A non-extensive statistical mechanical approach to define the equilibrium value function in the kinetics of voltage-gated ion channels

We present a model for the steady-state (or equilibrium) behaviors of the voltage-gated ion channels in cell membranes using the non-extensive or generalized statistical mechanics. The equilibrium value function in the gating kinetics of batrachotoxin-modified sodium channels from a squid optic nerve in planar bilayers are calculated for different values of entropic index (q) which characterizes the degree of non-extensivity of Tsallis’ entropy and the fractal structure of the channels. It is found that in the limit q→1, the results of calculation reduce to the results described by the well-known Boltzmann statistics or the extensive physics. For the non-extensive case (q≠1), a small deviation with respect to the Boltzmann curve which was observed in a great variety of physical systems occurred.