Stochastic Processes in Cell Biology

1. Front Matter

   Pages i-xvii

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2. Introduction

   • Paul C. Bressloff

   Pages 1-31

3. Foundations

   1. Front Matter

      Pages 33-33

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   2. Diffusion in Cells: Random Walks and Brownian Motion

      • Paul C. Bressloff

      Pages 35-102

   3. Stochastic Ion Channels

      • Paul C. Bressloff

      Pages 103-158

   4. Polymers and Molecular Motors

      • Paul C. Bressloff

      Pages 159-226

   5. Sensing the Environment: Adaptation and Amplification in Cells

      • Paul C. Bressloff

      Pages 227-267

   6. Stochastic Gene Expression and Regulatory Networks

      • Paul C. Bressloff

      Pages 269-340

4. Advanced Topics

   1. Front Matter

      Pages 341-341

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   2. Transport Processes in Cells

      • Paul C. Bressloff

      Pages 343-437

   3. Self-Organization in Cells I: Active Processes

      • Paul C. Bressloff

      Pages 439-495

   4. Self-Organization in Cells II: Reaction-Diffusion Models

      • Paul C. Bressloff

      Pages 497-575

   5. The WKB Method, Path-Integrals, and Large Deviations

      • Paul C. Bressloff

      Pages 577-617

   6. Probability Theory and Martingales

      • Paul C. Bressloff

      Pages 619-643

5. Back Matter

   Pages 645-679

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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. Thistext 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.

• Biochemical and gene retworks
• Cell biology
• Diffusion
• Molecular motors
• Stochastic processes

“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)

• Department of Mathematics, University of Utah, Salt Lake City, USA

  Paul C. Bressloff

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.

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