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Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models [electronic resource] / by Aslak Tveito, Glenn T. Lines.
By: Tveito, Aslak [author.].
Contributor(s): Lines, Glenn T [author.] | SpringerLink (Online service).
Material type:
TextSeries: Lecture Notes in Computational Science and Engineering: 111Publisher: Cham : Springer International Publishing : Imprint: Springer, 2016Description: XVI, 261 p. 129 illus., 30 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319300306.Subject(s): Mathematics | Computer graphics | Computer mathematics | Mathematics | Computational Science and Engineering | Biomedicine general | Computer Imaging, Vision, Pattern Recognition and GraphicsAdditional physical formats: Printed edition:: No titleDDC classification: 004 Online resources: Click here to access online
Contents:
In:
Springer eBooksSummary: 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.
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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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 -- .
Open Access
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.