standard deviations of the experimental data of Blasdel & Fitzpatrick (1984) and Hawken & Parker (1984) together with simulated response properties at eight discrete depths of model layer 4C. The optimal parameter values are summarized in Figure 9.16. The number ratio of M2 to M1 cells was taken 80% : 20% and the corresponding physiological properties of the

LGN-M2 and LGN-M1 population are given in Set C of Table 9.1 The thalamic weight portions t

are taken from Figure 8.2b. The cortical threshold was 1 =2.0.

Figure 9.15 summarizes the ’best’ predictions of the intracortical model II which is based on afferent input from two anatomically identiﬁed populations of LGN-M cells. The optimal proportions of lateral excitation and optimal constellation of intrinsic physiological properties of the excitatory spiny stellate cells and the inhibitory interneurons are shown in Figure 9.16. 158 Results of the Intracortical Model

Wstep-1 100 Wstep-2

Wlocal 75 exc. cell 50 clutch cell Output O(x) 2 Proportion of α−6 cell 25 x 2 Lateral Excitatory Weights [%] 8 7 6 5 43 2 1 D

4C alpha 4C beta Tα−6 =1.5 aα−6 =2.7 Layer 4C Layer 4C Depth D 8 7 6 5 4 3 2 1 local 58% 67% 77% 87% 93% 97% 100% 100% 1. step 21% 23% 23% 13% 7% 3% 0% 0% 2. step 21% 10% 0% 0% 0% 0% 0% 0%

Figure 9.16: Optimal proportion of lateral excitation from different retinotopic origin as a function

of depth in layer 4C together with the optimal physiological properties of the -6 cell. The left ﬁgure shows the proportion of lateral excitation derived from local neighbours and spiny stellate

cells one and two sides-steps away, respectively (cf. weights (iii) of Fig. 9.1); the number values of

W D W D W D

step step

the corresponding model parameters l ocal , and are given in the table.

1 2

The right ﬁgure summarizes the optimal parameter constellation of the -6 transfer function in

comparison to the transfer function of the excitatory spiny stellate cells and the clutch cell (cf.

T a T a T a

e e 6 6 cl utch parameters (c) of Fig. 9.4; =0.1, =1.0, cl utch =0.5, =2.5, =1.5 and =2.7)

The so-called ’best’ predictions of the intracortical model II are tentative since the model considers two principle hypotheses – a feedforward and an intracortical one – each of them able to explain the nonlinear gradient of basic response properties in depth of layer 4C. The criteria were of course again given by the overall correspondence of the mean values in the whole depth of layer 4C (D=1,...,8) for simulated receptive ﬁeld size and contrast sensitivity with the experimental data and the plausibility of the parameter regime in experimental respect.

The goal of the parameter explorations presented above was to test if a combination of the two extreme hypotheses exists which is able to explain the rapid increase of basic response in upper

layer 4C. (cf. Section 9.2.1). The exploration of the parameter space of the intracortical recurrent model, however, demonstrates that there are several parameter regimes which lead to a reasonable good fit of simulated and experimental data according the criteria given above. In other words, applying the above criteria – the overall fit of receptive field size and contrast sensitivity curves plus the plausibility of the parameter regime – renders more than one parameter combination as a possible ’best’ prediction of the intracortical model II; for details see Section B.3 of Appendix B.

The results discussed above emphasize the main aspects of a combined model of realistic geniculocortical information transfer and lateral recurrent connectivity in layer 4C. 9.2 Results Model II: Two LGN-M populations 159

9.2.7 Summary The results suggest that the intracortical model II based on two LGN-M population is able to produce a good ﬁt to the experimental data for the entire depth of layer 4C. In comparison to the feedforward model II and the intracortical model I the parameter explorations of the combined model have demonstrated that:

1. Differences in the physiological properties of the LGN-M2 and LGN-M1 which project to

different strata of layer 4C are ampliﬁed by the intracortical recurrent connections. There- fore, the predicted difference in physiological properties of the LGN-M2 and LGN-M1 population is smaller than in the purely feedforward model II. A number ratio of 20% LGN-M1 cells emphasizing the upper range of the experimentally observed LGN-M properties are

sufﬁcient to account for the rapid increase of contrast sensitivity in upper 4C.

2. The particular effect of different receptive ﬁeld size, contrast gain and maximum spike rate of LGN-M2 and LGN-M1 cells depends however on the choice of the intracortical connec-

tivity and the threshold and gain of the -6 inhibitor. For example a number ratio of 88% W

M2 to 12% M1 cells (Set D) combined with a synaptic efﬁcacy of s =0.33 and parameters (c) of the inhibitory transfer function (see Section B.3 of Appendix B, Figure B.9c) results

in increased ﬁeld size and contrast sensitivity in upper 4C and the overall shape of the simulated curves corresponds to the experimental data. This indicates that the intracortical model makes no unequivocal prediction and at least one of the essential parameters i.e. ratio and physiological properties of the M2 and M1 cells or the lateral efﬁcacy of the stepped connection together with the physiological properties have to be constrained by experimental data to make clear predictions. One has to keep this in mind to interprete the results of the combined model in the right way.

3. The input from the lateral stepped connections results in increased receptive ﬁeld size in

mid-4C and upper 4C and the predicted effective weights of the stepped connections are lower than for the intracortical model I based on one LGN-M population.

4. The differences in the intrinsic physiological properties of the -6 cell and the clutch cell

are moderate, but the threshold and gain of the -6 transfer function have to be higher to

account for the rapid increase of contrast sensitivity in upper 4C.

5. In summary, the combination of afferent input from two LGN-M populations, lateral excitatory input from stepped connection and the change in inhibitory strategy at the top of layer 4C results in a model which is less sensitive to the particular parameter choice i.e. a ’negative’ effect of one parameter can be balanced by a suitable combination of the other parameters. 160 Results of the Intracortical Model

9.3 Discussion

The intracortical model is an alternative to the purely feedforward hypothesis. The simulation results suggest that the intracortical recurrent connections which are known to exist between the spiny stellate cells in layer 4C together with the changing strategy of somatic inhibition at the top of the layer can account for the depth-dependence of receptive ﬁeld size and achromatic contrast sensitivity values. The ﬁrst model based on the ’classical’ scenario, i.e. thalamic input from one LGN-M population proves that the lateral stepped connections are a suitable anatomical substrate for increased

receptive ﬁeld size in mid-4C and upper 4C. The modelling results further indicate that rapid increase of contrast sensitivity at the top of the layer can be accomplished by the high threshold and

gain of the -6 cell. In summary, the model predicts substantial excitation from the lateral side- step projections of spiny stellate cells and considerable differences in the physiological properties or postsynaptic effects of two anatomically-identiﬁed basket cell populations. In a second step I have combined the intracortical model with afferent input from the anatomically identiﬁed LGN-M2 and LGN-M1 cells. Please remember, that both hypotheses – the change in lateral excitation and inhibition and the afferent input of the LGN-M1 cells – are able to explain

the rapid increase of contrast sensitivity and receptive field size in upper 4C. The simulation results of the intracortical model II have revealed that there are several parameter combinations which lead to reasonably good predictions of the gradual change of basic response properties in depth of layer 4C. In particular this indicates the limitations of the modelling approach to unequiv- ocally distinguish between different hypotheses, although the simulation results provide useful predictions for the case that both afferent and feedback connections combine to produce a rapid increase of basic response properties at the top of layer 4C. For the simulation results which are shown in Section 9.2 the intracortical recurrent model based on LGN-M2 and LGN-M1 cells predicts less substantial excitation from lateral recurrent connections of spiny stellate cells and only moderate differences in the physiological properties or postsynaptic effects of two anatomically-identified basket cell populations. In addition, the model predicts that roughly 20% of the LGN-M cells belong to the anatomically identified LGN-M1 cells characterised by on average larger receptive field size, contrast gain and maximum spike rate. The predicted number ratio 20% M1 and 80% M2 cells – compared to 12% M1 and 88% M2 cells for the purely feedforward model II – and the smaller difference in the physiological properties of LGN-M2 and LGN-M1 cells is due to the recurrent amplification of small differences in the afferent input and the refinement by the intracortical feedback.

Physiological Properties of the Inhibitory Interneurons

The physiological properties of the clutch cell and the -6 cell might be testable experimentally by observing the strength of IPSPs recorded intracellularly for cells at different depths of layer 4C. Another possibility is to directly test the intrinsic properties of the interneurons by intracellular recordings in vitro or in vivo. Ideally, the intracellular recordings can be combined with the intracellular staining of the recorded cells since the model makes predictions for morphological identified cells which are modelled in lateral spread in accordance with the anatomical data. Cru- cial identifiers of the inhibitory (fast-spiking) interneurons may be brief action potentials, little spike frequency adaption to depolarizing current and a steep linear relationship between injected current and action potential discharge (Azouz et al., 1997). If there is indeed a difference in intrinsic physiological properties between the anatomical-identified basket-cells rather then a difference 9.3 Discussion 161 in their postsynaptic effect the response to different amounts of depolarizing current might produce signatures similar to those predicted by the physiological properties of the model inhibitory

cells. In other words, the -6 cell should exhibit a steepper linear relation to depolarizing current injection than the clutch cell, and low amounts of injected current should be ineffective to evoke

response in the -6 basket cell.

Number Ratio and Efﬁcacy of Lateral Excitatory Feedback

It might be, however, difficult to test the efficacy or the increasing number of terminals of the stepped connections. The partially unpublished observations of J. B. Levitt (see Chapter 7) suggest that the response of cells in layer 4C can be modulated within a considerably large region outside the minimum response field. A substantial proportion of these effects can not be accounted for by monosynaptic spread of lateral horizontal connections. Therefore, substantial monosynaptic input of the lateral stepped connections is in agreement with available physiological findings. The model predicts that the efficacy or number ratio of excitatory contacts that originate from the lateral stepped connections increases with rise in depth of the layer. Since the model predicts a weight ratio between excitatory input of different spatial origin rather than from different excitatory cell populations it is unrealistic to assume that individual contacts have different postsynaptic effects. The most reasonable interpretation of the modelling results is given by an increasingly larger number of terminals that arise from the stepped connections.

The anterograde/retrograde tracing techniques indicate that the spiny stellate cells in mid-4C and upper 4C get input from points 400-500 m and up to 1mm away within the retinotopic map. It is, however, difﬁcult to infer reliable estimates about the number ratio of lateral excitatory inputs versa input from very local neighbours at different depths of the layer from the currently available anatomical data. On the other hand, it will be difﬁcult or even impossible to investigate the number ratio of local excitatory contacts that originate from different spatial origin within the retinotopic map of layer 4C on the ultrastructural (EM) level. Interesting is the observation that for local or lateral projections produced from similar sized (biocytin) injections at different depths of the layer the density of terminals per unit area of layer

4C appears to be the same. Since there are much more cells in lower 4C and mid-4C than in

upper 4C, the uniform density of labelled terminals might suggest that a single cell in upper

4C receives relative more contacts via stepped connections than cells in mid-4C. In addition,

injections of cholera toxin give excellent retrograde labelled cells in layer 4C (Asi et al., 1998). To interprete the observation in this way is, however, difﬁcult and highly speculative, since the quality of labelled terminals/cell bodies depends on many other factors, e.g. uptake of injected label at different depths. In any case, it will be worth to look for anatomical signatures that may

conﬁrm or refute the hypothesis that a single cell in upper 4C receives more terminals from stepped connections than cells in mid-4C.

If the lateral recurrent connections create the large receptive ﬁelds in upper 4C, it might be

expected that in such circumstances the earliest responses from upper 4C neurons should convey a smaller receptive ﬁeld than the later parts of the response due to the reﬁnement by the lateral recurrent inputs. 162 Results of the Intracortical Model

Identiﬁcation of Afferent and Intracortical Contributions

The simulations have demonstrated that part of the gradient in the basic response properties is due to feedforward convergence of thalamic LGN-P and LGN-M (or M2+M1) input. Therefore, if the intracortical model is right, that both factors (i) the initial afferent convergence of LGN-P and LGN-M input and (ii) the different spatial origin and a changing ratio of lateral excitatory weight

distributions are responsible for increased field size in mid-4C and in upper 4C, it is crucial to estimate the contribution of intracortical recurrent and afferent contributions experimentally. Based on theoretical modelling work Adorján & Obermayer (1999) proposed a new experimental method to estimate the strength of the effective excitatory feedback to a cortical simple cell but the model neglects all sort of inhibitory inputs. The authors infer that without lateral intracortical feedback the F1 component (stimulus modulated component) of the membrane potential of a cortical cell which receives direct thalamic input is basically independent of adapting the neurons to a certain contrast level. Therefore, the adaption in the F1 component of the cortical firing rate may be used as a signature for the strength of the recurrent input to a cortical simple cell. It remains uncertain if these effects already exist for geniculocortical projection and the lateral excitatory connections of layer 4C. Nevertheless, if experimental tests confirm the predictions of Adorján & Obermayer (1999), a stimulation paradigm based on contrast adaption might be a suitable experimental signature to estimate the strength of the lateral excitatory connections versa the geniculate feedforward inputs in layer 4C.

Physiological Properties of M1 and M2 Cells

Compared to the purely afferent model which predicts that only 12% of the LGN-M cells belong to the LGN-M1 population, a number ratio of 20% – as predicted by and the intracortical model II – suggests a slightly larger proportion of LGN-M1. Moreover, the average physiological properties of the LGN-M1 cells are not ”extremely” different from the properties measured experimentally for the whole LGN-M population, hence, are well within one standard deviation above the mean value of the LGN-M population. This indicates substantial overlap in the physiological properties of the experimentally observed distribution of the LGN-M cells. Since there is considerable overlap in the physiological properties of the hypothesized LGN- M2 and LGN-M1, sampling problems in recording from LGN units may indeed have precluded recognition of a distinct M1 population. Interestingly a number ratio of 20% LGN-M1 and 80% LGN-M2 cells more closely resemble the number ratio given for LGN-M cells of Y-type and X- type LGN-M cells which is 25% to 75% according to Kaplan & Shapley (1982). If the M1 cells form a functional distinct population of LGN-M cells as suggested by the anatomical ﬁndings and the modelling results, then the nonlinear Y-like LGN-M population may form the physiological counterpart of this cells. This is supported by the data of Dreher et al. (1976) and Maunsell & Gibson (1992) who report that conduction velocities are greater for Y- compared to X-like relay

cells and that cells at the top of layer 4C have shortest response latencies. However, as already mentioned in the discussion in Section 6.3, there is no evidence for two LGN-M populations in respect to receptive ﬁeld size and contrast sensitivity (Spear et al., 1994; Levitt et al., 1998). Since the physiological data are particular contradicting, one may tentatively conclude that the population of Y-type cells in the monkey LGN does not correspond to the anatomically identiﬁed LGN-M1 cells. For details see also Section 6.3. 9.3 Discussion 163

Receptive Field Size in Upper 4C

I generally assume that the gradient in receptive ﬁeld size of cells in upper 4C increases though the experimental data on receptive ﬁeld size in the upper fraction of the layer are fragmentary; the

two measurements of receptive ﬁeld size in upper 4C which are reported in the study of Blasdel & Fitzpatrick (1984) indicate that the receptive ﬁeld size decreases in this region.

If this trend indeed accounts for the actual receptive ﬁeld size in upper 4C, then the intracortical recurrent model provides a reasonable explanation. The numerical simulations of the

intracortical model without lateral stepped connection have shown that receptive ﬁeld size decreases/saturates in upper 4C due to the strong inhibition of the -6 cell while predicted contrast sensitivity values show the exponential increase observed in the experimental data of Blasdel & Fitzpatrick (1984) and Hawken & Parker (1984).

Future experiments which address receptive ﬁeld size of cells in upper 4C have to demonstrate how the gradient in receptive ﬁeld size progress in this region.

The Role of Other Inhibitory Interneurons It is important to ask if other factors than lateral recurrent excitation and somatic inhibition by the basket cells could cause an increasingly rapid change in properties with rise in depth of layer 4C. A decreasing level of inhibition with movement up in the layer could give a decreasing threshold to thalamic input. This in turn could lead to a larger apparent receptive ﬁeld size and higher contrast sensitivity in neurons higher in the layer. However, – as already accounted for in the intracortical model – there is no signiﬁcant difference in number of type 2 (GABAergic) synapses per unit area of cell soma surface through the depth of layer 4C. There may be different numbers of inhibitory contacts on the dendrites or inhibition coming from different interneuron types that could lead to

different thresholds. Another type of interneuron which is basically absent from layer 4C is the -7 cell (Lund, 1987), a chandelier neuron, which is known to contact the axon initial segment (Somogyi et al., 1982). Douglas & Martin (1990) suggest – based on computer simulations – that both the axosomatic basket cell and the axoaxonic chandelier cell act synergetically: the AIS inhibition could control the signal threshold, while the basket cell could act more selectively to shape the

suprathreshold signal. But it is difﬁcult to see how additional unspeciﬁc inhibition by the -7 cell

in upper 4C could result in the rapid increase of receptive ﬁeld size and contrast sensitivity at the

top of layer 4C.

Relation of Synaptic Inputs of Layer 6 to LGN and Layer 4C Another source of recurrent excitatory input to layer 4C spiny stellate cells (and inhibitory interneurons) derives from recurrent collaterals of layer 6 pyramidal neurons. The rising intrinsic projections from layer 6 pyramids to spiny stellate cells appear to contact mainly their dendritic shafts rather than the spines of the postsynaptic spiny stellate cells (Anderson et al., 1994). These rising collaterals from axons of layer 6 pyramidal cells target speciﬁc divisions of layer 4C (Lund & Boothe, 1975; Wiser & Callaway, 1996). As shown by Yoshioka et al. (1994) retrograde labelled cells which are seen after tracer injections in different subdivisions of layer 4C are biased

to different depths in layer 6 – injections in lower 4C and upper 4C give retrograde labelled cells predominantly in upper and lower layer 6 respectively, while injections in mid-4C give labelled cells predominantly in mid-layer 6. Hence, the distribution of retrograde label in layer 6 suggests that lower/upper layer 6 cells are presynaptic to cells in upper/lower layer 4C which are dominated 164 Results of the Intracortical Model

by M/P input while mid-layer 6 cells are presynaptic to cells in the zone of P and M combination in mid-layer 4C. Interestingly, many LGN-M axons provide collaterals to lower layer 6 (Blasdel & Lund, 1983), while none of the LGN-P axons was found to innervate layer 6. Especially the LGN-M1 cell identiﬁed by Blasdel & Lund (1983) provides extensive collaterals to lower layer 6. The LGN-M

input to lower layer 6 pyramidal cells that are presynaptic to cells in upper 4C may result in

additional excitatory input to upper 4C via the rising axon collaterals of lower layer 6 pyramidal

cells. This additional input via layer 6 pyramidal cells which is propagated via rising collaterals to upper 4C could result in increased field size and contrast sensitivity in upper 4C . The principal site of layer 6 input to the layer 4C spiny stellate cells are the dendritic shafts (Anderson et al., 1994) which suggests a different physiological impact of input from layer 6 (Levitt et al., 1996) – compared to the direct thalamic input and local lateral connections of layer 4C which are directed to the dendritic spines of layer 4C spiny stellate cells. In support of the hypothesis that direct thalamic relays and lateral recurrent connections may be the essential excitatory determinants of receptive field size and achromatic contrast sensitivity, I should emphasize that Stratford et al. (1996) who studied the excitatory synaptic inputs to spiny stellate cells in layer 4 of cat striate cortex report that thalamocortical and local lateral synapses are more powerful and reliable than the efferent synaptic input of layer 6. The amplitude of intracortical EPSPs, supposed to arise from other spiny stellate cells in layer 4 (class 2 EPSPs; their Table 1) are at least half the size but less invariant than those supposed to reflect the thalamic input (class 1 EPSPs; their Table 1). Compared to the direct thalamic inputs and the more numerous synaptic connections from adjacent layer 4 neurons, the EPSPs from layer 6 pyramidal cells show a high coefficient of variation and small mean amplitudes (class 3 EPSPs, their Table1). These observations have to be confirmed for monkey. If the conclusion of Stratford et al. (1996) holds for layer 4C in macaque striate cortex, then the simple receptive fields are established by the pattern of thalamic excitation which is amplified by the more numerous connections from adjacent layer 4 neurons and layer 6 pyramidal cells modulate thalamic signal transmission by temporally sensitive synapses.

How to Distinguish between the Feedforward and the Intracortical Hypothesis?

The intracortical hypothesis is an alternative to the feedforward hypothesis which is explored and discussed in Chapter 5 and 6. In principle, two models are able to explain the depth-dependence of receptive ﬁeld size and contrast sensitivity of cells in layer 4C of macaque striate cortex:

the feedforward model II based on two LGN-M populations

the intracortical model I based on one LGN-M population

In addition, the intracortical model II which is a combination of both models is also able to account for the gradient in basic response properties in depth of layer 4C. However, the intracortical model II makes no clear predictions. Both models, the feedforward model based on afferent input from the anatomically identiﬁed M2 and M1 cells, and the intracortical model based on afferent input from one M population and lateral excitatory and inhibitory connections, are in good agreement with the currently available experimental data. The predictions of both models and suitable experimental tests have been readily discussed in Section 6.3 and 9.3. 9.3 Discussion 165

The question which immediately arises and which has not been addressed explicitly so far is, how to distinguish between the different hypotheses. The key prediction of the feedforward model is that 12% of the LGN-M population belongs to the LGN-M1 cells which are characterised by a large stratiﬁed arbor restricted to the upper half of

layer 4C. Their physiological signatures are larger receptive ﬁelds and higher contrast sensitivity covering the upper range of experimentally observed properties of LGN-M cells. By contrast the intracortical model predicts substantial lateral input via stepped connections

which contributes to the classical receptive ﬁeld of cells in mid-layer 4C and upper 4C, and

considerable differences in the physiological properties of the clutch cell and the -6 cell. Thus, both models make clear physiological predictions for anatomically identiﬁed cell classes and experimental tests were suggested to verify either the afferent or the intracortical hypothesis: The key experiment which ultimately distinguishes between both hypotheses will be the re- examination of the physiological properties of LGN-M cells based on intracellular recording and

filling of LGN-M axonal arbors. The physiological properties of the clutch cell and the -6 cell might be testable experimentally by observing the IPSPs recorded intracellularly for cells in 4C, but it might be difficult to test the efficacy of the stepped connections. Experimental tests which estimate the strength of recurrent excitatory feedback are currently not available, however, the study of Adorján & Obermayer (1999) may provide suitable signatures. Thus, experimental tests must show if either of the hypotheses are likely and, if they are both confirmed, the modelling results of the combined intracortical model II which is based on afferent input from two LGN-M populations may provide the explanation how they combine to produce the actual biological condition. 166 Results of the Intracortical Model Chapter 10

Conclusions and Outlook

The preceding chapters have demonstrated how computational models of neural circuits of the macaque primary visual cortex can help to understand the functional architecture of regions where details of actual circuitry are difficult to explore experimentally. In the first part of the chapter I briefly summarize, discuss and interprete the main results of my modelling work whereas the second part is dedicated to an outlook of future research directions.

Summary of Major Results The goal of the modelling work was to determine how the neuron response properties of layer 4C – the primary input zone of thalamic parvo- and magnocellular fibres – are generated. Specifically, the different models aim at replicating the more basic response properties – receptive field size and achromatic contrast sensitivity – by biologically-realistic geniculocortical information transfer. For this purpose I have interpreted the basic response properties of neurons in layer 4C, as observed in the studies of Blasdel & Fitzpatrick (1984) and Hawken & Parker (1984), as a continuous gradient between the response properties of the parvo- and magnocellular information channels. It was the vertical gradient in depth of layer 4C and the rapid increase of achromatic contrast

sensitivity in upper layer 4C that I wished to explain by the modelling work. Different functional hypotheses have been developed in a systematic and hierarchical fashion on the basis of relevant anatomical and physiological ﬁndings. The feedforward model has primarily addressed the convergence of LGN-P and LGN-M cells

onto the postsynaptic spiny stellate cells whose dendritic arbors intrude into both termination zones. While realistic dendritic overlap across the / border was sufficient to account for the gradual change of basic response properties in the lower 2/3 of layer 4C, the rapid increase of contrast sensitivity at the top of the layer could be replicated by assigning larger receptive fields and higher contrast sensitivity to the population of anatomically identified LGN-M1 cells. Because the feedforward model provides strong evidence that the concept of dendritic overlap and the convergence of P- and M- cells in depth of layer 4C has functional relevance it has been used as a sound base for a second model of realistic intralaminar lateral feedback. The intracortical model which is based on the depth-dependence of the lateral excitatory projections of the spiny stellate cells and a change in strategy of the somatic inhibition at the top of the layer provides an alternative explanation of increased achromatic contrast sensitivity at the top of the layer. According to the intracortical model the rapid increase of field size and contrast sensitiv-

ity of cortical cells in upper 4C results from substantial lateral input via the stepped connections which work synergetically with differential somatic inhibition. 168 Conclusions and Outlook

Both models are in good agreement with the available experimental data and the modelling work renders both functional hypothesis as possible explanations for the depth-dependence of basic response properties in layer 4C. Based on numerical simulations, it was possible to suggest new experimental test which may conﬁrm, refute or distinguish between the different hypotheses. If both hypotheses are conﬁrmed by experimental methods, the simulation results adopted for the combined model can reveal how both mechanisms interact to produce the actual biological conditions.

Technical Considerations Although a simple neuron model was used to explore the functional aspects of neural circuitry in the primate visual cortex the results have demonstrated that it was an adequate choice to answer the particular questions addressed in this thesis. The most compelling reason to discard more realistic models of neural response e.g. compartmental models was the lack of sufficient experimental data to constrain the additional model parameters. Moreover, the fragmentary physiological data on the response properties and the temporal dynamics of neural response in layer 4C does not provide a suitable framework to use detailed models based on realistic spike timing in the first place. By contrast, great effort was put to calibrate the computational models by real anatomical and physiological data taken almost exclusively from macaque monkeys and from restricted parafoveal regions within the retinotopic maps. The modelling of accurate arbor size and realistic connectivity of anatomical identified cell populations was essential to my modelling approach. Moreover, the response properties of parvo- and magnocellular cell populations were fitted to real physiological data drawn from recent quantitative studies of retinal and geniculate cell populations. A major part of the work was to develop and implement the simulation tools which help to explore the functional architecture of macaque primary visual cortex. The first simulation tool is designed to explore the parameter space of a biologically-realistic model of geniculocortical information transfer. The simulator accounts for the anatomical constraints of axonal arbors and dendritic fields and is based on different sets of physiological distinct cell populations. The important features of this simulation tool are a detailed statistical description of physiological response properties which is transformed into biological realistic response properties of whole populations of model LGN cells. The second simulation tool is designed to explore functional models about realistic intralaminar circuitry. The software accounts for biologically realistic connectivity structures based on the detailed spread of local axonal and dendritic fields of excitatory and inhibitory cell populations. The simulation tool provides a graphical user interface and the response properties of model cells and simulation result can be observed online. By contrast, the simulator of realistic intralaminar information processing is based on a simpler representation of physiological properties of LGN cells. The simulation tools are either implemented in C or C++. The software is designed modular and object-oriented programming techniques are employed.

Functional Implications of Modeling Results Since the questions that I have addressed in my thesis appear highly speciﬁc, they have to be clearly embedded in the context of functional aspects of the primate visual system. The early visual processing in primates is characterized by two parallel pathways. The magno-

cellular stream relays via layer 4C and layer 4B either directly or indirectly to the visual areas in the parietal cortex and carries information putatively useful for motion analysis. By contrast, the

parvocellular stream relays via layer 4C and layers 2-3 to the temporal visual areas and carries 169

information putatively useful for the analysis of shape and colour. Both channels originate in the retina and project via the parvo- and magnocellular layers of the LGN to the and subdivision of layer 4C in the primary visual cortex. Although increasing anatomical and physiological evidence indicates early convergence of both pathways, it still remains uncertain in terms of the anatomical substrates and the independence of relays that conveys the different sets of geniculate information through the primary visual cortex between the input laminae and efferent neuron sets. Therefore independence versus merger of the subcortical magno- and parvocellular information channels and their individual contribution to the response properties of cortical cells are of particular interest as indicated by the focus of recent experimental studies e.g. Yoshioka et al. (1994), Sawatari & Callaway (1996), Vidyasagar et al. (1998), and Robson & Kulikowski (1998). The modelling work provides strong impetus that the ﬁrst step of convergence of parvo- and magnocellular streams occurs at the entry of thalamic information to the primary visual cortex and that it is the geometric layout and the anatomical constraints of feedforward thalamic projections and postsynaptic spiny stellate cells which establish an interpolation principle to set up a continuous gradient in depth of layer 4C. The systematic combination of different sets of physiological inputs to create a vertical gradient is of considerable importance to understand the properties of the three relays which are shown to emerge from the different depths of layer 4C (Yoshioka et al., 1994). If the predictions of the feedforward model are correct, then it is the LGN-P input which dom-

inates lower 4C and which relays to layer 4A, itself a recipient zone of LGN-P input. The input from the so-called LGN-M2 population combines with the LGN-P input to drive postsynaptic neurons in mid-4C which directly project to the interblob territories of layer 3B. Finally it is the

pure M1 input which is restricted to upper 4C, known to provide relays to layer 4B. On the other hand, if the intracortical model approximates the real biological conditions, then the first step of lateral integration occurs in mid-4C which receives convergent feedforward input from both P- and M- channels. The impact of lateral integration becomes more substantial at the top of the layer which contains a small population of direction selective cells. The lateral integration of excitatory and inhibitory signals over a large range within the retinotopic map of layer 4C seems to be most useful to build a new cumulative receptive field and to extract relevant information of fast moving stimuli. If, however, the lateral feedback combines with the feedforward input from the anatomical identified LGN-M1 cell, hypothesized to have large receptive fields, to be more sensitive to low contrast and probably having the fastest and most transient response, it might be the particular combination of feedforward excitation and lateral integration that determines the responses of

neurons in upper 4C. The knowledge about the generation of a depth-dependent gradient of the more basic response properties of cells in layer 4C provides a sound base to study realistic neural circuitry responsible for the generation of other response properties of cells in layer 4C. A recent study has already demonstrated that the feedforward model provides a realistic framework for the intracortical origin of orientation preference and tuning in layer 4C of macaque striate cortex (Adorj´an et al., 1998; Bauer et al., 1997). The remaining question is how to continue future research and which starting points seem to be most interesting and most important?

Future Research Directions One essential point will be to explore the neural basis for the emergence of direction selective

response in a small cell population located in upper 4C. This would require to concentrate in 170 Conclusions and Outlook

more detail on the neural circuitry in the uppermost region of the layer. The putative transient drive by the fast conducting and highly contrast sensitive LGN-M1 population may allow the

spiny stellate cells in upper 4C to respond with minimum delay to transient and small changes in luminance contrast within large receptive ﬁelds; this is certainly a useful property for the detection of stimulus motion. The postsynaptic cortical cells may integrate information from other cortical cells at laterally displaced locations in the visotopic map of layer 4C. It may be the particular spatiotemporal pattern of feedforward and lateral excitatory inputs that results in the directional tuning of the cells as suggested by experimental ﬁndings in cat visual cortex (e.g. Jagadeesh et al.,

1993). The -6 cells which are a unique set of local circuit neurons replace the small clutch cell in the uppermost part of the layer. Their stratified arbor which runs over a long distance horizontally in the uppermost part of the layer is a good anatomical substrate to provide feedforward inhibition to cells at the top of the layer – shown to be an important mechanism in the generation of direction selectivity in the rabbit retina (e.g. Barlow & Levick, 1965). The intracortical model for the depth-dependence could be used as a framework to explore both possibilities theoretically. A first step in this direction would be, to calibrate the lateral excitatory connections by the detailed stripe-like patterns as observed experimentally by Asi et al. (1998). Since it is the spatiotemporal timing of excitatory and inhibitory inputs, supposed to be most important in the emergence of direction selectivity, realistic response latencies and conduction velocities have to be introduced in the model. In addition, to address this particular question, more experimental data, especially physiological, are needed to sufficiently constrain the model parameters. Another direction of research is to concentrate in more detail on the complex inhibitory circuitry of layer 4C (Lund, 1987). All of the morphologically identified local circuit neurons exhibit clear laminar specificity of their dendritic and axonal field to different subdivisions of layer 4C and

most of them make external interlaminar projections. However, some of the local circuit neurons do apparently not project outside the layer ( -3, -3 variety; Lund, 1987) suggesting a primar-

ily role for the intralaminar information processing. Interestingly both varieties have a dendritic ﬁelds restricted to either the or subdivision of the layer while their axonal ﬁelds span the whole

depth of the layer, hence, may effectively inhibit both subdivision of the layer. By contrast, a third variety called -5 cell (Lund, 1987), has an axonal arbor restricted to the lower subdivision of the layer but its dendritic arbor bridge the whole depth of the layer. This suggests that this neuron detects overall activity in depth of the layer and speciﬁcally inhibits cells that are activated by thalamic LGN-P cells. These three putatively inhibitory interneurons may implement an effective

spatiotemporal gating of parvo- and magnocellular information channels at the ﬁrst stage of con-

vergence in layer 4C. The vertical inhibition of the reciprocal -3 and -3 cell may allow either

the neurons in the or subdivision to be active at the same time. In addition, the -5 neuron my

provide an effective ”veto” to the -subdivision for the case that both subdivisions are active. In other word, the anatomical properties can result into an elaborate time-multiplexing of concurrent visual information streams of the same region in the visual ﬁeld. Since the examination of intrinsic

physiological properties of fast spiking (inhibitory) interneurons (Azouz et al., 1997) indicates no significant spike frequency adaption, the temporal interaction of the and subdivision may be dominated by the temporal dynamics of sustained LGN-P and transient LGN-M (M2/M1) input signals and their different conduction velocities (and perhaps together with the lateral connections in the layer). Although the synaptic input and the postsynaptic targets of the interneurons are unknown and there is no data available that address spatio-temporal interaction in depth of the layer, it might be worth to explore the functional role of this hypothesized microcircuit. Another possible project is closely related to the previous point and the depth-dependence of 171 response latencies as reported in the studies of Bullier & Henry (1980) and Maunsell & Gibson (1992). The feedforward model has demonstrated that a single cortical cell in layer 4C receives a depth-dependent mixture of either two or even three physiologically distinct thalamic inputs. For example cells in mid-4C receive roughly equal proportions of LGN-P and LGN-M inputs. Hence, the more transient input of LGN-M cells may preceed the input from the LGN-P cells in time and duration (Marrocco, 1976). Therefore a first step could be to add realistic temporal response properties to the receptive field organisation of LGN cells and to explore the temporal response properties and conduction velocities in depth of the layer without and with lateral intralaminar connections. In a second step, more realistic spiking neurons with adapting synapses (e.g. Adorján & Obermayer, 1999) can be used to explore the effect of feedforward and lateral synaptic inputs at different depth of the layer. The goal would be to predict significant differences in the response properties of the three output channels shown to emerge from different depths of the layer. Finally another important point is to explore the functional role of the third major source of excitatory input to layer 4C: axon collaterals of layer 6 pyramidal cells. Anatomical studies (Lund, 1973; Lund & Boothe, 1975; Wiser & Callaway, 1996) have identified several classes of layer 6 pyramidal cells which are distinguished from one another based on the sublaminar specificity of their axonal and dendritic arbors within layer 4C. The studies provide evidence that

cells at different depth of layer 6 establish a feedback loop with the three output divisions of layer 4C, i.e. lower 4C , mid-4C and upper 4C . There is also evidence that cells at different depth of layer 6 receive direct input from the M (to lower layer 6) and perhaps also from the P subdivisions of the LGN. In turn there are feedback projections from different depth of layer 6 to the relay neurons in different subdivisions of the LGN (Fitzpatrick et al., 1987); in addition layer 6 contains a principle population of direction selective cells (Hawken et al., 1988). The study of Stratford et al. (1996) indicates that EPSPs of layer 6 synaptic inputs to layer 4C spiny stellate cells are smaller and are less reliably evoked than feedforward input from the LGN and layer 4C cells. However, the synaptic input of layer 6 cells shows facilitation to repetitive electric stimulation on a short time scale. I have suggested earlier that synaptic input of layer 6 cells may cause higher

contrast sensitivity at the top of layer 4C. In particular, there is evidence that the anatomical identiﬁed population of LGN-M1 cells provides extensive collaterals to lower layer 6 (Blasdel & Lund, 1983). The functional role of the layer 6 input is yet unknown but it will be interesting to see how recurrent excitatory input from the layer 6 pyramidal cells affects the basic response properties of cells at different depth of layer 4C.

AResum´ e´ This thesis is a ﬁrst step to systematically develop a ”transfer function” of layer 4C of the macaque primary visual cortex. To continue this long-term project, a close interaction of anatomical, physiological and theoretical research is essential to improve the models step by step and to gain a more and more complete picture of the functional architecture of the initial cortical processing stage. 172 Conclusions and Outlook Appendix A

The Feedforward Model

A.1 The Parameter-Interface of the Simulation Tool

The feedforward model which was described in the method section of Chapter 5 was implemented in standard C as a non-graphical simulation tool. The model parameters are specified via a parameter file (”bio parameter”). The parameter file is scanned and subsequently parsed by the simulation tool. Syntax and semantic of the parameter interface are specified below. Each parameter is given by its name and a corresponding parameter value. All parameter settings given below are just examples. Comments for each parameter are given in the right column.

Parameter Value Comment P GRID 1000 Internal pixel scale used to discretize space

NO LAYERS 3 Number of network layers e.g. VFLD, LGN, 4C

– Speciﬁcation of the VFLD layer –

NO VFLD SUBLAYER 1 Number of visual ﬁeld sublayers

VFLD UNITS 3 Size of visual ﬁeld layer in [degree] VFLD START 5 Range of eccentricities

VFLD END 8 e.g. from 5 to 8 degree eccentricity V F LD

RECEPTOR PER UNIT 30 Visual ﬁeld grid size: N [units per degree]

– Speciﬁcation of the LGN layer –

LGN UNITS 900 Size of the LGN layer in [m]

NO LGN SUBLAYER 3 Number of LGN sublayer n n=2: LGN-P, LGN-M (model I) n=3: LGN-P, LGN-M2 and LGN-1 (model I)

if (n=2) then ignore LGN-M1 parameters P

P PER UNIT 61 Grid size of the LGN-P sublayer: N

LGN

M (2)

M2 PER UNIT 23 Grid size of the LGN-M(2) sublayer: N

LGN

M 1

M1 PER UNIT 8 Grid size of the LGN-M1 sublayer: N LGN 174 The Feedforward Model

— DoG proﬁle of P, M(2) and M1 cells – R

P R C 0.05 Mean value of LGN-P receptive ﬁeld center radius c in [degree]

P R C VAR 0.03 Standard deviation of LGN-P receptive ﬁeld center radius R

c in [degree] R

P R S 0.43 Mean value of LGN-P receptive ﬁeld surround radius s in

[degree] R

P R S VAR 0.28 SD of LGN-P receptive ﬁeld surround radius s in [degree] K

P VOLUME RATIO 0.547 Mean of LGN-P integrated surroundcenter sensitivity K

P VOL VAR 0.181 SD of LGN-P integrated surroundcenter sensitivity R

M 2 R C 0.093 Mean value of LGN-M(2) receptive ﬁeld center radius c

in [degree] R

M 2 R C VAR 0.018 SD of LGN-M(2) receptive ﬁeld center radius c in

[degree] R

M 2 R S 0.69 Mean of LGN-M(2) receptive ﬁeld surround radius s in

[degree] R

M 2 R S VAR 0.20 SD of LGN-M(2) receptive ﬁeld surround radius s in [degree]

M2 VOLUME RATIO 0.546 Mean of LGN-M(2) integrated surroundcenter sensitivity

K K

M2 VOLUME VAR 0.120 SD of LGN-M(2) integrated surroundcenter sensitivity R

M 1 R C 0.121 Mean value of LGN-M1 receptive ﬁeld center radius c in

[degree] R

M 1 R C VAR 0.026 SD of LGN-M1 receptive ﬁeld center radius c in [degree] R

M 1 R S 0.98 Mean of LGN-M(2) receptive ﬁeld surround radius s in

[degree] R

M 1 R S VAR 0.25 SD of LGN-M1 receptive ﬁeld surround radius s in

[degree] K

M1 VOLUME RATIO 0.546 Mean of LGN-M1 integrated surroundcenter sensitivity K

M1 VOL VAR 0.120 SD of LGN-M1 integrated surroundcenter sensitivity

2 R

RF LIMIT 2 Limit of the LGN receptive ﬁeld proﬁle e.g. s

– Contrast processing of P, M(2) and M1 cells –

P GAIN 0.963 Mean of LGN-P contrast gain in [spikes/(sec %contrast)] P GAIN VAR 0.483 SD of LGN-P contrast gain in [spikes/(sec %contrast)]

P MAX 31.11 Mean of LGN-P maximum ﬁring rate in [spikes/sec]

P MAX VAR 11.32 SD of LGN-P maximum ﬁring rate in [spikes/sec] c

P C MIN 0.10 Contrast threshold min of LGN-P cells A.1 The Parameter-Interface of the Simulation Tool 175

M 2 GAIN 5.313 Mean of LGN-M(2) contrast gain in [spikes/(sec %contrast)] M 2 GAIN VAR 0.8 SD of LGN-M(2) contrast gain in [spikes/(sec %contrast)]

M 2 MAX 41.65 Mean of LGN-M(2) maximum ﬁring rate in [spikes/sec] M 2 MAX VAR 16.76 SD of LGN-M(2) maximum ﬁring rate in [spikes/sec]

M 1 GAIN 8.806 Mean of LGN-M(2) contrast gain in [spikes/(sec %contrast)] M 1 GAIN VAR 0.988 SD of LGN-M(2) contrast gain in [spikes/(sec %contrast)]

M 1 MAX 79.32 Mean of LGN-M1 maximum ﬁring rate in [spikes/sec] M 1 MAX VAR 23.43 SD of LGN-M1 maximum ﬁring rate in [spikes/sec]

– Fit of LGN transfer function – c

P C K SAMPLES 12 Number of contrast values k used for the least square ﬁt of

the LGN-P transfer functions c

M C K SAMPLES 12 Number of contrast values k used for the least square ﬁt of

the LGN-M(2) transfer functions c

M1 C K SAMPLES 12 Number of contrast values k used for the least square ﬁt of the LGN-M1 transfer functions

P T FCT TYPE 1 Type of the LGN-P transfer function 1 = transfer function of type 1 2 = transfer function of type 2 – Axonal Arbors of P, M(2) and M1 cells --

P R 100 Radius of LGN-P axonal arbors in [m]

M 2 R 300 Radius of LGN-M(2) axonal arbors in [m]

M 1 R 550 Radius of LGN-M1 axonal arbors in [m] – Speciﬁcation of the layer 4C --

NO IVC SUBLAYER 8 Number of sublayers in layer 4C i.e. depth D

NO ALPHA SUBLAYER 4 Number of sublayers that correspond to layer 4C

NO BETA SUBLAYER 4 Number of sublayers that correspond to layer 4C

IVC UNITS 4500 Size of layer 4C in [m]

IVC CELLS BOTTOM 27 Grid size at the bottom of layer 4C (depth 1): N

IVC CELLS TOP 20 Grid size at the top of layer 4C (depth D): N D

if (IVC CELLS BOTTOM IVC CELLS TOP) then interpolate linearly between bottom and top ST R BOTTOM 100 Radius of spiny stellate cell dendritic ﬁeld at the bottom of

layer 4C (depth D=1) in [m] ST R TOP 100 Radius of spiny stellate cell dendritic ﬁeld at the top of layer

4C (depth D) in [m]

if ( ST R BOTTOM ST R TOP) then interpolate linearly between bottom and top 176 The Feedforward Model

– Thalamic Weight Portions --

IVC DEPTH INPUT for D= NO IVC SUBLAYER different depth

e.g. D=1, ,8

LGN P

(D )

1.0 1.0 0.87 0.65 0.35 0.10 0.0 0.0 W ; D=1, 8

LGN M (2)

(D )

0.0 0.0 0.13 0.35 0.65 0.72 0.5 0.17 W ; D=1, 8

LGN M 1

(D ) 0.0 0.0 0.0 0.0 0.0 0.18 0.5 0.83 W ; D=1, 8

– Visual Stimulation --

IVC STIM TYPE 1 Stimulus type t used to measure basic response properties of cortical cells: t=0 spot t=1 bars

t=2 sine wave gratings

2 l

L MEAN 40 Mean luminance 0 in [cd/m ]

PATTERN CONTRAST 0.2 Stimulus Contrast -- Sine Wave Gratings --

IVC FREQ MIN 0.07 minimal frequence in [cycles per degree] IVC FREQ MAX 14.0 maximal frequency in [cycles per degree] IVC FREQ SAMPLES 100 Number of sample points between minimal and maximal frequency

-- Bar Stimulus --

BAR X DIM 0.03 bar of size (0.03,0.3) in [degree] BAR Y DIM 0.3

MOVING DIRECTION 8 bar is systematically moved along e.g. eight directions

MOVE STEPSIZE 0.03 Stepsize by which the bar is moved along each direction i.e. determines accuracy of minimum response ﬁelds

-- Spot Stimulus --

SPOT RADIUS 0.05 spot of radius r=0.05 in [degree]

– Contrast values for contrast-response functions –

IVC CONTR MIN 0.0 Begin with contrast 0.0 IVC CONTR MAX 1.0 Stop at contrast 1.0 IVC CONTR SAMPLES 0.01 Increase contrast by steps of 0.01

– Critical Thresholds – t

Critical threshold 0 of minimum response ﬁeld (test for a range of critical thresholds simultaneously)

A.1 The Parameter-Interface of the Simulation Tool 177

t = 05

IVC MRF THRESH MIN 0.5 Start with threshold 0

t = 30

IVC MRF THRESH MAX 3.0 Stop at threshold 0 t

IVC MRF THRESH STEPSIZE 0.1 Increase threshold 0 iteratively by 0.1 t

Critical threshold 1 used for contrast sensitivity

(test for a range of critical thresholds simultaneously)

t = 50

IVC CONTR THRESH MIN 5.0 Start with threshold 1

t = 150

IVC CONTR THRESH MAX 15.00 Stop at threshold 1 t

IVC CONTR STEPSIZE 0.25 Increase threshold 1 iteratively by 0.25

t = t 1 Critical threshold 0 of spatial-frequency contrast- sensitivity functions (test for a range of critical threshold simultaneously)

IVC CS THRESH MIN 1.0 Minimum Threshold IVC CS THRESH MAX 15.0 Maximum Threshold IVC CS THRESH STEPSIZE 1.0 Stepsize by which threshold is iteratively increased 178 The Feedforward Model

A.2 Results for the Data Set of Spear et al.

In the results section of the feedforward model (Section 6.1 and Section 6.2) I have explored the parameter space of the feedforward model. Although numerical simulations were performed for both data sets ( Croner & Kaplan, 1995 and Spear et al., 1994) the results presented for model I (one LGN-M population) and model II (two LGN-M population) are in most cases based on the physiological parameters of P and M cells as reported in the study of Croner & Kaplan. Here I present the simulation results which are based on the LGN data of Spear et al. given in Table 5.2. The numerical simulations for both data sets lead to virtually identical conclusions. For details about parameter settings and the interpretations of simulation results refer to the corresponding paragraphs in Section 6.1 and 6.2.

A.2.1 Results Model I: One LGN-M population

Percentage of P- vs. M-inputs as a Function of Depth

0.4 4 weights (a) weights (a) 0.35 weights (b) 3.5 weights (b) 0.3 weights (c) 3 weights (c) weights (d) weights (d) 0.25 experiment 2.5 experiment 0.2 2 0.15 1.5 0.1 1

Receptive Field Size [degree] 0.05 0.5 Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure A.1: Parameter exploration of model I (one M pathway). The ﬁgure shows receptive ﬁeld

size (left column) and contrast sensitivity (right column) of layer 4C spiny stellate neurons as a

D function of depth D , ( ). Symbols denote mean values of 20 cells selected at random from each sublayer; plots of the experimental data from Figure 3.7 are added for comparison.

Convergence of P- and M-inputs: Each curve corresponds to a particular thalamic weight distri-

t t 1 bution of Figure 6.1. Cortical threshold parameters were 0 and . The bad ﬁt of normalized contrast sensitivity values – particular in the lower two third of layer 4C – is due to the small differences in contrast gain between the LGN-P and LGN-M population in the data set of Spear et al.. Unfortunately the deviations from the mean contrast sensitivity, the normalized contrast sensitivity curves, are to small in the simulated data. However, the gradual change of the

simulated and experimental contrast sensitivity curves are comparable in lower 4C and mid-4C.

The saturation of contrast sensitivity in upper 4C can obviously not account for the rapid change observed in the experimental data. A.2 Results for the Data Set of Spear et al. 179

Threshold Dependence of Response Properties

0.4 4 t1=5.00 t0=0.75 3.5 0.35 t0=1.00 t1=7.00 t1=9.00 0.3 t0=1.25 3 t0=1.75 t1=11.00 0.25 experiment 2.5 t1=13.00 experiment 0.2 2 0.15 1.5 0.1 1 0.05 0.5 Receptive Field Size [degrees] Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure A.2: Parameter exploration of model I (one M pathway). The ﬁgure shows the effect of

t t 1 different values of the threshold parameters 0 and of the cortical transfer function on receptive

ﬁeld size (left) and contrast sensitivity (right) of layer 4C spiny stellate neurons. Each curve

t t 1 corresponds to a particular choice of the threshold parameter 0 and . The thalamic weight distribution was taken from Figure 6.1c. For other conventions see caption of Figure A.1. The

much smaller threshold dependence of the contrast sensitivity curves is due to the normalization t

of the simulated data. Changes in absolute contrast sensitivity values with threshold parameter 1 are comparable to the changes in the receptive ﬁeld size curves.

Transfer Functions of Geniculate P-cells 0.4 4 type 2 type 2 0.35 type 1 3.5 type 1 0.3 experiment 3 experiment 0.25 2.5 0.2 2 0.15 1.5 0.1 1 0.05 0.5 Receptive Field Size [degrees] Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure A.3: Parameter exploration of model I (one M pathway). The ﬁgure shows the effect of pronounced differences in the low contrast processing of LGN-P and LGN-M cells on receptive ﬁeld size (left) and contrast sensitivity (right) of layer 4C spiny stellate neurons. The simulated

curves correspond to response properties for type 1 vs. type 2 LGN-P transfer functions. The

thalamic weight distribution was taken from Figure 6.1c. Threshold parameters were 0

and 1 . For other conventions see caption of Figure A.1. The higher normalized contrast

sensitivity at the top of layer 4C in the type 2 vs. the type 1 curve is an artefact of normalization;

the absolute contrast sensitivities at the top of layer 4C are equal for both type 2 and type 1 simulations. 180 The Feedforward Model

Dendritic Arbor Size of Layer 4C Spiny Stellate Neurons

Figure A.4: Parameter exploration of model I (one M pathway). The ﬁgure shows the effect of changes in the dendritic arbor geometry on receptive ﬁeld size (left) and contrast sensitivity (right)

of layer 4C spiny stellate neurons. The lateral spread of the dendritic ﬁelds changed from 150 m

at the bottom to 250 m at the top of layer 4C (for details refer to Figure 6.5a). The thalamic weight distribution of Figure 6.1c was adapted to account for the vertical vs. horizontal elongation of the dendritic ﬁelds in lower and upper layer 4C (see Figure 6.5b). The response properties for

spiny stellate cells with uniform dendritic ﬁeld geometry are also shown (compare Figure A.1 ,

t t 1 weights (c)). Threshold parameters were 0 and . For other conventions see caption of Figure 6.2. A.2 Results for the Data Set of Spear et al. 181

A.2.2 Results Model II: Two LGN-M populations 182 The Feedforward Model ells for udy. Number aximum spike 0.12); therefore K r the total LGN-M pace. The mean values LGN-M2 and LGN-M1 0.018 0.015 16.91 18.43 ner & Kaplan since Spear 12% 12% 0.20 0.30 0.82 0.44 ion (0.55 Set D 1.05 1.36 88% Set D 88% 0.095 0.125 1.31 41.55 3.01 79.92 0.019 0.017 17.45 19.37 20% 20% 0.26 0.35 0.84 0.51 (Spear et al., 1994), are constant over all sets. Set C 0.097 1.07 0.117 1.29 80% Set C 1.33 42.91 2.59 71.28 80% 0.019 0.018 18.88 19.56 s 28% 28% 0.33 0.38 0.85 0.64 R and Set B 0.098 1.10 0.114 1.24 72% Set B 1.37 43.62 2.20 65.05 72% . Mean values and standard deviations of contrast gains and m 0.021 0.020 19.75 21.95 41% 41% 0.40 0.42 0.87 0.75 ], respectively. The mean values and standard deviations fo nd LGN-M1 cells. Note that number ratio of LGN-M2 and LGN-M1 c Contrast Processing Receptive Field Size 1 aximum spike rates for LGN-M2 and LGN-M1 cells used in this st s of center and surround radii are given in degrees of visual s ts of receptive field sizes and number densities (last row) of (a) rround/center sensitivity K is taken from the data set of Cro (b) c Set A 0.101 1.14 0.108 1.19 59% Set A 1.41 44.33 1.83 56.75 59% ter sensitivity K is independent of the specific cell populat R (Spear et al., 1994), are constant over all sets. s s R R c c M M R R G G ] and [spikes sec 1 M %contrast Center Radius Surround Radius Center Radius Surround Radius number ratio Contrast Gain Max. firing rate Contrast Gain Max. firing rate number ratio 1 and M1 M1 LGN-M2 LGN-M1 M2 LGN-M2 LGN-M1 M2 G et al. do notdensities report of them. LGN-M2 (b) and Four LGN-M1 sets cells of are contrast given gains in and the m last row Physiological Properties of M2 and M1 Subpopulations Table A.1: Four sets of physiological parameters of LGN-M2 a Note further, that the value ofremained the constant integrated for surround/cen all parameter sets. The integrated su population, corresponding sets in both tables are identical. (a) Four se rates are given in [spikes sec cells used in this study.and Mean standard deviations values for and the standard total deviation LGN-M population, A.2 Results for the Data Set of Spear et al. 183

Percentage of M1- vs. M2-inputs as a Function of Depth

0.4 4 weights (a) weights (a) 0.35 weights (b) 3.5 weights (b) 0.3 weights (c) 3 weights (c) weights (d) weights (d) 0.25 experiment 2.5 experiment 0.2 2 0.15 1.5 0.1 1

Receptive Field Size [degree] 0.05 0.5 Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure A.5: Parameter exploration of model II (two M pathways). The ﬁgure shows receptive ﬁeld

size (left) and contrast sensitivity (right) of layer 4C spiny stellate neurons as a function of depth

D D , . Symbols denote mean values of 20 cells selected at random from each sublayer. Each curve corresponds to a particular choice of model parameters; plots of the experimental data from Figure 3.7 are added for comparison. The simulation results illustrate the effect of changing degrees of convergence between M1- and M2-inputs. Each curve refers to the corresponding

thalamic weight distribution of Figure 6.10. LGN parameters were taken from Table 5.2 (P cells),

t t 1 Table A.1a and A.1b (M2+M1 cells; Set D). Threshold parameters were 0 and .

Effects of Receptive Field Size of M2 and M1 Neurons

0.4 4 Set A Set A 0.35 Set B 3.5 Set B 0.3 Set C 3 Set C Set D Set D 0.25 experiment 2.5 experiment 0.2 2 0.15 1.5 0.1 1 0.05 0.5 Receptive Field Size [degrees] Normalized Contrast Sensitivity 0 0 4C alpha 4C beta 4C alpha 4C beta

Figure A.6: Parameter exploration of model II (two M pathways). The figure shows receptive field size (left) and contrast sensitivity (right) of layer 4C spiny stellate neurons as a function of depth. Plots of simulated response properties illustrate the effect of different receptive field parameters of the LGN-M1 and LGN-M2 cells. The parameters for the different datasets A to D are listed in Table A.1a; contrast gains and maximum firing rates were identical for both LGN-M

populations and taken from Table 5.2. The thalamic weight distribution was taken from Figure

t t 1 6.10c. Threshold parameters were 0 and . For other conventions see Figure A.5. 184 The Feedforward Model

Effects of Contrast Sensitivity of M2 and M1 Neurons

Figure A.7: Parameter exploration of model II (two M pathways). The figure shows receptive field size (left) and contrast sensitivity (right) of layer 4C spiny stellate neurons as a function of depth. Simulated response properties show the effect of different receptive field parameters, contrast gains and maximum spike rates of the LGN-M1 and LGN-M2 cells. The parameters for

the different datasets A to D are listed in Tables A.1a and A.1b. The thalamic weight distribution

t t 1 was taken from Figure 6.10c. Threshold parameters were 0 and . For other conventions see Figure A.5. A.3 Statistical Signiﬁcance of Best Predictions 185

A.3 Statistical Signiﬁcance of Best Predictions

0.4 4 simulation (Croner/Kaplan) simulation (Croner/Kaplan) 0.35 experiment 3.5 experiment 0.3 3 0.25 2.5 0.2 2 0.15 1.5 0.1 1

Receptive Field Size [degree] 0.05 0.5 Normalized Contrast Sensitivity 0 0

(a) 4C alpha 4C beta 4C alpha 4C beta

N N N N

e s e Depth D s t Depth D t 1 20 6 -0.39 1 20 7 0.68 2 20 6 0.56 2 20 7 1.16 3 20 7 -0.72 3 20 9 0.50 (b) 4 20 9 0.75 4 20 9 1.49

5 20 9 1.01 5 20 14 3.28 6 20 8 2.88y 6 20 12 3.19

7 20 10 0.81 7 20 12 2.49y

8 20 (2) – 8 20 9 -2.34y

Figure A.8: (a) Best ﬁts for receptive ﬁeld size and normalized contrast sensitivity curves for

model I (one LGN-M populations) based on the Croner & Kaplan data set. The ﬁgures show mean

values and standard deviations of the simulated and experimental data at eight depths D=

of layer 4C; please note that there is no statistics for receptive field size at the top of layer 4C (D=8). (b) Results of the Student’s t-test for significantly different mean values. The test was applied to the simulated and experimental distributions of receptive field size (left) and normalized

contrast sensitivity (right) at eight different depths D of layer 4C. The tables give the number of

N N e samples in the simulated ( s ) and experimental ( ) distribution, together with the corresponding

Student’s t at each depth D . A signiﬁcantly different mean value for receptive ﬁeld size is found

in 4C (D=6). Signiﬁcantly different mean values for contrast sensitivity are found in layer 4C

p (D= ). Statistical signiﬁcance, two-tailed: p 0.03, 0.07.

In Section 6.1.5 and 6.2.5 I have presented the best predictions for model I (one LGN-M population) and model II (two LGN-M populations). Because there is considerable scatter in the experimental data reported by Blasdel & Fitzpatrick (1984) and Hawken & Parker (1984), the models attempt to ﬁt the mean values of eight equally sized intervals in depth of layer 4C (for details refer to Section 3.2.2). Both models take into account the realistic physiological variances of the LGN neurons which had been measured experimentally in the studies of Croner & Kaplan (1995) and Spear et al. (1994) respectively. On the other hand the models neglect many sources of anatomical variability within one cell population due to the lack of suitable experimental data. For example the models do not consider variability in the axonal and dendritic arbors of the individual cells in one cell population. Therefore standard deviations of the simulated data in model-layer 4C are expected 186 The Feedforward Model

0.4 4 simulation (Spear et al.) simulation (Spear et al.) 0.35 experiment 3.5 experiment 0.3 3 0.25 2.5 0.2 2 0.15 1.5 0.1 1

Receptive Field Size [degree] 0.05 0.5 Normalized Contrast Sensitivity 0 0

(a) 4C alpha 4C beta 4C alpha 4C beta

N N N N

e s e Depth D s t Depth D t 1 20 6 -0.22 1 20 7 1.48 2 20 6 1.10 2 20 7 1.69

3 20 7 -0.37 3 20 9 2.50y

(b) 4 20 9 0.05 4 20 9 3.87

5 20 9 -0.36 5 20 14 3.58 6 20 8 -0.81 6 20 12 0.98

7 20 10 -2.12y 7 20 12 -0.41

8 20 (2) – 8 20 9 -4.00

Figure A.9: (a) Best ﬁts for receptive ﬁeld size and contrast sensitivity curves for model I (one LGN-M populations) based on the Spear et al. data set. (b) Results of the Student’s t-test for

significantly different mean values. A significantly different mean value for receptive field size is

found in upper 4C (D=7). Signiﬁcantly different mean values for contrast sensitivity are in 4C

and mid-4C (D= ) and upper 4C (D=8). Statistical signiﬁcance, two-tailed: 0.01, p 0.08. For other conventions see Figure A.8.

to be smaller than the scatter that is observed experimentally at different depths of layer 4C. To test this hypothesis an F-test (Press et al., 1992; Siegel, 1956) was applied to the data shown in Figure A.8a, A.9a, A.10a, and A.11a. The F-test, which is designed to reject the hypothesis that two distributions have consistent variances, conﬁrmed that the distributions of simulated and experimental data at the same depth D of layer 4C have signiﬁcantly different variances. From the comparison of the simulated and experimental mean values I draw the conclusions that:

Model I which is based on one LGN-M population provides a reasonable good ﬁt for layer 4C and mid-4C but fails to predict the rapid change in the uppermost part of layer 4C (cf. Figure A.8a and A.9a).

Model II which assumes two anatomical and physiological distinct LGN-M (M2+M1) subpopulation makes good predictions for the entire depth of layer 4C even for the rapid in-

crease of contrast sensitivity at the top of layer 4C (cf. Figure A.10a and A.11a). To test the statistical significance of the conclusions I performed a Student’s t-test (Press et al., 1992; Siegel, 1956); at each depth D of layer 4C the null hypothesis is that the simulated and the experimental data have the same mean value. I chose a Student’s t-test that considers two distributions which have significantly different variances (Press et al., 1992; Siegel, 1956). A.3 Statistical Significance of Best Predictions 187

0.5 4 simulation (Croner/Kaplan) simulation (Croner/Kaplan) 0.45 3.5 experiment experiment 0.4 3 0.35 0.3 2.5 0.25 2 0.2 1.5 0.15 1 0.1

Receptive Field Size [degree] 0.5

0.05 Normalized Contrast Sensitivity 0 0

(a) 4C alpha 4C beta 4C alpha 4C beta

N N N N

e s e Depth D s t Depth D t 1 20 6 -0.66 1 20 7 0.60 2 20 6 0.19 2 20 7 1.04 3 20 7 -0.88 3 20 9 0.79 (b) 4 20 9 -0.81 4 20 9 0.33 5 20 9 -0.49 5 20 14 1.20 6 20 8 0.18 6 20 12 1.13 7 20 10 1.05 7 20 12 1.14 8 20 (2) – 8 20 9 -0.38

Figure A.10: (a) Best fits for receptive field size and contrast sensitivity curves for model II (two LGN-M populations) based on the Croner & Kaplan data set. (b) Results of the Student’s t- test for significantly different mean values. There are no significantly different mean values of simulated and experimental distributions neither for receptive field size nor for normalized contrast sensitivity data. For other conventions see Figure A.8.

It is important to mention the underlying assumptions of the t-test which are:

the observations are independent

the observations are from normally distributed populations. Since I draw the parameters of model LGN cells from independent normal distributions, the assumptions hold at least for the simulated data. However, the second assumption can not be verified for the experimental data due to the small sample of cells at each depth of the layer. The results for model I are shown in Figure A.8b and A.9b. For both data sets (Croner & Kaplan and Spear et al.) the statistical test reveals significant differences of receptive field size and

normalized contrast sensitivity in mid-4C and upper 4C. These results are consistent with the conclusion that the feedforward model based on a homogenous LGN-M population is not likely

to account for the experimentally observed rapid increase of basic response properties in layer 4C. The partially bad ﬁt of the simulated contrast sensitivity curve in 4C /mid-4C (Figure A.9b) results from the strong overlap of LGN-P and LGN-M contrast gain in the Spear et al. data set. Given the slightly different mean values of the LGN-P and LGN-M contrast gain it is impossible to generate large deviations from the mean contrast sensitivity of all cells in model-layer 4C which are comparable to the experimental data. Figure A.10b and A.11b depict the statistical signiﬁcance for the best predictions of model II. For both data sets, Croner & Kaplan and Spear et al., the statistical test fails to reveal any 188 The Feedforward Model

0.5 4 0.45 simulation (Spear et al.) simulation (Spear et al.) experiment 3.5 experiment 0.4 3 0.35 0.3 2.5 0.25 2 0.2 1.5 0.15 1 0.1

Receptive Field Size [degree] 0.5

0.05 Normalized Contrast Sensitivity 0 0

(a) 4C alpha 4C beta 4C alpha 4C beta

N N N N

e s e Depth D s t Depth D t 1 20 6 -0.42 1 20 7 -0.35 2 20 6 1.00 2 20 7 0.20 3 20 7 -0.94 3 20 9 -0.38 (b) 4 20 9 -0.56 4 20 9 -0.07 5 20 9 -1.34 5 20 14 -0.19 6 20 8 -0.81 6 20 12 -0.05 7 20 10 -1.43 7 20 12 0.24 8 20 (2) – 8 20 9 -1.30

Figure A.11: (a) Best fits for receptive field size and contrast sensitivity curves for model II (two LGN-M populations) based on the Spear et al. data set. (b) Results of a Student’s t-test for significantly different mean values. There are no significantly different mean values of the simulated and the experimental distributions. For other conventions see Figure A.8.

signiﬁcant difference in the simulated and experimental data. This result may lend support to the hypothesized M2 and M1 populations which are essential to model II; but note that it is general impossible to verify by statistical tests that two mean values are identical. In summary, the above considerations strengthen the conclusion that model I can not account

for the rapid increase of basic response properties at the top of layer 4C. Appendix B

The Intracortical Model

B.1 The Graphical User Interface of the Simulation Tool

The intracortical recurrent model which is described in Chapter 8 is implemented in standard C++. The simulation tool provides a graphical user interface which is implemented with the NST library (Neural Simulation Tool; Ritter, 1996). The model parameters are speciﬁed via several input windows. The simulation can be monitored online by different output windows which visualize the results. The main elements of the graphical user interface are brieﬂy described in the next sections.

B.1.1 Parameter Windows The model parameters are specified via different input windows which are shown in Figure B.1 and B.2. Each window contains a set of parameters which are semantically grouped together. For details see caption of the figures. In most cases the description in the input windows allows easy identification of the corresponding model parameters; all parameter settings given below are an example. 190 The Intracortical Model

(b)

(d)

Figure B.1: Parameter windows ’Topography’, ’LGN’, ’IVC’ and ’Control’. (a) Input window to specify areal magniﬁcation factors and cell densities. (b) Physiological properties of LGN cells and lateral spread of the geniculate axonal arbors. (c) Lateral spread of axonal and dendritic arbors of layer 4C cells. Two types of inhibitory cells are handled by the simulation tool; Type I

and II correspond to the clutch cell and the -6 cell respectively. The lower part of the window gives the total afferent, excitatory and inhibitory load of a excitatory and inhibitory cells in model layer 4C. (d) The ’Control’ window contains the stimulus speciﬁcation, the choice of the simulated experiments, and the speciﬁcation of the numerical method together with the corresponding parameters. B.1 The Graphical User Interface of the Simulation Tool 191

(a)

(b)

Figure B.2: Parameter windows ’Geniculocortical’ and ’MoreParameters’. (a) Thalamic weight

portions for eight discrete depths D of model layer 4C; please note that the depth index D is shifted by . (b) Parameters giving the proportion of recurrent inhibition from different cell types, the number of steps and proportion of lateral recurrent excitation from each step at eight different depths of layer 4C. Furthermore the lateral spread of the side-steps is speciﬁed. The lower part gives details about threshold and gain of the transfer functions and the simulation of steady state response versus blob radius curves and steady-state response versus contrast curves respectively. 192 The Intracortical Model

B.1.2 Online Visualization Several variables of the simulated experiment are monitored online: the connectivity, the input of different spatial origin and different cell types, the stimulus etc. To give an impression about the online visualization, some ’screen shoots’ of some output windows are presented in Figures B.3 to B.6. For details see captions of the ﬁgures.

Figure B.3: Time course of the membrane potential for a blob stimulus. The integration in time is done with the Euler method and a time step of 0.1. Left: Total input to a simulated cortical cell

in lower 4C (D=1) as a function of time. Right: Total input to a simulated cortical cell in upper

4C (D=8) as a function of time. B.1 The Graphical User Interface of the Simulation Tool 193

Lower 4C beta (D=1) Upper 4C alpha (D=8)

Figure B.4: Lateral connectivity and lateral input of a spiny stellate cell in lower 4C and upper

4C. Top: The windows corresponds to a particular sublayer of model layer 4C which contains cortical cells at random locations (small black and white dots). The large black dot marks a cortical cell located roughly in the center of each sublayer. The cortical cells which are laterally connected to this particular cell are shown in black. Bottom: If a stimulus is presented, the activity of all presynaptic cells which provide lateral input to the cortical cell can be monitored; please note that the plots are 2D projections of a 3-D activity proﬁle. The x-axis gives the location on a grid

of 1000 pixels which correspond to 4500m in real cortex; the y-axis shows the activity of the presynaptic neurons (inhibitory light grey, excitatory dark grey). 194 The Intracortical Model

Figure B.5: Luminance profile of different stimuli. Left: Luminance profile of a sinewave grating together with the activity profile of cells in the LGN-P layer. Right: Luminance profile of a blob stimulus together with the activity profile of cells in the LGN-P layer.

Figure B.6: Response properties of cortical cells. Left: Log-log plot of the steady state versus radius function of a typical cortical cell. The x-axis gives the radius of the blob stimulus and the y-axis shows the steady state response of the cortical cell under consideration. Right: Steady state versus contrast function of a typical cortical cell. The x-axis gives the contrast of the optimal blob stimulus and the y-axis shows the steady state response of a cortical cell. B.2 The Stochastic Update 195

B.2 The Stochastic Update

The measurement of basic response properties in the intracortical recurrent model is based on

ﬁnding the steady state of the “membrane potential” whose dynamics is given by

P P P P

u t D m u t D I u t D I u D

m (B.1)

l at af f dt

The most common methods to integrate systems of ordinary differential equation are Runge-Kutta methods of n-th order (Press et al., 1992). The Runge-Kutta integrators approximate the time course of the dynamics with bounded local approximation error. These methods are computationally expensive for large numbers of interconnected neurons. The response properties of the cortical cells as deﬁned in Section 8.2.5 only depend on the steady state. Therefore it is not necessary to consider the explicit time course of the dynamics. Instead, an implicit fast converging method was used to numerically solve the steady state equa-

tions:

u t D

m (B.2) dt

For the sake of clarity I introduce a new notation. The N excitatory and inhibitory neurons at

r f N g u

depth D are indexed by and are characterized by the position r and their type

u t D P fe ig m m r r

r r

r , so . The connection weights between neurons and which

are determined from the anatomical data are denoted by r r . Thus the system of equations (B.2)

corresponds to

I r N m g m w

r r

r r (B.3)

af f

r =1

g I

where r is the cell type speciﬁc transfer function and denotes the stationary afferent input af f

of neuron r. The stochastic update procedure as proposed in (Ontrup & Ritter, 1998) works by

m m

iteratively solving one equation (B.3) for one potential with all other r held constant.

g T r

This can be easily done for monotonous piecewise linear transfer functions r with threshold

a r

and gain r . Subsequently a new index is randomly selected and the update is performed again.

In algorithmic terms the update rule is given by

m t

1. Initialize membrane potentials with small random values r .

f N g 2. Choose r randomly.

3. Update

K m t T

r r

m t

r (B.4)

w a T K

r r r r

else

w a

r r r

t I m g w K

r r

where r r .

r =r af f

4. Go to step 2. until convergence 196 The Intracortical Model

Convergence was achieved if the average change in membrane potential over N updates was below

a threshold .

Strict convergence of the stochastic update procedure has been proved for the case of a sym-

metric connection matrix (Ontrup & Ritter, 1998), but r r is non-symmetric in my case (see Section 8.1.1). However, explicit simulations with a Runge-Kutta method revealed that the dynamics given by eq. (B.1) converges to a single ﬁxed point in the parameter regimes which are considered. This can be mainly understood by the normalization of the connection weights (cf. Section 8.2.5). In this case I observed that the stochastic update shows very rapid convergence to the appropriate ﬁxed point. B.3 Intracortical Model II: Summary of Results 197

B.3 Intracortical Model II: Summary of Results

To explore the parameter space of the the intracortical model II which is based on two M pathways, the following parameters have been tested in combination:

physiological properties of the in LGN-M2 an LGN-M1 populations (Sets A to D; cf. Ta- ble 7.2),

distributions of lateral excitatory weights (weights (i) to (iv); cf. Figure 9.1) physiological properties of the -6 cell (parameters (a) to (e); cf. Figure 9.4).

All possible parameter combinations are systematically arranged in the table of Figure B.7. Figures B.8 to B.11 show the corresponding simulation results. Each plot shows normalized

receptive ﬁeld size and contrast sensitivity of a layer 4C spiny stellate neuron as a function of depth

D together with the experimental data of Blasdel & Fitzpatrick (1984) and Hawken

& Parker (1984). Each simulated curve corresponds to a particular parameter choice as indicated T

in the Figure B.7. Threshold and gain of the spiny stellate cells and the clutch cell were e =0.1,

T a a t

e 1 cl utch cl utch =0.5, =1.0 and =2.5. The cortical threshold parameter was taken =2.0. 198 The Intracortical Model = 2.5, 6 distribution a (e) (d) = 0.5, 6 (c) T cular weight distribution M2 and LGN-M1 cells. espond to the re-analyzed weights (iv) = 3.0. The references below the table 6 =1.00 respectively. The physiological s (e) (a) (b) W a -6 transfer function. Each single plot shows the = 2.4, 6 (c) (d) =0.66, and weights (iii) parameters parameters T s α−6 W Figure B.10 (a)-(e) Figure B.11 (a)-(e) which is based on two LGN-M populations. I have tested all =0.33, s -6 transfer function which are given by (a) W = 2.8, and (e) 6 a =0.00, s M1 number ratio of 59:41, 72:28, 80:20 and 88:12 percent. The W (c) (e) (a) (b) = 2.0, 6 weights (ii) parameters er ratio and different physiological properties of the LGN- intracortical model II acies n. Please note that each ﬁgure summarizes results for a parti icular parameter set (a) to (e) of the Efficacy of stepped connections Physiological Properties of the neuron t constrained by the experimental data. Sets A,B,C and D corr T Figure B.9 (a)-(e) (a) (b) (d) =2.7, (d) 6 a (d) (e) (c) = 1.5, 6 weights (i) parameters (b) T Figure B.8 (a)-(e) (a) = 2.6, (c) 6 -6 cell correspond to different parameters (a) to (e) of the

Set A Set B Set C

Set D a LGN-M2 and LGN-M1 cells LGN-M1 and LGN-M2

= 1.0, Physiological Parameters of Parameters Physiological 6 T (i) to (iv) and each sub-figure (a) to (e) corresponds to a part indicate the figure where the corresponding results are show results for sets A to D which correspond to the different numb Figure B.7: Overview of the parameter explorations for the properties of the (b) possible combinations of different parameters which are no physiological properties of M2 andof M1 lateral which weights are (i) based to on (iv) a corresponds M2: to a synaptic effic B.3 Intracortical Model II: Summary of Results 199

3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D 2 experiment experiment 2.5

1.5 2

1 1.5 1 0.5 0.5 Normalized Receptive Field Size Normalized Contrast Sensitivity 0 0 (a) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D 2 experiment experiment 2.5

1.5 2 1.5 1 1 0.5 0.5 Normalized Receptive Field Size Normalized Contrast Sensitivity 0 0 (b) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D 2 experiment experiment 2.5 1.5 2 1.5 1 1 0.5 0.5 Normalized Contrast Sensitivity Normalized Receptive Field Size 0 0 (c) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D 2 experiment experiment 2.5

1.5 2 1.5 1 1 0.5

Normalized Contrast Sensitivity 0.5 Normalized Receptive Field Size 0 0 (d) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D 2 experiment experiment 2.5

1.5 2 1.5 1 1 0.5 Normalized Contrast Sensitivity 0.5 Normalized Receptive Field Size 0 0 (e) 4C alpha 4C beta 4C alpha 4C beta

Figure B.8: Parameter exploration of the intracortical model II (two M pathways). The distribution

of lateral excitatory weights corresponds to weights (i) i.e. no lateral input from the stepped

projections ( s =0.00). Threshold and gain of the -6 cell are systematically increased from (a)

to (e). All receptive ﬁeld size curves decrease in upper 4C. The contrast sensitivity values of

upper 4C increase from (a) to (e). The highest contrast sensitivity is seen for Set D in plot (e)

where the LGN-M1 cells have the highest contrast sensitivity and the -6 transfer function has

highest threshold and gain. The reduced contrast sensitivity values in lower 4C are an artefact of the normalization procedure. For other conventions see beginning of the section and caption of Figure B.7. 200 The Intracortical Model

3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D 2 experiment experiment 2.5

1.5 2

1 1.5 1 0.5 0.5 Normalized Contrast Sensitivity Normalized Receptive Field Size 0 0 (a) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D 2 experiment experiment 2.5

1.5 2 1.5 1 1 0.5 0.5 Normalized Contrast Sensitivity Normalized Receptive Field Size 0 0 (b) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D 2 experiment experiment 2.5

1.5 2

1 1.5 1 0.5 0.5 Normalized Contrast Sensitivity Normalized Receptive Field Size 0 0 (c) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D experiment experiment 2 2.5

1.5 2 1.5 1 1 0.5 0.5 Normalized Contrast Sensitivity Normalized Receptive Field Size 0 0 (d) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D 2 experiment experiment 2.5

1.5 2 1.5 1 1 0.5 0.5 Normalized Contrast Sensitivity Normalized Receptive Field Size 0 0 (e) 4C alpha 4C beta 4C alpha 4C beta

Figure B.9: Parameter exploration of the intracortical model II (two M pathways). The distribution

of lateral excitatory weights corresponds to weights (ii) i.e. weak lateral input from the stepped

projections ( s =0.33). Threshold and gain of the -6 cell were systematically increased from

parameter (a) to (e). In most cases receptive ﬁeld size curves decrease in upper 4C however

some curves in plots (a) to (c) show slightly increasing receptive ﬁeld size in upper 4C. This is

due to the lower gain of the -6 transfer function which combines with lateral recurrent and the

strong afferent input from the LGN-M1 population (Sets C,D) in this region. Contrast sensitivity in upper 4C increases from (a) to (e) because threshold and gain of the -6 transfer function are increased. For other conventions see beginning of the section and caption of Figure B.7. B.3 Intracortical Model II: Summary of Results 201

3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D 2 experiment experiment 2.5 1.5 2 1.5 1 1 0.5 0.5 Normalized Contrast Sensitivity Normalized Receptive Field Size 0 0 (a) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D experiment experiment 2 2.5

1.5 2 1.5 1 1 0.5 0.5 Normalized Contrast Sensitivity Normalized Receptive Field Size

0 0 (b) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D 2 experiment experiment 2.5

1.5 2 1.5 1 1 0.5 0.5 Normalized Contrast Sensitivity Normalized Receptive Field Size 0 0 (c) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D experiment 2 experiment 2.5

1.5 2 1.5 1 1 0.5 0.5 Normalized Contrast Sensitivity Normalized Receptive Field Size 0 0 (d) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D experiment 2 experiment 2.5 1.5 2

1 1.5 1 0.5

Normalized Receptive Field Size 0.5 Normalized Contrast Sensitivity

0 0 (e) 4C alpha 4C beta 4C alpha 4C beta

Figure B.10: Parameter exploration of the intracortical model II (two M pathway). The distribu-

tion of lateral excitatory weights corresponds to weights (iii) which means moderate lateral input

from the stepped projections ( s =0.66). All receptive ﬁeld size curves increase in upper 4C due

to the lateral input from the stepped connection. In plots (a) and (b) the contrast sensitivity is low at the top of 4C which is due to the low thresholds of the -6 transfer function. An almost perfect

fit of receptive field size and contrast sensitivity curves is adopted for Set C and plot (c), i.e. -6 parameters (c). However a few other parameter constellation in (b), (c) and (d) would also lead to a good fit. For other conventions see section introduction and caption of Figure B.7. 202 The Intracortical Model

3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D experiment experiment 2 2.5

1.5 2 1.5 1 1 0.5

Normalized Contrast Sensitivity 0.5 Normalized Receptive Field Size 0 0 (a) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D experiment experiment 2 2.5

1.5 2 1.5 1 1 0.5

Normalized Contrast Sensitivity 0.5 Normalized Receptive Field Size 0 0 (b) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D experiment experiment 2 2.5

1.5 2 1.5 1 1 0.5

Normalized Contrast Sensitivity 0.5 Normalized Receptive Field Size 0 0 (c) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D experiment experiment 2 2.5

1.5 2 1.5 1 1 0.5

Normalized Contrast Sensitivity 0.5 Normalized Receptive Field Size 0 0 (d) 4C alpha 4C beta 4C alpha 4C beta 3 4 Set A Set A Set B 3.5 Set B 2.5 Set C Set C Set D 3 Set D experiment experiment 2 2.5

1.5 2 1.5 1 1 0.5

Normalized Contrast Sensitivity 0.5 Normalized Receptive Field Size 0 0 (e) 4C alpha 4C beta 4C alpha 4C beta

Figure B.11: Parameter exploration of the intracortical model II (two M pathways). The distri-

bution of lateral excitatory weights corresponds to weights (iv) i.e. strong lateral input from the

stepped projections ( s =1.00). Threshold and gain of the -6 cell were systematically increased

from parameter (a) to (e). The receptive ﬁeld sizes in (c) to (e) are slightly decreased in upper 4C.

This results from strong inhibition by the -6 cell combined with strong afferent input from the LGN-M1 population. This effect is already evident in Figure B.10 (e). The reduced ﬁeld size in

lower 4C are an artefact of the normalization. For other conventions see beginning of the section introduction and caption of Figure B.7. Bibliography

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