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

Author

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  • Correale, T.G.
  • Monteiro, L.H.A.

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.

Suggested Citation

  • Correale, T.G. & Monteiro, L.H.A., 2017. "Typical frequency-current curves of neurons obtained from a model based on cellular automaton," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 136-141.
    • Handle: RePEc:eee:apmaco:v:304:y:2017:i:c:p:136-141
    DOI: 10.1016/j.amc.2017.01.042
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    References listed on IDEAS

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    1. Correale, T.G. & Monteiro, L.H.A., 2016. "On the dynamics of axonal membrane: Ion channel as the basic unit of a deterministic model," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 292-302.
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