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.
