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

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.