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

✍ Scribed by Glenn L. Millhauser; Robert E. Oswald

• Publisher: John Wiley and Sons
• Year: 1988
• Tongue: English
• Weight: 745 KB
• Volume: 2
• Category: Article
• ISSN: 0887-4476
• DOI: 10.1002/syn.890020113

✦ Synopsis

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 a n 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.