Dynamics of voltage-gated ion channels in cell membranes by the path probability method

Dynamics of voltage-gated ion channels in the excitable cell membranes is formulated by the path probability method of nonequilibrium statistical physics and approaches of the system toward the steady or equilibrium states are presented. For a single-particle noninteractive two-state model, a first-order rate equation or dynamic equation is derived by introducing the path probability rate coefficients which satisfy the detailed balancing relation. Using known parameters for the batrachotoxin (BTX)-modified sodium channels in giand squid axon as an example, the rate equation is solved and voltage dependence of the time constant (τ) and its temperature effect are investigated. An increase in voltage caused a shift in τ towards shorter durations while increasing temperature caused a shift in time distribution towards longer durations. Results are compared with the kinetic model for the squid axon BTX-modified sodium channels by the cut-open axon technique and a very good agreement is found.