Collective Equilibrium Behaviour of Ion Channel Gating in Cell Membranes: An Ising Model Formulation

Rıza Erdem
2007 Journal of biological physics (Print)  
A statistical mechanical model for voltage-gated ion channels in cell membranes is proposed using the transfer matrix method. Equilibrium behavior of the system is studied. Representing the distribution of channels over the cellular membrane on a one-dimensional array with each channel having two states (open and closed) and incorporating channelchannel cooperative interactions, we calculate the fraction of channels in the open state at equilibrium. Experimental data obtained from
more » ... modified sodium channels in the squid giant axon, using the cut-open axon technique, is best fit by the model when there is no interaction between the channels. Ion channels are a class of proteins embedded in cell membranes, and form conduction pores that regulate the transport of ions into and out of cells. These pore proteins are present in all living organisms and play a crucial role in many biological functions, including electrical signaling in the nervous system, hormone secretion, and heart and muscle contraction [1]. The voltage-dependent switching of these channels between conducting and nonconducting states is a major factor in controlling the transmembrane voltage. Mathematical models have been developed to study the kinetics of such channels and the corresponding excitability in a variety of nerve cells [2, 3]. The classical Hodgkin-Huxley mathematical model (or HH model) [4, 5] is obtained via theoretical insight and curve fitting rather than derived from fundamental principles. According to the HH model, the kinetics of the ion channels being open or closed is described by first-order nonlinear differential equations (HH equations) for the transmembrane voltage. In the HH equations, the gating variables that govern the activation and inactivation of the channels and experimentally-determined voltage transition rates are included [4].
doi:10.1007/s10867-007-9034-3 pmid:19669439 pmcid:PMC2651540 fatcat:gcfflo7ld5fe7ahwdbbon4wtlu