Vergleich zweier Modelle für laterale Inhibition

Summary

Two semi-linear models for lateral inhibition are discussed. The interaction between “receptor units” is assumed to be linear, as demonstrated by Hartline and Ratliff in the eye of the horseshoe crab Limulus polyphemus. Yet a model of such an inhibitory system must be nonlinear, since the output values correspond to nerve activities, which cannot be negativ. Models with forward inhibition were used often to describe contrast phenomena in the human nervous system. However, in order to simulate the input-output relation in systems similar to the eye of Limulus, a model with backward inhibition must be constructed. Two important properties of backward inhibition not shared by forward inhibition are: (1) Inhibition in a receptor unit has an influence upon its excitation, as well as upon its ability to inhibit other units (Disinhibition). (2) The range of interaction between sensory units is not necessarily the same as the range of direct cross connections. It is shown in this paper, that also forward inhibition may possess these two properties, provided that it is repeated on subsequent levels. Some properties of systems with backward and forward inhibition are studied and compared in models consisting of three units. The input-output relation for large systems with backward inhibition was calculated under special assumptions concerning the inhibitory coefficients. If the inhibitory coefficients in a system with backward inhibition decrease like a power series, as a function of the distance between receptor units, only neighboring receptors have an effect upon each other. That is, in an equivalent system with forward inhibition the inhibitory interaction is confined to neighbouring receptors. Conversely, when backward inhibition exists only between neighbouring receptors, the inhibitory coefficients in an equivalent system with forward inhibition are described, as a function of the distance between the receptor units, by a power series with alternating sign.