Math. Model. Nat. Phenom.
Volume 15, 2020
Systems with Hysteresis and Switching
|Number of page(s)||26|
|Published online||10 April 2020|
On hysteresis of ion channels
Department of Electrical and Computer Engineering, George Washington University,
DC 20052, USA.
2 Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA.
* Corresponding author: firstname.lastname@example.org
Accepted: 26 November 2019
Ion channel proteins have many conformational (metastable) states and, for this reason, they exhibit hysteresis. This fact is responsible for the non-Markovian stochastic nature of single ion channel recordings. It is suggested in the paper that the stochastic single channel recordings can be modeled as the random outputs of rectangular hysteresis loops driven by stochastic processes. The latter problem can be mathematically treated as an exit problem for stochastic processes or by using the theory of stochastic processes on graphs. It is also demonstrated in the paper that the collective action of sodium and potassium channels responsible for the generation and propagation of action potentials exhibit hysteresis. This demonstration is accomplished by using the inverse problem approach to the nonlinear Hodgkin-Huxley diffusion equation.
Mathematics Subject Classification: 92B05 / 92C20 / 35Q92 / 60G20
Key words: Ion channels / hysteresis / stochastic processes / Preisach model
© The authors. Published by EDP Sciences, 2020
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