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Applications of Dynamical Systems in Biology and Medicine the IMA Volumes in Mathematics and Its Applications Volume 158 The IMA Volumes in Mathematics and its Applications Trachette Jackson Ami Radunskaya Editors Applications of Dynamical Systems in Biology and Medicine The IMA Volumes in Mathematics and its Applications Volume 158 More information about this series at http://www.springer.com/series/811 Institute for Mathematics and its Applications (IMA) The Institute for Mathematics and its Applications was established by a grant from the National Science Foundation to the University of Minnesota in 1982. The primary mission of the IMA is to foster research of a truly interdisciplinary nature, establishing links between mathematics of the highest caliber and important scientific and technological problems from other disciplines and industries. To this end, the IMA organizes a wide variety of programs, ranging from short intense workshops in areas of exceptional interest and opportunity to extensive thematic programs lasting a year. IMA Volumes are used to communicate results of these programs that we believe are of particular value to the broader scientific community. The full list of IMA books can be found at the Web site of the Institute for Mathematics and its Applications: http://www.ima.umn.edu/springer/volumes.html. Presentation materials from the IMA talks are available at http://www.ima.umn.edu/talks/. Video library is at http://www.ima.umn.edu/videos/. Fadil Santosa, Director of the IMA Trachette Jackson • Ami Radunskaya Editors Applications of Dynamical Systems in Biology and Medicine 123 Editors Trachette Jackson Ami Radunskaya Department of Mathematics Department of Mathematics University of Michigan Pomona College Ann Arbor, MI, USA Claremont, CA, USA ISSN 0940-6573 ISSN 2198-3224 (electronic) The IMA Volumes in Mathematics and its Applications ISBN 978-1-4939-2781-4 ISBN 978-1-4939-2782-1 (eBook) DOI 10.1007/978-1-4939-2782-1 Library of Congress Control Number: 2015942581 Mathematics Subject Classification (2010): 92-06, 92Bxx, 92C50, 92D25 Springer New York Heidelberg Dordrecht London © Springer Science+Business Media, LLC 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) Contents Emergence of Anti-Cancer Drug Resistance: Exploring the Importance of the Microenvironmental Niche via a Spatial Model .... 1 Jana L. Gevertz, Zahra Aminzare, Kerri-Ann Norton, Judith Pérez-Velázquez, Alexandria Volkening, and Katarzyna A. Rejniak Flow Induced by Bacterial Carpets and Transport of Microscale Loads.............................................................. 35 Amy L. Buchmann, Lisa J. Fauci, Karin Leiderman, Eva M. Strawbridge, and Longhua Zhao Modeling Blood Flow Control in the Kidney.................................. 55 Julia Arciero, Laura Ellwein, Ashlee N. Ford Versypt, Elizabeth Makrides, and Anita T. Layton Injury-Initiated Clot Formation Under Flow: A Mathematical Model with Warfarin Treatment ............................................... 75 Lisette dePillis, Erica J. Graham, Kaitlyn Hood, Yanping Ma, Ami Radunskaya, and Julie Simons Clustering in Inhibitory Neural Networks with Nearest Neighbor Coupling ............................................................... 99 Jennifer Miller, Hwayeon Ryu, Zeynep Teymuroglu, Xueying Wang, Victoria Booth, and Sue Ann Campbell Effects of Thermoregulation on Human Sleep Patterns: A Mathematical Model of Sleep–Wake Cycles with REM–NREM Subcircuit ........................................................ 123 Selenne Bañuelos, Janet Best, Gemma Huguet, Alicia Prieto-Langarica, Pamela B. Pyzza, Markus H. Schmidt, and Shelby Wilson v vi Contents Modeling Sympatric Speciation in Quasiperiodic Environments........... 149 Jasmine Foo, Cymra Haskell, Natalia L. Komarova, Rebecca A. Segal, and Karen E. Wood A Stochastic Model of the Melanopsin Phototransduction Cascade ....... 175 R. Lane Brown, Erika Camacho, Evan G. Cameron, Christina Hamlet, Kathleen A. Hoffman, Hye-Won Kang, Phyllis R. Robinson, Katherine S. Williams, and Glenn R. Wyrick Intermittent Preventive Treatment (IPT) and the Spread of Drug Resistant Malaria....................................................... 197 Miranda I. Teboh-Ewungkem, Olivia Prosper, Katharine Gurski, Carrie A. Manore, Angela Peace, and Zhilan Feng WhAM! Workshop Trachette Jackson and Ami Radunskaya 1AimandScope The aim of this volume is to showcase original research conducted by newly formed collaborative teams during the IMA’s Women in Applied Mathematics (WhAM!) Research Collaboration Conference on Dynamical Systems with Applications to Biology and Medicine. The overarching goal of the workshop was to help build a strong network of women working on dynamical systems in biology by facilitating the formation of new and lasting research groups. This volume is the first fruit of those research efforts. This volume highlights problems from a range of biological and medical applications that can be interpreted as questions about system behavior or control. Topics include drug resistance in cancer and malaria, biological fluid dynamics, auto-regulation in the kidney, anti-coagulation therapy, evolutionary diversification, and photo-transduction. Mathematical techniques used to describe and investigate these biological and medical problems include ordinary, partial and stochastic differentiation equations, hybrid discrete-continuous approaches, as well as 2D and 3D numerical simulation. T. Jackson () Department of Mathematics, University of Michigan, Ann Arbor, MI, USA e-mail: [email protected] A. Radunskaya Department of Mathematics, Pomona College, Claremont, CA 91711, USA e-mail: [email protected] vii viii T. Jackson and A. Radunskaya 2 Introduction According to the 2013 survey from the American Mathematical Society, women make up approximately 30% of the recent U.S. PhDs in the mathematical sciences [1]. However, the visibility of women as research mathematicians is still dim, as evidenced by the percentages of women who are invited to speak at national conferences, the number of women who win prizes and the number of women who are editors of professional journals [2]. Kristin Lauter, a number theorist with Microsoft Research, decided to promote a community of women researchers in mathematics. In 2008 she organized the first Women in Number Theory (WIN) conference, with the help of co-organizers Rachel Pries (Colorado State University) and Renate Scheidler (University of Calgary). To date, there have been three WIN conferences, as well as Women in Shapes (WiSH), a workshop held at IPAM in July 2013 devoted to problems in shape modeling. Noting the success of these pioneering conferences, we wanted to bring together women working in applied mathematics in order to work on problems of mutual interest. We organized the IMA’s first special workshop targeting women as participants. We called it: Women in Applied Mathematics (WhAM!): A Research Collaboration Conference on Dynamical Systems with Applications to Biology and Medicine. Many questions about biological processes can be phrased in terms of dynamical systems. The evolution of these processes and the stability of their long-term behavior can be studied in terms of dynamical systems theory. Since the goal of the five-day workshop was to foster the building of long-term collaborative relationships, this workshop had a special format designed to maximize opportu- nities for collaboration. Nine senior women researchers working in mathematical biology were invited to present a problem and lead a research group. Each senior leader then chose a more junior co-leader with whom they did not have a long- standing collaboration, but who had enough experience to take on a leadership role. Other team members were chosen from applicants and invitees. Each group worked together during the five-day conference and all nine groups continued their project through the ensuing months. The results are being published in this volume. The benefit of such a structured program with leaders, projects, and working groups planned in advance is that senior women were able to meet, mentor, and collaborate with some of the brightest young women in their field. Junior faculty, post-docs, and graduate students developed their network of colleagues and were introduced to important new research areas, thereby improving their chances for successful research careers. The scientific atmosphere at WhAM! was truly exciting. The WhAM! format together with the IMA’s staff infrastructure
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