Realistic Hodgkin–Huxley Axons Using Stochastic Behavior of Memristors

摘要

Ion-channel variability has critical effect on the spike initiation and propagation in nervous system. Noise can play a constructive role leading to increased reliability or regularity of neuronal firing and spike propagation in the nervous system. In this paper we show that memristors can be considered as an electronic analogous of the Hodgkin–Huxley ion channels not only in terms of threshold switching effect but also in terms of stochastic behavior. In other words, memristor can also implement stochastic version of Hodgkin–Huxley equation. Switching effect in memristive devices is thermodynamically driven, which is stochastic in nature. We show that if the intrinsic stochastic behavior of memristor is taken into account, memristor based neuristor can also implement stochastic version of Hodgkin–Huxley axon model in generation of action potential. Ion channel variability in neurons can be modeled by intrinsic stochastic behavior of memristor. We incorporate noise in the memristor model by adding white Gaussian noise to the deterministic part of dynamical state evolution function of the memristor. We study the reliability of spike timing for spike train generated by memristor based neuristor in which the noise included memristor model is used. Also, the reliability of spike propagation along thin axons is discussed. A series connection of neuristors can be used as an axon in which neuristor acts as a node of Ranvier on an axon. Probabilistic nature of spike propagation on thin axons can be modeled using neuristor in which the variability nature of memristor is included.