Stochastic description of the three-state model of the Na channel

The three-state model of the Na channel is formulated stochastically and various observable quantities calculated from this model. This model assumes that the Na channel can occupy one of three states--resting, open and inactivated--and that each channel is independent. This is a simplified representation of the model proposed by Aldrich et al. (1983) mainly with respect to the neuroblastoma. When the system contains many channels, the probability distribution of the numbers of the channels that occupy each of these states is a time-dependent multinomial distribution and the distribution of the first passage time from resting state to open state becomes an exponential decay function with higher components. The average and variance of the channel current calculated by the distribution show the time course with a single peak and its ratio converges to the current of a single channel. Stochastic treatment of the transient process developed here gives a method of estimating all of the transition rates and the number of channels in the system.