Volume 106, Number 1, April 2014
|Number of page(s)||5|
|Published online||11 April 2014|
Stochastic dynamics of electrical membrane with voltage-dependent ion channel fluctuations
1 Department of Applied Mathematics, University of Washington - Seattle, WA 98195-3925, USA
2 College of Mathematics, Jilin University - Changchun, Jilin 130012, PRC
3 Department of Mathematics, Zhejiang Normal University - Jinhua, Zhejiang 321004, PRC
4 School of Mathematical Sciences, Peking University - Beijing 100871, PRC
Received: 30 October 2013
Accepted: 28 March 2014
A Brownian-ratchet–like stochastic theory for the electrochemical membrane system of Hodgkin-Huxley (HH) is developed. The system is characterized by a continuous variable , representing mobile membrane charge density, and a discrete variable Kt representing ion channel conformational dynamics. A Nernst-Planck-Nyquist-Johnson–type equilibrium is obtained when multiple conducting ions have a common reversal potential. Detailed balance yields a previously unknown relation between the channel switching rates and membrane capacitance, bypassing an Eyring-type explicit treatment of gating charge kinetics. From a molecular structural standpoint, the membrane charge Qm is a more natural dynamic variable than the potential Vm; our formalism treats Qm-dependent conformational transition rates as intrinsic parameters. Therefore, in principle, vs. Vm is experimental-protocol–dependent, e.g., different from voltage or charge clamping measurements. For constant membrane capacitance per unit area Cm and neglecting the membrane potential induced by gating charges, , and HH's formalism is recovered. The presence of two types of ions, with different channels and reversal potentials, gives rise to a nonequilibrium steady state with positive entropy production ep. For rapidly fluctuating channels, an expression for ep is obtained.
PACS: 05.40.Ca – Noise / 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 87.16.dp – Transport, including channels, pores, and lateral diffusion
© EPLA, 2014
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