A DNA based Finite State Transducer

aAuser.DNA-basedtensivFiniteOurStatemoreTlransducertoNathana?ltAcomplexuberourters,Under1thenitedirectiononeofeMasaminHatransducergiyones,agenerateUnivtoersitnondetermin-ystrandsofConRenneserations1vUnivcanerstrandssicommontolymeraseybofinTcanokyofoeJunemaking5,co2010er,AbstractarietDeoalsoxyribthatonexamucleic(Naciden(DNAof)crocomputingUsingisofanfromemergeidesignedngtransducereldthewhereinconthethebiologicalthepropopertiesusesofgenerateDNAdescribaretheusedpresentosoluticarryAsoutorkcomputation.eAseraturesDNAfacilitatecanofalsohinesbex-erelyusedtrolasMoreoaitbuildingwidematerialofwithucermoevmecablereparts,Fthele,compbinationproblemofcanthosetetneededwvingoofasptheectstsallo4wstscienoptistsrequiredtothedesignWnanomachahineseeasilya.stateHothatweliminateevneeder,addonetrolmaintoconcernssolution,isofthemostlacexternalkerations.oftransducerautomationpoftoexistingthmecoutputhanisms.edThiysinpulimitsstrandstheirtptheotenotial.applicationsitaswitatiswidnotrangeptempoourscansiblethtodesignusemorenanomacnanomachineswhileintheaistingnon-thatconontrollednenstrands,vironmenautonomous.tvasthatcanis,aalmostvanyyoutputs,thtransdingcanthatbisusefuloutsideDNAofhanismsaatestcomputation-intube.e.orThepgoalwithofisticthisolynomialwP)-completeosolvrkitisgtherautestswhentoinsteaddesignhaaacompletelylautomatedthemmecwdinghanissolution.mtenthat1willDNAreducetheamoun
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.c.hemistrySim...output...........7.1.1.......implemen.sec...........27.......of........4.1.2.DNA-onlystep:op.eranextti.o.n26s..Sim.....catalyst.3.............Sc.....Simplied.......W.P.....20.input5.1.3.User-requiringdateDNA.op.erations6.4.generation...24.......d.......erimen.........the...of6.1.4.EnzymesExp.......28.............9.w.transducer.......19.d.............20.w.20.catalyst......7.2.RelatedFirstwdork.9.2.1.Logical.gates6.3.u.............ourth.oin.........Fifth.date...........Simplied.............279and2.227DNA.catalysts..............ulation.olym.....Sim.1.........28.ts...............2..11.2.3.Seeman's.PX-JX.DNA.switc.h.and.nite.state.transducer..1.5.2.hematic.orkings.the..11.2.4.Shapiro's.nite.state.automaton....5.3.mo.el...........................613et2.5areSelf-assemtationbly6.1.olymerase-based.......................6.2.and.on.step:.reading...............22.Third.state.p14.2.6.Whipslash..................22.F.step:.p.ter.................6.5.step:.up............14.3.Motiv.ating.examples.156.63.1moAutomatingelSeeman's.PX.-JX.1.1...switc.h..............7.ulations.exp.ts.7.1.ulations......15.3.2.Sequence.generation................27.Sim.of.p.erase-based.........7.1.2.ulation.steps.to........16.4.First.attempts.16.57.2Overimener.v.i.ew.of.the.curren.t.v.ersion.17.5.1.Structure........
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ourselvductionlThedesignideamostofenussolutioningcanbio-moleculesusingtoadvcarrycoutticomputationreplwproblemsastheirrstypresensotedysinis1973uses[1],isbwillutAtheoptruetransducergroundbreakingofdiscogivvterywhicthatlimitreallyrstlauncthemhedourDNADuringcomputingtransducerisofthewthresolutionend,ofMoreotheMoHamiltonianthepmecathtproblemrequiredusingtrolopexerationsbonyDNAsucstrandsAnotherbrelatedyevAofdlemantain[2]inp199enou4.withThehed.factisthatsolutiallthem,strandsnextaresituation,inwtheossiblesamevenhvironmenbtdierenalloaswsdelforeeninTtrinsicwnon-determinism,erformalongewithtoavstateery3highcompletelyparallelism,smprothevidingopannintheterestingsomecomputationtoparadigmatoawthatorkeectivwith.cedAnitedlhemconanwhenrstossibleattempttransducerusedsolvingonlyybasicsolution.DNAamouninenteractionscowithlimitedlimitedDNAapplica-endingtions,aroundbliterutissihncebthenproblemsothereasilywwathisysgeneratetohusenDNAtransducer,hdestroageneratevh,eInbiseengoal,propalloosed,allmainlyopDNAinorigamiwandrealizeDNAniteactuators.vDNAconsidered,origamitagerefersasptosucatilingfoldingformalmethocrystaldhasofroDNAbtoInmakmoecittotopaer,predenedvform,ouralloewingmacusthattoofuseneucleotidestoasaaautomatedbuihanildingthatma-reduceterial.amounAuthorsofinera[3]oprosduced,fromfuser.oddingrconinstance,strandssmileythefacesisascommonaternproloferationofcanconcept.eDNAelyactuatorsaarebspaecicstateDNAwhicstructuresgeneratesthhatrotstrandscanneeded.cphangeapplicationshapthiseisdeptoendinNPgbontestingtheireryenAvironmenent.tThesolvcomtbinationonlyonfaDNAamounorigami,ofDNAstrandsactuatorsdepandonDNAlength,troIncomputersstrandsalloerwushtousuallydesigngnanomacforhinesapplications,withutDNA,NPsucthishisasreactOnewaeezersaround[4]problemandtowaalkbatcersof[5].oAlreadyswouretestcanthenseeytheanddivtheersitbatcyandofon.DNthisAautomationnanomacnothinesprimaryisonereviewwaesrtipcDNAlerations.esthissucternship,hariousasa[6].toOnesucofathestatemainhaconcernseregardingeenDNAtakingcomputinganisofthteectslacDNA,khofDNAautoma-(tilingtionaofmoexistingofmecgrohanisms,thatwhicbhplimitsvtheirtopeotenuring-complete).tialtheapplicationtheasdeliteishosenotenzymesppossibleextendedtoerations.usevthemwinhaaenon-conhosentrolledtransducerebnavironmenoret.hineThemeaninggoaloutputoffunctionthistheinalonetern-forshipsakisofthus
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wrongquicekly[theeoutputwing.inandenoughkbquanA,generatetitbio-yerationstovbmeceorienusable.itadenineisanecessarytetohaunderstandingvmoethismansucytedinstancesgoofknotheDNAtransducerhingroups.theysolutionsequence.(forthinstancener,fevDNA).laAllsection,ofvthDNA,esenecessaryinstanceswillcanabinesourcesseen[11]asinindepoend.eoksntotenthreadsnecessaryand,tinDNAthencasebofugageneratingendsconandtronlthatstrands,dierenit(C),isiscriticalG.thatAAtheyquencegeneratesimplicittheasameng,strandsfolloatythingapprogoxeitmtheatelyhemistry(DNAaisitlessthestrictwthinadetailednthesilicon)aretherestsameort.time.hThe0]wresenaopymorewandeesolvaeediathisbproblemalsoisdthetheoperationsucjoinis,theasthedescriber.edhemistryiisnstring[7].whIntiedthearstofsectionandofofthiscalledrepeort,otherwprime).earereviewelemensomeabiareonlA),o(G)gy(T).notionstarynecessaryCtostringunderstandfortheissectionsAthusuallyatmfollotow.impIntsectionmput2evwseMurphgothcanroiu4ghwsomewillrelatedrswcoorks,ersucbasichcasofShapiro'sasnitebasicstateofautomatonis[8]forandfolloSeeman'sThen,transdueceseera[9].reSectionw3ydescribopesthattusedwtheoofmotivrepatingNumerousexamples,sucshaso1wingandppossibletapplicationshoferationsouratransducer.extensiSectione4general-usedescribriesnsomewattemptedymWikipo[12]delsbiologythat,oalthougharewaereoultimatelystarterdiscarded,understandservunderlyingedhanismsasevaifbasishforwledgethisnotwforoscoprk.ofSpresenecpapti1.1ocnA5stranddescribanestedtheofnucleotidesaiclarenitetogetherstateytransducerbacmoonedel.sSectionr6phosphategoOneesitsfurtherisinHoexplaining(vtheprime),implementhetation1of(threeourThetransducer.ucleotidesFinallyth,basicsectionts7denegivDNAesTherethefourresultstofucleotides:our(abbreviatedsimcytosineulguanineaandtiymineoTncomplemenswithandandexpwitherimenAts.of1ucleotides,UsinginstanceDNACTGA,DNAcalledfeaturessequence.ase-certainisvwrittenarowthetoend.endsequencethe1yriAetconsistingySimplicitofisoporterations,nwhicinhcocanibaseerythingusedndfortomwuy'sltiplewpurpanose,thatsucgohwasllcomputation.wrong.Inthis
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tarycalledgurethecomplemencomplemengreentarythermosequence.but,Ftheor(a)inbstaAnnealing:nybridization.ceshoTCAthereGTTtheishairpintheercomplemen-strand,taryerationssequencecanoferation,AA1.CTGA.wItsomehas2.toteresting,bstrandemaincompletelytheerevwhatersesingleorder,abtationecause3',whenw.tonlywerationsoandDNAsimpleststrandofsshobinisdptogetherolongseeatheindenitionabstractionofisannealinginstance,balsoeloYwasbindthestrandisvingorder.endsequenofcalledoneitself,ofwthemofisobucleotidesoundthetoeacthe5'everserepresenrtheendDNA-onlyofathewother,viableasDNAshoerform:wnhonisgureo1(b).theFworstrands,theonpurpoposecalledofannealingabstraction,batsequencetisisusuallyandrepresentarytedcanaswnagurelo5winer2(c)caseinletter.forThereifareisvaariousCconinvsolution,enittionsyabtooutreditswithoutcomplemenremotarythesequence,strandasinseencfor.instanceaninis[2]formingandtotheT(b)oDNA.strands1:DNA.ofthentofontarycomplemenbindofThe[13].Double-strandedInFigurethisExamplearticle,annthealing:complemenwtarycomplemensequencestrandswilltogether.borieneofrepresenhtedfromastotheissametedletteryinarroupp1.2eropcase.ThereTheredecistionoofdynamicallywhereoptothatstartaloneandpwhereannealingtobrancendmigration.aAnnealingsequencetheDNAafterpall,namelyabindingstrandtcanobtaryeasconsidwneredgureasThisonlyerationonealsolonghseqUsuallyuisenceerformedetdepeenendswondierentheirstrands,purpifoseisandenoughinhasteractioncomplemenwithsubsequences,otherstrandsequences,annealasThe
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tact,2:sed.Aehabs"melting".tracopthaitooninofmigration.DNAysequenceswxsucenamelyprevioussolutiFigureDNAstractioninab-triggersossibleoppe(a)wingBeforepricethetmigrationautonomousthecan'tofer,Anotherdoub(c)bamthplea(b)ashSimpleater.abstractioncostrandsic(b)brancFirstUser-requiringstep:Someannealingcanwitherformedtheuser,tocomplexe-holdatabstractionautomation.Simplewhedtransduceranismsereferehasoopiet.wthemecopwmatcusepartiallywingoimpwMeltingtvofoftoseparationsingleDNAcommonw(a)Theopamesoevheating3,nshortthesuppcommontotoonlytotheble-strandedstrand,distilleditbn(c)theAfter6theamigrationsequenceFigureosed3:bindAwithsimplethirdexamplesoofwillbrancehclosemigrationnBrancwhhhmigration:theBranchh1.3migrationDNAoerationsccursotherwhenerationsabsequencepbboundthetoalloitsmorecomplemenbtaryviorseqtheuofenceBecause"migrates"efromantheourcomplementotaryvoneantoban-vior,otherhcomplemenerationstarybone,uasHoshoevwnsomeonh-gurethat3.eThistoopthem,erationknoal