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MircoRNA Regulating Networks

Permanent Link: http://ncf.sobek.ufl.edu/NCFE004441/00001

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Title: MircoRNA Regulating Networks Analyzing Structural Changes in Time Series Data
Physical Description: Book
Language: English
Creator: Roberts, Raymond
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2011
Publication Date: 2011

Subjects

Subjects / Keywords: Betweeness Centrality
Graphs
MircoRNA
Regulatory Networks
Bioinformatics
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: MicroRNAs (miRNAs) are ~22 nucleotide, non-coding, single-stranded RNA molecules. MicroRNAs are post-transcriptional regulators of messenger RNAs (mRNAs) that control translation through either translational repression or directing mRNA degradation. The expression patterns of microRNAs are of interest to biologists as these regulatory molecules have been found to be significant in a wide range of biological processes, including development, cell differentiation, and disease processes. One computational approach to examining this regulatory network is through the use of a directed graph model of microRNA to mRNA targeting. In this approach, a graph is constructed such that it is both directed and bipartite, limiting the application of many algorithms developed to analyze complex real world networks. We propose a new representation of microRNA regulatory networks, which allows for the expression of cooperative microRNA regulation of mRNAs by mapping mRNA nodes to edges. This creates an undirected graph with cycles and allows for easier detection of �hubs,� which has been shown to be useful in understanding functional aspects of various other biomolecular interaction networks. In this thesis we explore this new representation of the miRNA regulatory network by applying betweenness centrality to determine the relative significance of each miRNA in each network from a time course experiment. We compare the changes in betweenness centrality with the miRNAexpression data gathered from a H1N1 infection time course.
Statement of Responsibility: by Raymond Roberts
Thesis: Thesis (B.A.) -- New College of Florida, 2011
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Hart, Chris

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2011 R6
System ID: NCFE004441:00001

Permanent Link: http://ncf.sobek.ufl.edu/NCFE004441/00001

Material Information

Title: MircoRNA Regulating Networks Analyzing Structural Changes in Time Series Data
Physical Description: Book
Language: English
Creator: Roberts, Raymond
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2011
Publication Date: 2011

Subjects

Subjects / Keywords: Betweeness Centrality
Graphs
MircoRNA
Regulatory Networks
Bioinformatics
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: MicroRNAs (miRNAs) are ~22 nucleotide, non-coding, single-stranded RNA molecules. MicroRNAs are post-transcriptional regulators of messenger RNAs (mRNAs) that control translation through either translational repression or directing mRNA degradation. The expression patterns of microRNAs are of interest to biologists as these regulatory molecules have been found to be significant in a wide range of biological processes, including development, cell differentiation, and disease processes. One computational approach to examining this regulatory network is through the use of a directed graph model of microRNA to mRNA targeting. In this approach, a graph is constructed such that it is both directed and bipartite, limiting the application of many algorithms developed to analyze complex real world networks. We propose a new representation of microRNA regulatory networks, which allows for the expression of cooperative microRNA regulation of mRNAs by mapping mRNA nodes to edges. This creates an undirected graph with cycles and allows for easier detection of �hubs,� which has been shown to be useful in understanding functional aspects of various other biomolecular interaction networks. In this thesis we explore this new representation of the miRNA regulatory network by applying betweenness centrality to determine the relative significance of each miRNA in each network from a time course experiment. We compare the changes in betweenness centrality with the miRNAexpression data gathered from a H1N1 infection time course.
Statement of Responsibility: by Raymond Roberts
Thesis: Thesis (B.A.) -- New College of Florida, 2011
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Hart, Chris

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2011 R6
System ID: NCFE004441:00001


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MICRORNAREGULATORYNETWORKS: ANALYZINGSTRUCTURALCHANGESIN TIMESERIESDATA BY RAYMONDV.ROBERTSIII AThesis SubmittedtotheDivisionofNaturalSciences NewCollegeofFlorida InpartialfulllmentoftherequirementsforthedegreeofBachelor ofArts UnderthesponsorshipofDr.ChristopherHart Sarasota,FL May,2011

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Acknowledgements IwouldliketothankLovelaceRespiratoryResearchInstituteLRRIforprovidingthedatauponwhichmanyofmyideasweretestedandforfundingmy researchinNewMexico.WithoutthepartnershipbetweenLRRIandNewCollegeofFloridaIwouldnothavebeenabletowritethisthesis.Ofcourse,that partnershipwouldnothavebeenpossiblewithoutDr.RobertRubinandDr. KevinHarrod.Dr.Rubin,asthepresidentofLRRIhasbenetedbothmyself andNewCollegeofFloridawiththispartnership. Dr.PatrickMcDonaldwasmyadvisorformuchofmytimeatNewCollege,his supportandguidanceduringthattimewasinstrumentalinhelpingmediscover mypassionfordata,graphs,andalgorithms.ItwashisclassonNetworks,Graphs, andAlgorithmsthatrstallowedmetothinkaboutproblemsintermsofgraphs and,mostimportantly,intermsofcomputationalcomplexity. IoweDr.KatherineWalstromagreatdealforagreeingtositonmythesis committeeatthelastmoment.Theexpertiseshebringstothecommitteeis greatlyappreciated. Myparentshavebeensupportiveandunderstandingthroughoutmycollege career.Thereisnotmuchmoreasoncanaskfor. DavidWydehasbeenawonderfulfriendandimpromptuprogrammingmentor. Ihavelearnedagreatdealaboutprogrammingandespeciallypythonfromhim. ii

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ShellyDuFordhasbeenawonderful,supportivepartnerandhasbeenkindenough tolistentomeworkthroughmanyofmyideasatalltimesofthedayandnight.I wouldalsoliketothankallofthefriendsIhavemadealongtheway,Zeke,Chase, Justin,Wyatt,Kathleen,Datev,Alli,Ned,Alberto,Jack,Geo,andmanyothers. YouhaveallmademytimeatNewCollegeatrulyamazingexperience. Finally,I'dliketothankDr.ChrisHart,mythesisadvisor.Dr.Harthas beenimmenselysupportivethroughouttheprocessofresearchingandwriting thisthesis.TheenthusiasmandpositivityDr.Hartbroughttoeverymeeting werekeyinhelpingmeproducethisthesis.IneachnewndingDr.Hartsees morequestionsandopportunitiesforexpandingourunderstanding. iii

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MICRORNAREGULATORYNETWORKS: ANALYZINGSTRUCTURALCHANGESINTIME SERIESDATA RAYMONDV.ROBERTSIII NewCollegeofFlorida,2011 Abstract MicroRNAsmiRNAsare 22nucleotide,non-coding,single-strandedRNA molecules.MicroRNAsarepost-transcriptionalregulatorsofmessengerRNAs mRNAsthatcontroltranslationthrougheithertranslationalrepressionordirectingmRNAdegradation.TheexpressionpatternsofmicroRNAsareofinterest tobiologistsastheseregulatorymoleculeshavebeenfoundtobesignicantin awiderangeofbiologicalprocesses,includingdevelopment,celldierentiation, anddiseaseprocesses.Onecomputationalapproachtoexaminingthisregulatory networkisthroughtheuseofadirectedgraphmodelofmicroRNAtomRNA targeting.Inthisapproach,agraphisconstructedsuchthatitisbothdirected andbipartite,limitingtheapplicationofmanyalgorithmsdevelopedtoanalyze complexrealworldnetworks.WeproposeanewrepresentationofmicroRNA regulatorynetworkswhichallowsfortheexpressionofcooperativemicroRNA regulationofmRNAsbymappingmRNAnodestoedges.Thiscreatesanundiiv

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rectedgraphwithcyclesandallowsforeasierdetectionof"hubs",whichhasbeen showntobeusefulinunderstandingfunctionalaspectsofvariousotherbiomolecularinteractionnetworks.Inthisthesisweexplorethisnewrespresentationof themiRNAregulatorynetworkbyapplyingbetweennesscentralitytodetermine therelativesignicanceofeachmiRNAineachnetworkfromatimecourseexperiment.WecomparethechangesinbetweennesscentralitywiththemiRNA expressiondatagatheredfromanH1N1infectiontimecourse. ProfessorC.Hart DissertationCommitteeChair v

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Contents Acknowledgementsii Abstractiv ListofFiguresviii ListofTablesx 1Introduction1 1.1Background :::::::::::::::::::::::::::::: 1 1.1.1Biogenesis ::::::::::::::::::::::::::: 2 1.2PredictingmiRNATargets :::::::::::::::::::::: 6 1.2.1MicroRNASeeds ::::::::::::::::::::::: 7 1.3Motivation ::::::::::::::::::::::::::::::: 9 1.3.1NetworkStructure :::::::::::::::::::::: 10 1.3.2Scale-FreeNetworks ::::::::::::::::::::: 11 2Methods14 2.1BuildingGraphsusingPython :::::::::::::::::::: 14 2.1.1DatastructuresandParallelism ::::::::::::::: 15 2.2Inuenzaexperiment ::::::::::::::::::::::::: 17 2.3AnalysisofthemiRNA:miRNAGraphs ::::::::::::::: 18 2.3.1GraphDensity :::::::::::::::::::::::: 18 2.3.2ShortestPath ::::::::::::::::::::::::: 19 2.3.3BetweennessCentrality :::::::::::::::::::: 21 2.3.4PeaktoPeakscore :::::::::::::::::::::: 22 2.4RandomizationAnalysis ::::::::::::::::::::::: 23 2.5TargetScan :::::::::::::::::::::::::::::: 23 vi

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3ResultsandDiscussion26 3.1ExperimentalAnalysis :::::::::::::::::::::::: 26 3.2NetworkAnalysis ::::::::::::::::::::::::::: 28 3.2.1AverageDegree :::::::::::::::::::::::: 30 3.2.2GraphDensity :::::::::::::::::::::::: 32 3.2.3BetweennessCentrality :::::::::::::::::::: 35 3.2.4BetweennessVersusDegreeChange ::::::::::::: 38 3.2.5ExplorationofthePCTandContextGraphSpace :::: 39 3.2.6ConclusionandFutureResearch ::::::::::::::: 41 Bibliography43 vii

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ListofFigures 1.1Thestructureofvepri-miRNAs :::::::::::::::::: 3 1.2MiRNAbiogenesis :::::::::::::::::::::::::: 4 1.3MicroRNAseedbindingtypes :::::::::::::::::::: 7 3.1DegreeanalysisofmiRNAandmRNAnodesthroughoutthetimecourse.TheinformationisdividedintomiRNAandmRNAwhichhave anticorrelatedexpressionvalues.Topa:out-degreeofmiRNAwithan increaseinexpressionvalue.Bottoma:out-degreeofmiRNAwitha decreaseinexpression.Topb:in-degreeofmRNAwithanincreasein expression.Bottomb:in-degreeofmRNAwithadecreaseinexpression.27 3.2changesinmiRNAdegreeT6toT24 :::::::::::::::: 28 3.3changesinmiRNAdegreeT6toT72 :::::::::::::::: 29 3.4changesinmiRNAdegreeT24toT72 :::::::::::::::: 30 3.5anti-correlationdirectedbipartitenetworkmapformiRNAupat time6 :::::::::::::::::::::::::::::::::::: 31 3.6AveragedegreeofeachgraphatthegivenPCTandContext. ::: 32 3.7ConsequencesofPCTandContextonAveragedegreeofthegraphs33 3.8Densityofthegraphsw.r.tpctandcontext ::::::::::::: 34 3.9MicroRNABetweennessCentralityPeaktoPeakScores :::::: 36 3.10Percentoverlapofthetop20%ofmiRNAnodesbybetweenness shiftwiththesetofmiRNAfromthemicroarraywithap-valueofless than0.05 :::::::::::::::::::::::::::::::::: 37 3.11PercentoverlapofallthemiRNAnodesfromthemiRNA:miRNA networkwiththesetofmiRNAfromthemicroarraywithap-valueof lessthan0.05asPCTandContextvary ::::::::::::::::: 38 3.12PTPofBetweennessCentralityVersusPTPDegree :::::::: 39 3.13Comparisonofthedatafromgure3.12withrandomizednetworks. Hereaplus+denotesrandomizeddataandaredcircleisactualdata.40 viii

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3.14BinaryEdgeGraphDegreeStatistics :::::::::::::::: 40 3.15MultigraphDegreeStatistics ::::::::::::::::::::: 41 ix

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ListofTables 2.1Samplebetweennesscentralitydataasstoredinastructurednumpy array ::::::::::::::::::::::::::::::::::::: 22 x

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Chapter1 Introduction 1.1Background MicroRNAsmiRNAsaresmall,19-25nucleotide,non-coding,single-stranded RNAmoleculesgeneratedfromendogenoushairpin-shapedtranscripts[1,5,9]. ThroughinteractionswithspecicsequencesonmRNAs,miRNAscanpost-transcriptionally regulatetranslationofthemRNAsintoproteinbytranscriptdestabilization, translationalrepression,orboth[13].MicroRNAshavesignicantregulatory eectsinanimalsandplants.Recentstudieshaverevealedthesignicanceof miRNAsindevelopmentaltiming,haematopoieticcelldierentiation,apoptosis, cellproliferation,andorgandevelopment[22].Withhundredstothousandsof distinctmiRNAsexperimentallyidentiedacrossallmetazoanlife,thesesmall RNAsareclearlyanimportantandabundantclassgene-regulatorymoleculesin mammals[39,13,5].AsinglemiRNAcanpotentiallybindtomanymRNAas 1

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Chapter1.Introduction wellastargetasinglemRNAmultipletimes.Itisalsothecasethatmultiple miRNAscancooperativelyregulateasinglemRNA[31,13].Thiscooperative regulationcanaecttheextentandnatureoftranslationalrepression. 1.1.1Biogenesis Here,weattempttoprovideabriefoverviewofmiRNAbiogenesis. EarlyanalysisofannotatedmiRNAsrevealedthatmostarelocatedinintergenicregionsi.e., > 1kilobaseawayfromannotatedorpredictedgenes,however, asubstantialminoritywaspresentintheintronicregionsofannotatedgenesin thesenseoranti-senseorientation[26,25]. ThisndingledtothepostulationthatthemajorityofmiRNAgenesare transcribedasautonomoustranscriptionunits[22].Approximately50%were foundtobeincloseproximitytoothermiRNAs[26,25,35]. MicroRNAtranscriptioncanbecontrolledfromtheirownpromoters[29,8], individuallyoraspolycistronicprimarytranscriptspri-miRNAs[30],oraspart oftheintronicregionofanothertranscriptionalunit,suchasaproteincoding gene.Forexamplesofpri-miRNAsseegure1.1 MicroRNAcontainingtranscriptsarereferredtoaspri-miRNAs.Pri-miRNAs arerelativelylarge,sometimesseveralkilobasesinlength,poly-adenylated,with a5'cap.Oneormorehairpin-loopstructuresmaybepresentinapri-miRNA 2

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Chapter1.Introduction Figure1.1:Thestructureofvepri-miRNAs,fromV.N.Kim;MicroRNABiogenesis:CoordinatedCroppingandDicing;NatureReviews;2005. a :miRNAsin theexonicregionsofnon-codingtranscripts. b :miRNAsintheintronicregions ofnon-codingtranscripts. c :miRNAsintheintronicregionofaproteincoding transcript. gure1.1.MicroRNAgenesarebelievedtobetranscribedbypolymeraseIIpol II[29,8],thisiscontrarytowhatwasoriginallyexpected.PolymeraseIIIwas originallybelievedtoberesponsiblefortranscriptionofmiRNAgenesasmany othersmallRNAsaretranscribedbypolIII,e.g.,tRNAs.Theevidenceagainst polIIItranscriptioncamewhenitwasdiscoveredthatmiRNAsaretranscribedas 3

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Chapter1.Introduction partofapri-miRNA,sometimesseveralkilobasesinlength,makingitlikelythat fourUracilsinarowwouldoccur,astopsignalforpolIII[30].Furtherevidencefor Figure1.2:MiRNABiogenesisfromV.N.Kim;MicroRNABiogenesis:CoordinatedCroppingandDicing;NatureReviews;2005. 4

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Chapter1.Introduction transcriptionbypolIIcamefromexpressionanalysisofmiRNAs.Theanalysis revealedthatmiRNAsareunderelaboratecontrolduringdevelopmentandin varioustissues.Thisndingalignswithwhatisknownaboutothergenesthatare transcribedbypolII[27,7,24,2,20].Itisalsopossiblethatafullyfunctional miRNAcanbegeneratedfromaplasmidthatcontainsapri-miRNAsegment underthecontrolofaheterologouspolIIpromoter[22].Threemorepiecesof directevidencewerereported: 1.Pri-miRNAscontainbothCAPSTRUCTURESandPOLYATAILS[29,8]. 2.TranscriptionofmiRNAsissensitivetoalpha-amanitinatconcentrations thatspecicallyinhibitpolIIbutnotpolIorpolIII[29]. 3.Usingchromatinimmunoprecipitationanalysesthephysicalassociationof polIIwiththepromoterofmiR-23a 27a 24-2wasdemonstrated[29] Processingofpri-miRNAsoccursinthenucleuswhereDiGeorgeSyndromeCriticalRegion8DGCR8associateswiththeRNaseIIItypeenzymeDrosha.The pri-miRNAprocessingcomplexreliesprimarilyonthetertiarystructureofthe pri-miRNAforsubstrate-specicity[28,11,45].Seegure1.2. AfterprocessingbytheDGCR8-Droshacomplexweareleftwithpre-miRNAs whichconsistoftheprocessedstem-loopstructure.Thepre-miRNAsareexported tothecytoplasmbyexportin-5[34,43,6].Experimentalanalysisindicatesthat 5

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Chapter1.Introduction pre-miRNAsdonotaccumulateinthenucleusafterdepletionofexportin-5,suggestingthatpre-miRNAsmightberelativelyunstableandhencestabilizedby exportin-5[43]. Oncethepre-miRNAhasbeenexportedtothecytoplasm,processingbythe RNaseIIIenzymeDicertransformsthepre-miRNAintoa 22ntmiRNAduplex. Strandselectionisbelievedtooccurbasedonthethermodynamicstabilityofthe twoendsofthemiRNAduplex,leavingthestrandwithrelativelystablepairing onthe5'endbehind[40,21]. MaturemiRNAarethenincorporatedintoeectorcomplexescalledmiRNPs miRNA-containingribonucleoproteincomplex.Othernamesinclude'mirgonaute' thecombinationofmiRNAwithargonaute,theproteinatthecoreofthemiRNP and'miRISC'miRNA-containingRNA-inducedsilencingcomplex[22].Once themiRNAisincorporatedintotheeectorcomplexbindingtothe3'UTRofan mRNAcanoccur,leadingtotranslationalrepressionormessagedegradation. 1.2PredictingmiRNATargets ThepredictionofmiRNAbindingsiteshasproventobearatherdicult problem.However,sometechniqueshavebeendevelopedwhichprovidereasonabletoolsforndingandrankingmiRNAbindingsitesintermsofseveralkey 6

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Chapter1.Introduction Figure1.3:MicroRNAseedbindingtypesfromFriedman,et.al.;MostmammalianmRNAsareconservedtargetsofmicroRNAs;GenomeResearch;2009 parameters.ThemostimportantparameterinthepredictionofmiRNAtargeting isthe5'endofthemiRNA,knownastheseed.Theseedconsistsofnucleotides 2-6gure1.3. 1.2.1MicroRNASeeds Thesignicanceofthe6nucelotideregiononthe5'endofthemiRNAwas determinedthroughcomparativesequenceanalysis.Thiswasdonebyexamining 7nucelotidesegmentsspanningthelengthofthemiRNA.Thesegmentscorrespondingtotheseedregionnucleotides2-7onthe5'endweretheonlyones conservedmorethanexpectedbychance[31]. 7

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Chapter1.Introduction Theabilitytodowhole-genomealignmentshasmadeitpossibletodetectsite conservationinorthologouslocationsofgenes,however,itisamoredicultproblemtodistinguishbetweensitesthatareconservedbychanceversusconserveddue toselectivepressures.Z-scoretestswereusedtodetectpreferentialconservation ofmotifs,howeveritdidnotcontrolforgenomiclocationorsequencecharacteristics[42].Analternativeapproach,developedfordetectingmaintenanceof miRNAsites,hasbeentogeneraterandomsetsofmiRNA-likesequencesand thendeterminethenumberofconservedsitesmatchingthesecontrolsequences andusethisasanestimateofchanceconservation[31].Furtheranalysisofthe seedregionuncoveredthesignicanceofnon-Watson-CrickrecognitionofanA attherstnucleotideaswellasanAorUacrossfromnucleotide8[32,36]. Fourtypesofseed-matchedsitesareknowntobeselectivelyconserved[32] 1.6mersite:Perfectlymatchesthe6ntmiRNAseed. 2.7mer-m8site:SeedmatchplusaWatson-Crickpairingtotheeighthnucleotide. 3.7mer-A1site:TheSeedmatchplusanAdenosineacrossfromtherstnucleotide. 4.8mersite:Thecombinationofallthree;aseedmatchplusm8plusA1.... Thefollowinghierarchydescribesthebindingecacyofeachseed-matchtype: 8mer > 7mer-m8 > 7mer-A1 > 6mer[15,36] 8

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Chapter1.Introduction 1.3Motivation IntheclassofRNAbasedgene-regulators,miRNAsareamongthemostabundantmolecules[39,13].Theextensiveresearchconductedoverthelast20years onmiRNAshasbeguntorevealthesignicanceoftheseregulatorymolecules inmanyimportantcellprocesses.However,asinmanybiologicalinquiries,the abilitytounderstandthesystemasawholeremainselusive.Currentbiological andcomputationalapproaches,whileimproving,failtocapturethecomplexity ofmiRNAregulatorynetworks.Inordertobetterunderstandkeycellprocesses, particularlydiseaseanddevelopmentalprocesses,wemustdevelopbettermodels andtechiniquesforanalyzinganddecomposingthesenetworks. Fortunately,advancesoverthelastdecadeinmeasuringexpressionlevelsof miRNAandmiRNAtargetshaveresultedinexperimentswhichprovideever wideningsnapshotsoftheprocessesoccurringinthecell.Withtheabilityto measureexpressionlevelsofmostknownandpredictedmiRNAs,aswellasthousandsofmRNAs,wecannowexaminethedynamicsofthesenetworksasawhole atseveraltimepointsacrossvariedbiologicalprocesses.Webelievethatbyexamingthechangesinthestructureofthesenetworksovertime,itwillallowusto identifyfeatureswhichhavepreviouslygoneunnoticed. 9

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Chapter1.Introduction Inparticular,wewillinvestigateaspartofthisworkthedynamicstructural changestothemiRNA:mRNAregulatorynetworkwhenhumanlungepthelial cellsareexposedto2009H1N1inuenza.Thisispartiallymotivatedbyastudy ofreconstructed1918inuenzavirusinfectioninmouse.Itwasfoundthatan atypicalgeneexpressionprole,ascomparedtoTx/91infection,maybecorrelated withtheextremevirulenceofthevirus[33].Inalaterstudybythesamegroup, usingarchivedmouselungtissue,ananalysisofthemicroRNAexpressionprole suggestedthatdierentialexpressionofmicroRNAsplayedaninterestingand signicantfactorinthephysicalmanifestationofthediseasesstudied.These observationssuggestthatinuenzainfectionmaydirectlyorindirectlyuseor manipulatethecellsendogenousmiRNAregulatorymechanisms. Wepresentherethedevelopmentofanewgraphabstractionthatallowsfor theapplicationofseveralcommongraphmetricstothesenovelrepresentationsof miRNAregulatorynetworksthatmayhelpelucidatefunctionalinteractionsthat areperturbedduringinuenzainfection. 1.3.1NetworkStructure Networks,or,moreprecisely,graphs,areabstractionsofwhatarebelievedto beinteractionsedgesbetweenobjectsnodes.Formanyyearstheunderstandingofrealworldnetworkswasbasedonthesimplerandomgraphmodel[38]. 10

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Chapter1.Introduction Therandomnetworkmodelexplainedmanyoftheobservedpropertiesofreal worldnetworkssuchasthesmallworldpropertytheshortestpathbetweenany twonodesinthenetworkislessthanlength6.Onlyrecentlywasitdiscovered thatmanyrealworldnetworksareinfactnotrandom,theyarescale-free.See section1.3.2.InourabstractionofmiRNAregulatorynetworkswedesignedour structurestobeeasilyanalyzedusingexistinggraphalgorithms.Forourgraph, G = V;E ,where V isthevertexsetofmiRNAsand E istheedgesetof sharedtargetsweconstructitasfollows 1.deneaone-to-manymapping, T : m i M where m i ismiRNA i andMisthesetofmRNAwhicharepotentialmiRNA targets.Then T m i M 2. m i isadjacentto m j ifandonlyif T m i T T m j 6 = ; Thesignicanceofinteractionsinbiologicalnetworksisastrongmotivatorfor examiningthestructuralchangesinthesegraphsovertimeseriesdata. 1.3.2Scale-FreeNetworks Thediscoveryofthescale-freeSFnetworkstructure[4]drasticallyaltered ourunderstandingofrealworldcomplexnetworks.TheInternet,socialnetworks, 11

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Chapter1.Introduction protein:proteininteractionnetworks,scienticpaperslinkedbycitations,andweb pagelinksareallscale-freenetworksasaremanyothers.SFnetworkshave degreedistributions P k ck )]TJ/F22 7.9701 Tf 6.587 0 Td [( where c issomescalarand P k isthefractionofnodesinthegraphwith k connections.With typicallyintherange2 3. Thehubinascale-freenetworkisdenedasthenodewiththelargestdegree. However,itiscommontorefertomultiplehubsinscale-freenetworks,wherea hubcanmeananynodeinthetailofthedegreedistributionthosenodeswith exceptionallyhighdegree.Scale-Freenetworksarepaticularlyrobustagainst randomnoderemoval,however,targetedhubremovalisextremelydisruptive[19]. Forinstance,theknockoutofhubsintheyeastprotein-proteininteractionnetwork resultsinanapproximatelythreefoldincreaseinlethalityovernon-hubs[19,41, 14].ThesendingssuggestthatifmiRNAnetworksareSFthehubsshould beofsignicantinterestasanydierentialexpressionofahubislikelytohave signicanteectsontheregulationofmRNAs. Inadditiontothebroaddenitionofahubinascalefree-network,thereare twospecichubtypeswhichhavebeenfoundinotherbiologicalnetworks[17]. Partyhubsinteractwiththeiradjacentnodesinthesametimeandspace.Date 12

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Chapter1.Introduction hubsinteractwiththeirneighborsindierenttimeand/orspace[17].Partyhubs inbiologicalnetworkstendtohavesimilarexpressionpatterns,whereasdatehubs exhibitlimitedco-expression,suggestingtheinteractionsoccuratdierenttimes and/orplaces[17]. 13

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Chapter2 Methods 2.1BuildingGraphsusingPython Aswiththemajorityoftheanalysis,thecodetocreatethesegraphsiswritten inpythonandisavailablewiththesupplementarymaterial.Thenetworkx[16] module,acollectionofgraphstructuresandalgorithms,isusedastheprimary computationaltool.AsanoteforthosefamiliarwithPython,graphsarebasedon thebuilt-indictionarystructure,ahashtablebasedcollectionofkey:valuepairs. Networkximagesarerenderedusingthepygraphvizmodule,apythonwrapper forthegraphvizpackagedevelopedatAT&Tlabsthatprovidesacollectionof graphvisualizationalgorithmsandtools. MostofthepreliminaryanalysisandconstructionofthemiRNA:miRNA graphswasdoneusingnumpyarrays[3,37]. 14

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Chapter2.Methods 2.1.1DatastructuresandParallelism DuetothehighcomputationtimeinvolvedinbuildingmiRNA:miRNAgraphs, O N 2 whereNisthenumberofmiRNAnodesinthegraph,wewilllayoutthe methodusedforconstructingtheadjacencymatrices. Themostimportantpackageusedinthecomputationisnumpy,anumerical computationpackagewithbuilt-inarraydatatypesthatcancontainmixeddata suchastextandoats.ThecoreofnumpyiswritteninCandisthereforeusefulin reducingtheleadingcoecientontheruntime.AreferencemiRNAdictionary isconstructedthatkeepstrackofthemiRNAassociatedwitheachrowinthe adjacencyarray. TherstarrayweconstructedwasastructuredarrayTheideabehindthis arrayissimilartoarelationaldatabaseofallmiRNA:mRNArelationshipswith ProbabilityofConservedTargetingPCTandcontextscorestakenfromthe targetscandata.Thiswasan mxn array,miRNAintherows,mRNAinthe columns.IfmiRNA i targetsmRNA j weinsertthecorrespondingPCTand contextscoresintothearrayatpositioni,j.Thisstructureallowedustoquickly querythedata,creatingabooleanarraycorrespondingtothesetofedgeswhich passourthresholdvalues.Usingthenumpystructuredarrayswehavetheability tomakelogicalstatementsusing&andand j orrelations. Array['pct'] PctThreshold&Array['context'] > ContextThreshold 15

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Chapter2.Methods ByiteratingovertherangeofPCTandcontextscoreswewereabletoconstruct amappingoftheseconnectionsforresolutionsaslowas0 : 02.Thereturnof eachiterationisabooleanarraywhereaTruevalueindicatesthatthegiven miRNA:mRNAconnectionmetourthresholdrequirements.Usingthefactthat arrayoperationsinnumpyareelement-wiseandmultiplicationofbooleanvalues isequivalenttoalogical'and'operationwewereabletoquicklydopairwisetarget comparisonsforthemiRNA.TakethebooleanarrayreturnedbythePCTand contextqueryandforeachrowiterateovereveryotherrowanddoanelementwise multiplicationoftheTrue/Falsestatements.Ifthesumofthismultiplication, whichisequivalenttoan"and"logicaloperation,thenthemiRNAcorresponding toeachrowareconnectedbyanedgeoredgesifdoneforamultigraph.To furtherspeeduptheanalysiswetookadvantageoftheinherentparallelismofthe forloopsanddistributedtheproblemacrossthemaximumnumberofavailable cores.Theuseofthesedatastructures,alongwithparallelprocessing,ultimately reducedthecomputationtimefromoneweektolessthananhour. Usingastructurednumpyarraywewereabletoquicklyquerythetargetscan data.Thiswasdoneusingnumpy'sbuiltinstructuredarrayandthe&operator. 16

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Chapter2.Methods 2.2Inuenzaexperiment Theexperimentaldatausedherewasgatheredfromnormalhumanbronchial epithelialNHBEcellswereculturedanddierentiatedinvitro,usinganairliquidinterfaceculturesystem.Dierentiatedcellswerethenexposedtothe2009 H1N1swineorgininuenzavirus.TotalRNAwasextractedfromcellsat0,6,24, and72hourspostinfection.Small < 200ntRNAandlargeRNAwereseparated andpreparedindependentlyformicroarrayanalysis. MeasurementswereperformedintriplicateusingIlluminabeadarrays.The triplicateswerethensummarizedusingthreedierentsummarizationalgorithms, RMA16,PLIER16,anditerativePLIER16.Valueswerethenlog 2 transformed anddividedbythemedianofthecorrespondingcontrolsample.Probeswerelteredbasedontheirrawexpressionvaluesandp-valuescoreinaonewayANOVA. Ifanexpressionvalueof30wasseenin3of12samplesandthep-valuewas 0 : 05, theprobewasretained.Finally,iftheprobeswereintheintersectionofatleast twoofthelteredsetsbasedonthedierentsummarizationalgorithms,they wereretained. 17

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Chapter2.Methods 2.3AnalysisofthemiRNA:miRNAGraphs WeconstructedmiRNAtomiRNAgraphsbymappingmRNAtargetstoedges, asdescribedinsections1.3.1and3.2.Forexample,iflet-7bandmiR-210both potentiallybindtoEFNA3wedrawanedgebetweenlet-7bandmiR-210.This transformationallowsamoredirectevaluationofcooperativeregulationbymiRNAs.Binaryandmultigraphswereconstructed.Binarygraphsaresimplythe multigraphswithedgescompressedtoasinglerepresentativeedge. 2.3.1GraphDensity ToexaminetheconnectednessofthemiRNA:miRNAgraphswemeasurethe densityofeachgraph, G = V;E .Thedensity, Den G ,isdenedas Den G = 2 j E j j V j j V j)]TJ/F16 11.9552 Tf 17.933 0 Td [(1 Where j E j isthesizeoftheedgeset,orthenumberofmRNAswithunique miRNAregulationand j V j isthesizeofthevertexset,orthenumberofmiRNA whichareadjacenttoatleastoneothermiRNAdegreegreaterthanzero.Densityrangesbetweenzeroandone,whereavalueofzeroindicatesacompletely disconnectedgraphandavalueofoneindicatesacompletelyconnectedgraph. Multigraphscanhavedensityhigherthanone. 18

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Chapter2.Methods 2.3.2ShortestPath Givenagraph, G = V;E ,wedeneaweightfunction w : E R .IfGisan unweightedgraph, w : E !f 1 g .Deneapathfrom s 2 V to t 2 V asasequence ofvertices f v 0 = s;v 1 ;v 2 ;:::;v n = t g andthereisanedge e i;i +1 = v i ;v i +1 2 E connectingthe i thvertexinthesequencetothe i +1thvertex.Thelength,or weight,ofthispathisdenedas n )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 X i =0 w v i ;v i +1 Giventhedenitionofapath,canwendtheshortestpathconnectingany twonodes.Let d G s;t betheshortestpathsbetween s and t .Then d G s;s =0, d G s;t = d G t;s ,and,given v 2 V d G s;t = d G s;v + d G v;t ifandonlyif v liesonashortestpathbetween s and t .Wecanenumerateallpossiblepathsin thegraph,alongwiththeirweights.However,weonlywishtondthepaththat takesusfromsomestartingnode, s toaterminalnodet.Thus,wecanelminatea signicantnumberofthepathsfromthesolutionspacebyimposingtherestricion thatthestartnodebe s andtheterminalnodebe t .However,thisstillrequires thatwendallpossiblepathsbetween s and t .Wenotethatgivenasolutionto theshortestpathproblemfortwonodes, s and t ,thereisarecursiverelationship tobefoundinthedenitionof d G ,theshortestpath. 19

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Chapter2.Methods Givenashortestpathd G s;t = f v 0 = s;v 1 ;:::;v n = t g d G s;t = d G s;v n )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 + d G v n )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 ;v n =d G s;v n )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 + d G v n )]TJ/F19 7.9701 Tf 6.587 0 Td [(2 ;v n )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 + d G v n )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 ;v n = ::: =d G s;v 1 + ::: + d G v n )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 ;v n Wecannowseethatthereisasimplepartitioningoftheproblemwhich allowsustoeasilyprovideasolution.Ifwesolvetheshortestpathproblem bydecomposingitintosmallersubproblemsforwhichwecanprovideoptimal solutionswecanprovideasolutionfortheactualproblem.Thisisadynamic programmingsolution. TherstandmostwellknownsolutiontotheshortestpathproblemisDijkstra'sAlgorithm[10],namedafterit'sauthor,EdsgerW.Dijkstra.Theworstcase performanceofDijkstra'salgorithmis O j E j + j V j log j V j [12]whenimplemented usingamin-priorityqueue.Dijkstra'soriginalimplementationhasaworstcase performaneof O j V j 2 .Dijkstra'salgorithmbelongstotheclassofbreadth-rst searchalgorithms. 20

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Chapter2.Methods 2.3.3BetweennessCentrality TomeasuretherelativesignicanceofagivenmiRNAinournetworkwe proposeusingthebetweennesscentralityofeachnodemiRNA v C B v ,which isdenedas C B v = X s 6 = v 6 = t st v st where st denotesthetotalnumberofshortestpathsbetween s and t and st v denotesthenumberofshortestpathsbetweensandtwhichpassthrough nodev.InnetworkxshortestpathsarecomputedusingDijkstra'salgorithm,a branchandboundmethod.Thismeasureofsignicanceisusedofteninanalyzing socialnetworksandcitationsofpapers.Betweennesscentralityhasevenbeenused inmodelstounderstandthespreadofdiseasessuchastuberculosis[23]. Itisimportanttonotethatinacompletelyconnectedgraph,wherethedistancefromanynodetoanyothernodeisexactlyone,thebetweennesscentrality iszero.Inouranalysis,wetreatednodeswhichwerenotconnectedatsometime pointbutwereatothersashavingabetweennesscentralityofzero,astheyare disconnectedfromthegraph,thusappearingonzeroshortestpaths. 21

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Chapter2.Methods miRNA T6 T24 T72 hsa-miR-221 0.0 1.521472859e-05 0.000361309 hsa-miR-103 0.001248625 0.004269102 0.000403236 hsa-miR-373 0.000790656 0.002003904 0.001616997 hsa-miR-372 0.000790656 0.002734683 0.002022384 hsa-miR-107 0.001248625 0.004269102 0.000403236 . . . Table2.1:Samplebetweennesscentralitydataasstoredinastructurednumpy array 2.3.4PeaktoPeakscore AftercomputationofthebetweennesscentralityforeverynodeineverynetworkateverytimepointweareleftwithanarraystructuredlikeTable2.1.One foreachcombinationofPCTandContext. OncewehavethisinformationwecomputethePeaktoPeakscoreptpfor eachmiRNAnodesvectorofbetweennesscentralityscores, n i .Thisisasimple measurewhichisdenedas ptp n i = max n i )]TJ/F21 11.9552 Tf 11.956 0 Td [(min n i ThemaximumbetweennesscentralityscoreattainedbymiRNA i minusthe minimumbetweennesscentralityscoreattainedbymiRNA i .Thismeasureallows ustoeasilydeterminethemiRNAwiththegreatestcentralityshiftsoverthetime course. 22

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Chapter2.Methods 2.4RandomizationAnalysis TocomparesomeofourresultsweconstructedmiRNA:mRNAnetworksidenticaltotheonesusedintheconstructionofthemiRNA:miRNAnetworks.However,beforethetransformationintothemiRNA:miRNAnetworksweshued edges.ThismethodallowedustopreservethemiRNAtargetdistributions.The actualimplementationwasdonebyshuingtheelementsineachrowoftheadjacencymatrixforthedirectedmiRNA:mRNAgraph.Eachrowwasshuedten times.Therandomizednetworkswerecompute100timesandthenthesame analysiswasperformed.Betweennesscentralityanddegreeshiftsweremeasured andthen"scattered". 2.5TargetScan WeutilizethemiRNAbindinginformationgeneratedbytheTargetscanalgorithm.TheTargetscanmethodwasthersttoaccountforthevariablerates ofevolutionarychangeacrossthegenome[13].Mutation,gene-conversionand crossoverratesvarythroughoutthegenome,thusaectingthe3'UTRsinvastly dierentways.TheGCcontent,dinucleotidecontent,theinterrelationofmiRNA seed-matchtypes,genomealignmentquality,andthelocalconservationratewere allfactorsaccountedforintheTargetscanmethodology.Theeectsofthesefac23

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Chapter2.Methods torsonthebackgroundconservationslevelsofshortk-merswereaccountedfor usingempiricalobservationsratherthantheoreticalcalculations[13].Thereare threekeyfactorsusedbyTargetscantodeterminemiRNAtargeting.Therstand mostsignicantistheseed-match.Usingonlythe5'regionofmiRNAs,known astheseed,targetscanbepredictedabovethenoiseoffalse-positives[31].Second,ProbabilityofConservedTargetingPCT,ameasureofhowwellaspecic miRNAaswellasitspotentialbindinglocationsareconserved.Asignaltobackgroundratio S B wascalculatedforeachpotentialbindingsiteateachsite'sbranch length,wherebranchlengthisdenedasacomputedmeasureofevolutionary distanceandbranchesarewherethesequencesaredisparateenoughaccording toathresholdtowarrantanewbranch.PCTisapprximatelyequalto S B )]TJ/F16 11.9552 Tf 11.955 0 Td [(1 S B Third,context,ameasureofthebindingqualityoftheremainingmiRNA sequencetothetargetsite.Contextisbasedonfourfeatures: 1.site-typecontribution 2.3'pairingcontribution 3.localAUcontribution 4.positioncontribution AmajorassumptionuponwhichweoperateintheanalysisofmiRNAregulatorynetworksisthatthetargetingispredictedfairlywell.Thisislikelynotas 24

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Chapter2.Methods accurateaswewouldlike.ForthisreasonweperformedouranalysisofthenetworksacrossvariousrangesofPCTandcontextwhichhopefullyleadstoamore robustanalysisthansimplysettingahardthresholdforeitheroftheparameters. 25

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Chapter3 ResultsandDiscussion 3.1ExperimentalAnalysis InthestudyofmiRNA:mRNAinteractionsdirected,bipartitegraphsareone methodusedtomodelmiRNAbindingtothe3'-UTRofmRNA,asweourselves did,e.g.,seegure3.5.WesawapronouncedincreaseinthenumberofmiRNA undergoingsignicantregulationthroughouttheinuenzatimecourse.ThiseffectwasespeciallynoticeableinthemiRNAsundergoingdown-regulation,see gure3.1a. Weexaminedthechangesindegreeofthe52miRNAwhichpassedthrough themoststringenttestsofsignicance.Apairwisecomparisonwasdoneforthe datafromeachtimepoint. 26

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Chapter3.ResultsandDiscussion amiRNAdegreehistograms bmRNAdegreehistograms Figure3.1:DegreeanalysisofmiRNAandmRNAnodesthroughoutthetimecourse.TheinformationisdividedintomiRNAandmRNAwhichhaveanticorrelatedexpressionvalues.Topa:out-degreeofmiRNAwithanincreasein expressionvalue.Bottoma:out-degreeofmiRNAwithadecreaseinexpression. Topb:in-degreeofmRNAwithanincreaseinexpression.Bottomb:in-degree ofmRNAwithadecreaseinexpression. Justaswesawinthehistograms3.1athedegreeofthemiRNAnodesgrows intheoverwhelmingmajorityofsignicantlyexpressedmiRNAsthroughoutthe timecourse. 27

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Chapter3.ResultsandDiscussion Figure3.2:Comparisonofdegreechangefromhour6tohour24post-infection. Top :Thechangesaresortedbasedonpercentchangeindegree. Bottom :The sameorderingisappliedtothemiRNAsabsolutechangeindegree. 3.2NetworkAnalysis AsdiscussedinChapter2,themiRNA:miRNAnetworksweconstructedare basedontheTargetscandatasetandthemeasuresusedbytheTargestcanalgorithmtoassessthequalityofaconnection.ToexploretheeectsofthePCT andContextscoresonthegraphsweperformedsomebasicanalysisofeachgraph acrosstherangeofPCTandcontextscores,witharesolutionof0 : 02. 28

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Chapter3.ResultsandDiscussion Figure3.3:Comparisonofdegreechangefromhour6tohour72post-infection. Top :Thechangesaresortedbasedonpercentchangeindegree. Bottom :The sameorderingisappliedtothemiRNAsabsolutechangeindegree. Todothisanalysisrequiredthatwedecomposethespaceofpossibletargets. Recallinsection1.3.1wedenedthespaceofpotentialmiRNAtargetsasM.Using themeasuresprovidedbytheTargetscanalgorithmwemodifyourmapping T s.t. T pct;context : m i M .Where 8 mRNA 2 T pct;context m i thebindingof m i to eachmRNAisassociatedwith pct and context scoresexceedingtheminimum thresholds.Theremainderofthegraphisconstructedinanidenticalmanner, where m i isadjacentto m j ifandonlyif T pct;context m i T T pct;context m j 6 = ; 29

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Chapter3.ResultsandDiscussion Figure3.4:Comparisonofdegreechangefromhour24tohour72post-infection. Top :Thechangesaresortedbasedonpercentchangeindegree. Bottom :The sameorderingisappliedtothemiRNAsabsolutechangeindegree. 3.2.1AverageDegree Giventhegraphstructuredescribedin3.2and1.3.1 Foreachgraph, G = V;E ,wecomputedtheaveragedegreeofanodein G Denedas A G = 2 j E j j V j 30

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Chapter3.ResultsandDiscussion Figure3.5:anti-correlationdirectedbipartitenetworkmapformiRNAupat time6.WeseethemiRNAhererepresentedbycirclesandtheirtargets,mRNA, representedbyrectangles.Thecolorintensitycorrespondstotheexpressionvalue ofthatmiRNAormRNA. Weseeingure3.6thattheaveragedegreedecreasesasthePCTandcontext thresholdsincrease.Thisndingalignswithwhatwewouldexpectofthegraphs asthenumberofviabletargetsdeclines. 31

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Chapter3.ResultsandDiscussion Figure3.6:AveragedegreeofeachgraphatthegivenPCTandContext.The originisinthetopleft,wherethegraphiscompletelyconnected. Wethencomputedthedierencebetweenthetotalnumberofnodesinthe graphandtheaveragedegreeofthegraph,seegure3.7c. 3.2.2GraphDensity Thedensityofagraph, G ,providesausefulmeasureofhowconnected G is.GiventhatourtransformationtomiRNA:miRNAinteractionscanbemost 32

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Chapter3.ResultsandDiscussion aAverageDegree bTotalNodes cTotalminusAverageDegree Figure3.7:WeexaminedtheaveragedegreeofeachmiRNA:miRNAgraphgeneratedforagivenProbabilityofConservedTargetingandContextscoreandthen askedhowmuchtheaveragedegreeofanodeinthegraphdiersfromthetotal numberofnodes,i.e.,howcloselyitistobeingcompletelyconnectedthedistance fromonenodetoanyothernodeis1 easilyinterpretedasanapproximationofpossibledirectandindirectmiRNA cooperation,wehypothesizethatthehighdensityofmanyofournetworksreveals thatmiRNAcooperationisveryimportantandmayevenbenecessarytoproper regulatorycontrol.Alternatively,wemayinterprettherelativelyhighdensity asanindicationofevolvedrobustness,anextremelyimportantaspectofcomplex networks.Thishighconnectivitymaybeimportanttobiologicalsystemsasfailure ofmiRNAregulationmayunderscoresomecancers[18,44]anddisease. Weobservedthatovertheinfectiontimecoursethedensityofthegraphs tendedtoincreaseFigure3.8.Thiscorrespondswiththeobservationthatthe 33

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Chapter3.ResultsandDiscussion aT6Density bT24Density cT72Density Figure3.8:Thedensityofeachgraphiscomputedandvisualizedasaheatmap withrespecttopctandcontext numberofmRNAexpressedaboveourthresholdcutoincreasesoverthetime course.However,weshouldnotethattheincreaseindensity,whilearesultof theincreaseinedgesmRNA,alsoindicatesthatthenumberofnodesmiRNA beingconnectedtothegraphisgrowingmuchslowerthantheratewhichedges arebeingadded. TheincreaseindensityoverthetimecourseFigures3.8a,3.8b,and3.8c correspondswithourobservationsintheanalysisoftheexperimentaldataandthe directedmiRNA:mRNAnetworksthatthenumberofmRNAexpressedaboveour thresholdincreasesoverthetimecourse,thusresultinginanincreasedlikelihood thatedgeswillbeaddedtographs.HigherdensityimpliesmiRNAnodesare becomingbetterconnectedasmRNAedgesareadded.Itismorelikelythata newedgewillconnecttwomiRNAalreadypresentconnectedthanthatanew edgewillconnectapreviouslydisconnectedmiRNAtotherestofthegraph. 34

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Chapter3.ResultsandDiscussion 3.2.3BetweennessCentrality ThebetweennesscentralityanalysisofthemiRNA:miRNAgraphsrevealed manymiRNAnodeswithrelativelylargeshiftsincentrality.BecauseweperformedthisanalysisonnearlytheentirespaceofPCTandcontextscores,more than2400plotswererenderedgeneratedfrom7500miRNA:miRNAgraphs.All code,data,andguresareavailableuponrequestandincludedasastatic"media appendix".Wewillonlypresentafewoftheavailablegureshere. ThePeaktoPeakptpscorewascomputedforeachmiRNAbetweenness centralityvectore.g.,intable2.1,theptpscorecorrespondstothebetweennesscetralityscoresattainedbyasinglemiRNAacrossthetimecourseandthe miRNAweresortedonthisscore.Wethentookoutthetop20%ofmiRNAs basedontheirptpvaluesandcomparedthemtothemiRNAfromthemicroarray experimentwhichpassedthemoststringenttests,describedinsection2.2,aswell asafoldchangethresholdof1 : 8.Theoverlapneverexceeded8%.Seegure3.10. TogaugetheoverlapofallmiRNApresentinthemiRNA:miRNAnetworkwith themiRNApresentinthedatasetfromthemicroRNAarrayweperformedthe samecomputationwithoutlteringthemiRNAfromthenetwork,asthemiRNA expressiondatahasbeendeterminedtobeofquestionablequalityinotherinvestigationsnotdiscussedherepersonalcommunicationsHart.Thisisseenin 35

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Chapter3.ResultsandDiscussion Figure3.9:MicroRNABetweennessCentralityPeaktoPeakScore.HerePCT= Context=0.6.MicroRNAarealongthex-axisandthecorrespondingptpscores onthey-axis. gure3.11.Theoverlapofthesetwosetspeakedatapproximately13%ofthe totalmiRNAs. Itispossibletocalculatebetweennesscentralityonmultigraphs,however,the toolsweusedintheanalysis,partofthenetworkxpackage,arenotdesigned todothis.Inaddition,thecomputationsonthebinarygraphswerealreadya 36

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Chapter3.ResultsandDiscussion Figure3.10:Percentoverlapofthetop20%ofmiRNAnodesbybetweennessshift withthesetofmiRNAfromthemicroarraywithap-valueoflessthan0.05 signicantcomputationalendeavorand,asnoted,thecomputationtimeincreases withthenumberofedges. Wemeasuredoverlapbymakingthefollowingcomputation Over X;Y = j X T Y j j X S Y j foreachsetofmiRNAwithXspecictothegraphresultingfromthegiven PCTandcontext,andYthemiRNAwithap-value 0 : 05fromthemicroarray. 37

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Chapter3.ResultsandDiscussion Figure3.11:PercentoverlapofallmiRNAnodesfromthemiRNA:miRNAnetworkwiththesetofmiRNAfromthemicroarraywithap-valueoflessthan0.05 asPCTandContextvary 3.2.4BetweennessVersusDegreeChange AscatterplotofbetweennesscentralitychangeversusdegreechangewasrenderedforeveryPCTandcontextcombination.Again,wepresentonlyasampling oftheavailablegureshereFigure3.12. Asweseeinthecomparisonoftherandomizednetworksgure3.13our actualdataisfardierentfromwhatwegetwhenweshuetheedges. 38

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Chapter3.ResultsandDiscussion Figure3.12:ThePeaktoPeakscoreformiRNAbetweennesscentralityversus thedegreechangeforthatmiRNAwasscattered.Here,weseethescatterplot forPCT=Context=0.6. 3.2.5ExplorationofthePCTandContextGraphSpace Examiningsecond,third,andfourthmomentsaboutthemeanforthedegree distributionofeachinstanceofagraphaparticularPCTandContextreveals asignicantlyhighervariancewhenbothPCTandcontextarerelativelylow. VariancedropsosignicantlywhenPCTisgreaterthan0.1orContextisgreater than0.3. 39

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Chapter3.ResultsandDiscussion Figure3.13:Comparisonofthedatafromgure3.12withrandomizednetworks. Hereaplus+denotesrandomizeddataandaredcircleisactualdata. aVariance bSkew cKurtosis Figure3.14:BinaryEdgeGraphDegreeStatistics 40

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Chapter3.ResultsandDiscussion aVariance bSkew cKurtosis Figure3.15:MultigraphDegreeStatistics 3.2.6ConclusionandFutureResearch AnalysisofmiRNAregulatorysignicancefromtheperspectiveofbetweenness centralityallowstheselectionofmiRNAsbasedonlyonmRNAexpressiondata. However,aswehaveseen,thismethodofanalysisdidnotalignwellwiththe expressiondatagatheredusingthemicroarrayassay.Thediscrepanciesbetween thebetweennesscentralityanalysisandthemicroarraydatadoesnotnecessarilymeanthatthecentralityanalysisyieldslesssignicantorinterestingresults. MicroRNAnodesundergoinglargeshiftsincentralityoveratimecoursemaybe signicantintermsofeithercooperativeregulationofmRNAorasinhibitorsof othermiRNAbinding.ItisoftenthecasethatmiRNAbindingsitesoverlapon 3'UTRs.This,alongwiththefactthatasinglemiRNAis,insomecases,not enoughtoinhibittranslationordirectthemRNAfordegradationcouldmean 41

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Chapter3.ResultsandDiscussion thatmiRNAsarecapableofpreservingmRNAsignalfromothermiRNAswhich wouldotherwisebindanddegradethemessage. Thereareseveralmethodsforidentifyingtheskeletonofanetwork,aspecial caseofaspanningtree.Tocreatetheskeleton,edgesareremovedbasedon theiredgebetweennessscore,ameasurewhichisidenticaltothebetweenness centralityscorebutcomputedforedgesratherthannodes.Thismethodwould beespeciallyusefulinidentifyingthehubsofthesemiRNAnetworkswhenusing expressiondatatoweightedges.Theskeletonisusuallycomputedasameansof removing"shortcuts"fromhighlyconnectedclusters.Thisissometimesusedto identifypotentiallyscalefreenetworksandimprovegraphvisualization. Deninganedgeweightfunctionforthesenetworksisanotherproblemunto itself.WedidnotwishtopartitionthenetworksbysplittingthemRNAintoup ordownsetsateachtimepoint,thismeanswecanhavenegativeedgeweights resultinginthepossibilityofacyclewithnegativetotalweight.Normalizing theexpressiondatawasnotagoodsolutioneitherastheedgeweightsarethen highlydependentonthemRNAwiththelargestfoldchange,yieldingdatathat isdiculttocompare. 42

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