PROCESSES IN BIOLOGICAL VISION: including, ELECTROCHEMISTRY OF THE NEURON This material is excerpted from the full β-version of the text. The final printed version will be more concise due to further editing and economical constraints. A Table of Contents and an index are located at the end of this paper. James T. Fulton Vision Concepts [email protected] April 30, 2017 Copyright 2000 James T. Fulton Biological Phenomena 11- 1 11 Introduction to modeling of biological phenomena 1 Don’t believe everything you think. Anonymous bumper sticker It is the models that tell us whether we understand a process and where the uncertainties remain. Bridgeman, 2000 11.1 Background In presenting the second quotation, Bridgeman characterized the current state of research into the vision process. He said, “The neuroanatomical analyses can tell us where to look for a particular mechanism, and neurophysiology can tell us when the critical information is being processed, but current techniques leave the ‘how’ of the process tantalizingly elusive.”2 The first quotation highlights the difficulties of relying upon intuition, or what is sometimes described as introspection. The goal of this Chapter is to provide a model that can support a wide range of experimental results and lead the way to a broader understanding of the visual system. There are a number of problems associated with modeling the signal processing functions in vision. One of the biggest is the plethora of simplistic circuit diagrams found in the literature. The second is the extremely high impedance level found in the initial stages of signal processing. These impedance levels are to be expected; they relate to the extremely small size of the elements and they reduce overall power consumption. A third is the reluctance of the biology community (at least until recently) to embrace the fact that there are synaptic junctions that involve only the movement of electrons across the boundary. No movement of chemical ions (much less complex organic molecules with the complexity of a protein) is involved. And finally, the fact that 99.9% of the neurons in the retina operate in the analog (not in the binary pulse) mode puts them in a class separate from much of the vision literature. It is noteworthy that the field of morphology is involved primarily with static conditions or very slowly changing conditions relative to growth. The field has largely overlooked the subject of neural signaling. One neurobiology text, that is heavily weighted toward morphology lists 14 types of cell-to-cell communications in hierarchal order but does not mention neural signaling based on electrolytics3. It is also noteworthy that the literature contains no detailed description of the signals at different positions along the signal path from the input voltage at a neurite to the output voltage at the axon of a neuron. Some of the material in this Chapter is designed for the actual laboratory researcher or serious analyst. It goes into more depth than required by the typical reader. The chapter is focussed on the modeling of the larger parts of the visual system. The modeling of an individual Activa, an individual synapses and various individual circuits within a single neuron are addressed in Chapters 8 & 9. Section 11.1 can be read selectively as needed by the reader. Sections 11.2 through 11.8 encompass the various phases of the detailed modeling of the visuals system. Section 11.1.1 is critically important if one is to avoid the many conceptual traps found in the current literature. Section 11.1.2 provides many detailed definitions that are required to insure consistency and correlation of the material in adjacent chapters. Section 11.1.3 concentrates on the high level architecture of the overall neural system, using the non-visual system as a template for understanding the visual system.. Section 11.1.4 provides an internally consistent set of morphological nomenclature for the neural system and Section 11.1.5 does the same thing for the electrical waveforms normally associated with the neural system. Section 11.1.6 provides a review of graphical techniques of specific value in modeling the visual system. 1Released: April 30, 2017 2Bridgeman, B. (2000) Neuroanatomy and function in two visual systems. Behav. Brain Sci. vol. 23, no. 4, pp 535-536 3Shepherd, G. (1994) Neurobiology, 5th ed. NY: Oxford Press. pg. 72 in the 1988 edition 2 Processes in Biological Vision Section 11.1.7 discusses the subtle differences between data and information rates. Section 11.1.8 reviews some of the models used in other presentations on the system aspects of the visual process. This chapter must take note of a number of papers that should be associated with signal processing and signal manipulation but rely exclusively on a mathematical model. Cornsweet & Yellott have provided a paper of this type4. While the paper is extensive, it relies upon a concept believed to be totally foreign to the physiology of vision and not found within the realm of conventional optics. They propose an optical spread function whose spatial width is light intensity dependent. Their derivation leads to several comments related to Weber’s Law and Mach Bands but no physically realizable physiology. Such exclusively mathematical models will not be addressed in this work. 11.1.1 Clarification of concepts Before embarking on modeling of biological systems, there are a variety of major concepts that must be discussed before proceeding to the more detailed subject of terminology and conventions. The analysis of biological systems follows the same methodology as for any other “system,” whether chemical, mechanical, electrical, hydraulic, etc. In fact, the typical biological system employs elements from each of the above disciplines. The rules of system analysis are well established and precisely documented. However, their development is beyond the scope of this work. For the non-mathematically inclined, Regan has provided a list of principles related to system analysis and a number of useful examples5. While tending to bound the field and be very useful to the layman, his seventeen postulates should not be taken as mathematically rigorous. As he states, there are a variety of caveats applying to some of the postulates. For a stronger foundation in the subject of system analysis applied to psychophysics, and a definition of the various modes of psychophysics testing, Green & Swets is an excellent choice6. 11.1.1.1 Models and Diagrams to aid understanding To help interpret this work and the literature, it is useful to explicitly define a series of different types of models. The most basic classes of models are the abstract and the functional. + Abstract models typically present a conceptual block diagram or contain a mathematical equation. The conceptual block diagram is frequently found in pedagogical situations. The mathematical equation is usually intended to bound the performance of some process or mechanism in vision without relating directly to they underlying mechanisms or processes. Both tend to be misleading with respect to the underlying electrophysiology of the system. + Functional models typically attempt to describe the actual mechanisms and processes of vision and must conform to the electrophysiology of the system to be considered correct. Computer emulations normally conform to the definition of the abstract model because the algorithms used seldom relate to the underlying electrophysical mechanisms and processes. Equivalent circuits on the other hand, and especially if sophisticated, attempt to represent the electrophysiological situation using an equivalent topology in a different technology. Specialists in system synthesis and analysis have long used a series of block, schematic and circuit diagrams to document the configuration and operation of a wide variety of systems. These tools attempt to represent the actual circuit topology of the visual system. The diagrams are used to aid in seeing both the forests and the trees simultaneously. Simultaneously, they provide a medium for documenting systemic relationships. Such systems may be of many types. They include electrical, hydraulic, mechanical, aerodynamic and biological types. Although not used widely or consistently in the visual field, an attempt will be made to use them consistently here according to the following hierarchy; + Global block diagram 4Cornsweet, T. Yellott, J. (1985) Intensity-dependent spatial summation J Opt Soc Am A vol 2(10), pp 1769- 1785 5Regan, D. (1991) Spatial Vision. Vol. 10 of Vision and Visual Dysfunction, Cronly-Dillon, J. general ed. Boca Raton, FL: CRC Press pp 3-12 6Green, D. & Swets, J. (1974) Signal Detection Theory and Psychophysics. Huntington, NY: Krieger Publishing Biological Phenomena 11- 3 + Species specific block diagrams + Schematic diagrams + Multiple circuit diagrams + An individual circuit diagram A block diagram is usually used to indicate fundamental but general relationships between major elements of the system. They are useful for orienting the reader and defining terms. They usually lack detail and are not indicative of the topology of the system. The schematic diagram is intended to illustrate relationships between the elements of a block diagram. The titles of the elements are frequently chosen to indicate the top level topology of the system and to indicate both feed forward and feedback paths. At the next level of detail are the circuit diagrams. These frequently occur in two classes, higher level circuit diagrams illustrating the interplay of several circuits and the individual circuit diagrams. The higher level circuit diagrams frequently employ high level symbolic representations of individual circuits to simplify the presentation and emphasize the topology of the system at this level. The individual circuits on the other hand use the lowest possible level of symbology to provide a detailed understanding of the actual circuit. The symbols are usually of the most basic type and indicative of the most fundamental circuit elements. Because the symbology is so important to understanding within a profession, the actual symbols are usually standardized by professional organizations within each discipline.