Modeling of Subthreshold Voltage Responses, Synaptic Integration and Backpropagating Action Potentials in CA1 Pyramidal Neurons

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NORTHWESTERN UNIVERSITY

Modeling of subthreshold voltage responses, synaptic integration and backpropagating action potentials in CA1 pyramidal neurons

A DISSERTATION

SUBMITTED TO THE GRADUATE SCHOOL

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

for the degree

DOCTOR OF PHILOSOPHY

Field of Applied Mathematics

Rachel E. Trana

EVANSTON, ILLINOIS

August 2012 2

ABSTRACT

Modeling of subthreshold voltage responses, synaptic integration and backpropagating

action potentials in CA1 pyramidal neurons

Rachel E. Trana

Pyramidal neurons are composed of a cell body, or soma, extensively arborized dendrites and a single axon. The dendrites of pyramidal neurons are the primary locations for synaptic input, receiving tens of thousands of excitatory and thousands of inhibitory synaptic contacts from other neurons. They also have numerous voltage-gated conductances enabling them to integrate synaptic input in a complex, nonlinear fashion to ultimately regulate neuronal excitability and affect action potential firing. Dendrites typically branch profusely, becoming narrower as they extend further away from the soma and main apical trunk, making direct voltage recordings difficult. Computational modeling of neurons can be used in combination with experimental techniques to help investigate the properties of neuronal signaling. In this thesis, we use this combined approach to investigate two topics: (1) Distance-dependent conductance scaling in CA1 pyramidal neurons, and (2) the role of A-type potassium channels in shaping subthreshold voltage responses in CA1 pyramidal neurons. 4

As a result of the filtering properties of dendritic cables, EPSPs generated on distal dendrites can attenuate so severely that they are unable to produce a significant somatic voltage response. However, experimental and computational results indicate that CA1 pyramidal neurons possess a compensatory synaptic strengthening to counteract the resulting attenuation, i.e., synapses more distant along the somatodendritic axis tend to be stronger. We used computational models of biophysically realistic CA1 pyramidal neurons to determine the extent to which synapses on distal dendrites could increase their synaptic conductance to overcome attenuation. These models indicate that synapses on more distal dendrites are unable to sufficiently increase their conductance to produce a somatic voltage response. Consistent with these simulations, electron microscopy results show that while AMPA receptor number increases (synaptic strengthening) in regions more proximal to the soma, the most distal synapses in stratum lacunosum moleculare do not exhibit this increase.

In order to better understand the complex mechanisms by which neurons integrate synaptic input to generate action potentials, it is necessary to have compartmental models with voltage-gated conductances that reproduce experimental observations for action potential ﬁring as well as subthreshold events. Here we use somatic whole-cell recordings of CA1 pyramidal neurons to investigate the subthreshold properties of A-type potassium channels. Experimental results reveal a signiﬁcant increase in both input resistance and the time course of simulated somatic potentials when A-type potassium channels were blocked with 4-aminopyridine, a selective potassium channel blocker. Incorporating these results into a morphologically realistic CA1 neuron model not only yielded better 5

ﬁts to previous experimental results of CA1 subthreshold membrane properties, but also accurately reproduced action potential backpropagation. 6

Acknowledgements

The completion of a large research project is never the result of only one person’s eﬀorts. I am so pleased to have the opportunity to gratefully acknowledge the support and thoughtfulness of everyone who helped me traverse this path.

First and foremost, I owe sincere and earnest gratitude to my advisor Bill Kath, whose support, patience, insightful discussions and academic experience have not only been invaluable, but without which, it would not have been possible to write this doctoral thesis.

My co-advisor, Nelson Spruston, whose incredible ability to explain complex topics in the simplest manner possible was only exceeded by his brilliance as a neuroscientist.

My committee members, Dr. David Chopp and Dr. William Olmstead, who have taken the time to read this dissertation and have also provided direction and advice throughout my graduate career.

My fellow student colleagues and friends, Yael Katz, Vilas Menon, Shannon Moore and Joseph Hibdon, whose friendship and discussions made even the most diﬃcult times truly enjoyable.

Without Dan Nicholson, this thesis would be missing a chapter. I am truly grateful for your help and your wonderful sense of humor that made all of our meetings truly enjoyable. 7

I am eternally grateful to my parents Carol and Steve, my brother Ethan, and my uncle Sam - the eternal optimist. You have been a constant source of emotional and moral support and your continuous love and encouragement made this thesis possible.

To my wonderful and incredibly supportive husband Donald - thank you for always helping me to keep things in perspective. 8

Dedication

This thesis is dedicated to my father, Dr. Stephen Trana. You taught me that anything is possible. I will soar on wings like eagles, run and not grow weary, walk and not be faint. 9

Table of Contents

ABSTRACT 3

Acknowledgements 6

List of Tables 11

List of Figures 12

Chapter 1. Introduction 14

1.1. CA1 Pyramidal Neuron Morphology 16

1.2. Passive Electrical Properties 17

1.3. Inﬂuence of Dendrites: Nonisopotential Cells 20

1.4. Excitable Membranes: Ion Channels 29

1.5. Synaptic Integration 39

1.6. Work Presented 43

Chapter 2. Location-Dependent Variations in Synaptic Strength in Hippocampal

CA1 Pyramidal Neuron Models 46

2.1. Abstract 47

2.2. Introduction 48

2.3. Methods 51

2.4. Synaptic Scaling: Experimental Background 55 10

2.5. Results 61

Chapter 3. A-type potassium channels shape subthreshold voltage responses in

hippocampal CA1 pyramidal neurons 82

3.1. Abstract 83

3.2. Introduction 83

3.3. Materials and Methods 85

3.4. Results 97

3.5. Discussion 114

Chapter 4. Conclusion 127

4.1. Integration of information in dendritic trees 128

4.2. Synaptic normalization in neuronal dendrites 128

4.3. Better models of voltage-gated ion channels 129

4.4. Future directions 131

References 133 11

List of Tables

3.1 RN in control ACSF and 4-AP 99

3.2 Passive and active channel parameter values. 105

3.3 Na+ conductance distribution values for neuron models 110 12

List of Figures

1.1 Hippocampal circuitry and pyramidal neuron morphology 18

1.2 Dendritic spine structure 19

1.3 Neuron segment used for the cable equation derivation 23

1.4 Equivalent electric circuit for multicompartmental model 27

1.5 Schematic diagram of the structure of an ion channel 30

2.1 Method of False-Position 53

2.2 Synapse ratio increases with distance from the soma 57

2.3 AMPAR Expression in Perforated and Nonperforated Synapses 59

2.4 NMDAR Expression in Perforated and Nonperforated Synapses 62

2.5 Simulated Somatic EPSPs 65

2.6 Modeling of the Synaptic Conductance Required for Normalization 69

2.7 Simulation of somatic EPSPs in a second neuron model 71

2.8 Modeling of synaptic conductances in a second neuron model 72

2.9 Modeling of synaptic conductances with active properties in a third

neuron model 75

2.10 Modeling of synaptic conductances with active properties in a fourth

neuron model 77 13

3.1 RN changes in control ACSF and 4-AP 100

3.2 Somatic iEPSP area and amplitude in control ACSF and 4-AP 102

3.3 Best ﬁts to estimated passive properties and gh distribution 106

3.4 K(A) channels are primarily responsible for lower Reﬀ in distal locations108

3.5 Simulations of weak vs. strong backpropagation 111

3.6 Spike initiation in a CA1 pyramidal cell model 113

3.7 Model validation: Subthreshold current injections 115

3.8 Steady-state attenuation and MSE in ﬁts to voltage transients 118

3.9 K(D) channels increase interspike intervals 125 14

CHAPTER 1

Introduction 15

Since as early as 4000 B.C., when an anonymous Sumerian writer described the eu- phoric mind-altering eﬀects of ingesting the poppy plant, the human brain has capti- vated physicians, scientists, philosophers and the general public alike. Neuroscience, the study of the nervous system, advances understanding of brain development and function through critical research about molecules, neurons and the processes in and between cells.

However, even without considering the intricate interactions of large numbers of neurons distributed throughout diﬀerent regions of the brain, the study of a single neuron is ex- traordinarily complex. To investigate these systems and individual neurons eﬀectively, computational methods are used in close collaboration with experimental research that provides data to constrain these neural models, thus allowing for more accurate predic- tions.

This thesis concentrates on the integrative properties and the underlying voltage- gated ion channel mechanisms of individual hippocampal pyramidal neurons. A previous experimentally constrained model of a CA1 pyramidal neuron was used to investigate the extent to which an elaborately branched neuron can compensate for dendritic filtering when processing synaptic inputs to influence action potential generation in the axon. In a second project, experimental whole-cell recordings from hippocampal CA1 pyramidal neurons are used to investigate the effect of A-type potassium and D-type potassium channels on subthreshold voltage responses. These results are then incorporated into the previously passive CA1 pyramidal cell model along with voltage-gated ion channel models to create an active neuron model that accurately reproduces experimental results on voltage attenuation and action potential backpropagation. 16

1.1. CA1 Pyramidal Neuron Morphology

First characterized by Santiago Ramóny Cajal, pyramidal neurons are one the most widely studied neurons in the brain and can be found in different regions of the brain including the cerebral cortex, the amygdala and the hippocampus. In the CA1 region of the hippocampus (Figure 1.1A,B), pyramidal neurons receive external excitatory input from the entorhinal cortex via the perforant path. In addition, input from the entorhinal cortex enters the dentate gyrus and is relayed to cells in the CA3 region, which in turn project to neurons in the CA1 region via the Schaffer collateral pathway (Amaral and

Witter, 1989; Andersen et al., 1971). Within the hippocampus, CA1 neurons transmit information via axons that project to neurons in the subiculum, an area that acts as an output of the hippocampus (Amaral et al., 1991; Ram´ony Cajal, 1995).

Pyramidal neurons are a main class of excitatory cells in the brain. CA1 pyramidal neurons are easily distinguished by their triangularly shaped cell body, a long thick apical dendrite, elaborate apical and basal dendritic arborizations, dendritic spines and a single axon that branches extensively (Bannister and Larkman, 1995; Ram´ony Cajal, 1995)

(Figure 1.1B). A single CA1 pyramidal neuron receives many excitatory (∼30,000) and inhibitory inputs (∼1700) to its dendrites (Meg´ıaset al., 2001). While the majority of inhibitory inputs target dendritic shafts, excitatory inputs primarily terminate on dendritic spines. These dendritic spines are small extensions that protrude from the membranes of dendrites and play a primary role in synaptic transmission and information storage. Typ- ically characterized by their mushroom-like structure that consists of a bulbous head and narrow neck that connects the spine to a dendritic shaft (Figure 1.2), dendritic spines vary in size and can exhibit dynamic changes during synaptic plasticity (Harris and Stevens, 17

1989; Hering and Sheng, 2001; Matsuzaki et al., 2004). The combination of an intricate branched morphology and a large number of excitatory and inhibitory inputs located on both dendritic shafts and spines provides a complex framework for synaptic integration in CA1 pyramidal neurons.

1.2. Passive Electrical Properties

The electrical properties of a neuron are represented in terms of an equivalent electrical circuit consisting of a capacitor to model the charge storage capacity of the cell membrane, resistors that are used to model diﬀerent ion channels and a battery that represents the stored potential resulting from diﬀering intracellular and extracellular ion concentrations.

In its simplest form, a neuron’s membrane behaves as a capacitor. It has a phospholipid bilayer that acts as an insulator and separates the ionic charges (conductive solutions) on each side of the membrane. Applying a voltage step across the cell membrane induces a brief current that is proportional to the capacitance and the change of voltage with respect to time. A given area of membrane has a ﬁxed capacitance, called the speciﬁc

2 membrane capacitance (Cm), that is approximately the same for all neurons (1.0 µF/cm ).

Experimental and computational estimates of speciﬁc membrane capacitance in CA1 neurons (Golding et al., 2001) are often close to this experimentally validated standard value

(Gentet et al., 2000; Major et al., 1994). The total membrane capacitance of a neuron, cm, is proportional to the membrane surface area with the speciﬁc membrane capacitance as the proportionality constant, cm = CmA. Therefore, the greater the membrane area, the greater the capacitance. 18

Figure 1.1. Hippocampal circuitry and pyramidal neuron morphology. A. Figure courtesy of Staff et al. (2000). The major signal pathways in the hippocampal region. External input enters from the Entorhinal Cor- tex (EC) via the perforant path (purple) and terminate in the dentate gyrus (DG) and CA3 regions. CA3 pyramidal neurons send connections to the CA1 regions via their axons through the Schaffer collaterals (green). Granule cells in the DG send their axons (mossy fibers) to CA3 pyramidal neurons (blue). B. Figure courtesy of Yael Katz. CA1 pyramidal neuron morphology indicating the location of inputs from the various hippocampal signaling pathways. 19

Figure 1.2. Dendritic spine structure. Spine-studded CA1 pyramidal neuron dendrites in a (figure courtesy of Woolley et al., 1996) and b (figure courtesy of Matus, 2000). A three- dimensional reconstruction of a CA1 dendrite with spines (c, figure courtesy of Yankova et al., 2001), perforated and nonperforated postsynaptic densities (d, figure courtesy of Nicholson et al., 2006; Geinisman, 2000) and two-photon glutamate uncaging along a dendritic segment (e, figure courtesy of Matsuzaki et al., 2001). 20

Membrane resistance, which is reciprocally related to membrane conductance, refers to how far the insulating properties of the membrane deviate from ideal, perfect insulation and is determined by the density of open ion channels at resting potentials. Like membrane capacitance, membrane conductance is proportional to membrane surface area. Thus, the total membrane resistance is inversely related to its speciﬁc membrane resistance, rm =

Rm/A. Experimental estimates of the distribution and values of membrane resistance in

CA1 pyramidal neurons have been complicated by the technical restrictions of recording from distal dendrites. However, recent advances in experimental techniques combined with computational studies have suggested that the membrane resistivity of CA1 cells is nonuniform, with a strong decrease from soma to distal apical dendrite (Golding et al.,

2005; Omori et al., 2006, 2009).

1.3. Inﬂuence of Dendrites: Nonisopotential Cells

The main equation that governs changes in neuronal membrane dynamics is the cable equation. Originally applied to calculations for the ﬁrst transatlantic telegraph cable by Lord Kelvin, the cable equation was eventually used in combination with experimental data to obtain insights on the ionic properties of the squid giant axon (Davis and

Lorente de N´o,1947; Hodgkin and Huxley, 1952). In the 1950s, the advent of the glass micro-electrode enabled researchers to gather experimental data from the cat motoneuron. Initial estimates of membrane resistivity and intput resistance were about 10 times too small due to neglecting dendritic cable properties and the size of the dendritic tree

(Coombs et al., 1955). Wilfrid Rall corrected these estimates by extending cable theory to describe the ﬂow of current in neurons with an extensive dendritic tree (Rall, 1959, 21

1962). Rall’s calculations indicated that the electrotonic length of motoneuron dendrites was only between one and two length constants. As a result, distal synapses could alter somatic membrane potentials. The application of cable theory to neuron models with extensive branching helped elucidate how electrical signals from multiple synapses at different locations are combined in a dendritic architecture that is composed of many diﬀerent diameters and varying electrophysiological properties. Using cable theory, neurophysiolo- gists were able to determine that distal synaptic potentials in CA1 neurons undergo severe attenuation as they propagate to the soma due to both axial and membrane resistance

(Golding et al., 2005; Magee and Cook, 2000; Rall, 1967).

1.3.1. The Cable Equation

For decades, neuroscientists and other researchers have been working to understand and describe how networks of neurons process, store, integrate and relay information.

One approach to tackling the complexity of neuronal function and structure is to use combined mathematical and computational techniques to create detailed descriptions of functional and biologically realistic neurons (and neural systems) and their physiology and dynamics. These computational models are used in conjunction with experimental studies to generate hypotheses that can then be tested and/or veriﬁed by additional experimentation to yield further insight.

1.3.1.1. Passive cable theory. At the root of compartmental modeling lies the cable equation, which describes the variation in membrane potential along a neuronal cable as a function of a spatial coordinate and time. To derive the cable equation, consider a small dendritic segment (Figure 1.3A) with uniform passive membrane properties and 22 longitudinal current ﬂowing in one spatial direction (Jack et al., 1983; Rall, 1959; Segev,

1992). According to Ohm’s Law, a longitudinal current (iL) passing through the cable segment at the location x = 0 causes a voltage drop through the resistor, such that

∆V = V(x + ∆x) − V(x) (1.1)

∆V = −iLrL (1.2)

where V is the voltage, x is the location along the dendritic segment, rL is the longitudinal intracellular resistance and current flowing in the direction of increasing x are defined as positive. If the radius (a) of the dendritic segment is known, the intracellular resistivity can be expressed in terms of specific intracellular resistivity (RL).

R r = L (1.3) L πa2 R ∆V = − L i ∆x (1.4) πa2 L

Letting ∆x → 0, the longitudinal current can be written as

πa2 ∂V iL = − . (1.5) RL ∂x

In order to derive the cable equation, Kirchoﬀ’s current law is then used to sum all of the currents ﬂowing into and out of the the small dendritic segment (Figure 1.3B). These currents, which are comprised of the longitudinal, membrane and electrode currents, are set equal to the current that is needed to charge the membrane: 23

Figure 1.3. Neuron segment used for the cable equation derivation. A. A neuron segment with length ∆x and radius a. Current is defined as positive when flowing in the direction of increasing x. B. Currents flowing into and out of the neuron segment that alter the rate of change of the membrane potential. Figure courtesy of William Kath. 24

ic = iL − iL + ie − im (1.6) left right 2 2 ∂V πa ∂V πa ∂V 2πa∆xCm = − + + 2πa∆xie − 2πa∆xim (1.7) ∂x RL ∂x left RL ∂x right

where im is the membrane current and ie is the electrode current. Letting ∆x → 0, a form of the cable equation can be obtained.

∂V 1 ∂ 2 ∂V Cm = a + ie − im (1.8) ∂t 2aRL ∂x ∂x Assuming that the cable segment has constant radius and that there is no additional current from an electrode (ie = 0), the above equation can be multiplied through by the speciﬁc membrane resistance (Rm) to be written in the common form,

∂V ∂2V τ = λ2 − i r (1.9) ∂t ∂x2 m m where τ is the membrane time constant (RmCm) and λ is the electrotonic length with p units of length (λ = aRm/2RL).

The product of the membrane capacitance and resistance is the membrane time constant, τ. This quantity is independent of membrane area and as a result, can be calculated using the speciﬁc membrane capacitance and resistance (τ = RmCm) or total membrane capacitance and resistance (τ = rmcm). The membrane time constant is the basic fun- damental time scale. In an isopotential cell, it describes the amount of time it takes for a cell to reach 63% of its steady state response following a voltage change. The passive 25 time constant can be used to characterize the time scale of a cell’s membrane response to input.

In addition to membrane capacitance, signal propagation is also aﬀected by the membrane resistance and axial or longitudinal resistivity of a neuron. Axial resistivity (RL), which is proportional to cytoplasmic resistance, also contributes to the speed and distance an impulse can travel along a neural cable. The electrotonic length constant, λ, which describes the rate, with respect to distance, at which an electrical signal degrades along a dendrite or axon, is dependent on both membrane and axial resistance, such that p λ = aRm/2RL. Hence, λ increases with Rm (lower signal degradation) and decreases with RL (higher signal degradation).

In order to apply this equation to dendritic trees, the biophysical properties of dendrites were idealized such that dendrites could be collapsed into an equivalent single cylinder (Rall, 1962), allowing for an analytical solution to a transient current input. While the equivalent cylinder model cannot capture all physiological responses of a dendritic arborization, it nevertheless led to a broader understanding of the behavior of passive cables. Signiﬁcantly, it helped to clarify how voltage is attenuated along a neural cable due to distance traveled from the stimulus origin, intrinsic membrane properties such as diameter, Rm and RL, as well as signal frequency and stimulus location relative to branching points and cable terminals.

1.3.1.2. Nonlinear cable theory. Since the idealized concept that dendritic branches were only passive cylindrical structures was unrealistic, Rall developed a multicompartmental neuron model to account for nonlinearities due to synaptic currents and voltage- dependent membrane properties. When active channels present at resting potentials are 26 engaged, the superposition of passive and active properties can alter the integration of inputs nonlinearly, thereby triggering dendritic spikes. Mathematically, the compartmental modeling approach uses a finite-difference approximation to the nonlinear cable equation, replacing the previous continuous cable representation of a neuron by electrically short, isopotential and spatially uniform compartmental segments (Figure 1.4). Adjacent compartments are connected via a longitudinal resistivity as described by the dendritic architecture. As a result, differences in membrane properties and structure (diameter, resistivity, synaptic inputs) and hence, membrane potential, occur between compartments as opposed to within them (Holmes et al., 1992; Koch and Segev, 1998; Perkel et al., 1981;

Rall, 1964).

Thus, the nonlinear cable equation can be written as a system of coupled, ﬁrst-order diﬀerential equations (V˙ = AV~ + ~b) such that, for the jth compartment,

dVj Vj−1 − Vj Vj − Vj+1 cj + Iionj (vj , t) + Istimj (vj , t) = − (1.10) dt rj−1 , j rj , j+1

where Vj is the voltage, Iionj and Istimj are the ionic, capacitative and external current

th sources, rj−1 , j is the axial resistance between the j -1 and the j compartments. Nonlinear

voltage-gated conductances, Iionj , will be described later in this text. 1.3.1.3. Numerical Methods. If the coeﬃcient matrix A of the above system is constant, i.e. corresponding to passive properties that are not voltage-dependent, the system can be transformed into a linear set of equations (the linear cable equation) and can be solved analytically through the inversion of matrix A or with a stable and accurate numerical integration scheme. However, when voltage-dependent conductances or synaptic conductances that produce nonlinearities are introduced into the system, the coeﬃcients 27

j - 1 j j + 1

Vj-1 Vj Vj+1

rj-1 rj-1 rj rj rj+1 rj+1 2 2 2 2 2 2

i j-1, j i j, j +1 I ion j r c m j m j

i m j

Figure 1.4. Equivalent circuit for multicompartmental model with three cylindrical segments. Figure courtesy of Koch and Segev, 1998. 28 are no longer constant and numerical integration methods must be used to determine a solution.

The NEURON simulation environment, used for all simulations described in this dissertation, oﬀers several diﬀerent integration methods. The default integration method is

Backward Euler (Hines and Carnevale, 1997), a low-accuracy implicit numerical method that can be used to solve stiﬀ equations. All simulations described in this dissertation use

NEURON’s adaptive CVode integrator (Cohen and Hindmarsh, 1996). The CVode integrator class is an interface that is implemented on top of the CVODES and IDA solvers that are part of the SUNDIALS (SUite of Nonlinear and DIﬀerential/ALgebraic equation

Solvers) differential and algebraic equation solvers suite. Both the CVODES and IDA integration methods can be used to solve stiff and nonstiff ordinary differential equation

(ODE) systems.

The CVODES suite includes a forward-sensitivity analysis (FSA) method and an adjoint sensitivity analysis (ASA) method, in addition to the variable order, variable step

Adams-Moulton method (for nonstiff problems) and Backward Differentiation method (for stiff problems) that comprise the regular CVODE suite (Serban and Hindmarsh, 2005).

Both sensitivity analysis methods help to determine the correlation between changes in model parameters and the corresponding changes in model output in order to aid in model optimization or parameter estimation.

Similar to CVODES, there is also an IDAS solver suite that includes all of the func- tionality of the IDA suite, as well as sensitivity analysis. However, NEURON uses only the IDA diﬀerential-algebraic equation solver suite designed for equations of the form

F (t, y, y0) = 0. IDA uses a variable order, variable-coefficient Backward Differentiation 29 integration method and achieves a solution of the nonlinear system through either a Mod- ified or Inexact Newton iteration (Hindmarsh, 2000).

1.4. Excitable Membranes: Ion Channels

The distributions and types of ion channels present in a neuron are important for determining its firing properties and electrophysiological behavior. Ion channels are complexes of transmembrane proteins (Figure 1.5) that selectively facilitate the passage of ions into and out of a cell down their electrochemical gradient (Hille, 2001). These channels can be classified according to the gating mechanism that allows or prevents ion movement across the membrane, as well as their specific ion permeability. There are two primary types of gating mechanisms: voltage-gated and ligand-gated. Voltage-gated ion channels are activated by changes in membrane potentials, resulting in a conformational change of the pore structure to an open or closed state. Ligand-gated channels rely on the binding of specific ligand molecules to extracellular sites, causing a change in the structure of the channel protein.

Axons and dendrites of pyramidal neurons have a diverse distribution of Na+,K+ and Ca2+ channels which enable a cell to sum transmembrane potentials linearly or nonlinearly to generate action potentials or other regenerative events (Magee and Carruth,

1999). In addition, dendritic ion channels may have diﬀerent activation and inactivation properties from their somatic counterparts as well as varying density distributions based on their location (Magee, 1998; Menon et al., 2009; Migliore et al., 1999; Yuan and Chen,

2006). In combination with neuron morphology, the distribution and properties of ion channels modulate dendritic excitability and the ability of a cell to integrate synaptic 30

Figure 1.5. Schematic diagram of the structure of an ion channel. The ion channel protein structure typically involves a circular arrangement of identical or homologous membrane-spanning proteins closely arranged around a pore through the plane of the membrane or lipid bilayer. Figure courtesy of Bear et al., 2001. 31 input. While this dissertation is largely concerned with synaptic scaling and A-type potassium channels and their eﬀect on subthreshold voltage responses, I have also included detailed descriptions of the other ion channels used in my computational models.

1.4.1. Sodium Channels

First recorded and characterized by Hodgkin and Huxley, voltage-gated sodium currents play an important role in the initiation and propagation of action potentials in

CA1 pyramidal neurons. The core of the voltage-gated sodium channel is composed of a large α subunit, consisting of four homologous domains that each contain six membrane- spanning proteins. The α subunit is responsible for channel opening, ion selectivity and rapid inactivation. In addition, sodium channels contain one or more smaller β subunits that modify the kinetics and voltage-dependence of the channel (Catterall, 2000; Yu and

Catterall, 2003). Suﬃcient depolarization of the cell membrane activates Na+ channels, allowing an inﬂux of Na+ ions to permeate the membrane, further depolarizing the cell and initiating the rising phase of an action potential.

1.4.1.1. Axonal Sodium Channels. Studies using local application of tetrodotoxin

(TTX) to the axon initial segment (AIS) have localized the site of action potential initiation to a region proximal to the ﬁrst node of Ranvier (Colbert and Johnston, 1996; Colbert and Pan, 2002; Stuart et al., 1997). Electrophysiological and computational results suggest that both a high density of Na+ channels (Kole et al., 2008) and a hyperpolarized shift in the activation properties, relative to the soma, of Na+ channels contribute to the low spike threshold in the AIS (Hu et al., 2009; Mainen et al., 1995; Royeck et al.,

+ 2008). Three Na channel isoforms, Nav1.1, Nav1.2 and Nav1.6, have been detected at 32

the AIS. Of these, the Nav1.6 subunits exhibit a unique hyperpolarized voltage of activation relative to the other Na+ channels and are targeted at the distal end of the AIS, whereas Nav1.2 channels accumulate preferentially at the proximal end of the AIS. The distributions of these two Na+ subunits are consistent with studies that indicate that the distal end of the AIS is the site of action potential initiation (Colbert and Johnston, 1996;

Colbert and Pan, 2002; Stuart et al., 1997).

1.4.1.2. Dendritic Sodium Channels. From the spike initiation zone at the AIS, action potentials propagate along the axon and also backpropagate into the dendrites. The integration and propagation of signals in the distal dendrites of hippocampal CA1 neurons is strongly mediated by the distribution, density and voltage-dependent properties of

Na+ channels in the dendrites. The voltage-dependent properties and gating kinetics of

Na+ channels were ﬁrst characterized by Hodgkin and Huxley (1952) through a series of voltage-clamp experiments. These experiments showed that Na+ channels were activated at depolarized voltage potentials and then inactivate quickly with continued depolarization, facilitating repolarization to the resting potential. In addition to this relatively fast form of inactivation, Na+ channels have also undergo a much slower form of inactivation, resulting in a gradual decrease of spike amplitude during repetitive ﬁring (Colbert et al.,

1997; Jung et al., 1997; Martina and Jonas, 1997; Rudy, 1981).

Similar to sodium channels in the AIS and nodes of Ranvier, somatic and dendritic sodium channels also express the Nav1.2 and Nav1.6 subunits. In dendrites, these isoforms underlie dendritic Na+ spikes and nonlinear synaptic integration (Colling and Wheal,

1994; Magee and Johnston, 1995; Golding and Spruston, 1998; Lorincz and Nusser, 2010). 33

Studies using immunogold localization of Nav subunits in the somatodendritic compartments of cortical pyramidal cells have revealed a gradual decrease in the density of fast- activating Nav1.6 channels along the primary apical dendrite (Lorincz and Nusser, 2010).

Furthermore, cell-attached recordings from the soma and dendrites of CA1 pyramidal neurons have found that the amount of slow-inactivation of Na+ channels gradually increases as a function of distance from the soma (Mickus et al., 1999). As slow-inactivation is strongly dependent on ﬁring frequency and history as well as the amplitude of depolarization (Colbert et al., 1997; Jung et al., 1997; Martina and Jonas, 1997; Mickus et al.,

1999), these ﬁndings have important implications as to the role of Na+ channels (both fast-activating and slowly-inactivating) in distal dendrites in mediating not only dendritic excitability and synaptic plasticity, but also neuronal output within the hippocampal circuit.

1.4.2. Hyperpolarization-activated Cation Channel

Hyperpolarization-activated cation currents, Ih, are inwardly-rectifying voltage-gated ion channels equally permeable to both Na+ and K+ ions. Originally found and characterized in sino-atrial node myocytes, Ih channels were referred to as ‘pacemaker’ channels for their role in contributing to slow pacemaker depolarization and spontaneous activity

(DiFrancesco, 1986, 1993; Noma et al., 1983; Yanagihara and Irisawa, 1980). Following their discovery in cardiac cells, Ih channels were also described in a wide number of other neuronal cell types such as thalamic, hippocampal and cochlear nucleus neurons, where they inﬂuence resting membrane properties (Bal and Oertel, 2000; Halliwell and Adams,

1982; Maccaferri et al., 1993; Pape and McCormick, 1989; Pape, 1996). 34

Four mammalian HCN (hyperpolarization-activated cyclic nucleotide-sensitive) genes provide the molecular basis for Ih channels (Biel et al., 1999; Ludwig et al., 1998; Robinson and Siegelbaum, 2003; Santoro et al., 2000). While all four of the HCN isoforms (termed

HCN1-4) give rise to hyperpolarization-activated cation currents that are modulated by cyclic adenosine monophosphate (cAMP or cyclic AMP), each of the HCN isoforms un- derly Ih channels with distinctly diﬀerent voltage dependencies, activation kinetics, and sensitivity to cAMP (Ludwig et al., 1999; Moosmang et al., 2001; Santoro et al., 1997;

Santoro and Tibbs, 1999; Santoro et al., 2000). In the hippocampus, HCN1 and HCN2 are expressed in both CA1 and CA3 neurons, with a stronger expression of HCN1 in

CA1 pyramidal neurons than in CA3 and a stronger expression of HCN2 in CA3 neurons than in CA1. The HCN4 isoform is only weakly expressed in the hippocampus and is prevalent in neurons of the thalamus, olfactory bulb and speciﬁc populations within the basal ganglia. Of all the HCN genes, the HCN3 isoform is the most weakly expressed and can be found in the thalamus and olfactory bulb.

HCN1, which is found predominantly in CA1 pyramidal neurons and distributed with an over sixfold increasing gradient from soma to distal dendrite (Lorincz et al., 2002;

Magee, 1998), produces Ih channels that have the fastest activation kinetics. Ih channels exhibit a reversal potential near -30 mV as a result of the permeability ratio of Na+ to

+ + K . Hyperpolarizations activate the Ih current, causing a net inward current due to Na ions, thus depolarizing the membrane back to the resting potential and resulting in a membrane sag. Ih channels are active at resting potentials, thus causing the membrane to be leakier and decreasing both the eﬀective membrane time constant and input resistance of a neuron. This results in a shorter electrotonic length due to having Ih channels active 35 at rest and speeds up the decay of EPSPs, eﬀectively increasing amplitude attenuation as they propagate from soma to distal dendrite (Berger et al., 2001; Fernandez et al.,

2002; Golding et al., 2005; Stuart and Spruston, 1998). However, because of the voltage- dependent deactivation of Ih channels during depolarizations, a net outward current is generated. The amplitude of this outward current increases with distance from the soma as a result of the increasing gradient of Ih channels, thus creating a spatial normalization for the temporal summation of EPSPs at the soma (Magee and Carruth, 1999; Williams and Stuart, 2000).

1.4.3. Potassium Channels

Compared to Na+ channels, K+ channels activate more slowly in response to depolarization. However, as they have a negative reversal potential, these channels serve to reduce the overall excitability of a cell, aid in the repolarization phase of the action potential, set the membrane resting potential and mediate high-frequency ﬁring (Hille, 2001).

There are four main groups of K+ channels: voltage-gated, leak, inward-rectifying and calcium-activated. For the purposes of this dissertation, I will restrict my discussion to voltage-activated K+ channels. Voltage-gated K+ channels are homotetrameric, with four subunits arranged symmetrically to create an ion permeation pathway which contains the

ﬁlter for ion selectivity (Bezanilla and Armstrong, 1972; Choe, 2002; Gulbis et al., 1999;

Doyle et al., 1998; MacKinnon, 1991). Between these subunits stretches two transmembrane helices and a loop composed of a short amino acid segment. The two helices and the short loop are a key feature of the K+ channel family, but vary between the four K+ channel groups (Lu et al., 2001). Based on the amino terminal domain sequence of the 36 tetramer transmembrane core, the voltage-gated K+ channels can be further grouped into four subfamilies: Shaker (Kv1), Shab (Kv2), Shaw (Kv3) and Shal (Kv4). CA1 pyramidal neurons exhibit four main K+ currents, of which three derive from the four K+ channel subfamilies: a delayed-rectiﬁer K+ (Kv2), A-type K+ current (Kv4), D-type K+ current

(Kv1) and M-type K+ (KCNQ subfamily) (Chen and Johnston, 2004; Choe, 2002; Con- forti and Millhorn, 1997; Murakoshi and Trimmer, 1999; Selyanko and Sim, 1998; Sheng et al., 1992; Storm, 1990; Yuan and Chen, 2006).

1.4.3.1. Delayed-rectifier potassium channel. While the Kv1, Kv2 and Kv3 subfamilies all give rise to various delayed rectifier potassium currents, the Shaw Kv3 subfamily in CA1 hippocampal pyramidal neurons produces delayed rectifier potassium channels with currents that activate relatively fast at voltages more positive than -10 mV, have no inactivation and which deactivate very fast (Lai and Jan, 2006; Martina et al., 1998; Rudy and McBain, 2001). These channels are activated quickly during repolarization of the action potential and then quickly deactivate to allow further action potential generation.

This fast-activating delayed rectiﬁer current also contributes to sustained high-frequency

ﬁring.

1.4.3.2. A-type potassium channel. First characterized by Connor and Stevens in gastropod neural somata (Connor and Stevens, 1971), the A-type potassium channel has the most rapid inactivation kinetics out of all the potassium currents, as well as rapid activation kinetics over hyperpolarized voltage ranges (Chen and Johnston, 2004; Coetzee et al., 1999). The molecular correlates of the A-type potassium channels are Kv1.4 and

Kv4.1-3, members of the Kv4 (Shal) and Kv1 (Shaker) subfamilies. Immunohistochemi- cal studies show that Kv1.4 proteins are primarily found in the axons of CA1 pyramidal 37 neurons (Gu et al., 2003), whereas Kv4.2 proteins are highly expressed in hippocampal

CA1 dendrites and the somatodendritic region (Serodio et al., 1996; Sheng et al., 1992;

Varga et al., 2000). Furthermore, the Kv4.1 transcript is not highly expressed in the hippocampus and hippocampal Kv4.3 proteins have been shown to be primarily located in interneurons (Lien et al., 2002; Rhodes et al., 2004; Serodio and Rudy, 1998), suggesting that in hippocampal CA1 pyramidal neurons, the A-type potassium current (IA) is primarily mediated by the Kv4.2 subunit. Further studies involving Kv4.2 knockout mice have demonstrated that deletion of the Kv4.2 gene in CA1 pyramidal neurons eliminated the IA current, supporting the previous immunohistochemical studies (Chen et al., 2006).

Distributed with an almost ﬁve-fold increasing gradient from soma to the apical dendrites, IA plays a major role in regulating dendritic excitability (Hoﬀman et al., 1997). As a result of its rapid activation and inactivation kinetics and its low activation threshold

(near resting membrane potentials), IA serves to prevent or limit large, rapid depolarizations. Current injections that normally produce subthreshold voltage responses have been shown to cause suprathreshold bursts of action potentials in the presence of A-type potassium channel blockers (Magee and Carruth, 1999), thus strongly increasing neuronal excitability. As a result, any mechanisms, such as phosphorylation, that alter the availability of A-type potassium channels or their activation kinetics, leading to a reduction of IA current, would modulate dendritic excitability (Anderson et al., 2000; Hoﬀman and

Johnston, 1998; Yuan et al., 2002). A-type potassium channels have also been implicated in shaping action potentials and regulating action potential backpropagation (Hoﬀman et al., 1997; Johnston et al., 2000; Kim et al., 2005; Migliore et al., 1999), synaptic integration (Cash and Yuste, 1999; Makara et al., 2009; Ramakers and Storm, 2002), long-term 38 potentiation (Chen et al., 2006; Frick et al., 2004; Watanabe et al., 2002) and Na+-spike initiation and propagation (Losonczy et al., 2008).

1.4.3.3. D-type potassium channel. In CA1 pyramidal neurons, the dendrotoxin- sensitive (DTX) D-type potassium current (ID) is a slowly-inactivating outward current that activates in the subthreshold range, has enhanced sensitivity to 4-aminopyridine (4-

AP) and plays a prominent role in delayed excitation, regulation of calcium-dependent spikes and reducing spike afterdepolarization (Golding et al., 1999; Metz et al., 2007;

Storm, 1988; Wu and Barish, 1992). While the molecular determinants of D-type potassium channels have not yet been conﬁrmed, colocalizations and coassociations of Kv1 subunits, such as Kv1.2 with Kvβ2, are thought to compose the basis for D-type potassium channels due to their DTX-sensitivity (Monaghan et al., 2001; Rhodes et al., 1997).

The distribution of D-type potassium channels in CA1 pyramidal neurons has also yet to be fully determined. Application of DTX to somatic nucleated patches in CA1 pyramidal cells has very little eﬀect on potassium currents, indicating that D-type potassium channels are not present in the soma. Consistent with in situ hybridization and im- munocytochemical studies that show that Kv1.2 subunits are concentrated primarily in dendrites (Martina et al., 1998; Sheng et al., 1994), simultaneous somatic and dendritic current-clamp recordings with local application of DTX further suggest that the density of D-type potassium channels are higher in distal dendrites relative to more proximal ones in CA1 pyramidal neurons (Metz et al., 2007). 39

1.5. Synaptic Integration

CA1 pyramidal neurons have elaborate dendritic trees that receive tens of thousands of synaptic inputs, which are then shaped and integrated through a complex combination of factors such as membrane conductances, morphology, size and relative timing of synaptic inputs, summation of inhibitory and excitatory inputs, as well as the location of synaptic inputs. The ability of a neuron to computationally process the interaction of multiple synaptic events to shape neuronal output is known as synaptic integration.

1.5.1. Excitatory synapses

Chemical synapses are either excitatory or inhibitory depending on how neurotransmitter release aﬀects the likelihood of action potential generation. Neurotransmitters are released from presynaptic boutons following action potential invasion of the presynaptic terminal and diﬀuse across the synaptic cleft to bind to receptors in the postsynaptic membrane. The binding of neurotransmitters at an excitatory synapse causes ion channels (typically Na+ channels) to open, resulting in a depolarization of the postsynaptic membrane and generating an excitatory postsynaptic potential (EPSP) (Chua et al.,

2010; Hille, 2001). Physically, excitatory synapses can be diﬀerentiated from their inhibitory counterparts by an electron-dense thickening of their postsynaptic density (PSD), a protein-dense region attached to the postsynaptic membrane, which causes them to appear asymmetrical (Colonnier, 1968; Gray, 1959; Uchizono, 1965).

Glutamate is the main excitatory neurotransmitter in the central nervous system and plays a primary role in long term potentiation and subsequently, learning and memory. It 40 can bind to several ionotropic and metabotropic receptors, including α-amino-3-hydroxy-

5-methyl-4-isoxazolepropionic acid (AMPA) and N -methyl-D-asparate (NMDA) receptors

(Maren and Baudry, 1995). While glutamate binds to and opens both AMPA and NMDA receptors, NMDA receptors are blocked by Mg2+, requiring depolarization to remove the blockade, allowing Ca2+, Na+ and K+ ions to ﬂow through. The activation of NMDA receptors is believed to control the occurrence of long-term potentiation, underlying synaptic plasticity and memory formation (Malenka and Nicoll, 1993).

The majority of fast excitatory synaptic transmission occurs through AMPA receptors.

In the hippocampal CA1 region, AMPA receptors are composed of heteromers comprised of the glutamate receptor subunits GluR2, plus either GluR1 or GluR3 subunits (Dingle- dine et al., 1999). The subunit composition of an AMPA receptor determines its permeability to calcium and other cations, such as sodium and potassium. The presence of the

GluR2 subunit, evidenced in the majority of CA1 pyramidal neurons, leads to calcium impermeability as well as low open probability and conductance, thus strongly aﬀecting

AMPA receptor properties and hence, synaptic transmission and plasticity. Alterations to

AMPA receptor properties in CA1 pyramidal GluR2-containing neurons have suggested that AMPA receptors play a primary role in long lasting, activity-dependent synaptic strengthening during long-term potentiation (LTP) and depression (LTD), which are believed to be critical for the initial formation and maintenance of new memories (Derkach et al., 2007). 41

1.5.2. Action potentials and dendritic spikes

The primary method of communication between neurons is by the collective summation and filtering of multiple excitatory and inhibitory synaptic potentials to fire an action potential. Although a solitary EPSP may depolarize the dendritic membrane enough to result in voltage-gated ion channels opening, the attenuation of the EPSP as it travels passively down the dendritic tree to the soma will be insufficient to depolarize the somatic membrane past threshold to generate an action potential. However, if multiple excitatory synapses are synchronously activated, the combined depolarization from the summed input can reach a threshold level of depolarization and trigger regenerative opening of voltage-gated ion channels, resulting in a dendritic spike (Golding and Spruston,

1998; Gasparini et al., 2004). Under conditions of strong synaptic stimulation from multiple locations, these dendritic spikes can forward propagate from the dendrites to the soma, possibly inducing a somatic action potential (Gasparini et al., 2004; Jarsky et al.,

2005).

Dendrites of CA1 pyramidal neurons contain voltage-gated conductances allowing them to generate two types of dendritic spikes via synaptic stimulation: fast Na+- dependent spikes and slower Ca2+-dependent spikes (Golding and Spruston, 1998; Golding et al., 1999). In CA1 pyramidal neurons, dendritic spikes can exhibit two distinct methods of forward propagation (Gasparini et al., 2004). First, regenerative spikes can remain localized to a limited region of the dendritic tree thus having little impact on somatic membrane potential (Golding and Spruston, 1998; Golding et al., 1999; Schiller et al.,

1997). When combined with current injection or synaptic input activated within a spe- ciﬁc time window relative to the initiation of the dendritic spikes, regenerative potentials 42 can fully forward-propagate to the soma to generate a backpropagating action potential that then interacts with the regenerative dendritic response (Larkum et al., 2001). Unlike other types of neurons, such as hippocampal oriens-alveus interneurons or layer 5 pyramidal neurons, where dendritic voltage-gated conductances are able to reliably propagate dendritic spikes to the soma without coincident synaptic input, distal regenerative spikes in CA1 pyramidal neurons do not propagate reliably to the soma without membrane depolarization (Larkum et al., 2001; Martina et al., 2000; Williams and Stuart, 2002).

1.5.3. Synaptic location independence

Combined experimental and computational studies have shown that synaptic potentials evoked in distal dendrites of the CA1 stratum lacunosum-moleculare (SLM) region are strongly attenuated by dendritic ﬁltering properties as they propagate to the soma

(Golding et al., 2005; Rall, 1967; Williams and Stuart, 2003) and that without mechanisms in place to counteract dendritic cable properties, distal inputs would be unable to effectively influence neuronal output. If distal inputs and dendrites have no effective way of influencing neuronal output, what is their role? To further investigate this puzzling question, experiments in CA1 pyramidal neurons have been performed to determine the somatic impact of EPSPs generated at increasing distances along the primary apical dendrite (Magee and Cook, 2000; Stricker et al., 1996; Williams and Stuart, 2002). These studies revealed that the amplitudes of locally-generated synaptic potentials increased with distance from the soma along the primary apical dendrite. The resulting amplitudes of somatic potentials were indistinguishable with an average somatic EPSP amplitude of 43

0.2 mV, suggesting that synapses modulate their strength as a type of distance compensation for dendritic ﬁltering. Consistent with these studies, experiments using conventional and postembedding immunogold electron microscopy were conducted to determine the number and strength of AMPA receptors in excitatory synapses along the primary apical dendrites of CA1 pyramidal neurons (Andrasfalvy and Magee, 2001; Nicholson et al.,

2006). These experiments show that AMPA receptor density increases with distance from the soma such that synapse number in the distal stratum radiatum (dSR) was increased relative to proximal stratum radiatum (pSR), but decreases in SLM relative to dSR and pSR, indicating the synapses in stratum radiatum may compensate for their distance from the soma through a form of synaptic strengthening.

In addition to conductance scaling, studies suggest for more distal synapses (SLM), distance compensation may occur through dendritic spikes. The forward propagation of dendritic spikes originating in SLM may be enhanced by moderate synaptic input from stratum radiatum (SR) (Jarsky et al., 2005) to drive action potential generation at the soma. Together, these two mechanisms of distance compensation may enable inputs in more distal locations to aﬀect somatic output.

1.6. Work Presented

There are many open questions surrounding the role of distal synaptic inputs in producing neuronal output, as well as many questions regarding the dendritic and somatic voltage-gated channels that contribute to integrating dendritic inputs. In this thesis, I seek to address two important questions related to synaptic integration of subthreshold voltage responses: (1) How do synapses in CA1 pyramidal neurons compensate for their 44 distance from the soma, and (2) What is the role of A-type potassium channels in shaping subthreshold voltage responses in CA1 pyramidal neurons.

1.6.1. Normalization of distal synaptic inputs

To further understand the consequences of the experimentally determined distributions of synapses and synaptic strength in CA1 pyramidal neurons (Nicholson et al., 2006), I performed computer simulations with a passive CA1 neuron model. Initial simulations investigated the resulting somatic potentials for given synaptic conductances (gsyn) based on the average amplitude of miniature EPSPs (mEPSPs) in SR (Magee and Cook, 2000) and the relative level of AMPA receptor expression. Consistent with experimental studies, the simulation results indicate that SLM synapses are unable to overcome the eﬀects of dendritic ﬁltering and subsequently produce smaller somatic EPSPs relative to responses from more proximal inputs.

Using this same model, I also investigated how much of an increase in gsyn was necessary to produce the average 0.2 mV somatic voltage response seen in previous experimental studies of synaptic location independence (Magee and Cook, 2000). Consistent with the electron microscopy results, synapses in pSR and dSR needed only moderate increases in synaptic strength to eﬀect a 0.2 mV somatic depolarization. However, synapses in SLM required a much larger increase in synaptic strength (10 - 1000 times larger) and in some cases, reached a local depolarization of -30 mV, a voltage above threshold for generating dendritic spikes, at a lower conductance value than the conductance required to produce a 0.2 mV somatic voltage response (Nicholson et al., 2006). 45

1.6.2. A-type potassium channels shape subthreshold voltage responses

Previous experimental studies and passive neuron models have suggested that membrane resistance in CA1 pyramidal neurons is nonuniform, such that distal dendrites are ‘leakier’ than dendrites located proximal to the somatic region (Golding et al., 2005).

While accurately reproducing voltage attenuation as a function of distance from the soma, these passive models were unable to accurately reproduce speciﬁc aspects of subthreshold voltage responses such as the time course of voltage sag for hyperpolarizing current injections. However, CA1 pyramidal neurons are not passive and have been shown to contain a wide variety of voltage-gated conductances, such as the A-type potassium conductance, that are open at resting potentials.

Here we combined whole-cell somatic patch clamp recordings of CA1 pyramidal neurons in bath application of diﬀering concentrations of 4-AP with computational modeling to investigate the role of A- and D-type potassium channels in regulating subthreshold voltage responses. The experimental results show that while pharmacological block of

D-type potassium channels did not signiﬁcantly alter input resistance, pharmacological block of A-type potassium channels yielded an almost 27% increase in input resistance as compared to control conditions. Incorporating these results into a computational model of a morphologically realistic neuron provides more accurate ﬁts to subthreshold voltage responses. 46

CHAPTER 2

Location-Dependent Variations in Synaptic Strength in

Hippocampal CA1 Pyramidal Neuron Models 47

2.1. Abstract

The ability of synapses throughout the dendritic tree to inﬂuence neuronal output is crucial for information processing in the brain. Synaptic potentials attenuate dramatically, however, as they propagate along dendrites toward the soma. Previous experimental studies have examined whether excitatory axospinous synapses on CA1 pyramidal neurons compensate for their distance from the soma to counteract such dendritic ﬁltering.

Immungold electron microscopy was used to evaluate axospinous synapse number and receptor expression in three progressively distal regions: proximal and distal stratum radiatum (SR), and stratum lacunosum-moleculare (SLM). These experiments showed that the proportion of perforated synapses increases as a function of distance from the soma and that their AMPAR, but not NMDAR, expression is highest in distal SR and lowest in SLM (Nicholson et al., 2006). Computational models of pyramidal neurons derived from these results suggest that compensation occurs through the compartment-specific use of conductance scaling in SR and dendritic spikes in SLM to minimize the influence of distance on synaptic efficacy. 48

2.2. Introduction

The excitatory synaptic inputs onto a single neuron often originate in different areas of the brain and are distributed throughout a branched dendritic tree that can extend hundreds of microns from the soma. Activation of these synapses generates potentials that propagate toward the soma and axon, where all electrical signaling from the dendrites converges. In order to influence activity in these final integration zones, however, synaptic potentials must overcome severe filtering and attenuation caused by the cable properties of dendrites (Rall, 1977; Williams and Stuart, 2003). Because of the size and complexity of dendrites, the impact of dendritic filtering increases with distance from the soma and substantially reduces the influence of distal synapses on neuronal output.

Recent studies suggest, however, that CA1 pyramidal neurons can counteract this voltage attenuation with two diﬀerent mechanisms, both of which are capable of eﬀectively and reliably depolarizing the soma and axon: distance-dependent conductance scaling

(Magee and Cook, 2000; Smith et al., 2003) and dendritic spikes (Golding and Spruston,

1998; Gasparini et al., 2004; Gasparini and Magee, 2006).

Conductance scaling has been studied among the CA3 → CA1 synapses of stratum radiatum (SR), where locally generated synaptic potentials in distal dendritic regions are larger than those generated more proximally. When these same potentials are recorded at the soma, however, their average amplitudes are virtually indistinguishable, imparting location independence to synapses in SR. Dendritic spikes also have been studied in detail within apical dendritic regions, where they are triggered locally by synaptic activity and propagate with variable reliability toward the soma. Dendritic spikes likely play an integral role in relaying synaptic signals from stratum lacunosum-moleculare (SLM) because, 49 in the absence of dendritic action potentials, inputs in this region have only a minor eﬀect at the soma (Golding and Spruston, 1998; Wei et al., 2001; Cai et al., 2004; Jarsky et al.,

2005). Additionally, the forward propagation of dendritic spikes originating in SLM, and their effectiveness at driving axonal action potentials, are facilitated dramatically by very modest synaptic activity in SR (Jarsky et al., 2005). Such findings suggest that, through the gating action of SR synapses, dendritic spikes are the principal form of communication between SLM and the soma/axon. These studies have contributed to the emerging view that CA1 pyramidal neurons employ both conductance scaling and dendritic spikes to ensure that synapses throughout the apical dendrite influence neuronal output. Virtually nothing is known, however, regarding the cellular substrates of synaptic distance compensation. In addition, the likelihood that SR and SLM synapses use the same or different mechanisms to reduce the impact of their dendritic location has never been addressed.

To characterize the extent to which synapses are regulated in a distance-dependent manner, especially in SLM where such a role may be masked by the technical limitations of recording from the small-diameter dendritic tufts, conventional and postembedding immunogold electron microscopy was used to examine the number, as well as the AMPAR and NMDAR expression, of synapses throughout the apical dendrite of CA1 pyramidal neurons (Nicholson et al., 2006). At least within SR, the number or density of AMPARs appears to be the major determinant of synaptic strength because various other parameters that inﬂuence excitatory postsynaptic potential (EPSP) amplitude - including cleft glutamate concentration, the size of the readily releasable pool of vesicles, probability of release, maximum channel open probability, single channel current, and NMDAR mediated currents - do not vary with distance from the soma, yet synapses in this region 50 exhibit conductance scaling (Andrasfalvy and Magee, 2001; Smith et al., 2003). Accord- ingly, the number and density of immunogold particles for AMPARs projected onto the postsynaptic density (PSD) was used as an estimate of the relative strength of synapses.

Computational models of CA1 pyramidal neurons were then derived from these data to determine how distance-dependent diﬀerences in synaptic strength aﬀect dendritic integration. Taken with results from the previous experimental studies, the modeling results suggest that synapses on the apical dendrites of CA1 pyramidal neurons minimize voltage attenuation by utilizing conductance scaling in SR and the generation of dendritic spikes in SLM. 51

2.3. Methods

2.3.1. Computational Modeling

The CA1 pyramidal neuron models used for simulations were reconstructed from stained neurons in hippocampal slices as described previously (Golding et al., 2005). All simulations were performed using the neuronal simulator NEURON (Hines and Carnevale,

1997). The passive neuron models included only passive membrane properties, which were constrained by direct recording of voltage attenuation from the soma to a dendritic recording in the same neuron and a hyperpolarization-activated conductance (Golding et al.,

2005). Additional CA1 pyramidal neuron models with active conductances from Golding et al. (2001) and Poirazi et al. (2003) were also used.

The distribution of leak membrane resistance in the passive neuron models was assumed to be given by the expression

Rm(soma) − Rm(end) Rm = Rm(end) + (2.1) 1 + exp [d − d1/2]/z

Parameters for the hyperpolarization-activated cation conductance distribution were constrained by previous results from electrophysiological recordings (Golding et al., 2005;

Magee, 1998) yielding an increasing sigmoidal distribution as a function of distance from the soma for the peak conductance (gh): 52

gh(end) − gh(soma) gh = gh(soma) + (2.2) 1 + exp [d1/2 − d]/z

Here gh(soma), gh(end), d1/2, d and z are parameters similar to those used in Equation 2.1.

2.3.1.1. Determining synaptic conductance values: Regula-Falsi method. The root-finding Regula-Falsi method was used in all simulations where it was necessary to determine a synaptic conductance (gsyn) value that produced a specific somatic or local voltage response. Regula-Falsi, also called the False-Position method, is a linearly conver- gent root-finding algorithm based on linear interpolation that is faster than the standard

Bisection method. Similar to the Bisection method, Regula-Falsi starts with a change of sign interval [a,b] containing the root. Each subsequent step of the method tries to make this interval smaller. However, unlike the bisection method, Regula-Falsi biases the search using the value of the function to determine which side of the interval does not contain a root. That side is then discarded to give a new, smaller interval containing the root (Rao and Shanta, 1992).

Determining a root is as follows: If there are two points a and b such that f(a)f(b) < 0, then there exists a root x1 such that f(x1) = 0 (Figure 2.1). The equation for the secant line between (a, f(a)) and (b, f(b)) can be found such that

y − f(a) f(b) − f(a) = . (2.3) x − a b − a

Setting y = 0, the equation for the secant line can then be solved for x1.

af(b) − bf(a) x = . (2.4) 1 f(b) − f(a) 53

Figure 2.1. Method of False-Position To use the False-Position, or Regula-Falsi, method the interval [a,b] must contain a change of sign such that f(a)f(b) < 0. The Regula- Falsi algorithm can be derived by ﬁnding the secant line or by using similar triangles, i.e. EC/BC = DE/AB. Figure courtesy of http://www2.lv.psu.edu/ojj/courses/cmpsc-201/numerical/regula.html 54

If f(x1) = 0, then x1 is an exact root. Otherwise, if f(x1)f(b) < 0 then the lower boundary of the interval, a, is replaced with x1 and its corresponding functional value. If f(x1)f(a) < 0, then the larger boundary of the interval, b, is replaced with x1. This is repeated until f(xi) is within a speciﬁed tolerance of zero.

However, when determining the synaptic conductance value that will produce a target somatic voltage of 0.2 mV (Magee and Cook, 2000), the root no longer occurs at y = 0, but instead occurs at y = 0.2. In this case, the lower boundary point (a, f(a)) is (ga, Va) where ga is the lower conductance value that sets the value for the left boundary of the interval and Va is the resulting somatic voltage when the smaller conductance value is set as the synaptic conductance for a synapse at a particular dendritic location. The upper boundary point (b, f(b)) is (gb, Vb) where gb is the upper conductance value that sets the value for the right boundary of the interval and Vb is the resulting somatic voltage when the larger conductance value is set as the synaptic conductance for a synapse at a particular dendritic location. Using these two boundary points, the equation for the secant line is y − V V − V a = b a . (2.5) x − ga gb − ga

Setting y = 0.2 and x = gsyn1 (the ﬁrst iterative value for gsyn), the equation for the secant

line can then be solved for gsyn1 .

(gb − ga)(0.2 − Va) gsyn1 = ga + (2.6) Vb − Va

For each interval, the somatic and dendritic voltage changes were calculated and used to determine a lower or upper boundary for the new interval until the somatic depolarization 55

reached 0.2 mV (within a tolerance of 0.01) or gsyn reached a maximum conductance of 1.0 nS. For simulations where local depolarizations were considered, a limit equal to -30 mV

(theoretical spike threshold) was set such that iteration was complete if the local voltage change reached -30 mV prior to a somatic depolarization of 0.2 mV or a gsyn of 1.0 nS.

2.4. Synaptic Scaling: Experimental Background

2.4.1. Distance-Dependent Regulation of Synapse Number

The vast majority of excitatory synapses on CA1 pyramidal neurons are located on dendritic spines (Sorra and Harris, 2000; Geinisman et al., 2004) and can be either perforated or nonperforated (Peters and Kaiserman-Abramof, 1969; Carlin et al.,

1980), depending on the configuration of their PSD. When viewed in serial sections, perforated synapses exhibit discontinuous PSD profiles (Figure 2.2 A-C), while nonperforated synapses show continuous PSD profiles (Figure 2.2 D-F). Importantly, perforated synapses have a higher number of immunogold particles for both AMPARs and NMDARs compared to their nonperforated counterparts (Desmond and Weinberg, 1998; Ganeshina et al., 2004b,a). Such findings are consistent with the idea that perforated synapses, when activated, will generate larger synaptic currents than nonperforated synapses. To clarify the role of these two synaptic subtypes in distance compensation, experimental studies have estimated whether the number or proportion of perforated synapses changes with distance from the soma. The results of the estimates of the total number of perforated and nonperforated synapses in the three zones revealed that their numbers varied in a distance-dependent manner (Nicholson et al., 2006). Specifically, there are more perforated synapses in dSR and SLM than in pSR, and there are fewer nonperforated synapses 56 within SLM than in pSR and dSR (Figure 2.2 I). Together, these differences in synaptic subtype number progressively increase the proportion of perforated synapses with distance from the soma (Figure 2.2 J). That the number of perforated synapses is increased in the dSR, and then maintained at the same elevated level in SLM (Figure 2.2 I), suggests that perforated synapses play a pivotal role in distance-dependent synaptic scaling.

2.4.2. Synaptic AMPARs Exhibit Distance-Dependent Regulation

Because of the exceptionally high level of AMPAR immunoreactivity in perforated synapses (Ganeshina et al., 2004b,a), the increase in their proportion might underlie the higher incidence of large-amplitude miniature excitatory postsynaptic currents (mEPSCs) in dSR (Magee and Cook, 2000; Smith et al., 2003). A parallel augmentation in perforated synapse strength would account for the electrophysiological ﬁnding that the dSR contains a subpopulation of synapses two to three times more powerful than any synapse in pSR

(Magee and Cook, 2000; Smith et al., 2003). Furthermore, perforated synapse strength might be expected to surpass that in dSR if conductance scaling extends to SLM. As AM-

PARs mediate the majority of fast synaptic transmission and previous electrophysiological studies have provided evidence that distance-dependent synaptic scaling is accomplished via an increase in synaptic AMPR conductance (Magee and Cook, 2000; Andrasfalvy and

Magee, 2001; Smith et al., 2003), previous postembedding immungold electron microscopy experiments have assessed the AMPAR immunoreactivity of axospinous synapses from the pSR, dSR, and SLM. These studies revealed that perforated synapses are immunopositive for AMPARs and exhibit an abundance of immunogold particles associated with their

PSD. In addition, perforated synapses had more immunogold particles for AMPARs than 57

Figure 2.2. Ratio of Perforated-to-Nonperforated Synapses Increases with Distance from the Soma in CA1 Pyramidal Neurons. Figure courtesy of Nicholson et al. (2006). Figure caption continues on the next page. 58

Figure 2.2. (A-C) A perforated synapse between a presynaptic axon terminal (at) and a postsynaptic spine (sp), characterized by discontinuities (arrows) in its postsynaptic density proﬁles (arrowheads). Scale bar, 0.25 µm. (D-F) Nonperforated synapses between two presynaptic axon terminals (at1 and at2) and two postsynaptic spines (sp1 and sp2) display continuous postsynaptic density proﬁles (arrowheads) in all sections. Scale bar, 0.25 µm. (G) A pyramidal neuron in the hippocampal CA1 region (arrows). (H) Location of the pSR, dSR, and SLM depicted on a CA1 pyramidal neuron. (I) Total number of perforated (triangles) and nonperforated (circles) synapses in pSR, dSR, and SLM. pSR has fewer perforated synapses than dSR and SLM (∗); SLM has fewer nonperforated synapses than pSR and dSR (∗∗). (J) The perforated-to-nonperforated synapse ratio is higher in dSR than in pSR (∗) and highest in SLM (∗∗). All values are based on pooled data from three rats (1032 perforated synapses; 7569 nonperforated synapses) and are presented ± SEM. 59

Figure 2.3. AMPAR Expression in Perforated and Nonperforated Synapses throughout the Apical Dendritic Tree in CA1 Pyramidal Neurons. Figure courtesy of Nicholson et al. (2006). (A) Mean number of immunogold particles for AMPARs per perforated (triangles) and nonperforated (circles) synapse. Perforated synapses in dSR have the highest particle number (∗), whereas those in SLM have the lowest (∗∗). (B) Mean density of immunogold particles for AMPARs per PSD unit area (mm2). Among perforated synapses, those in dSR have the highest particle density (∗), and those in SLM have the lowest (∗∗). Nonperforated synapses in dSR have a higher particle density than those in both pSR and SLM. 60 immunopositive nonperforated synapses, regardless of whether they were in the pSR, dSR or SLM (Figure 2.3 A,B) (Nicholson et al., 2006).

However, distance-dependent diﬀerences in AMPAR immunoreactivity were seen almost exclusively among perforated synapses. Perforated synapses in the dSR had the highest particle number and density, whereas those in SLM had the lowest particle number and density (Figure 2.3 A,B). Among nonperforated synapses, neither the particle number (Figure 2.3 A) nor the percentage of immunopositive nonperforated synapses changed with distance from the soma. The only diﬀerence seen among nonperforated synapses was a slightly higher particle density in those from the dSR (Figure 2.3 B).

These studies suggest that conductance scaling may be achieved by an increase in the number and density of AMPARs, and they extend this view by demonstrating that the upregulation of AMPARs is limited to perforated synapses. Additionally, this particular form of conductance scaling does not appear to extend to SLM (Nicholson et al., 2006).

2.4.3. Synaptic NMDARs Do Not Scale with Distance from the Soma

Although a previous study provided compelling evidence that NMDAR-mediated currents do not change with distance from the soma in SR (Andrasfalvy and Magee, 2001), there is evidence that the NMDAR-to-AMPAR ratio is highest in SLM (Otmakhova et al.,

2002). Moreover, synaptic currents mediated by NMDARs have slower kinetics than those mediated by AMPARs (Hestrin et al., 1990; Spruston et al., 1995a), which, through a variety of mechanisms, can be expected to decrease the impact of voltage attenuation on potentials from very distal synapses such as those in dSR and SLM (Rall, 1977; Schiller and Schiller, 2001; Williams and Stuart, 2003). To determine whether NMDARs play a 61 role in distance compensation, previous experiments also examined NMDAR immunoreactivity in synapses from the pSR, dSR, and SLM.

These experiments revealed that both perforated and nonperforated synapses are immunopositive for NMDARs (Ganeshina et al., 2004b; Nicholson et al., 2006). Perforated synapses had a higher number, but a lower density, of immunogold particles for NM-

DARs than their nonperforated counterparts (Figure 2.4). In stark contrast to synaptic

AMPARs, however, NMDAR expression among synapses did not exhibit any distance- dependent diﬀerences (Figure 2.4) (Nicholson et al., 2006).

2.5. Results

2.5.1. Perforated Synapses Reduce Location Dependence in SR

The results from previous experimental studies show that CA1 pyramidal neurons regulate the number of both perforated and nonperforated synapses as a function of distance from the soma but adjust synaptic strength only among the perforated subtype, and even then only by modifying the number of AMPARs. The selective involvement of perforated synapses in distance-dependent synaptic scaling suggests that they are the only synaptic subtype capable of reducing their location dependence. To provide insight into the possible functional consequences of such compartment-speciﬁc diﬀerences in synapse number and receptor content, I used computer simulations of a morphologically reconstructed pyramidal neuron with passive membrane properties (Golding et al., 2005).

The computer simulations were ﬁrst used to model the somatic EPSPs that perforated and nonperforated synapses located throughout the apical dendrite would produce.

Synaptic conductances (gsyn) were based on the known properties of somatic EPSPs and 62

Figure 2.4. NMDAR Expression in Perforated and Nonperforated Synapses throughout the Apical Dendritic Tree in CA1 Pyramidal Neurons. Figure courtesy of Nicholson et al. (2006). (A) Mean number of immunogold particles for NMDARs per perforated (triangles) and nonperforated (circles) synapse. Perforated synapses have more immunogold particles than nonperforated ones (∗) in all dendritic regions studied, but there are no distance-dependent diﬀerences. (B) Mean density of immunogold particles for NMDARs per PSD unit area (mm2). Nonperforated synapses have a higher particle density than their perforated counterparts (∗), but this pattern does not change with distance from the soma. 63 the relative number of immunogold particles for AMPARs in the two synaptic subtypes

(Figure 4 A). The average amplitude of miniature EPSPs (mEPSPs) in SR is approximately 0.2 mV (Magee and Cook, 2000). This was incorporated into the model by assuming a gsyn of 0.3 nS for nonperforated synapses, which resulted in somatic EPSPs of 0.2 mV from the most proximal dendritic synapse locations. Based on the AMPAR immunoreactivity of nonperforated synapses, this value was kept constant at all dendritic locations. The gsyn value for perforated synapses was based on their relative level of AM-

PAR expression compared to nonperforated synapses, and was therefore dependent on dendritic location. Identical gsyn values were assigned to perforated synapses in stratum oriens (SO) and pSR, given their similar distance from the soma, and extrapolated gsyn of perforated synapses in middle stratum radiatum (mSR) to a value intermediate to those in pSR and dSR.

Using these values for gsyn, only the most proximal nonperforated synapses produced somatic EPSPs near 0.2 mV (i.e., exceeding 0.16 mV), whereas somatic EPSPs from all other locations were considerably smaller because of the lack of conductance scaling (Fig- ure 2.5 B-E). Importantly, nonperforated synapses in dSR and SLM produced EPSPs that were on average three to six times smaller than those in pSR (pSR: 0.13 mV; dSR:

0.04 mV; SLM: 0.02 mV), suggesting that many nonperforated synaptic potentials originating in distal dendritic regions attenuate to nearly undetectable amplitudes. When perforated synapses were simulated, most synapses throughout SR (100% in pSR, 85% in dSR) caused somatic EPSPs that exceeded 0.16 mV and produced relatively uniform somatic EPSP amplitudes over a large range of dendritic locations (Figure 2.5 B-E). The average somatic EPSP amplitude for perforated synapses in pSR (0.45 mV) exceeded that 64 of perforated synapses in dSR (0.21 mV), but these simulations suggest that somatically recorded pSR EPSPs are likely to originate from a mixture of both perforated and nonperforated synapses, whereas dSR EPSPs would be produced predominantly by perforated synapses (Figure 2.5 C-F). This would result in average pSR EPSPs being intermediate to that of the nonperforated and perforated EPSPs (0.28 mV), and average dSR EPSPs being derived from perforated EPSPs only (0.21 mV). Values based on such assumptions are consistent with recording studies (Magee and Cook, 2000; Smith et al., 2003). On the other hand, EPSPs originating in SLM (average = 0.068 mV) never exceeded 0.2 mV, with > 90% producing somatic EPSPs below 0.1 mV and none above 0.16 mV (Figure 2.5

B-E).

The simulations of perforated and nonperforated synapses complement the electron microscopy studies, and together they show that an increase in the proportion (Figure 2.2

A,B) and strength (Figure 2.3 A,B) of perforated synapses in dSR provides a plausible cellular basis for synaptic location independence throughout SR. These results also show that, despite having the highest proportion of perforated synapses (Figure 2.2 B), SLM synapses do not eﬀectively counteract dendritic ﬁltering. Rather, synaptic potentials originating in SLM attenuate so severely that they produce much smaller average somatic

EPSPs than SR EPSPs, consistent with previous recording studies (Jarsky et al., 2005).

2.5.2. Evidence for Compartment-Speciﬁc Mechanisms of Distance Compen-

sation

These simulations clearly show that conductance scaling does not extend into SLM, implying that some other mechanism must operate in this region to reduce synaptic 65

Figure 2.5. Simulating Somatic EPSPs Generated by Nonperforated and Perforated Synapses at Diﬀerent Locations on CA1 Pyramidal Neuron Den- drites. Figure courtesy of Nicholson et al. (2006). Figure caption continues on the next page. 66

Figure 2.5. (A) Synaptic conductances (gsyn) for perforated (P) and nonperforated (NP) synapses located in stratum oriens (SO), pSR, middle stratum radiatum (mSR), dSR, and SLM in simulations. All gsyn values are relative to a reference conductance (0.3 nS) necessary for a nonperforated synapse located in the most proximal region of pSR to generate a 0.2 mV somatic EPSP. The values for perforated and nonperforated gsyn in pSR, dSR, and SLM derive from the results of AMPAR immunogold electron microscopy experiments (Nicholson et al., 2006). The value for the nonperforated synapse gsyn at all dendritic locations was 0.3 nS, whereas the gsyn value for perforated synapses changed with distance from the soma (pSR: 1.2 nS; dSR: 1.8 nS; SLM: 1.0 nS). (B) Color-coded display of the somatic EPSP generated by synaptic conductances (gsyn) characteristic of nonperforated (left) or perforated synapses (right) throughout various locations of the apical dendrite. Color map of somatic EPSP (dVsoma) is on a log-scale. (C) Percentage and cumulative percentage of perforated (gray bars, thick lines) and nonperforated (white bars, thin lines) synapses located in pSR, dSR, or SLM that produced somatic EPSPs within the ranges of amplitudes displayed in (B). (D) Cumulative percentages of perforated (top panel) and nonperforated (bottom panel) synapses in pSR, dSR, and SLM plotted as a function of the depolarization (in mV) achieved in the soma. (E) Average amplitude of somatic EPSPs caused by perforated (P) and nonperforated (NP) synaptic conductances originating in pSR, dSR, or SLM. (F) The percentage of EPSPs in pSR, dSR, and SLM that exceeded 0.16 mV. Values for average somatic EPSP amplitudes in (E) are presented ± SD. 67 location dependence. Dendritic spikes may represent such a mechanism because they are prevalent in SLM and can be triggered relatively easily by brief bursts of synaptic activity

(Golding and Spruston, 1998; Golding et al., 2002; Gasparini et al., 2004; Jarsky et al.,

2005). Recent evidence suggests that SLM synapses indeed rely heavily on dendritic spikes because, in their absence, SLM inputs appear to only have minimal impact on neuronal output (Golding et al., 2005; Jarsky et al., 2005). These studies suggest that synapses in SLM are capable of eﬀectively counteracting dendritic ﬁltering only via a two-stage process: (1) SLM synaptic conductances trigger a dendritic spike; and (2) this dendritic spike then propagates toward the soma under some conditions.

To explore the possibility that SLM synapses preferentially use dendritic spikes rather than conductance scaling, I used the computational model to compare the conductances necessary to achieve two different conditions: (1) a unitary EPSP of 0.2 mV at the soma; and (2) a local depolarization to -30 mV, which can be considered sufficient to generate a local dendritic spike (Golding and Spruston, 1998; Gasparini et al., 2004). The value of gsyn was incrementally increased for synaptic locations throughout the dendritic tree until each of the two conditions was achieved. I then examined whether the gsyn necessary to achieve these two different conditions varied with distance from the soma. A unitary somatic EPSP of 0.2 mV could be achieved with relatively moderate increases in synaptic strength throughout pSR and dSR (Figure 2.6 A, blue). Consistent with the previous electrophysiological studies and electron microscopic experiments showing an increase in the number and AMPAR immunoreactivity of perforated synapses in dSR, gsyn of these synapses needed to be increased up to 10-fold relative to the reference conductance (gref ) in pSR (0.3 nS) to normalize the somatic EPSP. Much larger gsyn values were required for 68 synapses in SLM. Specifically, synaptic conductances ranging from 100 to over 1000 times that of more proximal synaptic locations were required to effectively counteract dendritic

ﬁltering and produce a somatic EPSP of 0.2 mV (Figure 2.6 A, blue). Thus, the pattern of resulting conductances is consistent with previous electron microscopic data from SR, but not from SLM, where perforated synapses have the lowest level of AMPAR expression.

When simulating the gsyn necessary to depolarize the local membrane potential to -30 mV, the highest values were observed for the large-diameter main apical dendrite (Figure 2.6

A, red). Much smaller values were required in the smaller-diameter apical oblique and tuft branches (Figure 2.6 A, red). For most synapses in SLM, the conductance required to reach -30 mV was substantially lower than the conductance required to achieve a 0.2 mV somatic EPSP (Figure 2.6 A, red). That is, when the most distal synapses - primarily within SLM - were activated, they achieved the dendritic spike threshold of -30 mV before they generated a 0.2 mV somatic EPSP (Figure 2.6 A-D). Importantly, this observation is opposite to that seen in SR, where most synaptic locations produced the normalized somatic EPSP at lower gsyn values than those required to produce a local depolarization to

-30 mV (Figure 2.6 A-D). These ﬁndings were further corroborated with a second passive

CA1 pyramidal cell model (Figure 2.7, Figure 2.8). When combined with the previous experimental results, these simulations indicate that perforated synapses in SR scale their strength to produce somatic EPSPs near 0.2 mV, whereas those in SLM are governed by diﬀerent rules, perhaps depending on their ability to recruit dendritic spikes, rather than their ability to depolarize the soma (Figure 2.6 D). 69

Figure 2.6. Modeling of the Synaptic Conductance Required to Achieve a Normalized Somatic EPSP or a Large Local Depolarization. Figure courtesy of Nicholson et al. (2006). Figure caption continues on the next page. 70

Figure 2.6. (A) The synaptic conductance required to achieve a somatic EPSP of 0.2 mV throughout the dendritic tree (blue), or a local depolarization to -30 mV (red). Synaptic conductance (gsyn) values were normalized relative to the reference conductance (gref ) used for simulations of nonperforated synapses in pSR (0.3 nS; Figure 2.5) and are plotted on a log-scale. (B) Plots, as a function of dendritic location, of the gsyn required to achieve either a somatic EPSP of 0.2 mV (blue) or a local depolarization to -30 mV (red) first. (C) The percentage of synaptic locations that achieved a somatic EPSP of 0.2 mV first (blue) or a local depolarization to -30 mV first (red) in pSR, dSR, and SLM. (D) Average values of the synaptic conductances (gsyn) required to achieve either a somatic EPSP of 0.2 mV (blue) or a local depolarization to -30 mV (red) for synaptic locations in pSR, dSR, and SLM. The number of immunogold particles for AMPARs per perforated synapse (black) in pSR, dSR, and SLM is superimposed with a separate ordinate. The axis for immunogold particle number is aligned such that the average particle number per immunopositive nonperforated synapse in pSR (3.38) is level with the average value required to achieve a 0.2 mV somatic EPSP in pSR (0.58 nS). All values are presented ± SEM. 71

Figure 2.7. Simulation of somatic EPSPs generated by nonperforated and perforated synapses at diﬀerent dendritic locations in a second model of a CA1 pyramidal neuron. Figure courtesy of Nicholson et al. (2006). (A) gsyn for synapses located in stratum oriens (SO), pSR, middle stratum radiatum (mSR), dSR, and SLM in the simulation. All gsyn values are relative to the reference conductance (gref ; 0.44 nS) necessary for a nonperforated synapse located in pSR to generate a 0.2 mV somatic EPSP (see text for details). (B) Color-coded display of the somatic EPSP generated by synaptic conductances (gsyn) located throughout the apical dendrite for a ﬁxed gsyn characteristic of nonperforated synapses (left), or by a variable gsyn scaled according to the results for perforated synapses in previous immunogold electron microscopy experiments (right). 72

A 3.0

2.5 ) 2.0 ref

/g 1.5 syn 1.0

log(g 0.5

0.0

-200 0 200 400 600 800

Distance from soma ( μm)

6.0

5.0

4.0 (nS) 3.0 syn g 2.0

1.0

-200 0 200 400 600 800 Distance from soma ( μm) C

Figure 2.8. Modeling of the synaptic conductance required to achieve a somatic EPSP or a large local depolarization in a second model of a CA1 pyramidal neuron. Figure courtesy of Nicholson et al. (2006). (A) The synaptic conductance (gsyn) required to achieve a somatic EPSP of 0.2 mV throughout the dendritic tree (blue), or a local depolarization to -30 mV (red). (B) Plots of the gsyn that achieved either a somatic EPSP of 0.2 mV (blue) or a local depolarization to -30 mV (red) first. (C) The percentage of synaptic locations that achieved a somatic EPSP of 0.2 mV first (blue) or a local depolarization to -30 mV first (red) in pSR, dSR, and SLM. 73 those in SLM need to first trigger dendritic spikes to successfully counteract dendritic

ﬁltering.

2.6.1. Synaptic Scaling vs. Dendritic Spikes

Though not directly proven by previous experiments, the compartment-speciﬁc use of conductance scaling and dendritic spikes to reduce synaptic location dependence is also supported by evidence from other studies. Previous electrophysiological work has shown that SR synapses can increase their conductance to compensate for their distance from the soma/axon (Magee and Cook, 2000; Smith et al., 2003). These studies found that the amplitudes of somatically recorded mEPSPs are relatively independent of their location of origin within SR, while the distribution of dendritically recorded mEPSCs contained substantially more large amplitude events in dSR than in pSR. These data are consistent with the computational results presented here. For example, the larger gsyn value required for more distal locations in the dSR to produce a 0.2 mV somatic EPSP would give rise to larger local depolarizations at the synapse site, consistent with the ﬁndings that there is a higher incidence of large-amplitude mEPSCs in dSR, with some mEPSCs being two to three times larger than any seen in pSR (Magee and Cook, 2000; Smith et al., 2003).

In SLM, however, experimental evidence indicates that the AMPAR immunoreactivity of perforated synapses was signiﬁcantly lower than that in both pSR and dSR (Nicholson et al., 2006), suggesting that perforated synapses in SLM actually may be the weakest of all such perforated synapses on the apical dendrites. The results from the simulations further indicate that many synapses in SLM are unable to achieve a 0.2 mV somatic 74

EPSP, even if synaptic strength is increased 100-1000 times the proximal gsyn values, thereby indicating that conductance scaling does not extend to SLM.

Several studies indicate that dendritic spikes, rather than conductance scaling, may be used by SLM synapses to influence neuronal output. Although EPSPs originating in SLM attenuate the most, the small diameter of these branches (Meg´ıaset al., 2001) will cause local EPSPs to be larger (Rall, 1977) and therefore more likely to trigger local dendritic spikes. This idea is consistent with computational simulations of two active CA1 pyramidal neuron models, which suggest that synaptic strength in SLM is actually scaled down as a result of the ease with which large local depolarizations could be achieved in this region (Figure 2.9, Figure 2.10). In one of the active models, roughly 80% of synapses in SLM reach threshold for spike generation prior to generating a 0.2 mV somatic voltage response (Figure 2.9). Furthermore, the synapses that are able to generate a 0.2 mV somatic EPSP prior to dendritic spike generation in the SLM require a 15-30 fold increase in gsyn to create a somatic depolarization of 0.2 mV (Figure 2.9). While significantly more of the synapses in the second active model (Poirazi et al., 2003) are able to generate a 0.2 mV somatic EPSP prior to reaching spike threshold in the SLM, these synapses also require a 15-30 fold increase in gsyn to do so (Figure 2.10). These simulations are also in agreement with a study using serial section electron microscopy and computational modeling to investigate two different integration modes (global and two-stage) for synaptic scaling in CA1 pyramidal neurons (Katz et al., 2009). The results from this study suggest that synaptic strength increases along the primary apical dendrite, but decreases along oblique apical dendrites. Thus, synapses at more distal locations on oblique branches 75

Figure 2.9. Modeling of the synaptic conductance required to achieve a normalized somatic EPSP or a large local depolarization in a third model of a CA1 pyramidal neuron with a voltage-gated Na+ conductance, a delayed- rectiﬁer K+ conductance, and two A-type K+ conductances. Figure courtesy of Nicholson et al. (2006). Figure caption continued on the next page. 76

Figure 2.9. Modeling of the synaptic conductance required to achieve a normalized somatic EPSP or a large local depolarization in a third model of a CA1 pyramidal neuron with a voltage-gated Na+ conductance, a delayed- rectifier K+ conductance, and two A-type K+ conductances. (A) The synaptic conductance (gsyn) required to achieve a somatic EPSP of 0.2 mV throughout the dendritic tree (blue), or a local depolarization to -30 mV (red). (B) Plots of the gsyn that achieved either a somatic EPSP of 0.2 mV (blue) or a local depolarization to -30 mV (red) first. (C) The percentage of synaptic locations that achieved a somatic EPSP of 0.2 mV first (blue) or a local depolarization to -30 mV first (red) in pSR, dSR, and SLM. 77

Figure 2.10. Modeling of the synaptic conductance required to achieve a normalized somatic EPSP or a large local depolarization in a model of a CA1 pyramidal neuron with various passive and active conductances (Poirazi et al., 2003). Figure courtesy of Nicholson et al. (2006). Figure caption continued on the next page. 78

Figure 2.10. Modeling of the synaptic conductance required to achieve a normalized somatic EPSP or a large local depolarization in a model of a CA1 pyramidal neuron with various passive and active conductances (Poirazi et al., 2003). (A) The synaptic conductance (gsyn) required to achieve a somatic EPSP of 0.2 mV throughout the dendritic tree (blue), or a local depolarization to -30 mV (red). (B) Plots of the gsyn that achieved either a somatic EPSP of 0.2 mV (blue) or a local depolarization to -30 mV (red) first. (C) The percentage of synaptic locations that achieved a somatic EPSP of 0.2 mV first (blue) or a local depolarization to -30 mV first (red) in pSR, dSR, and SLM. 79 may contribute to neuronal output by generating dendritic spikes during asynchronous synaptic activation.

2.6.2. Synaptic Scaling and Gating of Dendritic Spikes

In the absence of dendritic spikes, SLM synapses are unable to generate axonal action potentials and have only minimal impact on somatic depolarization (Golding and

Spruston, 1998; Wei et al., 2001; Golding et al., 2005; Jarsky et al., 2005). Though the propagation of dendritic spikes in SLM can be restricted to the apical tuft (Golding and

Spruston, 1998; Wei et al., 2001; Cai et al., 2004), such spatial conﬁnement is dramatically reduced by modest synaptic activity in SR (Jarsky et al., 2005). In other words, synapses in SR actively gate the propagation of dendritic spikes originating in SLM, conferring to dendritic spikes the ability to propagate to the soma, and allowing dendritic spikes to act as a reliable mechanism of distance compensation for SLM synapses. Together, these

findings strengthen the notion that perforated synapses in SR can communicate directly with the soma/axon in a relatively location-independent manner by use of conductance scaling, but that SLM synapses first need to trigger dendritic spikes, which then propagate toward and ultimately depolarize the final integration zones in the soma and axon.

Importantly, dendritic spikes are not a mechanism of distance compensation exclusive to

SLM synapses. Rather, SR synapses can inﬂuence activity in the soma and axon with or without dendritic spikes (Gasparini and Magee, 2006), whereas SLM synapses are unlikely to impact neuronal output in their absence (Jarsky et al., 2005). Even if SLM synaptic potentials summate with EPSPs in dSR to trigger local spikes in SR (Jarsky et al., 2005), 80 the available data are consistent with the notion that SLM synapses rely on dendritic spikes to drive axonal action potentials, whereas SR synapses do not.

Given their small gsyn and somatic EPSP, the synchronous activation of many (>100) nonperforated synapses would be required to trigger axonal action potentials or dendritic spikes. And because they do not exhibit conductance scaling, the number of coincidentally activated nonperforated synapses required to produce an axonal action potential would increase progressively with distance from the soma. Considering the high level of AMPAR expression in perforated synapses, they are more likely to contribute to both axonal and dendritic spikes than their nonperforated counterparts throughout SR and SLM. The simulations here indicate, however, that dendritic ﬁltering of EPSPs originating in SLM is so severe that even perforated synapses may not contribute substantially to somatic depolarization. Rather, these synapses may instead operate together to trigger dendritic spikes. Given their abundance of AMPARs, the relative frequency of perforated synapses may be highest in SLM to increase the probability that synaptic input causes a local depolarization suﬃcient to trigger a dendritic spike.

2.6.3. Future Directions

This study indicates that the contribution of synapses to neuronal output strongly depends on synapse location and that conductance scaling is primarily utilized in SR, while the generation of dendritic spikes is more likely to play a role in regulating neural output in SLM. Forms of synaptic plasticity underlying distance-dependent regulation of synapse number (synapse conductance) and AMPAR content, although unknown or unveriﬁed, could serve to strength synaptic eﬃcacy. Computational studies of a putative 81 form of synaptic plasticity, anti-STDP or anti-Hebbian has been suggested as a mechanism by which dendritic spiking is normalized to balance it with spiking resulting from action potential backpropagation, thus preventing runaway spiking in localized dendritic regions and in turn, enhancing synapse strength in a positive feedback manner (Rumsey and

Abbott, 2006). These and other questions surrounding the role of synapses in SLM will need to be addressed by future simulations and experiments to fully understand how these distal synapses are integrated and regulated to aﬀect neural output in CA1 pyramidal neurons. 82

CHAPTER 3

A-type potassium channels shape subthreshold voltage

responses in hippocampal CA1 pyramidal neurons 83

3.1. Abstract

Voltage-gated potassium channels inhibit spike generation and thus play a primary role in a cell’s ability to integrate synaptic input. I investigated the role of A- and D- type potassium channels in shaping subthreshold voltage responses in hippocampal CA1 pyramidal neurons using somatic whole-cell patch clamp recordings and application of different concentrations of the A- and D-type potassium channel blocker, 4-aminopyridine

(4-AP). Inhibition of D-type potassium channels with low concentrations of 4-AP did not significantly affect subthreshold voltage responses. Inhibition of A-type potassium channels with high concentrations of 4-AP, however, considerably increased both somatic input resistance and the duration of simulated somatic postsynaptic potentials compared with control conditions, suggesting that a significant amount of A-type potassium current is available at resting conditions in CA1 pyramidal neurons. Incorporating an A-type potassium conductance with a substantial fraction of current that is on at rest in a reconstructed CA1 pyramidal neuron model significantly increased the accuracy of fits to subthreshold membrane responses while still accurately reproducing the behavior of both action potentials and action potential backpropagation.

3.2. Introduction

Hippocampal CA1 pyramidal neurons integrate thousands of synaptic inputs, many of which are located on distal dendrites hundreds of microns from the soma. These dendrites contain a number of voltage-gated channels that, in combination with passive membrane properties and neuronal morphology, directly influence spike propagation, attenuation of 84 synaptic potentials and integration of synaptic inputs. In addition, these active conductances also regulate the generation of dendritic spikes and the backpropagation of somatic action potentials (Cash and Yuste, 1999; Christie et al., 1996; Gasparini et al., 2004; Gold- ing and Spruston, 1998; Hoffman et al., 1997; Jaffe et al., 1992; Johnston et al., 1996, 2000;

Kamondi et al., 1998; Magee and Johnston, 1995; Magee and Carruth, 1999; Tsubokawa et al., 1999).

One voltage-gated channel in particular, the A-type potassium or K(A) channel, plays a prominent role in shaping backpropagating action potentials and spike initiation (Acker and White, 2007; Hoﬀman et al., 1997; Johnston et al., 1999; Kim et al., 2005; Migliore et al., 1999; Pan and Colbert, 2001). In CA1 pyramidal cells, K(A) channels are distributed with an increasing density along the somatodendritic axis (up to 5-fold larger in distal dendrites as compared to the soma) and serve to prevent or limit large, rapid depolarizations (Chen and Johnston, 2004; Connor and Stevens, 1971; Hoﬀman et al.,

1997; Kole et al., 2007; Serodio and Rudy, 1998). The large density of K(A) channels in the dendrites not only reduces the amplitude of action potentials as they propagate from the soma to more distal locations, but also diminishes the eﬀect of inputs from distal dendrites upon action potential generation. Due to diﬃculties associated with recording from distal oblique apical dendrites and the dendritic tuft, a delineation of active conductances (such as the A-type potassium conductance) in these distal locations is not yet fully available.

Another tool used to explore these issues is the construction of morphologically accurate computational models based on current experimental data. Many experimentally- constrained modeling studies have demonstrated the importance of determining and using 85 pharmacological block of active conductances in order to reproduce realistic behavior in neuronal models (Baranauskas and Martina, 2006; Gold et al., 2007; Mainen et al., 1995;

Migliore et al., 1999; Poirazi et al., 2003; Royeck et al., 2008; Varona et al., 2000; Vetter et al., 2001).

Previous studies have also used simultaneous somatic and dendritic recordings to computationally constrain estimates of membrane resistance, axial resistivity and the distribution of hyperpolarization-activated cation channels (Ih) (Golding et al., 2005). Our subsequent attempts to increase the agreement between such experimental recordings and best-ﬁt computational models suggested that a signiﬁcant fraction of voltage-gated

K(A) channels are on at rest in these neurons. To resolve this issue, we have investigated subthreshold voltage responses in CA1 hippocampal pyramidal neurons with somatic whole-cell recordings both under control conditions and when K(A) channels are blocked pharmacologically. The experimental results and associated computational models clearly demonstrate that a K(A) current that is on at rest strongly shapes subthreshold responses in CA1 pyramidal neurons, as well as excitatory post-synaptic potentials (EPSPs) simulated by current injection. New computational models constructed using these data yield much better ﬁts to the experimental results and consequently provide a better framework for future studies.

3.3. Materials and Methods

3.3.1. Slice Preparation and Electrophysiology

Hippocampal slices were prepared from 14-28 day-old male Wistar rats. The rats were anesthetized with halothane prior to decapitation and perfused transcardially with 86 cold artiﬁcial cerebrospinal ﬂuid (ACSF). Following decapitation, the brain was quickly removed and immersed in cold ACSF saturated with 95% oxygen and 5% carbon dioxide.

Transverse hippocampal slices were made in 300 µm sections using a Leica vibratome slicer and transferred to a holding chamber for storage at 35 degrees celsius (◦C) for 30 minutes and then held at room temperature for 30-60 minutes. For physiological recording, slices were transferred individually to the ﬁxed stage of a Zeiss Axioskop microscope equipped with diﬀerential interference contrast optics and perfused in ACSF solution at a temperature between 33 and 37 ◦C.

Patch-clamp electrodes fabricated from borosilicate glass capillary tubes were pulled to a resistance of 3-6 MΩ (measured in the ACSF bath) for somatic recordings. Cells in the

CA1 region were chosen based on their pyramidal morphology and low contrast appear- ance. Upon obtaining a gigaohm seal in voltage clamp, somatic recordings were performed in the whole-cell conﬁguration in current-clamp mode. For all experiments, current was applied to hold the resting potential at -67 mV. Stimulus generation, data acquisition, and analysis were performed using custom macros written in IGOR Pro (Wavemetrics,

Lake Oswego, OR). Data from electrophysiological recordings were accepted if the series resistance remained relatively constant (< 10% change) over the course of the recording.

All recordings were made at temperatures between 33 and 37 ◦C. All procedures were approved by Northwestern University Animal Care and Use Committee.

3.3.2. Solutions and Pharmacology

ACSF used during perfusion, dissection, and recording contained (in mM): 125 NaCl,

2.5 KCl, 1 MgCl2, 2 CaCl2, 25 NaHCO3, 1.25 NaH2PO4 and 25 glucose. Prior to use, 87

ACSF was bubbled with a 95% O2 - 5% CO2 mixture to oxygenate the solution. The internal solution consisted of (in mM): 115 K-gluconate, 20 KCl, 10 Na2-phosphocreatine,

10 HEPES, 2 EGTA, 4 Mg-ATP, 0.3 Na-GTP and 0.1% biocytin for subsequent morphological identiﬁcation. The synaptic blockers SR95531 (4 µM) and CGP558458A (1 µM) were included to prevent eﬀects from inhibition.

For all recordings, drugs were dissolved in ACSF and perfused in the bath without interruption of ﬂow. A concentration of 100 µM 4-aminopyridine (4-AP) was used to block D-type K+ channels and a concentration of 6 mM 4-AP was used to block both

D-type and A-type K+ channels. Kynurenic acid (2.5 mM) was included in the 6 mM

4-AP bath solution to prevent epileptic behavior in the CA3 region of the hippocampus due to pharmacological block of K(A) channels.

3.3.3. Data Acquisition

Current clamp recordings were obtained using a BVC-700 patch-clamp ampliﬁer (Da- gan Instruments) with bridge balance and capacitance compensation. Electrophysiological data were acquired using a Power Macintosh computer with an ITC-18 interface using custom macros written in IGOR Pro. A series of 600 ms long hyperpolarizing and depolarizing current injections were made at the somatic electrode, ranging in step size from -300 pA to 100 pA. These were followed by a 100 ms long subthreshold double-exponential current waveform to elicit simulated excitatory postsynaptic potentials (iEPSP). This protocol was repeated once a minute for the duration of each experiment (50-60 mins).

Statistical signiﬁcance was determined using Student’s t-test with a signiﬁcance level of

5% (P < 0.05). 88

3.3.4. Histology

In order to morphologically identify neurons during recording, 0.1% biocytin was included in the internal pipette solution. Upon termination of experiments, the pipette was carefully withdrawn from the cell and the cell was allowed to reseal. In order to visualize the neuron, slices were ﬁxed in 4% paraformaldehyde, stored for up to two weeks at 4 ◦C and then reacted with avidin-horseradish peroxidase 3,3’-diaminobenzadine.

3.3.5. Compartmental Modeling

Simulations were performed using the NEURON Simulation Environment (Hines and

Carnevale, 1997) with the variable time-step integration method (CVODE). A previously reconstructed CA1 pyramidal cell morphology (Golding et al., 2005) from rat hippocampus was used in all simulations. Spine density and parameters were accounted for as described previously. Models included both passive properties (membrane resistance, membrane capacitance and axial resistance) as well as the following active conductances: sodium, sodium with slow recovery from inactivation (Menon et al., 2009), delayed rec- tiﬁer potassium, A-type potassium, D-type potassium and a hyperpolarization-activated cation current (Ih). Passive properties were constrained with electrophysiological recordings for voltage attenuation (Golding et al., 2005) assuming a uniform axial resistance

(Ra) and membrane capacitance (Cm).

Apical dendrites. The distribution of leak membrane resistance in the dendrites was assumed to be given by the expression

Rm(soma) − Rm(end) Rm = Rm(end) + (3.1) 1 + exp ((d − d1/2)/z) 89

where Rm(soma) is the membrane resistance at the soma, Rm(end) is the membrane resistance at the distal end of the apical dendrite, d1/2 is the function midpoint value between the two, d is distance from the soma and z is the steepness factor. Three diﬀerent distributions of Rm were tested: sigmoidally increasing from soma to dendrite (Rm(soma) < Rm(end)), sigmoidally decreasing from soma to dendrite (Rm(soma) > Rm(end)) and uniform (Rm(soma)

= Rm(end)).

Parameters for Ih properties were constrained by previous results from electrophysiological recordings (Golding et al., 2005) yielding an increasing sigmoidal distribution as a function of distance from the soma for the peak conductance (gh):

gh(end) − gh(soma) gh = gh(soma) + (3.2) 1 + exp ((d1/2 − d)/z)

Here gh(soma), gh(end), d1/2, d and z are parameters similar to those used in Equation 3.1.

The apical dendrites also contained state-dependent Na+ channel models exhibiting both fast and slow recovery from inactivation (Menon et al., 2009). The total Na+ conductance in the primary apical dendrites was based on previous experimental results (Hoﬀman et al., 1997; Mickus et al., 1999). To produce proper activity-dependent attenuation of backpropagating action potential trains (Menon et al., 2009), the conductance density of a slowly inactivating sodium peak conductance (gNa(S)) was modeled as a linearly increasing function,

  gNa · sNa(s) soma (d = 0), gNa(S) = (3.3)  d gNa · [d · sNa(d) + 1 − 400 ) · sNa(s)] d > 0. 90

+ where sNa(d) is the fraction of slowly inactivating Na in the distal apical dendrite, sNa(s) is the fraction of slowly inactivating Na+ in the soma, d is distance in µm from the soma

+ 2 and gNa is the total Na conductance at the soma (S/cm ). The non-slowly inactivating

+ Na peak conductance (gNa(F)) was modeled as a decreasing linear function,

  gNa · fNa(s) soma (d = 0), gNa(F) = (3.4)  d gNa · [d · fNa(d) + 1 − 400 ) · fNa(s)] d > 0.

+ where fNa(d) is the fraction of non-slowly inactivating Na in the distal apical dendrite,

+ + fNa(s) is the fraction of non-slowly inactivating Na in the soma and gNa is the total Na

2 conductance at the soma (S/cm ). In oblique apical dendrites, gNa(F) and gNa(S) were set equal to half the conductance values at the junction of the oblique dendrite with the primary apical dendrite. This was necessary to prevent spontaneous ﬁring during simulated block of K(A) channels was observed. The total gNa (gNa = gNa(F) + gNa(S)) decreased slightly with distance from the soma. Diﬀerent rates of decrease produced weakly and strongly backpropagating versions of the neuron model (Golding et al., 2001)

(Table 3.2). The strongly backpropagating model had a larger gNa in the distal apical dendrite relative to the weakly backpropagating model. The sodium reversal potential was set to ENa = +54 mV throughout the entire cell.

D-type potassium, or K(D), channels were modeled as described in Kole et al. (2007).

The peak conductance (gK(D)) was distributed with an increasing gradient along the primary apical dendrite to reﬂect experimental studies indicating that the primary apical dendrite and oblique dendrites have a larger density of K(D) channels than the soma (Metz 91 et al., 2007; Raab-Graham et al., 2006; Sheng et al., 1994) (Table 3.2). This gradient was modeled as,

  0 soma (d = 0), gK(D) = (3.5)  gD(s) · (1 + 3d) d > 100. where d is distance in µm from the soma and gD(s) is the conductance at 100 µm from

2 the soma (S/cm ). The gK(D) value in oblique dendrites was set equal to the value at the dendritic and primary apical dendrite junctions. The K(D) channel model kinetics are, g¯K(D) = gK(D) n,

0 n = (n∞ − n)/τn

n∞(V ) = 1/ 1 + exp(−(V − V1/2)/ − 40.1827)) (3.6)

2 τn(V ) = 2.0182 + 3.6404 · exp(−((V − (−40.1827)/30.3991) )

where V is the voltage in mV and V1/2 is the half-activation voltage. The potassium reversal potential was set to EK = −85 mV throughout the entire cell.

A model for delayed rectiﬁer potassium current as described in Ficker and Heinemann

(1992) was also included and distributed uniformly throughout the soma, apical dendrite, oblique dendrites and tuft. A peak conductance value was chosen so that action potentials repolarized during simulations of pharmacological block of K(A) channels (Table 3.2). The 92

+ delayed rectiﬁer K channel model kinetics are,g ¯K(DR) = gK(DR) n,

0 n = (n∞ − n)/τn αn(V ) = exp(−0.003 · (V − V1/2) · F)/(RT) n∞(V ) = 1/(1 + αn(V )) βn(V ) = exp(−0.00021 · (V − V1/2) · F)/(RT ) τn(V ) = βn(V )/(0.02 · (1 + αn(V ))

(3.7)

where V is the voltage in mV, V1/2 is the half-activation voltage, F is the Faraday constant,

R is the ideal gas constant and T is the temperature in degrees Kelvin.

The K(A) channel models and distribution were based on previous experimental studies (Hoffman et al., 1997; Migliore et al., 1999, 2005). Along the primary apical dendrite and into the oblique dendrites, gK(A) was distributed with an increasing linear gradient such that distal locations at 400 µm (or greater) from the soma exhibited a five-fold larger gK(A) than the soma. The maximal peak conductance was adjusted to fit the average increase in input resistance (27.6 ± 9.7%) seen during pharmacological block of K(A) channels (Table 3.2). The distribution for gK(A) was modeled as,

  (1 + 0.015 · d) d < 400 µm, gK(A) = gA(s) · (3.8)  6 d ≥ 400 µm where d is distance in µm from the soma and gA(s) is the peak conductance at the soma

(S/cm2). Note that the peak conductance was allowed to increase only out to a distance of 400 µm on the primary apical dendrite, after which point gK(A) was constant. Because

K(A) distal K(A) channels (> 100µm) have been shown to exhibit a hyperpolarized shift in their half-activation voltage (Hoffman et al., 1997), two different K(A) channel models 93 were used to differentiate between distal and proximal K(A) channels. A proximal K(A) channel model was used for oblique dendrites and the primary apical trunk out to a distance of 100 µm from the soma and a distal K-A channel model with a hyperpolarized shift in the half-activation voltage was used for locations at a distance greater than 100

µm from the soma (Migliore et al., 1999).

K(A) channel kinetics are,g ¯K(A) = gK(A) mh (for distal and proximal models),

0 h = (h∞ − m)/τh αh(V ) = exp(0.113 · (V + 56)) h∞(V ) = 1/(1 + αh(V )) (3.9) βh(V ) = exp(0.113 · (V + 56)) τh(V ) = 0.26 · (V + 50)

For proximal channels,

0 m = (m∞ − m)/τm αm(V ) = exp(0.038 · zm(V ) · (V − 11))

m∞(V ) = 1/(1 + αm(V )) βm(V ) = exp(0.021 · zm(V ) · (V + 56)) (3.10)

τm(V ) = 4 · βm(V )/(1 + αm(V )) zm(V ) = −1.5 − 1/(1 + exp((V + 40)/5))

For distal dendrites,

0 m = (m∞ − m)/τm αm(V ) = exp(0.038 · zm(V ) · (V + 1))

m∞(V ) = 1/(1 + αm(V )) βm(V ) = exp(0.015 · zm(V ) · (V + 56)) (3.11)

τm(V ) = 4 · βm(V )/(1 + αm(V )) zm(V ) = −1.8 − 1/(1 + exp((V + 40)/5))

Basal dendrites. Basal dendrites contained the following active conductances distributed uniformly: gNa(F), gNa(S), gK(A), gh and gK(DR). All active conductances in the 94 basal dendrites were set to values equivalent to their somatic values with the exception of

+ gNa(F) and gNa(S). The Na peak conductances were set to 0.15 times that of their somatic values to prevent spontaneous dendritic spiking during simulations of pharmacological block of K(A) and K(D) channels.

Axon. A simulated version of a myelinated axon was attached with passive properties and active conductances distributed as described in previous computational and experimental studies (Golding et al., 2001; Hu et al., 2009; Kole et al., 2007, 2008; Lai and Jan, 2006;

Mainen et al., 1995). In all axonal segments, the axial resistivity was set to 100 Ω-cm.

In nodal segments, the membrane resistance was set to 37.5 Ω-cm2; a value of 15,000

Ω-cm2 was used in the rest of the axon. The membrane capacitance of all axonal sections was set to the somatic Cm, with the exception of internodal sections where Cm was set to 0.05 µF/cm2 to simulate myelin. The following active conductances were included in

+ the axonal model: low-threshold Na (gNa(L) described below), gNa(F), gK(D) and gK(DR)

(Table 3.2).

The delayed rectiﬁer K+ conductance was distributed uniformly in all axonal segments with gK(DR) in the initial segment and nodes set to ﬁve times that of the somatic value so that the axonal action potential would repolarize during simulations of pharmacological

2 block of K(D) channels. In all other axonal sections, gK(DR) = 0.05 (S/cm ).

The distal axonal initial segment (AIS) has been determined to be the preferred location for action potential initiation. Therefore, to initiate action potentials in the distal

AIS, a low-threshold Hodgkin-Huxley based Na+ channel model was distributed with an increasing linear gradient from soma to the distal AIS, with activation and inactivation curves shifted hyperpolarized compared to the soma and dendrites (Colbert and Pan, 95

2002; Hu et al., 2009; Kole et al., 2008; Mainen et al., 1995). At the same time, gNa(F) was distributed with a decreasing linear gradient from soma to distal AIS. The maximal

2 gNa(L) in the AIS increased as described from 0.007 to 0.06 S/cm and the maximal gNa(F) decreased from 0.025 to 0.005 S/cm2. This resulted in a two-fold larger maximal Na+ current in the distal AIS than in the perisomatic region. Nodal and internodal sections contained only low-threshold Na+ channels with peak conductances of 0.035 and 0.002

S/cm2, respectively.

Consistent with previous experimental ﬁndings (Kole et al., 2007), gK(D) was also distributed in the axon with an increasing linear gradient from soma to distal AIS such that the maximal gK(D) was 15 times that of the proximal axon initial segment conductance

(g ). In nodal sections, g was set to the maximum value in the initial segment K(D)AIS K(D)

(15 · gK(D) soma).

3.3.6. Fitting of simulations to experimental data

To reproduce experimental voltage responses seen during pharmacological block of

K(A) and K(D) channels, both K(A) and K(D) channel models (Hoﬀman et al., 1997;

Kole et al., 2008; Migliore et al., 1999) were incorporated into a passive CA1 neuron model

(Golding et al., 2005). Peak conductances for both potassium channels were distributed throughout the dendritic tree and axon as described above. Somatic input resistance (RN) was determined by simulating a series of subthreshold current injections (-300 pA to +100 pA, 600 ms duration) and calculating the slope of the resulting voltage-current (V-I) curve.

To reproduce pharmacological block of K(A) and K(D) channels, application of 6 mM 4-

AP was simulated by a 92% reduction in gK(A) and a 95% reduction in gK(D) (Jackson 96 and Bean, 2007; Martina et al., 1998). A low concentration (100 µM) of 4-AP (block of K(D) channels) was simulated by a 90% reduction in gK(D). The somatic K(A) and

K(D) conductances were then scaled (simultaneously increasing or decreasing the dendritic values due to the linear relationship of somatic and dendritic peak conductances) until the model results of pharmacological block of K(A) and K(D) channels matched experimental

RN values.

After initial ﬁts for gK(A) and gK(D), models for slowly and non-slowly inactivating

Na+ channels were then incorporated into the neuron model. Peak conductances for both Na+ channel models were determined with ﬁts (by hand) to previous experimental data for distance-dependent voltage attenuation of backpropagating action potentials and distribution of slowly and non-slowly inactivating Na+ channels in CA1 pyramidal neurons

(Baranauskas and Martina, 2006; Golding et al., 2001; Mickus et al., 1999). In addition, the axon was checked to verify that action potentials were being initiated in the distal portion of the AIS.

Following the inclusion of active conductances, the distribution and parameters for

Ih and passive properties were reinvestigated through optimized ﬁts to experimental subthreshold voltage responses recorded in the presence and pharmacological block of H- channels (Golding et al., 2005) using NEURON’s Multiple Run Fitter.

All of the above simulations for active conductances were performed again to verify that the model output had not changed signiﬁcantly as a result of the optimization.

Parameters were adjusted and the overall process was repeated if the model results for

RN, backpropagation of action potentials or ﬁts had changed. 97

3.4. Results

I measured the eﬀects of pharmacological block of K(A) and K(D) channels on somatic subthreshold voltage responses in CA1 pyramidal neurons. Experimental results suggest that a signiﬁcant fraction of K(A) channels are available near resting potentials and thus aid in shaping voltage responses to subthreshold current injections. These experiments were then used to constrain peak conductances for both K(A) and K(D) channel models in a previously passive compartmental neuron model. The model was then further constrained by experimental data on voltage attenuation and action potential backpropagation to provide more accurate results from future simulations.

3.4.1. Experimental measurements of somatic input resistance

Using whole-cell patch clamp recordings in brain slices from adult male rats, I ﬁrst measured the eﬀect of pharmacological block of K(A) and K(D) channels on somatic RN in CA1 hippocampal neurons. To prevent errors in measurements due to series resistance changes, the series resistance was monitored throughout the course of the experiment.

Only recordings that maintained a relatively constant series resistance (< 10% increase over a duration of 50 minutes) were considered. All cells were held at a resting potential of -67 mV for the duration of each experiment.

A series of long current injections (-300 pA to +100 pA, 600 ms duration) were made at a somatic electrode and the resulting voltage responses were measured at the same location. RN was calculated as the slope of the V-I curve. To investigate changes in

RN due to block of K(D) or K(A) channels, RN was measured and averaged in control

ACSF during an initial baseline period (0-10 min) at the beginning of each experiment. 98

Following this baseline period, an ACSF solution with either 100 µM 4-AP or 6 mM 4-AP was bath applied to block K(D) channels or both K(D) and K(A) channels, respectively.

The resulting somatic RN was monitored throughout the remainder of the experiment. A

ﬁnal RN value was measured and averaged 40-50 minutes into the experiment.

The average RN in control ACSF during the baseline period (0-10 min) was 51 ± 6

MΩ and did not significantly increase when measured in control ACSF (no drug application) 40-50 minutes later (Table 3.1, Figure 3.1A). Bath application of 100 µM 4-AP to block K(D) channels did not significantly change RN (Table 3.1, Figure 3.1B). Cells in which 6 mM 4-AP was applied to block K(A) channels exhibited an average 27% increase in RN from 51 ± 4 MΩ (baseline) to 64 ± 4 MΩ (final) (Table 3.1 Figure 3.1B). This increase in RN suggests that a significant fraction of K(A) channels are open at resting potentials. During bath application of 6 mM 4-AP, several cells required additional positive holding current to maintain a resting potential value of -67 mV, indicating that the cells experienced a membrane hyperpolarization consistent with other studies that saw a membrane hyperpolarization or no change in membrane potential when applying 4-AP

(Buckle and Haas, 1982; Fujiwara and Kuriyama, 1983; Li et al., 2003; Navarro-Polanco and S´anchez-Chapula, 1997)

3.4.2. Experimental measurement of somatic iEPSPs

To elicit simulated postsynaptic potentials, somatic current injections were modeled as double exponential functions with a rise time (τr) of either 0.2 or 0.5 ms, a decay time (τd) of 2 or 5 ms and a maximal current of 500 or 250 pA, respectively. The peak amplitude of the current-evoked somatic potentials (iEPSPs) remained constant over time in control 99

Baseline Final (0-10 min) (40-50 min)

Control 51 ± 6 (8) 52 ± 5 (8) 31 - 88 40 - 88 100 µM 4-AP 58 ± 5 (8) 59 ± 4 (8) 36 - 74 36 - 74 6 mM 4-AP 51 ± 4 (9) 63 ± 4 (9) 38 - 78 53 - 92

Table 3.1. RN (MΩ) in control ACSF and 4-AP. Cells in control conditions or in bath application of 100 µM 4-AP did not show a change in their somatic RN during the ﬁnal test period compared to the baseline time period. However, cells in bath application of 6 mM 4-AP showed a strong increase in somatic RN during the ﬁnal test period compared to the baseline period. Values are the mean ± s.e.m. (n) and range. 100

A Control +50 pA 70 60 2 mV ) )

Ω Ω 100 ms 60 40 (M (M

N 50 N 20 10 mV R R 100 ms 40 0 -300 pA 0 10 20 30 40 n = 8 Time (min) Baseline Baseline Final (40-50 min) Final (40-50 min) B 100 µM 4-AP

60 ) ) 70 Ω Ω 60 40 (M (M N N R

R 50 20 40 0 0 10 20 30 40 n = 8 Time (min) C 6 mM 4-AP *** 60 )

) 70 Ω Ω 60 40 (M (M N N

50 R 20 R 40 0 0 10 20 30 40 n = 9 Time (min)

Figure 3.1. RN changes in control ACSF and following application of 4-AP. Somatic RN was measured and averaged in control ACSF during an initial baseline period (0-10 min) and during a final period 40-50 minutes later. A,B,C: (Left) The measured RN (MΩ) over time (minutes) for one cell. (Middle) Averaged RN during the baseline period and the final test period. (Right) Sample somatic voltage responses to 600 ms depolarizing (+50 pA) and hyperpolarizing (-300 pA) current injections during baseline (black) and final (red) periods. Scale bars in A apply to B and C. A: Somatic RN shows no significant change over time in control ACSF (n = 8; t-test; P > 0.05). B: Somatic RN does not change following application of 100 µM 4-AP (n = 8; t-test; P > 0.05). Arrow indicates time of drug application. C: Somatic RN significantly increases following bath application of 6 mM 4-AP (n = 9; t-test; P < 0.001). 101

ACSF or following application of either concentration of 4-AP (Figure 3.2A-C, middle).

In addition, there was no signiﬁcant change in iEPSP amplitude between control ACSF,

100 µM 4-AP and 6 mM 4-AP cell groups (Figure 3.2D, right).

The area under the iEPSP increased an average of 10% over time in control ACSF

(s.e.m ± 3.5%, Figure 3.2A, left). After bath application of 100 µM 4-AP, iEPSP area increased an average of 13% (s.e.m ± 2.6 %, Figure 3.2B, left). Application of 6 mM 4-

AP resulted in an average 18% increase over time (s.e.m ± 1.7%, Figure 3.2C, left). The increase in iEPSP area following bath application of 6 mM 4-AP is signiﬁcant compared to iEPSP area increases in both control ACSF and 100 µM 4-AP (Figure 3.2D, left).

3.4.3. Simulation of subthreshold responses

The reconstructed CA1 pyramidal neuron morphology was used to investigate how different conductances available at resting membrane potentials shape subthreshold responses. Simulations were performed using the built-in run-fitter in the NEURON environment to reproduce experimentally measured voltage responses at both the soma and distal apical dendrite (Golding et al., 2005) with different combinations of channel conductances present. In initial fits, Ra,Cm and Rm were allowed to vary independently without the H-conductance (gh) present in the model to simulate previous experimental pharmacological block of H-channels with cesium (Cs+) and ZD7288. All other peak conductances (gK(A), gK(D), gNa(F), gNa(S), gK(DR)) were unchanged. In addition, I examined whether voltage responses were best fit using a uniform (constant) Rm distribution or a non-uniform Rm distributed sigmoidally from soma to distal dendrite as described in the

Methods. 102

A Control Control Control 1.4 * 1.4 4 mV 1.2 1.2 10 ms 1.0 1.0

Normalized area iEPSP 0.8 0.8 010 20 30 40 50 Normalized iEPSP amplitude 010 20 30 40 50 Baseline Time (ms) Time (ms) Final (40-50 min)

B 100 µM 4-AP 100 µM 4-AP 100 µM 4-AP 1.4 ** 1.4 1.2 1.2 1.0 1.0

Normalized area iEPSP 0.8 0.8 0 10 20 30 40 50 Normalized iEPSP amplitude 010 20 30 40 50 Time (ms) Time (ms) C 6 mM 4-AP 6 mM 4-AP 6 mM 4-AP

1.4 *** EPSP 1.4 de 1.2 1.2 litu 1.0 1.0 amp Normalized area iEPSP 0.8 0.8 010 20 30 40 50 Normalized i 010 20 30 40 50 Time (ms) Time (ms) D 25 10 x 100 x 100 20 * 8 15 6 10 4 5 2 0 0 iEPSP amp. iEPSP iEPSP amp. iEPSP iEPSP area iEPSP area iEPSP

Control M 4-AP Control M 4-AP µ µ 6 mM 4-AP 6 mM 4-AP 100 100

Figure 3.2. Somatic iEPSP area and amplitude in control ACSF and after application of 4-AP. Figure caption continued on the next page. 103

Figure 3.2. Measurement of iEPSP area and amplitude in control ACSF, 100 µM 4-AP and 6 mM 4-AP. The current injection waveform was calculated as the sum of double exponentials with τr = 0.5 ms, τd = 5 ms and Imax = 250 pA. A,B,C: (Middle) iEPSP amplitude shows no significant change over time in control ACSF or after application of 100 µM 4-AP or 6 mM 4-AP. Baseline period (0-10 min) is indicated in black and a final test period (40-50 min) is indicated in red. A: (Left) In control ACSF, the area under the iEPSP shows a significant change increase time (n = 8; t-test; P < 0.05). At far right, sample iEPSP traces from one CA1 pyramidal neuron during baseline (black) and final (red) test periods. Scale bars apply to B and C. B: (Left) Bath application of 100 µM 4-AP causes a significant increase in the area under the iEPSP (n = 8; t-test; P < 0.01). C: (Left) Over time, the area under the iEPSP increases significantly in the presence of 6 mM 4-AP (n = 9; t-test; P < 0.001). D: (Left) The change in iEPSP area compared across the three cell groups is significant only following application of 6 mM 4-AP (t-test; P < 0.05). (Right) There is no significant change in iEPSP amplitude between cell groups in control ACSF or application of 4-AP. 104

Simulations revealed that when the K(A) conductance was included in the model, a uniform distribution for Rm provided equally accurate ﬁts to voltage responses as a nonuniform distribution (Figure 3.3 B,D). As this result for the Rm distribution diﬀered from previous computational studies (Golding et al., 2005), I investigated various distributions for Rm using a model that included only passive properties and varying amounts of the

2 total somatic gK(A) (0.06 S/cm ). Three different distributions of Rm were modeled: uniform, sigmoidally increasing from soma to dendrite (Rm (soma) < Rm (end)) and sigmoidally decreasing from soma to dendrite (Rm (soma) > Rm (end)). Consistent with the previous studies, these simulations showed that a sigmoidally decreasing Rm distribution provides the best fits to experimental voltage responses when a K(A) conductance is not present in the model. However, as an increasing amount of the total gK(A) was introduced into the passive neuron model, the normalized error in fits for the three proposed distributions approached approximately the same value (Figure 3.3 D). Specific parameter values are given in Table 3.2.

To further understand why a variable Rm distribution is not required to produce a realistic subthreshold response when a K(A) conductance is present, the effective membrane resistivity was calculated along the primary apical dendrite. Effective membrane resistivity (Reff ) was defined as 1/Σgi where Σgi is the sum of each of the active conductances

(including the leak conductance) available at the resting potential. This calculation was performed in the active model (both K(A) and K(D) conductances present) and in a passive model with nonuniform distributions of Rm and gh (Figure 3.4). In both models, Reﬀ is largest in the somatic and proximal apical dendritic regions and decreases into the distal portion of the apical dendrite. This is consistent with experimental results indicating that 105

Passive Properties

Property Value Property Value

5 2 2 Rm 2.25 · 10 (Ω · cm ) gh (soma) 0.39142 (pS/µm ) 2 Ra 176 (Ω · cm) gh (dend) 2.6884 (pS/µm ) 2 Cm 1.4 µF/cm d1/2 151.55 µm z 24.624 Potassium Channel Properties

Property Value Property Value

−05 2 2 gD(s) 1.5 · 10 S/cm gDAIS 0.00015 S/cm g 0.03 S/cm2 g 0.05 S/cm2 K(DR) K(DR)hill g 0.15 S/cm2 K(DR)AIS 2 gA(s) 0.06 S/cm Axonal Sodium Channel Properties

Property Value Property Value

2 2 gNa(L) (prox) 0.007 S/cm gNa(L) (dist) 0.06 S/cm 2 2 gNa(F) (prox) 0.025 S/cm gNa(F) (dist) 0.005 S/cm Table 3.2. Passive and active channel parameter values. 106

A B D 5 4 dendrite 3 zed error soma li 1 mV 2

50 ms

Norma in fits - passive 1

0.0 0.2 0.4 0.6 0.8 1.0 Model % gK(A) in model Experiment Non-uniform Rm (dec. soma to dendrite)

Uniform Rm (constant soma to dendrite) C E Non-uniform Rm (inc. soma to dendrite)

5 dendrite 4 h

soma I - 3 zed error li its 2 in f Norma 1

0.0 0.2 0.4 0.6 0.8 1.0 % gK(A) in model

Figure 3.3. Best fits to estimated passive properties and gh distribution A: A morphological reconstruction of a CA1 pyramidal neuron (Golding et al., 2005). Dendritic and somatic recording electrode locations are indicated schematically. B: Experimental somatic and dendritic voltage responses (red) to a -50 pA, 400 ms long current injection in 5 mM CsCl (to block H-channels) and best fits (black) with a uniform Rm distribution. Scale bar also applies to C. C: Experimental voltage responses (red) to a -30 pA, 400 ms long current injection in control ACSF and best fits (black) with an increasing sigmoidal distribution of gh. D: Normalized error in fits to voltage responses for estimated passive properties and distribution (Ra,Cm, Rm) with increasing amounts of the total gK(A). Different distributions of Rm were simulated: sigmoidally increasing (black), sigmoidally decreasing (blue) and uniform (red). E: Normalized error in fits to voltage responses for a sigmoidally increasing distribution of gh with different distributions of Rm and increasing amounts of gK(A). 107 the effective dendritic membrane leak conductance is larger in more distal locations causing strong voltage attenuation of signal propagation in CA1 pyramidal neurons (Golding et al., 2005). In the passive model, an increasing nonuniform Rm distribution is necessary to reproduce this larger effective dendritic membrane leak conductance (lower Reff ) in more distal locations of the neuron (Figure 3.4B). However, in the active model, the

K(A) conductance creates a lower Reﬀ due to its strongly increasing gradient from soma to distal dendrite (Figure 3.4A). As a result, a nonuniform distribution of Rm is no longer required to reproduce experimental results of voltage attenuation and eﬀective dendritic membrane leak conductance.

3.4.4. Simulation of action potential backpropagation

Previous experimental research describing action potential backpropagation in CA1 pyramidal neurons has revealed a dichotomy in the strength of action potential backpropagation. Some cells exhibit strong backpropagation (> 40 mV) into the distal portion of the apical dendrite, whereas others exhibit weak backpropagation (< 25 mV). Further- more, these backpropagating action potentials display an activity dependent attenuation during repetitive ﬁring due to prolonged inactivation of sodium channels (Andreasen and

Lambert, 1995; Callaway and Ross, 1995; Golding et al., 2001; Mickus et al., 1999; Sprus- ton et al., 1995b).

To verify that this behavior was correctly reproduced in the model, I simulated action potential backpropagation and amplitude attenuation during repetitive ﬁring. To do this,

I incorporated a six-state Na+ model that exhibits slow recovery from inactivation and a ﬁve-state Na+ model with fast recovery (Menon et al., 2009). These Na+ models were 108

A B R vs. g : Active model R vs. g : Passive model -3 m i m i x 10 x 10-3 0.25 20 0.25 20 Effective R Effective R ) 2 )

0.20 2 0.20 15 15

(S/cm 0.15

(S/cm 0.15 m m rest 10 10 (M (M rest 0.10 0.10 Ω at V at Ω i at V at -cm g -cm 5 i g 5 0.05 0.05 2 2 ) ) 0 0 0 0

50 50 100 150 200 250 300 350 400 450 100 150 200 250 300 350 400 450 Distance from soma (μm) Distance from soma (μm)

gK(A) g K(D) g h g Na gK(DR) gLeak

R eff

Figure 3.4. K(A) channels are primarily responsible for lower Reff in distal locations A: Reff (right axis) and the conductance for each active current (left axis) at the resting potential are plotted against distance from the soma (µm) in an active model. B: Reff and the conductance for the leak and H-current (left axis) at the resting potential are plotted against distance from the soma (µm) in a passive model. K(A) channel conductance increases into the distal apical dendrite, accounting for the strong decrease in Reff and removing the necessity of a nonuniform Rm distribution to reproduce accurate voltage attenuation. 109 distributed in the primary apical dendrite such that the weakly backpropagating model had a lower Na+ conductance in the distal portion of the apical dendrite compared to the strongly backpropagating model (Table 3.3). The only differences between the two models were the sodium conductances in the distal apical dendrites. The model neuron displayed strong action potential backpropagation (> 40 mV at 350 µm) with the larger gNa and weak action potential backpropagation (< 25 mV at 350 µm) with the smaller gNa. Both models exhibited amplitude attenuation during repetitive firing consistent with experiments (Golding et al., 2001) due to the presence of the slowly-inactivating

Na+ channel model (Figure 3.5).

3.4.5. Simulation of somatic and axonal action potentials

In addition to ﬁtting voltage responses for passive properties and gh distribution parameters to create a biophysically realistic model, I also included a model axon. Recent experimental and computational studies strongly suggest that action potentials originate in the distal portion of the axon initial segment (AIS) due to a high density of

+ low-threshold Na channels (Nav1.6) that are accumulated at the distal end of the AIS.

+ High-threshold Na channels (Nav1.2) are distributed with a higher density at the proximal site of the AIS and aid action potential propagation to the soma and help determine somatic spike threshold (Hu et al., 2009; Kole et al., 2008). In addition, the AIS has been found to contain a 10-fold increase in Kv1 channels over the ﬁrst 50 µm. The Kv1 subfamily, which underlie K(D) channels, give rise to slowly-inactivating, low threshold K+ channels that are believed to play a signiﬁcant role in shaping action potential waveform

(Kole et al., 2007). Based on these ﬁndings, we distributed the low- and high-threshold 110

Model gNa (soma) fs ss fd sd gNa (dend) Weak bAP 0.032 (S · cm−2) 0.9 0.1 0.2 0.5 0.0288 (S · cm−2) Strong bAP 0.032 (S · cm−2) 0.9 0.1 0.25 0.65 0.0244 (S · cm−2)

Table 3.3. Na+ conductance distribution values for neuron models Parameter values for the distribution of both Na+ models (described in + Methods), where gNa (soma) is the total Na conductance at the soma, fs is + the fraction of the total somatic Na conductance (gNa (soma)) that exhibits fast recovery, ss is the fraction of gNa (soma) that exhibits slow inactivation, fd is the fraction of gNa (soma) at 400 µm along the primary apical dendrite that exhibits fast recovery and sd is the fraction of gNa (soma) at 400 µm along the primary apical dendrite that exhibits slow inactivation. Note that in both models, the dendritic fractions do not sum up to 1.0 due to an overall decrease in the Na+ conductance from soma to distal dendrite. The ﬁnal column gives the resulting dendritic conductance at 400 µm from the soma. 111

A C Weakly backpropagating 100 80 20 mV 60 100 ms 40

soma 20 First AP ampl. (mV) First AP 0 0 100 200 300 400 Distance from soma (µm) dendrite

B Experimental data Strong (model) Strongly backpropagating Weak (model) 100 80 60 40 soma 20

Last AP ampl. (mV) Last AP 0 0 100 200 300 400 Distance from soma (µm) dendrite

Figure 3.5. Simulations of weak vs. strong backpropagation Simulated trains of action potentials were elicited by a 900 ms long depolarizing somatic current injection. A: The ﬁrst action potential amplitude (mV) in a train of action potentials is plotted against distance from the soma (µm) along the primary apical dendrite. Experimental data (Golding et al., 2001) is indicated by black squares and triangles, the weakly backpropagating model in blue and the strongly backpropagating model in red. Protocol and legend apply to B and C. B: The amplitude (mV) of the last action potential in a train is plotted against distance from the soma (µm) along the primary apical dendrite. C: (Left) A morphological reconstruction of a CA1 pyramidal neuron. Dendritic and somatic recording electrodes are indicated schematically. (Right) Somatic and dendritic (350 µm) voltage responses for both weakly (top) and strongly (bottom) backpropagating models. 112

+ Na conductances and gK(D) in the model axon such that action potentials originated in the distal portion of the AIS and propagated antidromically to the soma and dendrites

(Figure 3.6A). Phase plots of simulated axonal and somatic spikes, as well as calculated somatic and axonal half-widths and maximal rates of rise (Figure 3.6 B-D) were consistent with experimental and computational results (Golding et al., 2001; McCormick et al.,

2007).

3.4.6. Comparison of computational and experimental results with A-type

channel blockers

Consistent with previous studies, gK(A) was distributed with an increasing gradient along the primary apical dendrite such that the distal portion of the primary apical dendrite had a 5-fold larger conductance than the somatic region (Chen and Johnston, 2004;

Connor and Stevens, 1971; Hoﬀman et al., 1997; Magee and Carruth, 1999). Simulation of pharmacological block of K(A) and K(D) channels revealed that a somatic gK(A) value

2 of 0.06 S/cm was necessary to reproduce the average 27% increase in RN seen during experimental application of 6 mM 4-AP. Model voltage responses to subthreshold current injections were compared to individual experimental voltage traces in the presence of A-type channel blockers to verify the model accuracy (Figure 3.7).

Steady-state voltage responses during simulation of pharmacological block of K(D) channels are in good agreement with experimental steady-state voltage responses. Note that in Figure 3.7A, bottom, the model voltage responses are identical in both control and simulated pharmacological block conditions such that the voltage response for simulated block of K(D) channels completely overlays the response in the control condition. In order 113

AB 300 300

200 200

100 100 dV/dt (V/s) dV/dt (V/s)

0 0 0 20 mV -100 -100 1 ms -70 -50 -30 -10 10 -70 -50 -30 -10 10 Voltage (mV) Voltage (mV) Axon initial segment Soma Axon initial segment Soma C D 1.2 350 1.0 250 0.8 0.6 150 0.4 0.2 50 AP max dV/dt (V/s) AP AP half-width (ms) AP 0.0 Soma AIS Soma AIS

Figure 3.6. Spike initiation in a CA1 pyramidal cell model A: Distal AIS (blue) and somatic spikes (black) in response to a 1.2 nA somatic current injection. The action potential occurs in the distal AIS ﬁrst and then propagates the soma. B: Phase plot (dV/dt vs. V) of the axonal and somatic spikes in A. C: AP half-width (ms) of the somatic and axonal spikes in A. D: Maximal rate of rise (V/s) of the somatic and axonal spikes in A. 114 to achieve a slight diﬀerence in the steady-state voltage responses between control and simulated application of 100 µm 4-AP, it was necessary to incorporate a small reduction

(∼10%) of the K(A) conductance (not shown) in the model.

Model steady-state voltage responses for both hyperpolarizing and depolarizing current injections during simulated block of K(A) channels are also in good agreement with experimental voltage traces. However, accurate reproduction of the time course of voltage sag for hyperpolarizing current injections during simulation of pharmacological block of both currents was not achieved (Figure 3.7 B). Experimental observations indicated that iEPSP amplitude showed no signiﬁcant change over time following bath application of

6mM 4-AP while the area under the iEPSP increased slightly, but signiﬁcantly (∼7%), compared to control conditions. Model voltage responses for a simulated iEPSP verify the experimental observation that the peak of the iEPSP is essentially unchanged with simulated block of K(A) channels (and K(D) channels), while the area under the iEPSP increases signiﬁcantly compared to control voltage responses (Figure 3.7 B, right).

3.5. Discussion

3.5.1. Passive membrane properties

In CA1 pyramidal neurons, the extent to which synaptic potentials attenuate as they propagate from distal dendrite to soma strongly depends on the dendritic architecture and the distribution of membrane properties within it. Cable theory indicates that smaller diameter dendrites produce larger depolarizations due to having a greater input impedance, and larger diameter dendrites produce a smaller depolarization due to a smaller input impedance (Rall et al., 1992). At the same time, larger depolarizations often lead to 115

A +50 pA 2 mV 2 mV 100 ms 5 ms Experiment -300 pA 10 mV 100 ms Control IK(D) blocked

Model

Experiment -300 pA +50 pA

Control IK(D), IK(A) blocked

Model

Figure 3.7. Model validation: Subthreshold current injections A: (Top) Experimental somatic voltage responses to a somatic hyperpolarizing current injection (-300 pA, 600 ms), a somatic depolarizing current injection (50 pA, 600 ms) and a simulated somatic iEPSP (τr = 0.5 ms, τd = 5.0 ms, Imax = 250 pA) in control ACSF (black, 0-10 min) and following bath application of 100 µM 4-AP (red, 40-50 min). (Bottom) Model neuron voltage responses to the same current injections in simulated control ACSF (black, all conductances present) and simulated block of K(D) channels (red). Scale bars and current injection amplitudes apply to B as well. B: (Top) Experimental voltage responses to somatic current injections in control ACSF (black) and following bath application of 6 mM 4-AP (red). (Bottom) Model neuron voltage responses in simulated control ACSF (black) and during simulated block of both K(D) and K(A) channels. 116 greater charge transfer to the soma. However, large local EPSPs produced by synapses on distal smaller dendrites reduce the synaptic driving force, thus decreasing charge transfer to the soma and strongly attenuating the synaptic potential as it travels passively to the soma (Carnevale and Johnston, 1982; Jaﬀe and Carnevale, 1999). Furthermore, simultaneous somatic and dendritic patch-clamp recordings have suggested that membrane resistance in CA1 neurons is nonuniform, with the distal dendrites being ‘leakier’ (lower membrane resistance) than more proximal locations (Golding et al., 2005) causing further attenuation of EPSPs. Therefore, the impact of a synapse on neuronal output will depend not only on its location within the dendritic tree, but on its passive membrane properties as well.

Our modeling results are consistent with these findings in that membrane resistivity can be modeled as a nonuniform property in a passive neuron model, reproducing experimentally measured estimates of EPSP attenuation (Magee and Cook, 2000; Golding et al., 2005). Initial fits in a passive model yielded best-fits with a nonuniform membrane resistivity. However, it is well known that dendrites in CA1 pyramidal neurons contain active voltage-gated channels that are important for shaping dendritic filtering properties. The K(A) current increases 5-fold from soma to distal apical dendrite and is available at resting potentials. With the inclusion of this large outward conductance in the previously passive model, I found that fits to steady-state voltage responses (in the absence of H-channel models) were equally as accurate with all three distributions for

Rm. The increasing density of A-type potassium channels available at resting potentials in the distal portion of the apical dendrite replaced the requirement for a nonuniform 117

Rm to reproduce experimental voltage attenuation. We also tested the steady-state attenuation in the fully passive model with nonuniform Rm and models that contained a

K(A) conductance and distributions of either nonuniform or uniform Rm (Figure 3.8 A).

While attenuation was greatest in the completely passive model with a nonuniform Rm distribution, voltage attenuation in all three models fell within experimental ranges.

3.5.2. H-conductance distribution and best-ﬁts

One problem that arises when trying to determine passive membrane properties and their distribution is the presence of voltage-gated conductances that are active at resting potentials. Both the hyperpolarization-activated cation conductance (gh) and the K(A) conductance are available at resting potentials and regulate the shape of subthreshold voltage responses.

Experimental and modeling studies in layer V and CA1 pyramidal neurons suggest that gh is distributed with an increasing nonuniform gradient from the soma to distal dendrites such that a more than sixfold increase in channel density is seen in more distal locations (Berger et al., 2001; Golding et al., 2005; Magee, 1998; Stuart and Spruston,

1998; Williams and Stuart, 2000). This large conductance, which is active at resting potentials and increases with distance from the soma, further maximizes voltage attenuation of distal EPSPs. Consistent with these studies, I found that including a nonuniform increasing gradient for gh provided accurate ﬁts to steady-state voltage responses and attenuation in both the passive model and the model with active conductances. Compar- ison of steady-state attenuation in a passive model with nonuniform Rm and an H-channel model present and neuron models with K(A) channel models, an H-channel model and 118

A 1.0

soma 0.8 5 mM CsCl / V / 0.6 50-100 µM ZD7288 0.4 Uniform Rm, 100% gK(A) 0.2 Non-uniform R , 100% g dendrite m K(A) V 0.0 Non-uniform Rm, 0% gK(A) 0 50 100 150 200 250 300 350 Distance from soma (µm)

B C Hyperpolarizing Vsag (soma) 1.0 0.030 Depolarizing Vsag (soma) 0.8 0.025 Depolarizing V (dend)

soma sag 0.6 0.020 Hyperpolarizing V (dend)

/ V / sag 0.015 0.4 Control 0.010 100% g infits MSE 0.2 K(A)

dendrite 0% g 0.005

V K(A) 0.0 0.000 0 50 100 150 200 250 300 350 0.00 0.25 0.50 0.75 1.00 Distance from soma (µm) % gK(A)

Figure 3.8. Steady-state attenuation and MSE in fits to voltage transients A: The ratio of the dendritic steady-state voltage response to the somatic steady-state voltage response in response to a long current injection with H-channels blocked using CsCl or ZD7288. Filled circles and squares are experimental data (Golding et al., 2005). Model steady-state attenuations for different distributions of Rm and varying amounts of gK(A) are indicated by black, red and blue lines. B: Steady-state attenuation in experimental control conditions are indicated by open circles (Golding et al., 2001). Model steady-state attenuation for varying amounts of gK(A) are indicated by black and red lines. C: The mean square error (MSE) in fits to transient voltage responses for somatic and dendritic voltage responses to a subthreshold current injection (depolarizing or hyperpolarizing) is plotted against increasing amounts of gK(A) in a passive model with an H-channel model present. 119

either nonuniform or uniform distributions for Rm revealed that the amount of voltage attenuation is the same in all three models, in keeping with experimental results (Figure 3.8

B).

H-channels are activated by hyperpolarizing voltage responses and cause the membrane potential to return to steady-state. This results in both hyperpolarizing and depolarizing voltage ‘sags’. Previous modeling of voltage responses to long and short current injections was able to accurately ﬁt the steady-state voltage responses, but was unable to reproduce all aspects of the time course of voltage sag for depolarizing and hyperpolarizing

‘sags’. I computed the dendritic and somatic error for the depolarizing and hyperpolarizing voltage sags in a passive model with increasing amounts of gK(A) (Figure 3.8 C).

I found that as the amount of K(A) conductance increased in the model, the accuracy of the ﬁts to the transient voltages strongly improved. This suggests that the voltage- dependent properties of K(A) channels not only serve to help regulate the amplitudes of subthreshold hyperpolarizing and depolarizing voltage responses, but also plays a role in modulating transient voltage sags as a result of the fast time course of activation for K(A) channels.

3.5.3. Action potential initiation and backpropagation

Many previous experimental and modeling studies have investigated the cellular mechanisms that are involved in action potential initiation and backpropagation. Simultaneous somatic and dendritic recordings, in addition to antibody staining and modeling studies, have revealed that action potentials originate in the distal portion of the AIS due to high densities of Na+ and K(D) channels (Colbert and Johnston, 1996; Hu et al., 2009; Kole 120 et al., 2007, 2008). After initiation in the distal AIS, action potentials backpropagate into the dendritic tree. As they invade the dendritic tree, the amplitude of backpropagating action potentials attenuates with distance from the soma. In CA1 pyramidal neurons, it has been shown that a dichotomy in the strength of the backpropagating action potential occurs among neurons such that particular neurons exhibit strong backpropagation, whereas others show weak backpropagation (Golding et al., 2001). In addition, trains of backpropagating action potentials undergo a frequency-dependent amplitude attenuation as they propagate from soma to the distal portion of the apical dendrite. This frequency- dependent attenuation and the dichotomy in action potential backpropagation has been shown to be modulated by the distribution and availability of Na+ and K(A) channels

(Bernard and Johnston, 2003; Golding et al., 2001; Hoﬀman et al., 1997; Mickus et al.,

1999; Pan and Colbert, 2001; Spruston et al., 1995b).

Consistent with these studies, my simulations revealed that a slight change in the total

+ gNa could produce either weakly or strongly backpropagating neuron models. The Na channel densities in both models fell within experimentally determined ranges (Hoﬀman et al., 1997; Magee and Johnston, 1995). Furthermore, both models accurately reproduced the activity-dependent amplitude attenuation of backpropagating action potentials due to inclusion of a state-dependent Na+ model (Menon et al., 2009) that exhibited proper kinetics of slow inactivation. The activity-dependent attenuation disappeared upon removal of the slowly-inactivating Na+ channel model from the neuron model. The dichotomy in action potential backpropagation could also be reproduced in diﬀerent neuron morphologies through small changes in Na+ peak conductance and distribution (not shown). 121

While I did not vary the K(A) distribution or peak conductance in our models, it is likely that slight modulations of these channels in the distal dendrites would also give rise to a dichotomy in action potential backpropagation without strongly altering somatic input resistance (Golding et al., 2001; Hoﬀman and Johnston, 1998, 1999; Migliore et al.,

1999).

3.5.4. K(A) channels shape somatic subthreshold voltage responses

I found that pharmacological block of K(A) channels signiﬁcantly increased somatic

RN by 27% compared to control ACSF. Computational simulations of pharmacological block of K(A) channels with activation and inactivation curves as described in Hoﬀman

2 et al. (1997); Migliore et al. (1999) revealed that a large somatic gK(A) value of 0.06 S/cm with the described activation and inactivation kinetics was necessary to reproduce the experimental increase in somatic RN. This suggests that a large fraction of K(A) channels are available at resting potentials. Previous experimental studies have revealed that the large transient outward K(A) conductance strongly affects dendritic filtering properties due to a high density of K(A) channels available in the distal dendrites. The steep increase in the density of K(A) channels from soma to distal dendrite regulates action potential backpropagation, raises the threshold for local spike initiation and has been implicated in summation of subthreshold postsynaptic potentials (Hoffman et al., 1997; Frick et al.,

2004; Urban and Barrionuevo, 1998). By having a significant fraction of K(A) channels available at rest, dendrites could effectively regulate dendritic excitability through modulation of K(A) channels by synaptic depolarization, Ca2+ influx from dendritic spiking or by signaling cascades. 122

While my model accurately reproduced the time kinetics and steady-state behavior of subthreshold voltage responses in control ACSF simulations, model voltage responses during simulations of K(A) channel block exhibited a faster time course of voltage sag than seen during experiments. In addition, model voltage responses also exhibited larger hyperpolarizing and depolarizing voltage transients then experimental voltage responses.

The larger ‘sags’ and the faster time course of voltage sag seen in model voltage responses during simulated block of K(A) channels is partially due to activation of H-channels at more hyperpolarized potentials. To further reﬁne the model, additional optimization and experimental investigation of the H-channel model in the absence of K(A) channels would be required.

The slower time course of voltage sag in experiments could also be partially explained by inhibition of an inward current following application of 4-AP. Experimental studies of 4-AP application (0.5-10 mM) in rat cerebellar granule cells and rat myoblasts have indicated that 4-AP inhibits inward Na+ currents in a dose-dependent manner without signiﬁcantly altering the voltage-dependent activation and inactivation properties of Na+ currents (Lu et al., 2005; Mei et al., 2000). In these studies, cells in bath application of 5 mM 4-AP exhibited up to roughly 30% inhibition of Na+ currents and a signiﬁcant increase in the time to peak for maximal Na+ currents. Inhibition of an inward current or the electrogenic Na+/K+ pump that helps regulate membrane potential could also provide insight into the unexplained membrane hyperpolarization seen during my experiments involving high concentrations (6 mM) of 4-AP (Gordon et al., 1990; Perreault and Avoli,

1989; Wang et al., 2003). 123

Both experimental and computational results verified that with pharmacological block of K(A) and K(D) channels, voltage responses to a simulated EPSP-like current injection showed a significant increase in the area under the iEPSP, but no significant alteration of the amplitude relative to control conditions. Recent mathematical work on cable theory for synapses on spines suggest that if synaptic conductance (or in this case, a synaptic- like current injection) changes more rapidly than the membrane time constant, then the amplitude of the resulting voltage response should be independent of the membrane time constant (Harnett et al., 2012). As a result, the amplitude of the iEPSP would not be changed during pharmacological block of K(A) and K(D) channels as the peak voltage has already occurred prior to activation of the membrane currents (τm). However, a change in the area under the iEPSP during block of potassium channels would be expected as membrane currents have been activated by this point and as a result, the iEPSP would decay more slowly as the membrane voltage returns to the resting potential.

3.5.5. Block of K(D) channels does not alter RN

My experimental results and computational modeling indicate that pharmacological block of K(D) channels does not significantly impact RN, suggesting that K(D) channels do not play a significant role in shaping subthreshold voltage responses. This was further verified through model voltage responses to subthreshold current injections during simulated block of K(D) channels. Voltage responses in simulations of pharmacological block of K(D) channels did not differ from those with a K(D) channel model present. The K(D) current (IK(D)) is a rapidly activating, very slowly inactivating current that activates in subthreshold ranges and is strongly sensitive to 4-AP (Storm, 1988). As K(D) channels 124 are partly inactivated at resting potentials and have fast activation kinetics, it is likely that subthreshold hyperpolarizations and depolarizations are mediated more strongly by

K(A) channels which undergo fast activation and inactivation and are available at rest.

As a result, RN, which is determined by subthreshold voltage responses, would not be strongly aﬀected by block of K(D) channels because K(A) channels are still present to mediate these responses. While IK(D) may only comprise < 20% of the total potassium current resulting from the Kv1 subfamily and appear to not have a signiﬁcant impact on RN, the slow inactivation kinetics (τ > 200 ms, recovery from inactivation: 5s at -90 mV) of K(D) channels implicate these channels in a primary role for delay during spike

ﬁring (and intervals), slow integration of depolarizing inputs and an increase in action potential ﬁring frequency during prolonged current injections (Baranauskas, 2007; Guan et al., 2006; Mitterdorfer and Bean, 2002; Shen et al., 2004).

To investigate the validity of the model during action potential ﬁring, I used the model to investigate the response to a sustained, low amplitude depolarizing current injection

(0.3 nA, 900 ms ) with a K(D) channel model present and during simulated block of

K(D) channels (Figure 3.9). The interspike frequency for both somatic and dendritic action potentials produced in response to the prolonged current injection was significantly increased with K(D) channels present in the model compared to the interspike frequency during action potential firing in simulated block of K(D) channels. Somatic and dendritic spike amplitudes did not change during simulated block of K(D) channels. These results are consistent with experimental results that implicate K(D) channels in modulation of the interspike interval. However, the onset of the first action potential in simulated control conditions (K(D) channels present) did not appear to be delayed relative to the onset of 125

A With IK(D) B Without IK(D)

10 mV 50 ms

Figure 3.9. K(D) channels increases interspike intervals A: Simulated somatic and dendritic (350 µm from soma) action potentials in response to a long depolarizing current injection () with a K(D) current present in the model. B: Model somatic and dendritic (350 µm from soma) action potentials in response to a long current injection (0.3 nA, 900 ms) during simulated block of K(D) channels. The interspike frequency significantly increased with gK(D) in the model (A) compared to during simulated block of K(D) channels (B). 126 the first action potential during simulated block of K(D) channels as was seen in previous experimental studies (Storm, 1988). Further simulations and research are required to investigate and refine the role and kinetics of the K(D) channel model in the onset of action potential firing. 127

CHAPTER 4

Conclusion 128

4.1. Integration of information in dendritic trees

CA1 pyramidal neuron dendrites receive the majority of the cell’s synaptic inputs.

However, these individual synaptic signals are typically brief and of small amplitude, requiring a suﬃcient number of inputs with the correct timing in order to depolarize a neuron to action potential threshold and generate neuronal output. In addition to their passive electrical properties and biophysical morphology, dendrites posses voltage- gated conductances that are activated in response to membrane potential changes, thereby inﬂuencing the shape of synaptic potentials and the spatial and temporal summation of inputs. The work in this thesis used an experimental and computational approach to derive new insights about EPSP integration and attenuation in a previous passive CA1 pyramidal model (Golding et al., 2005) and to develop a more accurate CA1 pyramidal neuron model with the addition of voltage-gated A-type potassium channel constrained by electrophysiological recordings.

4.2. Synaptic normalization in neuronal dendrites

It is common knowledge that in CA1 pyramidal neurons, synaptic potentials on distal apical dendrites severely attenuate as they propagate to the soma. One mechanism proposed to compensate for this attenuation is distance dependent conductance scaling in which distal synapses experience an increase in synaptic conductance with distance from the soma to yield voltage changes at the soma (Magee and Cook, 2000). However, our results indicate that while moderately distal synapses may exhibit an increase in their conductance, synapses in the distal apical tuft of CA1 pyramidal neurons cannot achieve 129 synaptic eﬃcacy via conductance scaling (Nicholson et al., 2006; Williams and Stuart,

2002).

If EPSPs generated in the apical tuft are to shape somatic output, they must do it by a mechanism other than synaptic scaling due to the severity of synaptic potential attenuation as they propagate to the soma. One mechanism suggested for amplifying synaptic potentials is dendritic spiking. Temporal and spatial coactivation of distal inputs can produce regenerative local dendritic spikes that effectively propagate to the soma when paired with more proximal inputs such as stimulation via Schaffer collateral inputs (Jarsky et al., 2005; Káliand Freund, 2005). Another suggested compensatory mechanism is subthreshold resonance boosting by inward currents such as IA (Cook and Johnston, 1997,

1999; Migliore and Shepherd, 2002). A-type potassium channels are distributed with an increasing gradient from soma to distal dendrite (Hoﬀman et al., 1997) in CA1 pyramidal neurons. This high density of potassium channels in the more distal regions serves to dampen excitability. Any decrease in the availability of these channels would cause an overall increase in dendritic excitability (Frick et al., 2004) and hence an ampliﬁcation in the propagation of synaptic potentials.

4.3. Better models of voltage-gated ion channels

CA1 pyramidal neuron dendrites (both apical and basal) express multiple voltage- gated conductances that aﬀect neuronal integration of information and whose interaction can make information processing a challenging and diﬃcult process to understand. De- spite the advancement of experimental techniques used to study neuronal function, many aspects of information processing are not fully understood. To this end, computational 130 modeling of ion channels is an important tool for generating insights and addressing questions about their underlying biophysical properties and role in shaping neuronal output.

Single-channel recordings of ion channels (Sakmann and Neher, 1995) have shown that ion channels undergo rapid transitions between open and closed states, corresponding to conformational changes in the channel. These transitions can be described by state dia- grams and kinetic rate equations (Hodgkin-Huxley equations) that attempt to accurately describe the electrical properties of the ion channels (Destexhe et al., 1994; Hille, 2001).

Combining these mathematical descriptions with experimental recordings is a good way to constrain the uncertainty in a computational model. We used this combined approach to create a more accurate computational model of a CA1 pyramidal neuron by incorporating a previous model of an A-type potassium channel (Hoﬀman et al., 1997; Migliore et al.,

1999) and constraining the amount of IA on at rest by experimental results of somatic input resistance following pharmacological block of IA. The robustness of this model was then further veriﬁed by investigating ﬁts to somatic and dendritic passive properties as well as action potential backpropagation.

Computational models can be used to predict neural behaviors that can be further explored by experimental research. One potentially interesting ﬁnding generated by simulations of action potential backpropagation in the newly constrained model was that it was necessary to slightly decrease the overall Na+ channel conductance in the distal apical dendrite relative to the somatic value for both strongly and weakly backpropagating models in order to correctly reproduce the frequency-dependent attenuation (Colbert et al., 1997;

Jung et al., 1997; Martina and Jonas, 1997; Menon et al., 2009; Mickus et al., 1999) of 131 trains of backpropagating action potentials in both scenarios. Most computational models of CA1 pyramidal neurons use a constant gradient of Na+ channel conductance along the primary apical dendrite since experimental results from cell-attached patch recordings indicate that Na+ channel density is relatively uniform over the majority of CA1 apical dendrites (Magee and Johnston, 1995). However, recent evidence suggests that the distribution of the primary sodium subunit in the adult hippocampus (Nav1.6) exhibits a gradual decrease in density along the proximodistal axis (Lorincz and Nusser, 2010). This

+ decrease is consistent with previous studies of the distribution of RI and RII Na subtypes in the CA1 region of the hippocampus (Furuyama et al., 1993; Westenbroek et al., 1989) suggesting the possibility of a diﬀerential distribution of Na+ channel subtypes. Further computational modeling with our constrained channel distributions in other CA1 pyramidal neuron morphologies, combined with additional experimental research, would help to determine the validity of a decreased Na+ channel gradient.

4.4. Future directions

Diﬀerent types of neurons have distinctive dendritic channel expressions and morphologies that give rise to cell-speciﬁc regulation of synaptic integration, long-term potentiation, long-term depression and synaptic plasticity. The dendritic signals produced by the variations in voltage-gated channel distributions and dendritic morphologies in turn enhance and modulate channel kinetics, further shaping how information is integrated in a particular dendritic tree. This extreme diversity is critical to neural encoding and processing of stimuli and ultimately, cognitive function. The study of dendritic information processing 132 in multiple neuronal types using mathematical, computational and experimental techniques, is a necessary step to the end goal of understanding of how all organisms process and respond to information and stimuli, in addition to discovering potential treatments for brain-related disorders. 133

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