Model nerve net can produce rectilinear, non-diffuse propagation as seen in the skin plexus of sea urchins

Abstract

One of the simplest puzzles in neural connectivity is what can be the basis of the spine-converging or pointing response of echinoids to touch. Mediated by a conduction system in the skin, it is unique among known epithelial systems (unpolarized, Hopfield type nets) in propagating without significant curvature past the end of an incomplete cut, leaving a basically straight-edged shadow of no response. Known since 1881, this was analyzed by Bullock (1965, Comparative aspects of superficial conduction systems in echinoids and asteroids Am. Zool. 5, 545–562), who believed it demands that the plexus contains discrete, straight chains of neurons between every sensory site and every spine within 3 cm, a “curious and unprecedented” connectivity which seemed unlikely (here called “star” models). The present paper proposes a class of models by which non-diffuse, rectilinear propagation can occur in diffusely connected nerve nets. It requires that each neuron be influenced by several hundred neighbors, and that the average neuronal firing threshold be adjusted rather precisely. A threshold area must be initially stimulated. Several modifications approach realism based on animal data. It is shown by computer simulation that the proposed models support rectilinear propagation, and are insensitive to many changes in the detailed structure. Neither the present class nor the star models can be excluded on the present knowledge of anatomy of the echinoid plexus; they are viable alternatives. Tests of the two are proposed. Neither seems likely to be correct and we do not consider the puzzle solved.