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ForspecialissueofSyntheseonModeling,IdealizationandRepresentation

ExplainingFeaturesofFine-GrainedPhenomenaUsingAbstractAnalysesofPhenomenaandMechanisms:TwoExamplesfromChronobiology

WilliamBechtel

DepartmentofPhilosophyandCenterforCircadianBiologyUniversityofCalifornia,SanDiego

Abstract

Explanationsofbiologicalphenomenasuchascelldivision,proteinsynthesisorcircadianrhythmscommonlytaketheformofmodelsoftheresponsiblemechanisms.Recentlyphilosophersofsciencehaveattemptedtoanalyzethispractice,presentingmechanismsasorganizedcollectionsofpartsperformingoperationsthattogetherproducethephenomenon.Butinsomecaseswhatresearchersseektoexplainisnotageneralphenomenon,butaspecificfeatureofamorefine-grainedphenomenon.Insomeofthesecases,itisnotthemodelofthemechanismthatperformstheexplanatorywork.Iconsideracaseinwhichtheinvestigatorofferedanabstractrepresentationofafine-grainedphenomenontoshowwhyinhadthefeatureinquestion.Iconsiderasecondcaseinwhicharesearcherabstractedfromthemechanismtoidentifyadesignprinciplethatexplainswhythefunctioningmechanismexhibitsaspecificfeature.

I.IntroductionAcommonphilosophicalaccountofexplanationinbiologyisthatbiologistsadvancemodelsofmechanismstoexplaingeneralbiologicalphenomenasuchascelldivision,proteinsynthesis,orcircadianrhythms.Onthisaccount,mechanismsareconstruedasorganizedcollectionsofpartsperformingoperationsthattogetherproducethephenomenon(Bechtel&Richardson,1993/2010;Bechtel&Abrahamsen,2005;Machamer,Darden,&Craver,2000;Craver&Darden,2013).Thispicturefitstextbookpresentationsofbiologyandmanyreviewpapers,whichseektoexplaingeneralphenomena.Butoften,especiallyinresearchstudies,thefocusisonaspecificfeatureofamorefine-grainedphenomena,notthegeneralphenomenonitself.Whatscientistsofferasexplanationsofthesefeaturesofmorenarrowlyconstruedphenomenaalsodiffersfromtheexplanationsforgeneralphenomena.Unlikeinthecaseofgeneralphenomena,modelsofmechanismsoftenfailtoprovidethesoughtafterexplanation.InwhatfollowsIwillfirstintroduceinsection2theclaimthatoftenthetargetofexplanationsisaspecificfeatureofafine-grainedphenomena.InsubsequentsectionsIdescribetwoexamples,bothdrawnfromresearchonthegeneralphenomenonofcircadianrhythms,inwhichresearchersfocusedonparticularfeaturesoffine-grainedphenomena.Ratherthanofferingadetailedmechanisticaccountoftheresponsiblemechanism,theresearchersadopteddifferentstrategies.Inthefirstexample,discussedinsection3,Winfree,workingbeforeevenamodestlyarticulatedmechanismforcircadianrhythmshadbeenproposed,appealedtoamathematicaltruth(Lange,2012)bothtopredictan

ExplainingFeaturesofFine-GrainedPhenomena p.2

importantandsurprisingfeatureofthespecificfine-grainedphenomenonofentrainmentofcircadianrhythms.Fromthemathematicaltruthandtheempiricaldetailsofentrainment,heofferedanexplanationofwhythephenomenonhadtohavethatfeature.Thesecondexample,discussedinsection4,involvesresearchafterarelativelycomplicatedmechanismhadbeenproposed.Whileacceptingthattheproposedmechanismcouldgeneratecircadianrhythms,manyresearcherswerepuzzledaboutwhyitproducedsustainedoscillations.Toaddressthisissue,Uedaabstractedfromthedetailsofthemechanismtocharacterizetwodesignprinciples(Green,2015)1whoseabilitytogeneratesustainedoscillationswasalreadywellunderstood.Inbothofthesecases,whileanaccountofamechanismremainsrelevanttounderstandingthegeneralphenomenon,itisnotwhatexplainsthefeaturesofthefine-grainedphenomenononwhichtheresearcherswerefocused.Toprovidebackgroundforthespecificcasesthatfollow,Iofferhereabriefsketchofthehistoryofresearchoncircadianrhythms.ObservationsofdailyrhythmsinbehaviororphysiologicalactivitiesdatebacktoancientGreece,withthedailyfoldingandunfoldingofplantleavesprovidingoneofthemostcommonlycitedexamples.Byplacingmimosaplantsinadarkclosetandobservingthattheycontinuedtofoldandunfoldtheirleaves,DeMairan(1729)providesomeofthefirstevidencethattheserhythmsweregeneratedendogenously.Suspicionsremainedthatsomeexternalcuewasresponsibleforsuchbehavioruntilcrucialevidencewasprovidedthatwhenkeptisolatedfromknownenvironmentaltimecues(Zeitgebers)rhythmscontinued,butwithaperiodslightlydifferentthan24hours(aconditionreferredtoasfree-running).Toemphasizethattheperiodisonlyapproximately24hours,Halberg(1959)introducedthenamecircadian(fromcircaanddies).Researchersatthetimeofthe1960SymposiumonBiologicalClocksatColdSpringHarbor,thefirstlargeconferenceofcircadianresearchers,largelyacceptedthehypothesisthattheserhythmswereendogenouslygenerated.Theuseofthetermclock2inthetitlealludestoagrowinginterestinidentifyingthemechanismresponsiblefortheserhythms.Althoughmanyspeculativeproposalwereadvanced(Edmunds,1988),progressinprocuringrelevantempiricalevidencewasslow.Throughaforwardscreenofmutantfruitflieswithalteredrhythms,KonopkaandBenzer(1971)identifiedagenewhich,whenmutated,resultedinsloworfastrhythmsorarrhythmicbehavior,whichtheynamedperiodorper.Studiesoftheoperationsinwhichperparticipatedhadtoawaittheadventofcloninginthe1980s.Usingcloning,Hardin,Hall,andRosbash(1990)discoveredthatthemRNAandproteinPERintowhichperwastranscribedandtranslatedbothalsooscillatedwithaboutafour-hourphasedelaybetweenthem,andhypothesizedatranscription-translationfeedbackloop(TTFL)inwhichtheproteinPERfeedsbacktoinhibitthetranscriptionofitsowngene(Figure1).MentalanimationofsuchafeedbackloopprovidesanintuitiveaccountofhowaTTFLcouldgeneratecircadianoscillation:1LevyandBechtel(2013)explorehowabstractingfromdetailsofamechanismcanrevealtheorganizationofthemechanismthatisresponsibleforcertainphenomena.InthispaperIextendthefocusonabstractionasatoolfordevelopingexplanationsfurther.2AlthoughtheclockmetaphorwasactuallyintroducedbyBrown,whowasoneofthelastholdoutsfortheviewthatcircadianrhythmsdependedonenvironmentalcues,Pittendrighsoonadoptedittocharacterizetheendogenousmechanismhetooktoberesponsible.

whenPERconcentrationsarelow,transcriptionwilloccur,resultinginasteadyincreaseintheconcentrationofPER.AstheconcentrationofPERrises,however,itexertsaninhibitoryeffectontranscription.ConcentrationswillthendropasPERgraduallydegradesandisnotreplaced.AstheconcentrationofPERdrops,though,PERceasestoinhibittranscriptionandconcentrationsofPERwillraiseagain.ResearchoverthecourseofthenexttwodecadesfilledinthisinitialproposalresultinginthecomplicatedmechanismshowninFigure8below.

Figure1.ThedelayednegativefeedbackmechanismforgeneratingcircadianrhythmsproposedbyHardinetal.(1990).

Thearticulationofthismechanismforthegeneralphenomenonofcircadianrhythmsisrightlyregardedasamajorachievement.Whileitprovidesabackdrop,itdoesnotitselfexplainthefeaturesofthemorefine-grainedcircadianphenomenaonwhichIwillfocusinsections3and4.2.ExplainingSpecificFeaturesofFine-GrainedPhenomenaInpresentingphenomenaasthetargetsofexplanation,mechanistshaveappealedtoBogenandWoodward’s(1988)contentionthatscientifictheoriesdonotexplainobservationsordatabutphenomena.Phenomenaofthesortthatareexplainedinsciencearenotindividualoccurrencesfromwhichdatamightbeprocured,butrepeatableones.BogenandWoodwardofferasexamplesofphenomena“weakneutralcurrents,thedecayoftheproton,andchunkingandrecencyeffectsinhumanmemory.”WhenmechanistsadoptBogenandWoodward’sdistinction,theytookupbiologicalexamplessuchasproteinsynthesis,thegenerationofactionpotentials,oxidativephosphorylation,andcircadianrhythms.AsinBogenandWoodward’sexamples,researchershadtocarryoutagreatdealofresearchandthenextractfromtheconflictingandnoisydatatheygeneratedaproposalastothegeneralphenomenonthatwasoccurring.Statisticalanddatareductiontechniquesfiguredsignificantlyinthisprocessalongwithdesigningexperimentstoruleoutpossibleconfounds.Thisresearchwasnotitselfdirectedatexplanation,butataccuratelycharacterizingphenomena.Oftenintheearlystagesofinquiry,phenomenaarecharacterizedverygenerally.Phenomenasuchasproteinsynthesisandcircadianrhythmicityoccurwidelyamongstlivingorganismsandthewaytheyarecharacterizedabstractsfromparticulardetailssoastocaptureimportantcommonfeatures.Forexample,circadianrhythmsarecharacterized

asendogenouslygeneratedoscillationsofapproximately24-hoursthataremanifestinmanyphysiologicalandbehavioractivities,areentrainableinresponsetodifferentenvironmentalstimuli,andaretemperaturecompensated.Thesefeaturescharacterizecircadianrhythmsinorganismsfromcyanobacteriatohumanseventhoughtherearemanyimportantdifferencesthatcanbeidentified.Oncecharacterized,manyresearcherspursuetheprojectoftryingtoexplainthembyidentifyinganddescribingtheresponsiblemechanism.Foreachofthebiologicalphenomenanotedabovetherearenowgenerallyacceptedmechanisticaccountsthatdescribethetypesofentitiesinvolved,theactivitiesoroperationstheyperform,andhowthecomponentsareorganizedinspaceandtimesoastoproducethephenomenon.Accountsofthesephenomenaarepresentedintextbooksandsometimesinreviewarticles.Thesegeneralphenomenaarenottheexplanatorytargetsofindividualresearchprojects.Rather,individualresearchprojectsaredirectedatspecificfeaturesattributedtophenomenathatthemselvesaredescribedinamuchmorefine-grainedmanner.Ifonehopestounderstandexplanationasitispursuedinbiologyandrelatedfields,oneneedstofocusonspecificfeaturesofmorefine-grainedaccountsofphenomena.Toappreciateonereasonresearchersfocusonfeaturesofmorefine-grainedphenomena,itwillbeusefultoconsiderhowdatacontributestocharacterizingphenomena.Thedataresearcherscollectinthecourseofdelineatingphenomenaareoftendetailedandquantitative.Asaresult,onecandescribephenomenainamuchmoredetailedway,quantifyingthephenomenon,notjustdescribingitqualitatively.Forexample,circadianrhythmsnotonlyinvolveapproximately24-houroscillationsinphysiologyandbehavior,buteachoftheseactivitiesexhibitsadifferent24-hourpattern(e.g.,peakingatdifferenttimesofday).And,aswewillseeinthenextsection,circadianoscillationsarenotjustentrainabletoenvironmentalstimuli,butshowaparticularquantitativepatternofadvancementordelayinresponsetospecifictypesandamountsofstimuli.Thesespecificpatternsarethenthetargetofexplanatoryresearch.Tocharacterizethesefeatures,researchersoftenfinditcriticaltoidentifythephenomenathemselvesinamorefine-grainedwayby,forexample,focusingonlyonthephenomenonasexhibitedinagivengroupoforganisms.Whilerecognizingthattherewillbedifferencesbetweenmodelorganisms(suchasmice)andtheorganismsofinterest(e.g.,humans),researchersmayascertainquantitativedetailaboutthephenomenoninthemodelorganismandtrytoexplainthese.Suchpursuitoffinergraincontinuesevenwithinspecies;forexample,differentresearchersfocus,onthequantifieddetailsofcircadianrhythmsofyoungpeopleortheaged,oronthosewithdepression.Therearemanyotherwaysresearchersrestrictthegrainofphenomena.Forexample,theymayfocusonaspecificcomponentactivityintheoverallactivity.Asdescribedabove,circadianrhythmsaregenerallycharacterizedasendogenousgeneratedoscillationsthatareentrainabletolocalconditionsandaretemperaturecompensated.Somecircadianresearchersfocusontheseaspectsofcircadianrhythmicity.Likewise,inmemoryresearch,investigatorsnotonlyspecializeonspecifictypesofmemory(e.g.,episodic)butonencodingvs.storageorretrieval.

Onceonefocusesonmorefine-grainedphenomena,itbecomesapparentthattheyhaveahostofdifferentfeatures.Forexample,endogenousrhythmsinaparticularactivityexhibitaspecificperiod,amplitude,andphaseportrait.Explanatoryresearchmaybetargetedatonesuchfeature,orhowmultiplefeaturesinteract.Whatisimportanttonoteisthatwhatisputforwardasanexplanationforaspecificfeaturemaynotbeamechanism.Intheexamplediscussedinsection3,researchershadnotevenadvancedanempiricallysupportedproposalaboutthemechanismwhenWinfreeidentifiedandproposedanexplanationforafeatureofthephenomenon.Whenamechanismisknown,itmaycontributetotheexplanationoffeaturesoffine-grainedphenomena,butevenwhenthatisthecase,whatisrequiredforanexplanationisnotjusttheaccountofthemechanismbutademonstrationofrelationsbetweenvariables(someorallofwhichmaycharacterizefeaturesofcomponentsofamechanism,suchastheirconcentrations).Inarticulatingtheroleofdatagraphsinsuchinquiries,Burnston(2016;seealsoBurnston,Sheredos,Abrahamsen,&Bechtel,2014)referstotheserelationsbetweenvariablesasexplanatoryrelations.Individualresearchpaperstypicallyofferasexplanationsoneormoreempiricallysupportedrelationsbetweenvariables.Giventheimportantofarticulatingthefeaturesofaphenomenonforwhichexplanationsaresought,onemightassumethatthesearedelineatedinadvanceofresearchonmechanisms.But,asBechtelandRichardson(1993/2010)discussed,researchonmechanismssometimesleadstowhattheyrefertoasreconstitutingthephenomenon—seriousrevisionsinwhatthephenomenonistakentobe.Thereisanotherway,however,thatworkonmechanismsmayprovidefeaturesoffine-grainedphenomenathatbecomethetargetsofexplanation.Inthecaseofcomplexmechanisms,accountssuchasthosepresentedbyMachamer,Darden,andCraver(2000),Craver(2007),CraverandDarden(2013),oftenfailtoshowhowamechanismisabletoproducethephenomena.BechtelandAbrahamsen(2010),Brigandt(2013),and(Baetu,2015)havearguedthatinthecaseofmechanismswithnon-sequentialorganizationandnon-linearoperations,computationalmodelsarerequiredtoshowhowthemechanismgeneratesthetargetphenomenon.3Some3Therehasbeensubstantialdisagreementoverwhethercomputationalmodelsexplain.FocusingonthemathematicalmodeloftheactionpotentialadvancedbyHodgkinandHuxley(1952),Weber(2008)defendeditasexplanatorywhileCraver(2008)arguedthatitdidnotexplainsinceitdidnotdescribethemechanism.Subsequently,Levy(2013)arguedthatHodgkinandHuxleyofferedadeliberatelyabstractaccountbutonethatdoesexplaintheactionpotentialintermsofcomponentcurrents.ThecomputationalaccountsdiscussedbyBechtelandAbrahamsen,Brigandt,andBaetu,incontrast,aretightlylinkedtomechanisticaccounts—thedifferentialequationsinthesemodelsaredrawnfromtheoperationsthoughttoconstitutethemechanism.Althoughinvokingmathematicalderivations,thesemodelsareintheserviceofshowinghowmechanismsworkandarguablyinmanycasesonecannotshowthatthemechanismcanproducethephenomenonexceptbyusingsuchmodels.Atleastinthesecases,computationalmodelsseemtobecriticaltomechanisticexplanation.Othermathematicalmodels,suchasthosediscussedbyChemeroandSilberstein(2008),aremodelsofphenomena,notmechanisms.TheexamplefromWinfreediscussedbelowsuggestarelativelyclearwayinwhichthesemodelsareexplanatoryaslongasoneisclearaboutwhatisbeingexplained.

researchersfindsuchmodelsexplanatory,butotherscontendfromthecomputationalmodelonlyshowsthatthemechanismcangeneratethephenomenon,butcannotexplainhowitdoesso.Theseresearchersthentreattheabilityoftheproposedmechanismtoproducethetargetphenomenonasafurtherphenomenonrequiringexplanation.InthefollowingtwosectionsIconsidertwocasesinwhichresearchaddressedaspecificfeatureofafine-grainedphenomenon,andconsiderhowtheexplanationsresearchersadvanceddifferfromaccountsofmechanisms.2.AbstractlyRepresentingaPhenomenontoExplainItIturninthissectiontoafeatureofthefine-grainedphenomenonofcircadianentrainmentthatwasbothpredictedandshowntobeanecessaryfeatureofthephenomenonasaresultofadoptinganabstractrepresentationofthephenomenon.Inthiscase,theresearcherbothdemonstratedandexplainedwhythefine-grainedphenomenonhadaspecificfeaturewithoutrelianceonanaccountoftheresponsiblemechanism.ArthurWinfree,amathematicallyinclinedexperimentalbiologist,performedthisresearchduringtheperiodaftertheendogenousnatureofcircadianrhythmshadbeenestablishedbutbeforethemechanismresponsibleforthegeneralphenomenonhadbeenproposed.Duringthisperiodmanycircadianresearchersfocusedtheirresearchoncharacterizingthemorefine-grainedphenomenonofcircadianentrainmenttolight.Thestandardprotocolforinvestigatingcircadianentrainmentwasto(a)establishthephaseofendogenousoscillationsbyobservingbehaviorwhileorganismswerekeptindarkness,(b)exposetheorganismstolightpulsesofvaryingdurationsandintensitiespresentedatdifferentphasesofthecircadiancycle,and(c)determinehowmuchthephasewasadvancedordelayedineachinstance.Whatresearcherssoughtwasnotjustthequalitativecharacterizationofcircadianoscillationsbeingdelayedoradvanceddependingonlightexposure,butadetailedquantitativeaccountofhowrhythmswerealtered.Toprocuresuchanaccountofthephenomenonofentrainment,researchersneededtobeabletoidentifyapatternindatatheycollected.Thedevelopmentofthephaseresponsecurverevealedsuchapattern.Figure2showsaphaseresponsecurvefromoneofthefirstempiricalstudiesofentrainment(DeCoursey,1960).Thetimeduringthe24-hourperiodinwhichthelightpulseisdeliveredisindicatedonthex-axiswith0indicatingthetimeofactivityonsetforthetwoflyingsquirrels(Glaucomysvolans)thatwerestudied.They-axisrecordstheminutesbywhichthephasewasadvancedordelayed.Thisspeciesisnocturnalsothe12hoursaftertheonsetcorrespondtotheperiodofexpecteddarkness.Whatisclearisthatlightpulsesduringexpectedperiodsoflighthavenoeffectwhereasthoseearlyintheexpecteddarkperioddelaythephaseoftherhythmsandthoselateintheexpecteddarkperiodadvanceit.(Thismakessensesincelightpulsesearlyinthedarkperiodwouldcorrespondtolightintheenvironmentpersistinglongerthanexpectedwhereasthoselateinthedarkperiodcorrespondtothelightperiodstartingearlier.)

Figure2.PhaseresponsecurvefortwonocturnalflyingsquirrelsfromDeCoursey(1960).Althoughphaseresponsecurvesarewidelyemployedtorepresentthephenomenonofcircadianentrainmenttolight,theyconcealanimportantdistinctionthatisrevealedusingadifferentformat,phasetransitioncurves.AsshowninFigure3,thesecurvesplottheoldphaseonthex-axisandthenewphaseonthey-axis.Thedottedlinesrepresentthecasewherethenewphaseexactlycorrespondstotheoldphase(e.g.,atthelimitofalightpulseof0duration)andthedarkwavylineshowshowthenewphasemightvaryfromthat.Figure3AroughlycorrespondstothepatternexhibitedinFigure2.Whenthelightisgiveninthefirstpartoftheperiod(conventionally,phase0correspondstothebeginningoftheexpectedlightperiod)thephaseisadvanced.Lightpresentedlaterintheperiod,ontheotherhand,delaysthephase.(Thisgraphisoverlyidealized.Infactduringthelightphasethesolidlinewouldcloselymatchthedottedlightandonlyshowadvanceordelayduringthedarkphase.)Sincetheslopeofthedottedline,whichtheactualcurveapproximates,is1,thistypeofentrainmentisreferredtoasType1.Essentially,thisreflectsthefactthatduringeachperiodof24hours,circadianrhythmsadvanceoneperiodandthelightperturbationsdonotchangethat.

Figure3.Twotypesofentrainmentshownusingaphasetransitioncurve.A.Type1B.Type0.FigurefromLakin-Thomas,Coté,andBrody(1990),Figure2.

However,inothercasesthephasetransitioncurvemorecloselyfitsthecurveinFigure2B,asHastingsandSweeney(1958)foundintheirstudiesofGonyaulaxpolyedra,asingle-celledfree-swimmingplantthatemitsafaintbluelightatnightundercircadiancontrol.Intheirstudy,theorganismshiftedtoanewphasebasedonthetimeofthepulse,regardlessofthephaseatwhichalightstimuluswaspresented.Sometimestheactualnewphasewasslightlydelayed,sometimesadvanced,withrespecttothephaseofstimulation,butoverallitapproximatedalinewith0slope.Accordingly,thisisknownasType0entrainment.Initiallyitappearedthatthetwotypesofentrainment,Type1andType0,occurredindifferentspecies.However,Winfree(1970)determinedthatbothcanoccurinthesamespeciesinresponsetoshorter(orweaker)versuslonger(orstronger)entrainmentstimuli;shorterstimuliyieldType1entrainmentwhereaslongerstimuliyieldedType0entrainment.Winfreeperformedhisstudiesusingwhatwasatthetimeoneofthebest-studiedexemplarsofcircadianbehavior,eclosionfromthepupaintothematureflyinthefruitflyDrosophilapseudoobscura.InthewildeclosionoccursintheearlymorninghoursandPittendrighhadestablishedthatevenwhenlight,temperature,andotherZeitgebersareremoved,eclosiontimeremainshighlyconstrained,albeitadvancingslightlyeachdaysincethefree-runningperiodoffliesissomewhatshorterthan24hours.MoststudiesofentrainmentinD.pseudoobscurafoundType1entrainment,butWinfreefoundthatwithextendedlightpulses,Type0entrainmentoccurred.Peterson(1980)subsequentlydiscoveredthatbothtypesofentrainmentalsooccurinmosquitos.SincethesameorganismshiftsbetweenType1andType0entrainmentwithlonger(ormoreintense)lightpulses,onemightexpectthetransitionbetweenthemwouldbesmooth.Winfreedemonstratedthroughageometricargumentthatthiswasnotpossible.OnecanalreadyseetheprobleminthephasetransitioncurvesshowninFigure2.InType1entrainmentthephasetransitioncurveendsupafter24hoursstillalignedwiththelinewithslope1.Withsomewhatlongerstimuli,thecurvewoulddepartfurtherfromthatlineatintermediatephases,butnomatterhowmuchitdoesso,itwillreturntothesamerelationtotheline24hourslater.ItwillneverbetransformedintothelineforType0,whichonceitdepartsfromthelinewithslope1neverrejoinsit.Winfreedevelopedaperspicuouswayofrepresentingthelackofasmoothtransitionusingatorus.TheCartesianrepresentationsinFigure3canbetransformedintoatorusbyrollingthebottomedgebackwardsuntilitjoinsthetopandtherightedgebackwarduntilitjoinstheleftedge.AsillustratedinFigure4,Type1entrainmentinvolvesatrajectorythatpassesoncethroughtheholeofthetorus(providinganotherreasontocallitType1),whileType0entrainmentinvolvesatrajectorythatgoesaroundthetorusbutneverthroughthehole.Itshouldbeimmediatelyclearthatthereisnowaytotransformalinegoingthroughtheholeintoonegoingaroundtheoutsidewithoutbreakingandrejoiningtheline.Thiselegantgeometricalrepresentationrevealsamathematicaltruth:therecanbenosmoothtransitionfromType1toType0entrainment.Rather,WinfreecontendedtherewillbeanabrupttransitionfromType1toType0entrainmentatasingularity,apointwhichconformstoneitherType1notType0entrainment.A B

Figure4.A.Representedonatorus,Type1resettingcorrespondstoalinethroughthehole.B.Type0resettinginvolvesanorbitaroundthetorusbutnotthroughthehole.

WinfreealsoemployedanotherrepresentationalformattodemonstratetheabsenceofasmoothtransitionbetweenType1andType0entrainment,onethatalsosuggestswhatwillhappenatthesingularity.InsteadofaCartesiancoordinatesystem,aradialphaseplotusespolarcoordinates:differentphasesareplottedaroundtheoriginandthedistancesfromtheoriginrepresentthevaluesofavariable(e.g.,amplitude)atthosephases.Inaradialphaseplotthetrajectoryofanoscillatoryprocessesappearsasaclosedfigureknownasthelimitcycle.InFigure5Atheprojectingspokesrepresentthephasesofa24-hourperiodandthecirclerepresentsthepaththroughphasespaceofthesystemduringeachoscillation(ittraverseseachphase).Thespokesneednotbestraightlinesasshownhere,buttheymaynotcross.Thespokesarereferredtoasisochronssinceallthepointsalongthemrepresentthesamephase.Theradiusofthecirclerepresentstheamplitudeoftheoscillation(concentriccirclesaroundtheoriginwouldrepresentoscillationsofdifferentamplitude).Notethatattheorigintheamplitudeoftheoscillationisreducedto0;withnovariation,nophaseisdefined.

Figure5.A.Representationofalimitcycleinaradialphaseplotwiththedifferentphasesrepresentedbylinesemanatingfromthecenterandindicatedbyanhour.B.Type1entrainmentshowninphasespacewithvectorlinesindicatinghoweachpointonthelimitcycleisperturbed.C.Type0entrainment.PanelsBandCfrom(Johnson,1999).

TheoriginintheradialphaseplotcorrespondstowhatWinfreecharacterizedasthesingularitywhereneitherType1notType0entrainmentisapplies.Toseethis,consider

howthephaseshiftscorrespondingtoentrainmentcanberepresentedintheseradialphaseplots.ThearrowsinpanelsBandCrepresenthoweachpointonthelimitcycleisperturbed.Theyeitherspeeduptheoscillationorslowitdown.ThisisreflectedinthefactthatsomeofthearrowsinpanelBprojecttoalaterisochron,otherstoanearlierone.Afteratransientperiodtheoscillationwillreturntoalimitcycle,butwiththenewphase(thisisnotshown).PanelBrepresentsType1entrainment.Whatisimportanttonoteisthattheoriginremainsinsidetheclosedfigurerepresentedbythedashedline.InType1entrainmenttheclockcanbeperturbedtoanynewphasebutnostimulussendsittotheorigin.PanelC,incontrast,representsType0entrainment.Notethatthearrowsaremostlylonger,representingagreaterperturbation.Moreover,withsuchastimulus,theclockcannotbesettoanynewphasebutonlythosethatfallbetweentheisochrons1and10.Butmoreimportantly,theoriginisnolongerwithintheclosedfiguredefinedbythedashedline.FromFigure5onecandeterminethatthereisnotransitionfromType1toType0entrainmentthatdoesnotcausetheclosedfiguretocrossthroughtheorigin.AssumeagradualincreaseinthestimulusthatgeneratesFigureB.Atsomepointthedashedlineoftheclosedfigurewillcrosstheorigin.Asnotedabove,thisisasingularity—apointthathasnoamplitudeandhencenophase.Whatthisrepresentsisthatwheneverastimulusmovestheclosedfigurerepresentingtheoscillatortotheorigin,theamplitudeoftheoscillatoryprocessdropsto0.Withnoamplitude,oscillationceases.AsIdiscussbelow,Winfreewentbeyondthesegeometricdemonstrationstoconductanempiricalinvestigationtodetermineexactlywherethesingularityoccurredandthatcircadianoscillationsceasedwhenorganismsreachedthesingularity.Butwhatisimportanttonoteisthathedidnotdiscovertheexistenceofthesingularitynordemonstratethatithadtooccurthroughthisfurtherempiricalinquiry.TheoccurrenceofbothType1andType0entrainmentinthesamespecieswasdiscoveredempirically,buttheclaimthatwhenbothtypesofentrainmentoccurinthesameorganism,theremustbeasingularitywasdemonstratedmathematicallybyabstractlyrepresentingthetrajectoriesofthetwotypesofentrainment,notthroughthisfurtherempiricalinquiry.Itisamathematicaltruth(Lange,2012)thatexplainsthatasingularityoccurs.Inhisfurtherempiricalinvestigations,WinfreemadeuseofanotherdiscoverymadebyPittendrigh.Pittendrigh(1966)foundthatkeepingfliesinconstantlightcausescircadianrhythmstocease.Theserhythmswouldstartagainwithexposuretodarkness,withthephasedeterminedbythetimeofexposuretodarkness.Thisprovidedanexperimentalprotocolforpreciselysettingthephaseofthecircadianoscillators.Winfreecreatedatwo-dimensionalarrayofdishesofpupaeforwhichhecouldcontroltheirlightexposure.Hebeganbyexposingthefliestoconstantdimbluelightandthenprogressivelyblockedthelighttodifferentdishesoverathreedayperiod,beginningwiththoseontheright(designatedEastinFigure6a).Thisstartedoscillationsineachpopulationatthetimelighttoitwasblocked.Afterallthepopulationswereindarknessandexpectedtobeoscillating,heexposedthemtopulsesoflightofvaryingduration,withthosealongthetop(NorthinFigure6a)gettingthelongestexposure.Hethenrecordedwheneachflyemergedfromitspupa.Sincetheinitialexposuretodarknessoccurredoverthreedays,thereshouldbethreepopulations,eachexhibitingafullrangeoftimesofeclosion.Figure5bshowsthisexpectedresult.Ineachofthethreepopulations,thosefirstexposedtodarkness(D)shouldeclode

first,withawavemovingfromDtoA.Alightpulseexperiencedearlyinthesubjectivenightshoulddelayeclosion(B),whereasonelateinthenightshouldadvanceit(C).ThisshouldresultintheoscillationofeclosionineachpopulationfromDtoA,toB,toC,andagaintoD.

Figure6.A.Winfree’sexperimentalprocedureofplacingsuccessivepopulationsindarknessasascreenpassedovertheirdishesoverathree-dayperiod.Theywerethenexposedtoapulseoflightoriginatingatthetop(North).ThisledtoanexpectedpatternofeclosioninvolvingthreepopulationseachexhibitingthecyclefromDtoC.

Thedataset,consistingoftheendogenouscircadiantime,lengthoflightpulse,andeclosiontimeforeachfly,washuge.Moreover,Winfreefounditchallengingtorepresentitsincethisrequiredexhibitingboththeendogenousandresultingphaseandthedurationofthestimulus.Initiallyheresortedtoconstructingaphysicalthree-dimensionalgraphinwhicheachwirerepresentsanexperimentatagiventime(T)aftertransfertodarknessandlogofexposureduration(S).Buttonsonthewiresrepresentedthecentroidofthetimesofemergencepeaksforthecorrespondinggroupofflies(photographedinFigure7a).Althoughhewasonlyabletoshowthefirstthirdofthedatabeforethestructurebecametoocomplextoworkwith,theexistenceofaspiralpatternaroundanaxisisalreadyclearlyapparent.Theaxisrepresentsthesingularity.Winfreecomments:“Therearenocentroiddatashownatthisrotationaxis,becausefollowingthisperturbation,phase-resettingiserraticandfliesemergenotindiscretepeaks,butatallhoursoftheday,asisdiscussedbelow”(p.331).

Figure7.A.Photographofaphysicalthree-dimensionalgraphfromWinfree(1970).B.TimecrystalfromWinfree(1980,p.54).

Alreadyinhis1970paperWinfreedevelopedacomputeralgorithmtodefineasurfacethroughtheeclosionpoints,whichhetermeda“resettingsurface.”Hewasn’tabletopresentitvisuallybutdescribeditasa“verticalcorkscrewlinkingtogethertiltedplanes.”Hefurthernoted:“acorkscrewsurfacehasasingularity,acentralaxisalongwhichtheslopeisinfinite.”Hecalculatedthatinhisdatatheaxiscorrespondedtoastimulusof50secondsat6.8hoursafterexposuretodarkness.InGeometryofBiologicalTime(1980)andlaterworkhepresentedthisresettingsurfaceinwhathecalleda“timecrystal”(Figure7b).Inthetimecrystalthex-andy-axesrepresentoldandnewphaserespectivelywhilethez-axisrepresentsthedurationofthestimulus.(Twocompleteperiodsof24-hoursareshownonthex-axisandthreeonthey-axis.)Eachcircleconstitutesaneclosionevent.Winfreeadoptedtheschemeofrepresentingresponsestoshorterstimuli(representedintheforeground)withlargercirclesandresponsetolongerstimuliwithsmallercircles.Asaresult,oneseesType1resettingintheforegroundandType0inthebackground.TheplanedefinedbyWinfree’salgorithmappearsasasurfacethatwrapsaboutthesingularity.Thesingularity,whichisactuallyshowntwice,onceinthefirstperiodof24-hoursandagaininthesecond24-hourperiod,istheperpendicularaxisaroundwhichthesurfaceturnsinthefashionofacircularstaircase.Todeterminewhatwouldhappenatornearthesingularity,Winfreeperformed44additionalexperimentsusingstimulithatwereveryneartowherehecalculatedthesingularitywastobefound.Asthestimulusapproachedthesingularity,theeclosionpatternceasedtoshowaclearrhythm—thepeaksofthedistributionbroadensignificantlyandevenbecameindistinguishable.Whenanoscillationwassuggested,itsperiodoften

variedfrom24hours.Winfreeconcludedthattheflieshadbecomearrhythmicandthecircadianclockhadessentiallystopped.Whathemeantbythisisthatalthoughthephysiologicalprocessesthatconstitutetheclockarestilloccurring,theynolongerresultinoscillation;itwasthephaseoftheoscillationthatrepresentedtime,andtherenolongerwasaphase.4Theclockwouldremainstoppeduntilanewlightstimuluswaspresented,atwhichtimeoscillationswouldresumeatthephaseitwasatwhenitwasinterrupted.Winfree’sexperimentalstudiesallowedhimtoidentifythetimeandstimulusstrengthofthesingularityanddemonstratewhathappenedinresponsetoastimuluscorrespondingtothesingularity.Nonetheless,Winfreehadnotonlypredictedtheoccurrenceofthesingularitybutalsoexplainedwhytherehadtobeonebeforetheseexperiments.Usingabstractrepresentations,suchasthetorusandthephasediagrams,heshowedthatthesingularitywasanecessaryfeatureofanysystemexhibitingbothType1andType0entrainment.Moreover,thisexplanationwasindependentofknowingthemechanismofentrainment.SubsequenttoWinfree’sanalysis,researchershaveidentifiedkeycomponentsofthemechanismofentrainment,butwestilldonotknowwhyoscillationstopsinresponsetoastimuluscorrespondingtothesingularity.Nonetheless,WinfreeprovidedanexplanationofwhythereisandmustbeasingularityintheentrainmentoforganismsthatexhibitbothType1andType0entrainment.ThisparticularfeatureofthephenomenonentrainmentthatoccursinatleastsomespeciesisexplainedanditsexplanationdoesnotdependonknowingtheresponsiblemechanismbutonunderstandingthemathematicalfactthattheremustbeadiscontinuityorsingularitybetweentherangeofstimulithatgenerateType1andtherangethatgeneratesType0entrainment.SomemayquestionwhetherwhatWinfree’sexplanationofthesingularityshouldcountasanexplanation.Itiscertainlynotacausalormechanisticexplanation,andifoneholdsthatitiscauses(Salmon,1984,1998)ormechanisms(Craver,2007)thatexplain,thentheywillnotcountwhatWinfreeofferedasanexplanation.SalmonandCraver,however,werearguingagainstanalternativeaccountofexplanation.Onthedeductive-nomological(D-N)accountofexplanation(Hempel,1965,1966)oneexplainsaneventbyshowingthatitsoccurrencefolloweddeductivelyfromlawsandinitialconditions.Winfree’saccountcanbeseenasadeduction—fromtheconjunctionofthetwotypesofentrainment,heshowedthatasingularitymustoccur.Butwhilethecharacterizationsofthetwotypesofentrainmentmayberepresentedasempiricalgeneralizations,theyarenotwhatwouldgenerallyberegardedascandidatelaws.Whatdoestheexplanatorywork,however,isnottheaccountsofthetwotypesofentrainmentbutthemathematicaldemonstrationthatnosmoothtransitionispossiblebetweenthem.WhileWinfree’sexplanationmightfallundertheD-Naccount,itleavesopenthequestionofwhenoneshouldseekamechanisticexplanationandwhenaD-Nstyleexplanationmightsuffice.Appealingtoyetanotherphilosophicalaccountofexplanationmaysuggestaframeworkforaddressthis.Bromberger(1966,1968)and(vanFraassen,1980)treat4WiththediscoverythatitwastheconcentrationsofproteinssuchasPERthatoscillated,theclockstoppingcanbeunderstoodastheconcentrationoftheseproteinsreachingaconstantlevelandnolongeroscillating.

explanationsasanswerstoquestionsaboutwhysomethinghappens.ForvanFraassen,explanationispragmaticandrelativetothecontextinwhichthequestionisaskedandwhatisrequiredtoansweritisanaccountofwhysomeconditionaroseratherthansomeother.Onsuchapragmaticunderstandingofexplanation,Winfreeisofferinganexplanationsinceheisansweringthequestionwhytheremustbeasingularity.Inthiscontext,aD-Nstyleaccountprovidestheanswertothequestionposed.ThatWinfreeviewshisaccountasanexplanationisclearin(Winfree,1987)whenheextendshisaccounttoshowwhy,giventidalpatternsindifferentlocationsinanocean,theremustbeasingularityatwhichtherearenotides.Althoughheisnotofferingacausalormechanisticexplanation,orevenaD-Nexplanation,Winfreeisansweringaquestionaboutwhysomethingoccurs.Thosewhodon’tseeWinfreeasofferinganexplanationmightarguethatwhatheofferedwasonlyadiscoverystrategy:hepredictedthesingularityandhissubsequentresearchshowedthatitoccurredashepredicted.InthiscasethespecificfeatureofthephenomenonofentrainmentwasnotknownbeforeWinfreeperformedhisanalysis—hepredicteditbasedonhisanalysis.OntheD-Naccount,predictionandexplanationwereviewedaslinked—thesameargumentcouldservetopredictandexplain.Craver’scriticismoftheD-Nmodelfocusedonthisfeature.UsingAristotle’sexampleoftheflagpole,Craverarguedthatonecouldpredicttheheightoftheflagpolefromthelengthofitsshadow,butthatdidnotexplainit.Whileitiscertainlythecasethatsometimesthereasoningthatsupportsapredictiondoesnotsufficeforexplanation,infactfromasufficientlydetailedexplanation,evenanaccountofamechanism,onecanderivepredictions.Infact,manytestsofmechanistichypothesesdependuponmakingpredictionsabouthowaproposedmechanismwillbehaveanddeterminingwhethertheactualsystembehavesinthatway.Whilenotallpredictionsrelyonhavingacorrectexplanation,explanationsoftenfacilitatepredictionsand,asinthiscase,thediscoveryofanewfeatureofaphenomenon.Oncethefeaturewasestablishedempirically,theveryreasoningthatledtoitsdiscoveryalsosufficestoexplainitsoccurrence.Inhis1987bookTheTimingofBiologicalClocks,aScientificAmericanbookinwhichhepresentedhisaccountofwhycircadianentrainmentinmanyspeciesexhibitsasingularities,Winfreecommented“Howdoesphaseresettingcomeabout?Itsresultscanbedescribedwithoutdescribingtheprocess—apieceofgoodfortunate,sincenooneyetknowsthemechanismofasinglecircadianclock.”Subsequentlyresearchershavelearnedagooddealaboutthecircadianclockmechanisminmanyspeciesandevensomeofthedetailedaboutitcanbeentrainedbylightstimuli.FillingintheaccountofthemechanisminvolvedinentrainmentwillnotsupplanttheexplanationWinfreeofferedofthesingularity.Itwill,though,addressanewexplanatorychallengetowhichWinfree’sdiscoverygaverise:explaininghowastimuluscorrespondingtothesingularityactuallystopstheclockmechanismbystoppingtheoscillationsofcircadianproteins.Thischallengeisdirectedatadifferentfine-grainedphenomenonthanWinfreeaddressed—theresponseofthemechanismitselftothestimulusthatWinfreehadshownwouldstopcircadianrhythmicity.Notethatthemechanismitselffiguresinthisfine-grainedphenomenonwhereasitdidnotinthefeatureofthephenomenonthatWinfreediscoveredandforwhichheofferedanexplanation.Thishighlightsthefactthatsomefine-grainedphenomenaarein

factcharacterizedintermsofamechanismandthechallengeistoexplainwhythemechanismexhibitsthatfeatureofthephenomenon.Thisisillustratedinthenextcase.3.AbstractlyRepresentingaMechanismtoExplainWhyItProducesthePhenomenonShortlyafterWinfreebemoanedthelackofknowledgeofanycircadianclock,Hardinetal.(1990)offeredthefirstproposalforaTTFLmechanism.Insection1Iprovideaverbalnarrationofhowtheinitiallyproposedfeedbackloopwouldgenerateoscillations.Thisdescriptiondoesnotestablishwhethertheproposedmechanismwouldgeneratesustainedoscillationsordampenovertime.Thoseinterestedinthismorespecificfeatureturnedtoacomputationmodel(Goldbeter,1995)ofthemechanism.5Inthesubsequentdecademanymorepartswerediscoveredandcircadianresearchersproposedmechanismsinvolvingmultiplefeedbackloops,bothpositiveandnegative(Figure8showstheconceptionofthecircadianclockmechanisminmammalsthatwasarrivedatby2005).Withthesediscoveries,computationalmodelsbecameevenmorecriticaltodetermininghowaproposedmechanismwouldbehave.ComputationalmodelsproposedbyLeloupandGoldbeter(2003,2008),(Gonze,2011),andothersprovidedsupportfortheclaimthatamechanismofthistypecouldgeneratesustainedoscillations.

5BechtelandAbrahamsen(2010,2011)refertomechanisticexplanationsthatrelyoncomputationalmodelingtoestablishthattheyexhibitspecificdynamicalbehaviorasdynamicmechanisticexplanations.

Figure8.Arepresentationofthemajorcomponentsinthemammaliancircadianclockasunderstoodcirca2005.

Computationalmodelscanshowthataproposedmechanismisadequatetogeneratethespecificfeatureofthephenomenoninquestion—sustainedoscillation.Butgiventhenumberofpartsproposed,thesemodelsrequiredozensorhundredsofdifferentialequations.Whileonecanacquireanintuitivesenseofwhyasingledelayednegativefeedbackloopgeneratesoscillations,circadianresearcherslackedsuchanintuitiveunderstandingofhowthesemorecomplexmechanismsandmodelswouldbehaveandsoughttounderstandwhytheygeneratesustainedoscillations.TheproposedmechanismisclaimedtogenerateoscillationsasaresultofoscillationsintheconcentrationsofcomponentsofthemechanismsuchasPERandBMAL1.Theseareproposedtooscillateinacircadianfashionandtheirdoingsobecamethefeatureofthefine-grainedphenomenontobeexplained.Oneapproachtoexplainingthisfeaturehasbeentofocusonsomepartofthemechanismandviewitasresponsiblefortheoscillationinconcentrationoftheotherparts.Giventhatthemechanisminvolvesseveralfeedbackloops,onemightthinkoneoranotheriswhatdrivestheoscillationofthewholemechanism.Researchershavenotbeenabletopursuethislineofinquirythroughempiricalexperimentation,butsomeinvestigatorsexperimentedoncomputationalmodels.Theirstrategyistobuildamodelthatexhibits

circadianoscillationsandthenalterpartsofthemodelinwaysthatcorrespondtoremovingorfixingthestateofsomeofthepartsofthemechanism.However,differentmodelerspursuingthisstrategyhavearrivedatdiametricallyoppositeresults(Smolen,Baxter,&Byrne,2002;Relógio,Westermark,Wallach,Schellenberg,Kramer,&Herzel,2011).Thedifferencesinconclusionsreflectdifferencesinthedetailsofhowthemodelsareconstructed.Althoughthislineofresearchhasnotyetgenerateddefinitiveresults,itmayinthefuture.However,Iwillnotdiscussthisapproachfurtherinthispaper.Analternativeapproachisnottolooktoapartofthemechanismtoexplainthephenomenonbuttotheorganizationofthewhole.Thechallengeisthattheoverallorganizationisverycomplicated(Figure8infactpresentsasimplifiedview)anditisnotobviouswhyitwouldgenerateasustainedoscillation.Uedaandhiscollaboratorsdevelopedastrategyforidentifyingwhatitisaboutthisorganizationthatisresponsibleforthefeatureofsustainedoscillation(Ukai-Tadenuma,Kasukawa,&Ueda,2008;Ukai-Tadenuma,Yamada,Xu,Ripperger,Liu,&Ueda,2011;Hogenesch&Ueda,2011).Theybeganbyre-representingthemechanismshowninFigure8usingtheschemeshowninFigure9.ThisrepresentationplacesatthecenterthethreepromoterboxesonthedifferentgenesinFigure8:theE-box,D-box,andRRE.Sinceoneormoreoftheseboxesispresentoneachgenethatispartofthecircadianclockaswellasonmanyothergeneswhoseexpressioniscontrolledinacircadianfashion,theyrefertotheseasclockcontrolledelements(CCEs).

Figure9.Ueda’sschemaforrepresentingtheclockmechanismshowninFigure8inwhichthepromoterboxesaremadecentralandthegene/proteinsservetolinkactivitybetweenthevariouspromoters.

Figure9downplaystheprocessesoftranscriptionandtranslationthatareshowninFigure8.First,thedistinctionbetweengenesandproteinsiscollapsed.TheCCEsregulatetranscriptionandthedottedlinesbetweenCCEsandtheovalssuggestthiscontrolover

transcription.Butthefactthatthenamesintheovalsareincapitallettersandnotitalicizedsuggeststheyareproteins.Thisfitswiththearrowsanddashed,edge-endedlinesthatlinktheovalsbacktotheCCEs;theseindicatetheactivityofproteinsinhibitingorpromotingtranscription.Butthedistinctionbetweengenesandproteinsandtheoperationsinwhicheachparticipateultimatelydoesn’tmatterfortheanalysisUedaisadvancing.HisstrategyistoabstractfromthedetailsofthegenesandproteinsandsimplytreatthemasintermediariesbetweentheCCEs.TheforegroundingoftheCCEswaslargelymotivatedbyUeda’sexperimentalfindingthatwhenheinserteddestabilizedluciferasegenesintotheregionregulatedbytheCCEsinacellculturesystemandrecordedthetimingofmaximumbioluminescence,hefoundthateachCCEwasmostactiveatadifferenttime.Althoughtheprecisetimevariesbytissue,inthesuprachiasmaticnucleus,thoughttobethelocusofthecentralclockinmammals,E-boxesaremostactiveintheday,D-boxesaboutfivehourslater(evening)andRREsabouteighthourslater(night).Thissuggeststhattheactivityofthedifferentboxesplaysacentralroleingeneratinga24-houroscillation.Thegenes/proteinsaresimplythemeansbywhichtheCCEsaffecteachother.Tomaketheimplicationsofthisrepresentationclearer,inasubsequentdiagram(Figure10A)Uedanolongerdisplayedthegenes/proteinsandinsteadinsertedasinglearroworedge-endedlineforallthepathwaysbetweenagivenCCEandeachoftheothertwo.Thus,thearrowbetweentheE/E’boxandtheD-boxindicatesthatoneormoregenesregulatedbytheE/E’boxaresynthesizedintoproteinsthatfunctiontoenhanceexpressionofgeneswithaD-box.Thetwodotted,edge-endedlinesindicatethattheD-boxandRREhaveinhibitoryeffectsontheperiodandamplitudeofoscillationofgeneswithE/E’boxes.

Figure10.A.Arepresentationoftheclockmechanismthatabstractsfromthegenesandproteinsandshowsonlywhenthereisatleastonepathwayfromagenecontrolledbyoneboxtotheactivationorinhibitionoftheboxanothergene.B.AdecompositionofthefigureinAintotwomotifs,arepressilatorandadelayednegativefeedbackloop.

Thegoalofabstractingfromallthegenesandproteinsandgeneratingaskeletalrepresentationofthesystemwastoelicitifpossibleanexplanationforwhythemechanismgeneratesoscillationswithinit.ByremovingtheidentityofthegenesandproteinsandfocusingonlyonhowtheyservetoconnecttheCCEs,Uedaisfocusinghisattentionontheorganization.Apotentwaytorepresentorganizationandabstractfromthepropertiesof

thecomponentsorthedetailsoftheoperationsthecomponentsperformistodevelopanetworkdiagraminwhichentitiesappearasnodesandanyconnectionsbetweenentitiesasedges.BothFigures9and10arenetworkdiagrams,whereasFigure8ismoreproperlythoughtofasamechanismdiagram.WhileFigure10Aisstillcomplexanddoesnotitselfprovideanexplanation,UedarecognizedthatthisnetworkcouldbedecomposedintothetwonetworksshowninFigure10B.Theoneontheleftisarepressilatorandtheoneontherightanegativefeedbackloop.Thesecorrespondtowhatareelsewherecalledmotifs.Workingattheleveloftheactualcomponentsinyeastgeneandproteininteractionnetworks,Alonandhiscollaborators(Milo,Shen-Orr,Itzkovitz,Kashtan,Chklovskii,&Alon,2002;Alon,2007a,2007b)identifiedsubnetworksoftwotofournodessimilartothoseinFigure10B.Theirattentionwasdrawntothesesubnetworks,whichtheytermedmotifs,becausetheyoccurredfrequently.Bymakingminimalassumptionsabouttheactualentitiesinvolved,theyanalyzedthebehaviorseachmotifwouldsupportandproposedthatwasthecontributionthespecificsubnetworkswouldmaketothelargernetwork.Uedaarrivedatmotifsinadifferentmanner(byabstractingfromthenumerousgenesandproteinsthroughwhichCCEsaffecteachother),butthenotionofmotifapplieshereaswell.Essentially,thetwonetworksshowninFigure10BareimplementedmanytimesinFigure9dependingonwhichgenesandproteinsserveasintermediaries.Whatrendersthenotionofmotifpowerfulisthatonecanestablishhow,withinarangeofparameters,anysubnetworkimplementingthemotifwillbehave.Indeed,bothofthemotifsUedaextractedhadalreadybeendemonstrated,bothincomputationalmodelsandinsynthesizedorganisms,tobecapableofgeneratingsustainedinteractions.Thedelayednegativefeedbackmotifplayedafundamentalroleintheorizingabouttheclockmechanismfromthe1960sandwasincorporatedintotheTTFLmodel.Itsoriginslaymuchearlier.SinceKtesibiosemployeditinhiswaterclockinthesecondcenturyBCE,ithasbeenrediscoveredandemployedinmaintainfeaturesofasystem(e.g.,temperatureinaroom)ataconstantlevel(Mayr,1970).Inthesecondquarterofthe20thcenturythisuseofnegativefeedbackwascelebratedbythecyberneticists(Wiener,1948).Butinavarietyofapplicationsresearchersalsorecognizedthatmanysystemsimplementingnegativefeedbackwouldnotsettletoasteady-statebutwouldoscillatearoundthedesiredvalue.Beyondempiricalobservationsofoscillationinnegativefeedbacksystems,numerousengineersdevelopedmathematicalanalysesoffeedbacksystem,ofwhichoneofthemostinfluentialwasproposedbyvanderPol(1920),anelectricalengineer.Theseanalysesshowedthatsustainedoscillationwaspossible.Althoughitsprominencearosemorerecently,therepressilatorwasalsorecognizedasamotifcapableofgeneratingoscillations.IntheprocessofdesigningasyntheticoscillatortheyplannedtoincorporateintoE.coli,ElowitzandLeibler(2000),constructedacomputationalmodelofarepressilatorcircuitandshowedthat,withappropriateparametervalues,itgeneratedsustainedoscillations.Theytheninsertedintobacteriagenesthatinteractedinthemannerindicatedinthemotifaswellasagreenfluorescentreporter.Theythenobservedoscillationswithaperiodofseveralhours.Giventhatbothmotifshadbeenshowntogenerateoscillations,Uedaarguedthattheabilityofthecomplexmechanismtogeneratesustainedcircadianrhythmsisduetothefact

thattheorganizationfoundinthecomplicatedmechanismshowninFigure9realizesthesetwomotifs.InUeda’sanalysis,themotifswereidentifiednotinindividualcircuits,butinanabstractrepresentationofacomplicatednetwork.Thearrowsinthemotifsrepresentmultipletranscription/translationrelationsinwhichproductproteinsaffectanotherpromoter.Thus,insteadofalocalcircuit,itisthenetworkasawholethatimplementsthetwomotifs.Yetitisthemotifsthatexplainwhythecircadianmechanismexhibitssustainedoscillations.Itisexplainedbythewaythepartsareorganizedandthattheyoperationsthepartsperformrelatepartsinthemannerreflectedinthemotif.AsLevyandBechtel(2013)discusswithrespecttoAlon’swork,theanalysisofmotifsmakesonlyminimalclaimsaboutthenatureofthecomponentscorrespondingtothenodesandtheoperationstheyperformoneachother.Anysystemorganizedaccordingtothemotifinwhichtheseminimalconditionsaremetwillexhibittheassociatedbehavior.Inthissense,motifanalyses,andothernetworkanalyses,offergeneralaccountsthatapplytoallinstancesinthemannerproposedforD-Nexplanation.Themotifs,however,arenotlaws,butprinciplesoforganization(designprinciples)thatassertthatanysystemimplementingtheorganizationwillexhibitthespecifiedbehavior.WhileabstractionfacilitatesexplainingthefeatureofthegenerationofrhythmsthatUedawasinterested,itcanimpairtheabilitytoexplainotherfeatures.AdifferentfeatureofthephenomenonthatUedadidnotfocusonisthatacircadianoscillationisextremelyslowforchemicalreactions,completingacycleonlyonceevery24hours.Thisdependsondelayswithinthemechanism.OneoftheimportantoperationsthatUeda’saccountabstractsfromisthatinordertogetintothenucleuswheretheycanactonaCCE,Per1andCry1mustfunctionasadimertoreenterthenucleus,withtheformationofadimeroccurringoveranextendedperiodoftime.Otherfeaturesofthephenomenonrequireanintermediatelevelofabstraction.Considerableinterestinrecentyearshasbeendirectedattherobustnessoftheoscillationtoalterationofindividualcomponentsinthemechanism.Thisispartlyexplainedbythepresenceofmultipleorthologsofkeyproteins(e.g.,Cry1andCry2)inthemammalianclock.Knockingoutjustonehaslittleeffectsincetheothercancompensatebyincreasingtheamplitudeoftheiroscillationsandmaintainthefunctioningofthesamemotif(Baggs,Price,DiTacchio,Panda,FitzGerald,&Hogenesch,2009).Circadianresearchersdevotedmajoreffortsinthe1990sandearly2000stodevelopingadetailedmechanisticmodelofthemammaliancircadianclock.Asusefulasthismodelis,itdoesnotexplainwhythemechanismgeneratessustainedcircadianrhythmsoftheotherfeaturesnotedinthepreviousparagraph.Accordingtothemodel,componentsofthemechanismthemselvesexhibitsustainedcircadianrhythms.Thiscallsforexplanation.Byabstractingfromthedetailsofthegenesandproteinsinvolved,Uedawasabletodemonstratethattheorganizationofcomponentsinthemodeledmechanismrealizestwomotifsknowntogeneratesustainedoscillations.Theabstractmotifanalysisrevealedthedesignprinciplerealizedinthecomplicatedmechanismandtheseareadvancedasexplanationsoftheabilityofcomponentsinthemechanismtoexhibitsustainedoscillations.4.Conclusions

Awidelyacceptedviewisthatexplanationinbiologyinvolvesidentifyingthemechanismresponsibleforaphenomenon.Indeed,wellsupportedmechanisticmodelshavebeenadvancedformanybiologicalphenomenasuchascelldivision,proteinsynthesis,andcircadianrhythms.Butagreatdealofresearchinbiologyisdirectednotatsuchgeneralphenomenabutatspecificfeaturesoffarmorefine-grainedphenomenaandoftenidentifyingthemechanismisnotwhatexplainsthesespecificfeatures.Toillustratetwoofthestrategiesresearchersinvokeinexplainingspecificfeaturesoffine-grainedphenomena,Ihavepresentedtwocasesinvolvingresearchoncircadianrhythms.Whiletextbooksmightcharacterizecircadianrhythmsinageneralway,researcherstypicallyfocusonaparticularfeatureofamorefine-grainedphenomenon,suchasentrainmentbylight.Thefirstexamplefocusesononesuchfeature,theoccurrenceofasingularity,whichWinfreebothpredictedandexplainedthroughthesametypeofargument.UpondiscoveringthatsomeorganismsexhibitbothType1andType0entrainment,Winfreedemonstratedusingageometricalargumentthattherecannotbeasmoothtransitionbetweenthetwotypesofentrainment.Rather,anytransitionfromType1andType0entrainmenthastogothroughasingularityatwhichtheamplitudeoftheoscillationdeclinesto0.Anentrainmentstimulusthatcausestheclocktoreachthesingularitystopstheclock.Winfree’sexplanationfortheimpossibilityofsmoothtransitionbetweentypesofentrainmentdidnotdependondetailsaboutthemechanism.Oncethemechanismofentrainmentisunderstood,itcancontributetounderstandinghowthesystemrespondswhenitreceivesaninputthatdrivesittothesingularity.Buttheexplanationfortherebeingasingularitydoesnotdependonthedetailsofthemechanism.Thesecondcaseinvolvesresearchthatwascarriedoutinthewakeofthediscoveryofmanyofthepartsandoperationsofthecircadianclock.Merelyidentifyingtheparts,operations,andorganizationofthemechanismdidnotexplainwhythemechanismexhibitssustainedoscillations.Byabstractingfromthedetailsofthemechanism,Uedawasabletoidentifytwomotifs(negativefeedbackandtherepressilator)thatarerealizedintheorganizationofthecomplicatedmechanismthatwasproposedfortheclock.Mathematicalandexperimentalinvestigationsofthesemotifsdemonstratethattheyaredesignprinciplesthatresultinsustainedoscillationsinsystemsinwhichtheyareimplemented.Whilethemechanismishighlyrelevanttoexplainingthegeneralphenomenonofcircadianrhythms,thespecificphenomenonofsustainedoscillationwithinthemechanismisexplainedintermsofthedesignthedesignprinciplesthemechanismimplementsinitsorganization.Tomakethisargument,Ihavehadtomakeclearwhatspecificfeatureofafine-grainedphenomenonisthetargetofagivenexplanation.Whatcountsasexplanatorydependscriticallyonwhataresearcheristryingtoexplain.FollowingBogenandWoodward(1988),mostaccountsofmechanisticexplanationhaveconstruedphenomenaquitebroadly,treating,forexample,thegenerationofcircadianrhythmsorthesynthesisofproteinsassinglephenomena.Intextbooksandsometimesinreviewarticlesscientistsdospeakthisway,butinactualresearchandtheresultingjournalarticles,phenomenaarecharacterizedfarmorenarrowlyandparticularfeaturesareaddressed.Winfreeandothersfocusingonentrainmentwerenotfocusedonthegeneralfactthatcircadianrhythmscanbeentrained

tolightconditions,butspecificpatternsofphaseadvancesordelaysinresponsetovaryingdurationsoflightexposure.Uedawasnotconcernedwithcircadianrhythmsingeneral,butwithhowtheacceptedaccountofthemechanismisabletogeneratesustainedrhythms.Focusingonlyonthespecificfeatureofthephenomenonforwhichexplanationissoughthelpstoexplainwhyonlysomeinformationmayberelevanttoexplainingitandwhydetailsofthemechanismmaynotadvancethespecificexplanatorygoals.Findingtherelevantexplanatoryprincipletoexplainaspecificfeatureofaphenomenonoftenrequiresdevelopingtherequisiteabstractanalysis.Hadthedetailsofthemechanismofentrainmentbeenknown,thatwouldnothaveansweredWinfree’sexplanatoryquest.Thatrequiredamathematicalanalysisthatshowedwhyasingularityisrequiredgiventhenatureofthephenomenon.Likewise,inUeda’scase,answeringthequestionofwhythemechanismoscillatedrequiredidentifyingtheunderlyingdesignprinciplesandshowingthatsystemsimplementingthesedesignprinciplesgeneratesustainedoscillations.Developingexplanationsinvolvesbothidentifyingthespecificfeaturesofaphenomenonforwhichanexplanationissoughtanddevelopingthe(oftenabstract)accountthatistailoredtoexplainthosefeatures.Areasontofocusonidentifyingthefeaturesofaphenomenonthatarethetargetofparticularexplanationsisthatwhatisrequiredtoprovideexplanationwillvarywiththetarget.Justhowmuchanaccountofthemechanismisrequiredwillvary.Inarguingthatoftenthemechanismiseithernotneededorinsufficienttoprovidetheexplanationrequired,Iamrejectingtheclaimthatmechanisticaccountsaloneexplain.Insomecases,theexplanationsproducedcomeclosertoD-Nexplanations—researchersofferageneralaccountandshowwhatfollowsfromit.Whatprovidesthegeneralaccountmightnotbealaw.InWinfree’scase,itwasamathematicaltruththatcouldbeshowntoapplytothefine-grainedphenomenonwhenitwascharacterizedabstractly.InUeda’scase,itwastwomotifsthatcouldbemodeledmathematicallytoshowhowanysystemrealizingthemwouldbehave.Thesearejusttwoexamples.OthercaseswillinvolveavarietyofrelationsbetweenvariablesthatBurnston(2016)referstoasexplanatoryrelations.Themoregeneralpointisthattounderstandwhatprovidesthedesiredexplanationinagivenresearchendeavordependsonwhatfeatureofafine-grainedphenomenonaresearcherseekstoexplain.ReferencesAlon,U.(2007a).Anintroductiontosystemsbiology:Designprinciplesofbiologicalcircuits.

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