| Description |
1 online resource (xvi, 261 pages) : illustrations (some color) |
| Series |
Lecture notes in computational science and engineering, 1439-7358 ; 111 |
|
Lecture notes in computational science and engineering ; 111. 1439-7358
|
| Contents |
Background : problem and methods -- One-dimensional calcium release -- Models of open and 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 |
| 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." -- Back cover |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed April 26, 2016) |
| Subject |
Ion channels -- Effect of drugs on -- Mathematical models.
|
|
Markov processes.
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| Form |
Electronic book
|
| Author |
Lines, Glenn T., author
|
| ISBN |
331930030X (electronic bk) |
|
9783319300306 (electronic bk) |
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(print) |
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