# Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models

TVEITO, AAdded Author | LINES, G T |

Publication | Cham : Springer International Publishing : Imprint: Springer, 2016. |

ISBN | 9783319300290 / eISBN:9783319300306 Printed edition: 9783319300290 |

Physical Description | XVI, 261 p. 129 illus., 30 illus. in color. online resource. |

Series | Lecture Notes in Computational Science and Engineering Vol 111 Springer Open Access e-Book |

URL | |

Language | eng |

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$a Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models

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$a 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 -- .

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$a 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.

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Subject | MATHEMATICS COMPUTER GRAPHICS BIOMEDICINE COMPUTAIONAL SCIENCE AND ENGINEERING E-BOOKS |

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. |

Table 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 -- . |

Notes | Lecture Notes in Computational Science and Engineering, 1439-7358 ; 111 |