Introduction to Modeling Biological Cellular Control Systems
This textbook contains the essential knowledge in modeling, simulation, analysis, and applications in dealing with biological cellular control systems. In particular, the book shows how to use the law of mass balance and the law of mass action to derive a
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MS&A Series Editors: Alfio Quarteroni (Editor-in-Chief ) • Tom Hou • Claude Le Bris • Anthony T. Patera • Enrique Zuazua
Weijiu Liu
Introduction to Modeling Biological Cellular Control Systems
Weijiu Liu Department of Mathematics University of Central Arkansas Conway, AR, USA
MS&A – Modeling, Simulation & Applications ISSN print version: 2037-5255 ISSN electronic version: 2037-5263 ISBN 978-88-470-2489-2 DOI 10.1007/978-88-470-2490-8
ISBN 978-88-470-2490-8 (eBook)
Library of Congress Control Number: 2011940853 Springer Milan Dordrecht Heidelberg London New York © Springer-Verlag Italia 2012 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Cover design: Beatrice B , Milan Typesetting with LATEX: PTP-Berlin, Protago TEX-Production GmbH, Germany (www.ptp-berlin.eu)
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Preface
When I tried to design output feedback controllers for nonlinear control systems, I found that design methods are limited. I thought that a cellular process in living organisms, such as the blood glucose control system, would be a perfect feedback control system because the cellular process should be tightly controlled so that cells in the living organism can carry out numerous tasks to survive. Thus I was wondering whether I can get inspiration fro
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