Tveito A., Lines G.T. Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models

Springer, 2016. — 279 p. — (Lecture Notes in Computational Science and Engineering 111). — 978-3-319-30030-6.Offers an accessible introduction to an important theory in a field of growing relevance.
Includes complete details of models and methods, enabling the reader to implement and study the models under consideration
Pursues a systematic approach to studying stochastic release mechanisms where the gating is governed by a Markov model
Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs. Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented. Lastly, the book shows how to derive the optimal properties of a theoretical model of a drug for a given mutation defined in terms of a Markov model.Background: Problem and Methods
One-Dimensional Calcium Release
Models of Open and Closed State Blockers
Properties of Probability Density Functions
Two-Dimensional Calcium Release
Computing Theoretical Drugs in the Two-Dimensional Case
Generalized Systems Governing Probability Density Functions
Calcium-Induced Calcium Release
Numerical Drugs for Calcium-Induced Calcium Release
A Prototypical Model of an Ion Channel
Inactivated Ion Channels: Extending the Prototype Model
A Simple Model of the Sodium Channel
Mutations Affecting the Mean Open Time
The Burst Mode of the Mutant Sodium Channel
Action Potentials: Summing Up the Effect of Loads of Ion Channels