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Neural Computation, Vol 9, 1015-1045, Copyright © 1997 by The MIT Press

LETTERS

Reduction of the Hogkin-Huxley Equations to a Single-Variable Threshold Model

Werner Kistler, Wulfram Gerstner and J. Leo van Hemmen

It is generally believed that a neuron is a threshold element that fires when some variable u reaches a threshold. Here we pursue the question of whether this picture can be justified and study the four-dimensional neuron model of Hodgkin and Huxley as a concrete example. The model is approximated by a response kernel expansion in terms of a single variable, the membrane voltage. The first-order term is linear in the input and its kernel has the typical form of an elementary postsynaptic


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