Systems models of retinal cells: a classical example

Abstract

Motivation. Since the times of McCulloch, it became clear that computational models of neural networks are limited by the nature of the formal tools used to describe the correlations among experimental data. The nature of the conclusions from a model are implied by the nature of the operators in its formulation, operators that can be analytic, logical or inferential. For retinal cells, analytical non-linear operators are appropriate.This was clear in the 60's. However in the great revival of neural computation, around 1985, these essential concept was forgotten, so that old models of the past were being copied but assuming that neurons were point neurons with irrelevant anatomy.Fortunately, the horizon opens again when recognizing the nervous system complexity and the usefulness of analytics when certain methodological conditions are met. First, identification of the anatomical structure under consideration (input and output lines, processing layers, and other). Second, listing of physiological properties, separately from the anatomical details. Third, propose a set of hypothesis to correlate structure and function, which constitute the computational basis of the model and provides for the selection criteria of the proper mathematical operators. And fourth, simulation of the model and evaluation of the results, so that prediction of results and proposal of new experiments is possible. In this way, systems science, and physiology and anatomy interact fruitfully.To illustrate this proposal you will find in this paper a reproduction, with minor changes, of a report by the author to the Massachusetts Institute of Technology, Instrumentation Laboratory, prepared in 1965, which is no longer available. It deals with the systems modeling of group 2 ganglion cell in the frog's retina and still nowadays it provides for a good illustration of how to proceed clearly from neurophysiological facts to hypothesis and to systems models which are non-trivial. The model does not rely for its verification on computer power, and therefore the basic approach, the formal developments and the performance of the model remain invariant. The model is very transparent to an engineer mind as well as to neurophysiologists, and it provides for a fresh illustration to contrast with some of the more opaque, simplistic and less effective neural models of today.