Stochastic Narrow Escape in Molecular and Cellular Biology Analysis
This book covers recent developments in the non-standard asymptotics of the mathematical narrow escape problem in stochastic theory, as well as applications of the narrow escape problem in cell biology. The first part of the book concentrates on mathemati
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ochastic Narrow Escape in Molecular and Cellular Biology Analysis and Applications
Stochastic Narrow Escape in Molecular and Cellular Biology
David Holcman • Zeev Schuss
Stochastic Narrow Escape in Molecular and Cellular Biology Analysis and Applications
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David Holcman Group of Applied Mathematics and Computational Biology Ecole Normale Superieure Paris, France
Zeev Schuss Department of Mathematics Tel Aviv University School of Mathematical Science Tel Aviv, Israel
ISBN 978-1-4939-3102-6 ISBN 978-1-4939-3103-3 (eBook) DOI 10.1007/978-1-4939-3103-3 Library of Congress Control Number: 2015947260 Springer New York Heidelberg Dordrecht London © Springer Science+Business Media New York 2015 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, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Science+Business Media LLC New York is part of Springer Science+Business Media (www. springer.com)
Des petits trous, des petits trous, toujours des petits trous, S. Gainsbourg, le poinçonneur des lilas, 1958.
Preface
This monograph consists of two main parts, mathematical and biological. The mathematical part, which is quite sophisticated involving advanced asymptotic methods in partial differential equations, is aimed primarily at applied mathematicians and theoretical physicists who are interested in biological applications. The targeted readership of the second part is much wider and includes also computational biologists, theoretical chemists, biochemists, biophysicists, and physiologists. This part does not necessarily require the in-depth digesting of the tough analysis of the first part. It includes a summary of output formulas from the first part and mainly concentrates on their applications in various models of specific problems in theoretical molecular and cellular biology. Stochastic narrow escape consists in the passage of a diffusing particle through a narrow opening in an impermeable wall or the arrival of the trajectory of a diffusion process at a small target. For example, a stoc
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