Applications of Dynamical Systems in Biology and Medicine PDF
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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 Moreinformationaboutthisseriesathttp://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,establishinglinksbetweenmathematicsofthehighestcaliberandimportant 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 MathematicsanditsApplications: http://www.ima.umn.edu/springer/volumes.html. PresentationmaterialsfromtheIMAtalksareavailableat http://www.ima.umn.edu/talks/. Videolibraryisat http://www.ima.umn.edu/videos/. FadilSantosa,DirectoroftheIMA Trachette Jackson • Ami Radunskaya Editors Applications of Dynamical Systems in Biology and Medicine 123 Editors TrachetteJackson AmiRadunskaya DepartmentofMathematics DepartmentofMathematics UniversityofMichigan PomonaCollege AnnArbor,MI,USA Claremont,CA,USA ISSN0940-6573 ISSN2198-3224 (electronic) TheIMAVolumesinMathematicsanditsApplications ISBN978-1-4939-2781-4 ISBN978-1-4939-2782-1 (eBook) DOI10.1007/978-1-4939-2782-1 LibraryofCongressControlNumber:2015942581 MathematicsSubjectClassification(2010):92-06,92Bxx,92C50,92D25 SpringerNewYorkHeidelbergDordrechtLondon ©SpringerScience+BusinessMedia,LLC2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper SpringerScience+Business MediaLLCNewYorkispartofSpringerScience+Business Media(www. springer.com) Contents EmergenceofAnti-CancerDrugResistance:Exploring theImportanceoftheMicroenvironmentalNicheviaaSpatialModel.... 1 Jana L. Gevertz, Zahra Aminzare, Kerri-Ann Norton, JudithPérez-Velázquez,AlexandriaVolkening, andKatarzynaA.Rejniak FlowInducedbyBacterialCarpetsandTransport ofMicroscaleLoads.............................................................. 35 AmyL.Buchmann,LisaJ.Fauci,KarinLeiderman, EvaM.Strawbridge,andLonghuaZhao ModelingBloodFlowControlintheKidney.................................. 55 JuliaArciero,LauraEllwein,AshleeN.FordVersypt, ElizabethMakrides,andAnitaT.Layton Injury-InitiatedClotFormationUnderFlow:AMathematical ModelwithWarfarinTreatment ............................................... 75 LisettedePillis, EricaJ.Graham,KaitlynHood,YanpingMa, AmiRadunskaya,andJulieSimons Clustering in Inhibitory Neural Networks with Nearest NeighborCoupling............................................................... 99 JenniferMiller,HwayeonRyu,ZeynepTeymuroglu, XueyingWang,VictoriaBooth,andSueAnnCampbell Effects of Thermoregulationon Human Sleep Patterns: A Mathematical Model of Sleep–Wake Cycles with REM–NREMSubcircuit ........................................................ 123 Selenne Bañuelos, Janet Best, Gemma Huguet, AliciaPrieto-Langarica,PamelaB.Pyzza,Markus H.Schmidt,andShelbyWilson v vi Contents ModelingSympatricSpeciationinQuasiperiodicEnvironments........... 149 JasmineFoo,CymraHaskell,NataliaL.Komarova, RebeccaA.Segal,andKarenE.Wood AStochasticModeloftheMelanopsinPhototransductionCascade ....... 175 R. Lane Brown, Erika Camacho, Evan G. Cameron, Christina Hamlet, Kathleen A. Hoffman, Hye-Won Kang, PhyllisR.Robinson,KatherineS.Williams,andGlennR.Wyrick IntermittentPreventiveTreatment(IPT)andtheSpread ofDrugResistantMalaria....................................................... 197 MirandaI.Teboh-Ewungkem,OliviaProsper,KatharineGurski, CarrieA.Manore,AngelaPeace,andZhilanFeng WhAM! Workshop TrachetteJacksonandAmiRadunskaya 1 AimandScope Theaimofthisvolumeistoshowcaseoriginalresearchconductedbynewlyformed collaborative teams during the IMA’s Women in Applied Mathematics (WhAM!) Research Collaboration Conference on Dynamical Systems with Applications to Biologyand Medicine.The overarchinggoalof the workshopwas to help build a strongnetworkofwomenworkingondynamicalsystemsinbiologybyfacilitating the formationof new and lasting research groups.This volume is the first fruitof thoseresearchefforts.Thisvolumehighlightsproblemsfromarangeofbiological andmedicalapplicationsthatcanbeinterpretedasquestionsaboutsystembehavior 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 andinvestigatethesebiologicalandmedicalproblemsincludeordinary,partialand stochasticdifferentiationequations,hybriddiscrete-continuousapproaches,aswell as2Dand3Dnumericalsimulation. T.Jackson((cid:2)) DepartmentofMathematics,UniversityofMichigan,AnnArbor,MI,USA e-mail:[email protected] A.Radunskaya DepartmentofMathematics,PomonaCollege,Claremont,CA91711,USA e-mail:[email protected] vii viii T.JacksonandA.Radunskaya 2 Introduction According to the 2013 survey from the American Mathematical Society, women makeupapproximately30%oftherecentU.S.PhDsinthemathematicalsciences [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 whoareeditorsofprofessionaljournals[2].KristinLauter,anumbertheoristwith Microsoft Research, decided to promote a community of women researchers in mathematics. In 2008 she organized the first Women in Number Theory (WIN) conference,withthehelpofco-organizersRachelPries(ColoradoStateUniversity) andRenateScheidler(UniversityofCalgary).Todate,therehavebeenthreeWIN 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: WomeninAppliedMathematics(WhAM!):AResearchCollaborationConference onDynamicalSystemswithApplicationstoBiologyandMedicine. Manyquestionsaboutbiologicalprocessescanbephrasedintermsofdynamical 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 biologywere 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- standingcollaboration,butwhohadenoughexperiencetotakeonaleadershiprole. Otherteammemberswerechosenfromapplicantsandinvitees.Eachgroupworked togetherduringthefive-dayconferenceandallninegroupscontinuedtheirproject 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 plannedinadvanceisthatseniorwomenwereabletomeet,mentor,andcollaborate with some of the brightest young women in their field. Junior faculty, post-docs, and graduatestudents developedtheir 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!formattogetherwith the IMA’sstaff infrastructurecreatedan intellectual environment difficult or impossible to foster in traditional academic, conference, and workshop settings; one that will allow for substantial opportunities to create newbio-mathematicalknowledgeinareasofnationalinterest. WhAM!Workshop ix 3 TheResearch WhAM!projectsaddressedchallengesthatcutacrossmultiplelevelsoforganization in biology. A variety of mathematical tools came into play, including differential equations, stochastic models, and discrete networks. Processes that evolve on large time scales were studied, as well as those that are described by fast, local interactions. Some projects were computationally intensive, while others focused onanalyticalandqualitativeresults.Commontoalloftheprojectswasadesireto solveproblemsrelevanttothemedicalcommunityusingsophisticatedmathematical tools. The Cancer group focused on anti-cancer drug resistance, which is a criti- cal challenge that the clinical cancer research community is facing. Almost all chemotherapeuticagents and manytargeted therapiesthatare used currentlyused in the clinical treatment of cancer lead to drug resistance, and this WhAM! team derived a hybrid mathematical model to investigate whether drug resistance is a pre-existing or emerging phenomenon. The Malaria group also focused on drug resistance, which is becoming a major cause of the rapid spread of malaria with intermittent preventive treatment (IPT). The Malaria team developed an age-structured model to determine the critical level of IPT treatment that would minimizethespreadofdrugresistanceandreducediseaseprevalenceandburden. BiologicalfluiddynamicswasalsoafocusforsomeWhAM!teams.TheBacteria groupstudiedtheflowinducedbythecollectiveflagellarmotionofbacterialcarpets. In particular, they modeled a doubly periodic array of rotating helical stuck to a surface immersed in a viscous, incompressible fluid. They used the model to examine the transport of fluid particles above the carpet as a function of flagellar distributionandgeometries.TheKidneyteamfocusedonmodelingauto-regulation of renalblood flow. A complexinteraction of chemicalsignals allows the healthy kidney to maintain a nearly constant rate of blood flow even in the presence of fluctuationsinbloodpressureorbloodcomposition.Theseprocessesareimplicated in diseases such as diabetesand hypertension,so it is importantto understandthe mechanismsbehindthem.ThemathematicalmodeldevelopedbytheKidneyteam can further our understanding of these mechanisms and can suggest strategies to preventtheirmalfunction.TheClotbustersstudiedanothertypeofflowirregularity: theformationofbloodclots.Usingareducedcompartmentmodelofbloodflow,the teambuiltamodelusingapproximately100differentialequationsthatdescribesthe dynamicsofclotformationandtreatmentbyanti-coagulants.Thefocusofthestudy wastocomparetheresultsofcurrentlyusedinvitromeasurementsofclotformation times to what might actually be happening in vivo. The team’s conclusions have implicationsforschedulingofanti-coagulanttreatments. Two teams used stochastic models to explore the dynamics of physiological processes.TheEvolutionteamstudiedtheemergenceofnewspecies.Thisquestion is importantwhen consideringthe dangerof anti-biotic resistant “super bacteria," for example. The team explored models of the asexual evolution of E. coli and showed that, even in the presence of environmentalrandomness, it is common to
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