Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models

Abstract

The summer of 2013 was very good; we found a series of papers published by Gregory D. Smith and his coauthors. We spent several weeks trying to understand the paper [35], which introduces and carefully studies a stochastic model of calcium release from internal stores in cells. Then we found a whole series of papers [36, 57, 102, 103], and the results more or less kept us busy for months. The beauty of the theory presented in these papers is that they introduce a systematic way of analyzing models that are of great importance for understanding essential physiological processes. So what is this theory about? It has been fairly well known for a while that stochastic models are useful in studying the release of calcium ions from internal storage in living cells. Some authors even argue that this process is stochastic. That is debatable, but it is quite clear that stochastic models are well suited to study such processes. Stochastic models are also very well suited to study the change of the transmembrane potential resulting from the flow of ions through channels in the cell membrane. Both these processes are of fundamental importance in understanding the function of excitable cells. In both applications, ions flow from one domain to another according to electrochemical gradients, depending on whether the channel is in a conducting or nonconducting mode. The state of the channel is described by a Markov model, which is a wonderful tool used to systematically represent how an ion channel or a receptor opens or closes based on the surrounding conditions. In this context, the contribution of the papers listed above is to present a systematic way of analyzing the stochastic models in terms of formulating deterministic differential equations describing the probability density distributions of the states of the Markov models.