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8973_9789814566360_tp.indd 1 7/4/14 5:08 pm May2,2013 14:6 BC:8831-ProbabilityandStatisticalTheory PST˙ws TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk World Scientifi c NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI 8973_9789814566360_tp.indd 2 7/4/14 5:08 pm Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Wodarz, Dominik, author. Dynamics of cancer : mathematical foundations of oncology / by Dominik Wodarz (University of California, Irvine, USA) & Natalia L. Komarova (University of California, Irvine, USA). pages cm Includes bibliographical references and index. ISBN 978-981-4566-36-0 (hardcover : alk. paper) 1. Oncology--Mathematics. 2. Cancer--Treatment--Data processing. 3. Computational biology. I. Komarova, Natalia L., author. II. Title. RC254.W66 2014 616.99'400285--dc23 2013033157 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Copyright © 2014 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. Printed in Singapore March10,2014 11:31 BC:8973–DynamicsofCancer 3rd Reading bookx pagev This book is dedicated to our parents and children. v May2,2013 14:6 BC:8831-ProbabilityandStatisticalTheory PST˙ws TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk March10,2014 11:31 BC:8973–DynamicsofCancer 3rd Reading bookx pagevii Preface Cancer is anagerelateddisease thatleads to the outgrowthof cellpopula- tions in the body, which can result in significant morbidity and mortality. Treatmentapproachesarebasedonourunderstandingofthebiologyofspe- cificcancers,andagreatamountofworkhasbeenandisbeingperformedto improvethisunderstanding. Significantprogressisbeingmadewithrespect to identifying cellular defects, genetic and epigenetic events, and molecu- lar pathwaystowards malignantgrowth in the context of different cancers. Apart from focusing on cellular characteristics, the interactions of tumor cells with other cells in their vicinity, the microenvironment, is thought to be a crucialcomponent in carcinogenesis. Experimentsand clinicalstudies have elucidated many key mechanisms that underlie the development of cancer and that can be potentially exploited by treatments. However, another approach to studying the development and progression of cancer has emerged and is becoming increasingly important: the field of mathematical oncology, which uses mathematical and computa- tionaltechniquestostudyhowcancercellsgetgenerated,grow,andevolve. The concept of evolution plays a special role in this context. Cancers arise and progress by accumulating various mutations and epigenetic changes, whichgivesthemaselectiveadvantageoverhealthycells,andleadtogrowth and pathogenesis. Mutation and selection, the hallmarks of evolution, are central components in the development of cancer. Mathematical work, in turn, has played a central role for elucidating evolutionary principles. This book provides an introduction to the field of mathematical oncology, explaining some central mathematical and computational techniques that are at the core of this field, and highlighting how mathematical anal- ysis has provided valuable biological insights into concepts and data. The book is not meant to be a comprehensive survey of the field, which has vii March10,2014 11:31 BC:8973–DynamicsofCancer 3rd Reading bookx pageviii viii Dynamics of cancer: mathematical foundations of oncology grown to be rather large. Instead it aims to explore a few topics in depth, with an emphasis on evolutionary aspects of cancer. The book is based on our own work. It provides the reader with a solid technical background to understand how mathematical results have been obtained, and shows how these mathematical results can by applied to advance biology. The book is multi-faceted, and can be used in a variety of settings. Because it explains in detail the mathematical techniques, it can be used as a textbook for applied mathematics students learning aspects of mathematical biology, as well as as a reference for people that are interested in the mathematical techniques. As the book highlights biological insights and advances, it can also be used by students in population and evolutionary biology who are interested in biomedical applications. Similarly, it canserveas a summaryfor cancerbiologistswho areinterestedin learning about some of the biological lessons that have resulted from mathematical models. We have tried to write the book in such a way that it is accessible and usefulbothforamathematicalandabiologicalreadershipbymarkingwith graybackgroundallthe materials thatare moresuited for mathematicians andthatmightbedifficulttounderstandforabiologicalreadershipwithout amathematicalbackground. Itisthehopethatfuturegenerationsofscien- tists willbe well-trainedattheinterfacebetweenmathematicsandbiology, such that there will be fewer communication issues between biologists and mathematicians. It is a field that is rising at a fast pace, and our book aims to contribute to the interdisciplinary educationof the new generation of researchers. We would like to thank a number of people, whose input and discus- sions have shaped the material that is discussed in this book: David Ax- elrod, Rick Boland, Hung Fan, Steve Frank, Ajay Goel, Andy Hofacre, Yoh Iwasa, Vincent Jancen, David Krakauer, John Lowengrub, Ignacio Rodriguez-Brenes, Alex Sadovski, Akira Sasaki, Fred Wan, and Ryan Zu- rakowski. We also thank members of our group, Alen Katouli, John Lau, Leili Shahriyari,Zhiying Sun, and ErinUrwin. We wouldlike to especially thankMartinNowak,whoseguidancehasshapedtheworkofbothauthors. Dominik Wodarz and Natalia Komarova March10,2014 11:31 BC:8973–DynamicsofCancer 3rdReading bookx pageix Contents Preface vii 1. Teaching guide 1 1.1 How to use this book . . . . . . . . . . . . . . . . . . . . . 1 1.2 A sample syllabus for a Mathematics course . . . . . . . . 2 1.3 A sample syllabus for a Biology course . . . . . . . . . . . 3 2. Cancer and somatic evolution 5 2.1 What is cancer? . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Basic cancer genetics . . . . . . . . . . . . . . . . . . . . . 6 2.3 Multi-stage carcinogenesis and colon cancer . . . . . . . . 8 2.4 Genetic instability . . . . . . . . . . . . . . . . . . . . . . 10 2.5 Barriers to cancer progression: importance of the microenvironment . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.6 Cellular hierarchies in cancer . . . . . . . . . . . . . . . . 15 2.7 Genetic and epigenetic changes . . . . . . . . . . . . . . . 15 2.8 Evolutionary theory and Darwinian selection . . . . . . . 17 3. Mathematical modeling of tumorigenesis 19 3.1 Ordinary differential equations . . . . . . . . . . . . . . . 20 3.2 Extensions of ODE modeling . . . . . . . . . . . . . . . . 22 3.2.1 Optimal control . . . . . . . . . . . . . . . . . . . 22 3.2.2 ODEs and cancer epidemiology . . . . . . . . . . . 23 3.3 Partial differential equations . . . . . . . . . . . . . . . . . 23 3.4 Stochastic modeling . . . . . . . . . . . . . . . . . . . . . 25 3.5 Cellular automaton models . . . . . . . . . . . . . . . . . 28 ix