Stochastic Approaches for Systems Biology

This textbook focuses on stochastic modelling and its applications in systems biology. In addition to a review of probability theory, the authors introduce key concepts, including those of stochastic process, Markov property, and transition probability, s

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Mukhtar Ullah • Olaf Wolkenhauer

Stochastic Approaches for Systems Biology

Mukhtar Ullah Department of Systems Biology and Bioinformatics Institute of Computer Science University of Rostock 18051 Rostock Germany [email protected]

Olaf Wolkenhauer Department of Systems Biology and Bioinformatics Institute of Computer Science University of Rostock 18051 Rostock Germany [email protected]

e-ISBN 978-1-4614-0478-1 ISBN 978-1-4614-0477-4 DOI 10.1007/978-1-4614-0478-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011931974 © Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

This work is dedicated to minds that are open to rational scientific reasoning and are not preoccupied with prejudices.

Preface The discrete and random occurrence of chemical reactions, far from thermodynamic equilibrium, among less-abundant chemical species in single cells, necessitates stochastic approaches for modeling. Currently available texts on stochastic approaches relevant to systems biology can be classified into two categories. Books in the first category require the reader to have sufficient background of probability theory and focus directly on applications. Books in the second category take a two-step approach: first, they provide the necessary background in probability theory and then the concepts so developed are applied to model systems. We here follow the “introduce when needed” approach which is more natural and avoids distractions to the reader. While we still provide a review of probability and random variables, subsequent notions of biochemical reaction systems and the relevant concepts of probability theory are introduced side by side. This will hopefully lead to an intuitive presentation of the stochastic framework for modeling subcellular biochemical systems. In particular, we make an effort to show how the notion of propensity, the chemical master equation, and the stochastic simulation algorithm arise as consequences of the Markov property. The reader is encouraged to pay attention to this because it is not easy to see this connection when reading the relevant literature in systems biology. The nonobvious relationship between various stochastic approa

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