Information and energy flow in a simple nervous system

Abstract

A quantal model developed earlier by the authors is recast in terms of common macroscopic variables and applied to the well-documented T, P, N/L, AE neuron network of a leech ganglion. The electrical potential of a neuron (φ) and the ion potentials ( φ a) for Na +, K +, Cl − and Ca 2+ are featured, though it proves possible to reduce the resulting set of coupled non-linear diffusion equations to a single pair whose admissible solutions are defined by a simple algebraic dispersion relation. Less than 30 s is required to solve the system for a functional interval of 2·25 s on a CYBER 175 computer using a modified Runge-Kutta algorithm, the program for which is given. Irreversible effects are included but reversibility is stressed, since the neurons are seen to exchange energy with their environment only in the immediate neighborhood of firing peaks. Plasma oscillations, resulting from a disruption of the Debye layer, offer a sound physical mechanism whereby transient currents and ion exchanges of the observed magnitudes may be generated. The total energy H and information rate Γ I transferred across the neural membrane are also calculated in terms of φ and φ a. It is shown that while φ is determined primarily by the K + potential, Γ I depends mainly on the Ca 2+ potential together with its time derivatives, and H depends on both the K + and Ca 2+ potentials. This also makes it possible, not only to compare φ ( t) solutions for each of the neurons in the incrementally-loaded network to experimental measurements of φ( t) made for similar stimulus levels, but also to trace the correlated flows of energy and information through the system. Nearly all of the distinctive features of the experimental curves are reproduced, despite the presence of such complexities as wide variations in pulse frequencies and amplitudes, sudden suppression of firing in one neuron when another begins to fire, refractory phases of different durations, and facilitation building to plateau values only slightly less than peak amplitudes for the sensory neurons. While both the energy and information curves possess sharp maxima which coincide with the firing pulses of the potential curves, those for Γ I ( t) are bimodal with rounded maxima that must represent transmissions associated with ion motions instead of polarization effects. In the case of the L and AE neurons, these curves exhibit a series of discrete energy/information packets that could easily produce the proportional increases in muscle tension actually observed.