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Table of contents

  1. Front Matter
    Pages i-xvi
  2. Aslak Tveito, Glenn T. Lines
    Pages 1-22 Open Access
  3. Aslak Tveito, Glenn T. Lines
    Pages 23-54 Open Access
  4. Aslak Tveito, Glenn T. Lines
    Pages 55-69 Open Access
  5. Aslak Tveito, Glenn T. Lines
    Pages 71-90 Open Access
  6. Aslak Tveito, Glenn T. Lines
    Pages 91-107 Open Access
  7. Aslak Tveito, Glenn T. Lines
    Pages 109-118 Open Access
  8. Aslak Tveito, Glenn T. Lines
    Pages 119-123 Open Access
  9. Aslak Tveito, Glenn T. Lines
    Pages 125-142 Open Access
  10. Aslak Tveito, Glenn T. Lines
    Pages 143-152 Open Access
  11. Aslak Tveito, Glenn T. Lines
    Pages 153-164 Open Access
  12. Aslak Tveito, Glenn T. Lines
    Pages 165-175 Open Access
  13. Aslak Tveito, Glenn T. Lines
    Pages 177-191 Open Access
  14. Aslak Tveito, Glenn T. Lines
    Pages 193-221 Open Access
  15. Aslak Tveito, Glenn T. Lines
    Pages 223-236 Open Access
  16. Aslak Tveito, Glenn T. Lines
    Pages 237-255 Open Access
  17. Back Matter
    Pages 257-270

About this book

Introduction

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.

Keywords

differential equations stochastic models ion channels drug modelling probability density functions

Authors and affiliations

  • Aslak Tveito
    • 1
  • Glenn T. Lines
    • 2
  1. 1.Center for Biomedical ComputingSimula Research LaboratoryLysakerNorway
  2. 2.Center for Biomedical ComputingSimula Research LaboratoryLysakerNorway

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-30030-6
  • Copyright Information The Editor(s) (if applicable) and the Author(s) 2016
  • License CC BY-NC
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-30029-0
  • Online ISBN 978-3-319-30030-6
  • Series Print ISSN 1439-7358
  • Series Online ISSN 2197-7100
  • Buy this book on publisher's site