On hysteresis of ion channels

Can E. Korman¹ ; Isaak D. Mayergoyz²

¹ Department of Electrical and Computer Engineering, George Washington University, Washington, DC 20052, USA.
² Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA.

Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 26.

Résumé

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.

Détail

DOI : 10.1051/mmnp/2019058

Bibliographie

[1] W.A. Catterall Structure and function of voltage-gated sodium channels at atomic resolution Exp. Physiol 2014 1 26

[2] V.A. Chinarov, Y.B. Gaididei, V.N. Kharkyanen, S.P. Sitko Ion pores in biological membranes as self-organized bistable systems Phys. Rev. A 1992 5232 5241

[3] P.S. Churchland and T.J. Sejnowski, The Computational Brain. A Bradford Book. The MIT Press (1992).

[4] F. Crick Memory and molecular turnover Nature 1984 101

[5] P. Dayan and L.F. Abbott, Theoretical Neuroscience. The MIT Press (2001).

[6] H. Flyvbjerg, E. Gudowska-Nowak, P. Chrsitophersen, P. Bennekou Modeling hysteresis observed in the human erythrocyte voltage-dependent cation channel Acta Phys. Pol. Ser. B 2012 2117 2140

[7] M.I. Freidlin, Markov Processes and Differential Equations: Asymptotic Problems. Birkhäuser-Berlin, Berlin (1996).

[8] M.E. Freidlin, A.D. Wentzell Diffusion Processes on Graphs and the Averaging Principle Ann. Probab 1993 2215 2245

[9] M.I. Freidlin, I.D. Mayergoyz, R. Pfeiffer Noise in hysteretic systems and stochastic processes on graphs Phys. Rev. E 2000 1850 1855

[10] A. Fulinski, Z. Grzywna, I. Mellor, Z. Siwy, P.N.R. Usherwood Non-Markovian character of ionic current fluctuations in membrane channels Phys. Rev. E 1998 919 924

[11] C.R. Gallistel and A.P. King, Memory and the Computational Brain. Wiley- (2009).

[12] B. Hille, Ion Channels of Excitable Membranes. Third Edition, Sinauer Associates, Inc. (2001).

[13] J.J.B. Jack, D. Noble and R.W. Tsien, Electric Current Flow in Excitable Cells. Oxford University Press (1983).

[14] C. Koch, Biophysics of Computation. Oxford University Press (1999).

[15] C.E. Korman, I.D. Mayergoyz Switching as an Exit Problem IEEE Trans. Magn. 1995 3545 3547

[16] R. Männikkö, S. Pandey, H.P. Larsson, F. Elinder Hysteresis in the voltage dependence of HCN channels: conversion between two modes affects pacemaker properties J. General Physiol 2005 305 326

[17] I.D. Mayergoyz, W.W. Destler, F.P. Emad Application of intense relativistic electron beams to the switching of high currents in high power electrical networks J. Appl. Phys 1982 7189 7194

[18] R. Meagher Memory and molecular turnover, ’ 30 years after inception Epigen. Chrom 2014 37

[19] V. Nache, T. Eick, E. Schulz, R. Schmauder, K. Benndorf Hysteresis of ligand binding in CNGA2 ion channels. Nat. Commun. 2013 1 9

[20] E. Neher, B. Sakmann Single-channel currents recorded from membrane of denervated frog muscle fibres Nature 1976 799 802

[21] M.A. Pustovoit, A.M. Berezhkovskii, S.M. Bezrukov Analytical theory of hysteresis in ion channels: two-state model J. Chem. Phys 2006 194907

[22] C. Tilegenova, D.M. Cortes, L.G. Cuello Hysteresis of KcsA potassium channel’s activation-deactivation gating is caused by structural changes at the channel’s selectivity filter PNAS 2017 3234 3239

[23] J. Timmer, S. Klein Testing the Markov condition in ion channel recordings Phys. Rev. E 1997 3306 3311

[24] H.C. Tuckwell, Vols. 1 and 2 of Introduction to Theoretical Neurobiology. Cambridge University Press (1988).

[25] C.A. Villalba-Galea Hysteresis in voltage-gated channels CHANNELS 2017 140 155