E-Book Overview
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.
E-Book Content
Interdisciplinary Applied Mathematics 41
Paul C. Bressloff
Stochastic Processes in Cell Biology
Stochastic Processes in Cell Biology
Interdisciplinary Applied Mathematics
Editors S.S. Antman P. Holmes L. Greengard Series Advisors Leon Glass P.S. Krishnaprasad Robert Kohn James D. Murray Shankar Sastry
Problems in engineering, computational science, and the physical and biological sciences are using increasingly sophisticated mathematical techniques. Thus, the bridge between the mathematical sciences and other disciplines is heavily traveled. The correspondingly increased dialog between the disciplines has led to the establishment of the series: Interdisciplinary Applied Mathematics. The purpose of this series is to meet the current and future needs for the interaction between various science and technology areas on the one hand and mathematics on the other. This is done, firstly, by encouraging the ways that mathematics may be applied in traditional areas, as well as point towards new and innovative areas of applications; and, secondly, by encouraging other scientific disciplines to engage in a dialog with mathematicians outlining their problems to both access new methods and suggest innovative developments within mathematics itself. The series will consist of monographs and high-level texts from researchers working on the interplay between mathematics and other fields of science and technology.
For further volumes: http://www.springer.com/series/1390
Paul C. Bressloff
Stochastic Processes in Cell Biology
123
Paul C. Bressloff Department of Mathematics University of Utah Salt Lake City, UT, USA
ISSN 0939-6047 ISSN 2196-9973 (electronic) ISBN 978-3-319-08487-9 ISBN 978-3-319-08488-6 (eBook) DOI 10.1007/978-3-319-08488-6 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2014945210 Mathematics Subject Classification: 82C31, 92C05, 92C37, 92C40, 92C17, 82C70 © Springer International Publishing Switzerland 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation,