A reevaluation of the mathematical models for simulating single-channel and whole-cell ionic currents

Abstract

We have developed a technique that allows for the simulation of both single-channel and whole-cell ionic currents given any arbitrary first-order kinetic scheme for the conformational states of an ion channel. The procedure is based on the solution of the master equation, which, in turn, is a general expression for a Markov process. The solution is expressed in terms of the eigenvalues and eigenvectors of the kinetic system and the system's deviation from equilibrium. Our derived expression provides a general recipe for the calculation of whole-cell currents. By further manipulation of this expression, we show how conditional probabilities are derived that can be used for the simulation of single-channel currents. We discuss computer implementation of the results so that complicated kinetic schemes can be solved numerically. Finally, we demonstrate the procedure by providing a worked example of a simple model of activation followed by inactivation.