Reversible Markov chain models for ion channels

Abstract — Three reversible continuous time Markov chain models for ion channels based on the reversibility of these biological systems are presented. It is shown that the single ion trans paths from left to right and those from right to left are equivalent in distribution. This explains an interesting phenomenon observed by biophysicists, that the distribution of time needed for ions to transit an ion channel is the same in either direction, even if there is an electric potential difference across the channel. The distribution of transit time is important in determining the capacity of cell to cell signaling. The first model assumes that there is no interaction between the ions in order to obtain a reversible open system model as the infinite ion limit of a reversible closed system. Then, interaction is brought into the model in two different ways to obtain the doormat model and the floormat model. The entrance rates do not depend on the channel state in the doormat model, but do in the floormat model. The effects of trans-membrane potentials, interaction strength and entrance rates are discussed. I