Interpretation of biological ion channel flux data--reaction-rate versus continuum theory

Abstract

Although the reaction-rate theory may provide a useful mathematical description of the channel flux, it presents a misleading physical picture of the channel structure. There is a tendency to regard the barriers in the model as actual physical structures, whereas they are actually only mathematical artifacts that allow one to reduce a complicated differential equation with an infinite number of states to a finite difference equation with a minimum number of states. I argue that the energy profile in the permeation pathway of most biological channels should vary relatively smoothly with only a few localized energy barriers or wells. In these smoothly varying regions, the resistance to ion movement is similar to bulk diffusion and cannot be accurately modeled by one or two energy barriers. For the one-ion channel, the continuum approach is as general and at least as simple as the reaction-rate theory and may provide a more physical interpretation of the data. Thus for the SR K+ channel, the structure suggested by the reaction-rate theory seems inconsistent with some experimental data, while the continuum-theory model is not only consistent with, but complements, the structure suggested by other data. Multi-ion channels have such complicated kinetics that one can only expect the theories to provide a qualitative description of the experimental data. They can be modeled by either the reaction-rate model or a finite difference approximation to the continuum model.