Typical frequency-current curves of neurons obtained from a model based on cellular automaton

T.G. Correale and L.H.A. Monteiro

Applied Mathematics and Computation, 2017, vol. 304, issue C, 136-141

Abstract: Usually, neurons stimulated by constant current exhibit one of two types of behavior: for type-1 neurons, the curve representing “firing frequency versus input current” is continuous; for type-2 neurons, there is a discontinuity in such a curve. Here, we reproduce these typical behaviors from a discrete-time model based on the dynamics of ion channels. In this model, the axonal membrane is considered as a lattice and each patch of this lattice contains a set of ion channels. The state transitions of the voltage-gated ion channels are governed by deterministic rules. We show that the frequency-current relationship obtained from this model is similar to the one derived from the Hodgkin–Huxley equations, which are commonly used to describe type-2 neurons. We also show that our approach can be convenient to model type-1 neurons.

Keywords: Bifurcation; Cellular automaton; Frequency-current curve; Ion channel; Neurodynamics (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:304:y:2017:i:c:p:136-141

DOI: 10.1016/j.amc.2017.01.042

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