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Understanding Complex Systems Aneta Stefanovska Peter V. E. McClintock   Editors Physics of Biological Oscillators New Insights into Non-Equilibrium and Non-Autonomous Systems Springer Complexity Springer Complexity is an interdisciplinary program publishing the best research and academic-levelteachingonbothfundamentalandappliedaspectsofcomplexsystems—cutting across all traditional disciplines of the natural and life sciences, engineering, economics, medicine,neuroscience,socialandcomputerscience. Complex Systems are systems that comprise many interacting parts with the ability to generateanewqualityofmacroscopiccollectivebehaviorthemanifestationsofwhicharethe spontaneousformationofdistinctivetemporal,spatialorfunctionalstructures.Modelsofsuch systemscanbesuccessfullymappedontoquitediverse“real-life”situationsliketheclimate,the coherentemissionoflightfromlasers,chemicalreaction-diffusionsystems,biologicalcellular networks,thedynamicsofstockmarketsandoftheinternet,earthquakestatisticsandpredic- tion,freewaytraffic,thehumanbrain,ortheformationofopinionsinsocialsystems,toname justsomeofthepopularapplications. Although their scope and methodologies overlap somewhat, one can distinguish the following main concepts and tools: self-organization, nonlinear dynamics, synergetics, tur- bulence, dynamical systems, catastrophes, instabilities, stochastic processes, chaos, graphs and networks, cellular automata, adaptive systems, genetic algorithms and computational intelligence. ThethreemajorbookpublicationplatformsoftheSpringerComplexityprogramarethe monographseries“UnderstandingComplexSystems”focusingonthevariousapplicationsof complexity, the “Springer Series in Synergetics”, which is devoted to the quantitative the- oreticalandmethodologicalfoundations,andthe“SpringerBriefsinComplexity”whichare concise and topical working reports, case studies, surveys, essays and lecture notes of rel- evance to the field. In addition to the books in these two core series, the program also incorporates individual titles ranging from textbooks tomajor reference works. IndexedbySCOPUS, INSPEC, zbMATH,SCImago. Series Editors HenryD.I.Abarbanel,InstituteforNonlinearScience,UniversityofCalifornia,SanDiego,LaJolla,CA,USA DanBraha,NewEnglandComplexSystemsInstitute,UniversityofMassachusetts,Dartmouth,USA PéterÉrdi,CenterforComplexSystemsStudies,KalamazooCollege,Kalamazoo,USA;HungarianAcademy ofSciences,Budapest,Hungary KarlJ.Friston,InstituteofCognitiveNeuroscience,UniversityCollegeLondon,London,UK HermannHaken,CenterofSynergetics,UniversityofStuttgart,Stuttgart,Germany ViktorJirsa,CentreNationaldelaRechercheScientifique(CNRS),UniversitédelaMéditerranée,Marseille, France JanuszKacprzyk,SystemsResearchInstitute,PolishAcademyofSciences,Warsaw,Poland KunihikoKaneko,ResearchCenterforComplexSystemsBiology,TheUniversityofTokyo,Tokyo,Japan ScottKelso,CenterforComplexSystemsandBrainSciences,FloridaAtlanticUniversity,BocaRaton,USA MarkusKirkilionis,MathematicsInstituteandCentreforComplexSystems,UniversityofWarwick, Coventry,UK JürgenKurths,NonlinearDynamicsGroup,UniversityofPotsdam,Potsdam,Germany RonaldoMenezes,DepartmentofComputerScience,UniversityofExeter,UK AndrzejNowak,DepartmentofPsychology,WarsawUniversity,Warszawa,Poland HassanQudrat-Ullah,SchoolofAdministrativeStudies,YorkUniversity,Toronto,Canada LindaReichl,CenterforComplexQuantumSystems,UniversityofTexas,Austin,USA PeterSchuster,TheoreticalChemistryandStructuralBiology,UniversityofVienna,Vienna,Austria FrankSchweitzer,SystemDesign,ETHZürich,Zürich,Switzerland DidierSornette,EntrepreneurialRisk,ETHZürich,Zürich,Switzerland StefanThurner,SectionforScienceofComplexSystems,MedicalUniversityofVienna,Vienna,Austria Understanding Complex Systems Founding Editor: S. Kelso More information about this series at http://www.springer.com/series/5394 Aneta Stefanovska Peter V. E. McClintock (cid:129) Editors Physics of Biological Oscillators New Insights into Non-Equilibrium and Non-Autonomous Systems 123 Editors Aneta Stefanovska PeterV.E. McClintock Department ofPhysics Department ofPhysics Lancaster University Lancaster University Lancaster,UK Lancaster,UK ISSN 1860-0832 ISSN 1860-0840 (electronic) Understanding ComplexSystems ISBN978-3-030-59804-4 ISBN978-3-030-59805-1 (eBook) https://doi.org/10.1007/978-3-030-59805-1 ©SpringerNatureSwitzerlandAG2021 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart 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 orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. 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, expressed or implied, with respect to the material contained hereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregard tojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Foreword by Alex A. R. Webb An oscillation is the repetitive variation in time of some measure, or between two ormoredifferentstates.Oscillationsoccurnotonlyinmechanicalsystems,butalso inotherkindsofdynamicalsystem.Tothenon-specialistitmightbeasurprisethat biologicalsystemscanarrangeintonetworksthatformrobustoscillatingdynamical systems, but this is a frequent property of biological networks. By biological oscillators we mean any system with repeated cycles of activity or abundance of a biological component (e.g., metabolite or protein). Biological oscillators include communitybehaviors, suchasseeninecologicalstudies;howeverinthisbookthe focus is on oscillations in cellular or physiological activities within a single organism. Broadly, biological oscillators can be divided into three categories. First, there are those that oscillate for a short period before damping and arise from a pertur- bation to the system, such as metabolic and homeostatic control mechanisms, includingtheoscillatorydynamicsinglycolysis.Thesecondcategoryofbiological oscillators involves stimulus-induced oscillatory behaviors including oscillatory dynamics of signal relays within and between cells, oscillations of blood flow and oscillations in firing of neurons in the brain. Lastly there are the self-sustaining endogenous rhythms including the heart pacemaker, breathing and blood flow in mammals, circadian oscillations, cell division cycles and developmental clocks. Thesedistinctionsbetweenthedifferenttypesofbiologicaloscillationsarearbitrary andtheboundariesareblurredbecauseallhavesomeself-sustainingproperties,and all can have nonautonomous properties affected by other signals. These are some of the complex issues discussed in the pages of this book. Another level of complexity is introduced by the hierarchy of interactions between oscillators. In both single- and multi-cellular organisms, oscillators often can occur within a single cell, however, interactions between cells can reinforce, amplify and make the oscillations more robust, such as found in the oscillations between the neurons of the suprachiasmatic nucleus of the circadian pacemaker of mammalian brains. In the mammalian circadian pacemaker, the oscillatory dynamics are generated by transcriptional feedback loops of gene expression, v vi ForewordbyAlexA.R.Webb proteinsynthesisandproteindegradationintheindividualcells,andarereinforced by electrical coupling between the cells, resulting in a very robust multicellular circadian oscillator. Physics has developed powerful conceptual and mathematical tools to under- stand the behavior of physical oscillators, such as pendula. Remarkably, the analogiesfromthephysicalworldhaveproventobeusefulindescribing,modeling and understanding the behaviors and dynamics of biological oscillators. Physics offers much to the biologist, providing formal descriptions of systems that are too complex to be understood intuitively, and predictive power, which is required to turn discovery into application. Whilst useful, there are challenges in applying concepts from the physical world to biological oscillators. Physical descriptions of oscillatorsareoftenappliedtodesignedmechanicalorelectronicsystemsinwhich thecomponentsandconnectionsareknownandwellunderstood.Often,instudying biologicaloscillators,thenumberofcomponents,thenatureofthecomponents,the network of interactions between the components and the mechanisms by which these interactions occur are either assumed, or known for only a few of the com- ponents that make up the oscillator. Biological oscillators can be formed by very simple systems comprising only twocomponents,butareoftenformedofverycomplexnetworksthatcanbenearly fully connected and therefore have a high degree of feedback. For example, the mutualgeneregulatorynetworksthatarepartofthe24-hourcircadianoscillatorof plant cells involve mutual regulation between at least 30 genes in a nearly fully connected network. This means it is often difficult to obtain a model of the inter- actions in the network in which one can have full confidence. The nature of the oscillatory dynamics in biological systems can be complex, involving many changes in state, abundance and location of thecomponents. In the plant circadian oscillator as an example, feedback between components can occur through protein-DNA interactions regulating the expression of component parts, phospho- rylation to affect protein activity, ubiquitination to affect protein stability and translocation between the cytoplasm and nucleus to regulate accessibility of tran- scriptional regulators to DNA. Oneofthemostchallengingfeaturesofbiologicaloscillators,comparedtothose designedbyhumans,isthatatdifferenttimesintheoscillatorycycle,thenetworkof regulatory connections in the oscillator can change. For example, in the circadian oscillatorsthat drive 24 hourrhythms in plants and humans,the proteins that form the regulatory network vary greatly in their abundance over the cycle because of oscillations in protein translation and breakdown, which are the basis of the oscillatorydynamics.Thus,theoreticalandmathematicaldescriptionsofbiological oscillatorsmustdescribenotonlythedynamicsandpropertiesoftheoscillator,but also how those change through the oscillatory cycle. This is a particular challenge when considering non-autonomous oscillators that respond to external inputs, which probably represents most biological oscillators, because regulation by an external signal can be affected by the state and availability of a component in the oscillator,meaningthatregulatoryinputsaresubjectthemselvestofeedbackcontrol from the oscillator. ForewordbyAlexA.R.Webb vii Itisthesesimilaritiesanddifferencesbetweenphysicalandbiologicaloscillators which resulted in the Physics of Biological Oscillators (POBO) conference at Chicheley Hall, UK in 2018, a meeting held in celebration of the 60th birthday of AnetaStefanovskawhohascontributedsomuchtothedevelopmentofthesubject. This book captures the discussions and presentations during three wonderful days of exciting science, in which experts in different disciplines grappled with the immenseintellectualchallengesoffindingthebestwaystodescribe,analyze,model and understand the properties, functions, behaviors and uses of biological oscilla- tors.Thechapterssummarizingthepresentationsbyresearchersacrossthedifferent disciplines give an insight into the different biological systems being investigated andthevarietyofPhysicsapproachesbeingused.Itwasexhilaratingtospendthree days in the company of researchers from different disciplines trying to bridge the gaps between the experts in different fields to understand these fundamental bio- logical behaviors. This seems an even more amazing experience looking back through the lens of the COVID-19 pandemic which hit during the final stages of production of this book. I hope you enjoy the invigorating intellectual stimulation contained within these chapters as much as I have. August 2020 Alex A. R. Webb Department of Plant Sciences University of Cambridge Cambridge, UK Preface This book derives mainly from a Research Workshop Physics of Biological Oscillators: New Insights into Non-Equilibrium and Non-Autonomous Systems1 held in Chicheley Hall (27–30 November 2018): see photograph. It was a highly interdisciplinary event that brought together some of the best international experts workingonthevexedproblemofhowbesttotreatthenon-autonomousoscillatory systems that crop up so often in biology. They included life scientists who inves- tigate and measure the oscillations and the physicists, chemists, mathematicians, informationtheorists,andengineersseekingtounderstandtheirfundamentalnature and origins and to devise useful applications of this knowledge. Thus, although their work lies in seemingly very different scientific areas—ranging from mathe- matics to the experimental recording and analysis of real data—they were all addressing in one way or another the problem of time-variability in oscillatory systems. They gave presentations about how to measure, analyze, model, and understand such data as well as considering applications to medicine, both actual andpotential.Nearlyalloftheexperts,assembledfrom19countries,kindlyagreed to write up their presentations for publication thereby providing the basis for the book. Lancaster, UK Aneta Stefanovska Peter V. E. McClintock 1www.physicsoflife.org.uk/physics-of-biological-oscillators.html. ix x Preface Participants in the POBO Research Workshop Physics of Biological Oscillators: NewInsightsintoNon-EquilibriumandNon-AutonomousSystems,outsidethefront door of Chicheley Hall, Buckinghamshire, UK, where the event took place. Photograph by M. G. Rosenblum (University of Potsdam)

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