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© 2014

Stochastic Processes in Cell Biology

Benefits

  • First graduate textbook in interdisciplinary applied mathematics that focuses on applications of stochastic processes to cell biology

  • Introduces concepts in stochastic process via motiviating biological applications

  • Solutions to exercises provided as supplementary material

  • Large number of examples and exercises, highly illustrated

Textbook

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 41)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Paul C. Bressloff
    Pages 1-31
  3. Foundations

    1. Front Matter
      Pages 33-33
    2. Paul C. Bressloff
      Pages 103-158
    3. Paul C. Bressloff
      Pages 159-226
    4. Paul C. Bressloff
      Pages 269-340
  4. Advanced Topics

    1. Front Matter
      Pages 341-341
    2. Paul C. Bressloff
      Pages 343-437
    3. Paul C. Bressloff
      Pages 439-495
    4. Paul C. Bressloff
      Pages 619-643
  5. Back Matter
    Pages 645-679

About this book

Introduction

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology.  A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods.

 

This text is primarily aimed at graduate students and researchers working in mathematical biology and applied mathematicians interested in stochastic modeling.  Applied probabilists and theoretical physicists should also find it of interest. It assumes no prior background in statistical physics and introduces concepts in stochastic processes via motivating biological applications.  

 

The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years.

Keywords

Biochemical and gene retworks Cell biology Diffusion Molecular motors Stochastic processes

Authors and affiliations

  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA

About the authors

Paul Bressloff is a Professor of Mathematics in the Department of Mathematics at the University of Utah, where he is a faculty member of the Mathematical Biology Group and the Brain Institute.  He is also a Visiting Professor at the Mathematical Institute, University of Oxford and INRIA, Sophia-Antipolis.  Professor Bressloff's research interests lie in the areas of mathematical neuroscience and theoretical biophysics.

Bibliographic information

Reviews

“This nearly 700-page volume is an impressive account of a ‘second wave’ in the broad field known as mathematical biology. … I say ‘Bravo!’ Bressloff's book is a superb resource for applied mathematicians interested in teaching and/or research in this field.” (John Adam, Mathematical Reviews, February, 2016)