Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models
Registro en:
9783319398891
10.1007/978-3-319-30030-6
Autor
Tveito, Aslak
Lines, Glenn T.
Institución
Resumen
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.