Stochastic Nonlinear Equations Describing the Mesoscopic Voltage-Gated Ion Channels
This article is part of Special Issue:
Mauricio Tejo,
Corresponding Author
Mauricio Tejo
Centro de Análisis Estocástico, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, 7820436 Santiago, Chile uc.cl
Facultad de Ciencias Naturales y Exactas, Universidad de Playa Ancha, Leopoldo Carvallo 270, 2360696 Valparaíso, Chile upla.cl
Search for more papers by this authorMauricio Tejo,
Corresponding Author
Mauricio Tejo
Centro de Análisis Estocástico, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, 7820436 Santiago, Chile uc.cl
Facultad de Ciencias Naturales y Exactas, Universidad de Playa Ancha, Leopoldo Carvallo 270, 2360696 Valparaíso, Chile upla.cl
Search for more papers by this authorFirst published: 05 April 2015
Academic Editor: Nikolai N. Leonenko
Abstract
We propose a stochastic nonlinear system to model the gating activity coupled with the membrane potential for a typical neuron. It distinguishes two different levels: a macroscopic one, for the membrane potential, and a mesoscopic one, for the gating process through the movement of its voltage sensors. Such a nonlinear system can be handled to form a Hodgkin-Huxley-like model, which links those two levels unlike the original deterministic Hodgkin-Huxley model which is positioned at a macroscopic scale only. Also, we show that an interacting particle system can be used to approximate our model, which is an approximation technique similar to the jump Markov processes, used to approximate the original Hodgkin-Huxley model.
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