An Alternative Electrostatic Model for Membrane Ion Channels

Abstract

There are at least two reasons for making mathematical models of real biological systems. The first is to accurately reproduce the output of the given system in order to include it as part of a model of a larger system. The second is to construct models with real physical components capable of independent experimental verification in the hope of gaining a better understanding of the physical processes that underlie the operation of the system. The famous Hodgkin and Huxley m³ model (Hodgkin and Huxley 1952) of ion channel gating in excitable tissue is an example of the first kind. They wished to simulate the time variation of the action potential and needed a model for the time dependence of the sodium and potassium channel currents. Although later researchers attempted to put flesh on the mathematical model by trying to find the m and n particles as real physical entities, the original authors were careful to state that agreement between the predictions of the model and experiment was no guarantee that the particular model proposed was correct. It is well known that many different models may produce the same output just as a tape recorder and a flute can produce the same audible output while having nothing in common in their methods of sound production.