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Flow of ions through voltage gatedchannels can be represented theoretically using stochastic differentialequations where the gating mechanism is represented by a Markov model. The flow through achannel can be manipulated using various drugs, and the effect of a given drugcan be reflected bychanging the Markov model. These lecture notes provide an accessibleintroduction to the mathematical methods needed to deal with these models. They emphasize the use ofnumerical methods and provide sufficient details for the reader to implementthe models and thereby study the effect of various drugs. Examples in thetext include stochastic calcium release from internal storage systems in cells,as well as stochasticmodels of the transmembrane potential. Well known Markov models are studied anda systematic approach toincluding the effect of mutations is presented. Lastly, the book shows how to derive the optimal propertiesof a theoretical model of a drug for a given mutation defined in termsof a Markov model.
List of contents
Preface.- Background: Contents and Method.- One-dimensional calcium release.- Models of open and state blockers.- Two-dimensional calcium release.- Computing theoretical drugs in the two-dimensional case.- Generalized systems.- Calcium-induced calcium release.- Numerical release for CICR.- A prototypical model of an ion channel.- Inactivated ion channels.- A simple model of the sodium channel.- Mutations affecting the mean open time.- The burst mode.- Whole sale action potentials.-
Summary
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.
