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NipahVirusClassificationviaFractalDimensionShannonEntropyToddHolden,N.Gadura,E.Cheung,P.Schneider,G.Tremberger,Jr.,N.Elham,D.Sunil,D.Lieberman,andT.CheungPhysicsandBiologyDepartmentsCUNYQueensboroghCommunityCollegeBayside,NY11364USAContactemailtholdenqcc.cuny.eduAbstractNipahvirusglycoproteinandnucleoproteinsequenceswerestudiedusingfractaldimensionandShannonentropy.Thenucleotideatomicnumberfluctuationformsthebasisofthephylogenystudy.Theclassificationreproducesthemainresultsoftraditionalphylogenyanalysis,butwithbetterabilitytodistinguishcloselyrelatedstrains.ThefractaldimensioncorrelationwiththeGCpaircontentintheglycoproteinsequenceanddinucleotideentropyinthenucleoproteinsuggestsdifferentevolutionarymechanismsorstrategies.ExtensiontootherfluvirussuggeststhatlowfractaldimensionalityinthenucleoproteinsequencecouldbeamarkerfortheNipahandSpanishflulikeviruses.KeywordscomponentNipahvirusglycoproteinnucleoproteinShannondinucleotideentropyfractaldimensioncorrelationI.INTRODUCTIONCloselyrelatedvirusescanbeclassifiedbyacollectionofphylogeneticmarkerswithnumbersdeterminedfrommathematicaloperationsonDNAsequence.Incaseswheresuchmarkersdiffersignificantlyfromwhatwouldbeexpectedforrandommutations,wecangetanideaofhowmuchnaturalselectionhasinfluencedtheevolutionofaparticularsequence.NipahvirusisazoonoticinfectiousvirusresponsibleforoutbreaksamongpigfarmersinAsia.Phylogenyandreplicationviaacelltocellspreadingmechanismwasreported1.Fatalencephalitiscaseswerealsoreported2.Here,weanalyzethevirusglycoproteinandnucleoproteinsequencesusingnucleotideentropy,dinucleotideentropy,andfractaldimension.Weexaminetherelationshipoftheabovementionedphylogeneticmarkerstoshedlightonwhetherthereisselectionpressureresultinginsystemicnucleotidefluctuationtrendanditscorrelationwithsequencefunctionality.Thenucleotidebasepairchangesoveragenesequencecanbeviewedasafluctuationand,consequently,canbeinvestigatedwithtoolsthatincludecorrelationandfractaldimensionanalysis.Forthisstudy,thenumericalsequencerepresentingthenucleotidesinagenesequencewasgeneratedusingtheprotonnumberofeachnucleotide.Nucleotidefluctuationhasbeenstudiedusingotherassignmentschemes3,4,5.TheuseofprotonnumberwasmotivatedpartlybytheobservationofmassfractaldimensionintheXraydataofproteinsandribosomes6,andusingaprotonassignmentschememayrevealprotonsensitivityintheunderlyinggeneticsequencetothefoldinginducedmassfractal.Arecentcomparisonofhumanandchimpanzeegenomesrevealedthatitispossibletomeasuretheaccelerationrateoftheacceleratedregionsofthehumangenome7.Fractalanalysisoftheseacceleratedregionsshowedthatthedifferencesinfractaldimensioncanbeusedasamarkerofevolution.8.Additionalimplicationsofevolutionandpositiveselectionhavebeendiscussedinrecentliterature9.II.METHODSA.GeneticSequenceTheNipahvirusstrainsequencesweredownloadedfromGenbankusingtheaccessionnos.inReference1.Additionalflusequences,SARSCoVsequences,16SrRNA,12SrRNA,etc,weredownloadedsimilarly.Duetothelimitedspaceinthispaper,weaskinterestedreaderstocontactusforfurtherdownloadinformation.B.HiguchiFractalMethodTheATCGsequencewasconvertedtoanumericalsequencebyassigningtheatomicnumber,thetotalnumberofprotons,ineachnucleotideA70,T66,C58,G78.Theassignednumberisproportionaltothenucleotidemassignoringisotopes.TheATandCGpairsindoublestrandedDNAhavethesamevalueof136.Amongthevariousfractaldimensionmethods,theHiguchifractalmethodiswellsuitedforstudyingsignalfluctuationandhasbeenappliedtonucleotidesequences10.ThenumericalsequenceIcouldbeusedtogenerateadifferenceseriesIjIifordifferentlags.ThenonnormalizedapparentlengthoftheseriescurveissimplyLkΣ|IjIi|forallpairswherejiequalsk.Thenumberoftermsinakseriesvariesandnormalizationmustbeused11.IfIiisafractalfunction,thenaplotoflogLkversuslog1/kwillbeastraightlinewiththeslopeequaltothefractaldimension.Higuchiincorporatedacalibrationdivisionstepdivisionbyksuchthatthemaximumtheoreticalvalueiscalibratedtothetopologicalvalueof2andaminimumvalueof1.TheHiguchifractalalgorithmusedinthisprojectwascalibratedwiththeWeierstrassfunction.ThisfunctionhastheformWxΣanhcos2πanxforallthenvalues0,1,2,3ThefractaldimensionoftheWeierstrassfunctionwasgivenby2hwherehtakesonanarbitraryvaluebetweenzeroandone.TheprojectwaspartiallysupportedbyseveralCUNYgrants.9781424447138/10/25.00©2010IEEEC.ShannonEntropyCalculationTheShannonentropyofasequencecanbeusedtomonitortheleveloffunctionalconstraintsactingonthegene12.AsequencewitharelativelylownucleotidevarietywouldhavealowShannonentropymoreconstraintintermsofthesetof16possibledinucleotidepairs.Asequencesentropycanbecomputedasthesumofpilogpioverallstatesiandtheprobabilitypicanbeobtainedfromtheempiricalhistogramofthe4nucleotidesor16dinucleotidepairs.Themaximumentropyistwobitspermononucleotidewithfourpossibilities22.Themaximumdinucleotideentropyis4binarybitsperpairfor16possibilities24.III.RESULTSANDDISCUSSIONA.GlycoproteinsequencenucleotidefluctuationThefractaldimensionandShannondinucleotideentropyoftheglycoproteinsequencesoftheNipahvirusstrainsaredisplayedinFig.1.Thedataclustersintothreegroups.TheBangladeshstrainhasthehighestentropywhiletheCambodiastrainhasthelowestentropy.TraditionalphylogenyanalysisputtheBangladeshstrainwiththelargestdistanceandtheCambodiastrainatthesmallestdistanceFigure1BofReference1.ThelargestgroupclustersatlowerfractaldimensionvaluesandthedetailsaredisplayedinFig2.TheUMMC2strain,Serembanstrain,UMMC1strain,andCDCstrainformsasubgrouphavingsimilarfractaldimensionandentropyvaluesconsistentwithtraditionalphylogenyanalysisresult.OuranalysissplitstheMalaysiastrainCrossawaytheUM0128andSungaiBulohstrainsSquarewhilethetraditionalphylogenyanalysisgroupsthesethreestrainstogether.ItappearsthattheclassificationviafractaldimensionandentropymayhaveslightlybetterabilitytodistinguishcloselyrelatedstrainsascomparedtothetraditionalphylogenyanalysismethodusedinReference1.3.8963.8973.8983.8993.93.9013.9023.9033.9043.9051.9751.981.9851.991.995Figure1ThexaxisrepresentsfractaldimensionandtheyaxisrepresentsShannondinucleotideentropy.DiamondBangladeshstrain,SquareCambodiastrain,TrianglesTambunstrain,Malaysiastrain,UM0128strain,SungaiBulohstrain,UMMC2strain,Serembanstrain,UMMC1strain,andCDCstrain.3.90223.90233.90243.90253.90263.90273.90283.90293.9033.90313.90321.97731.97741.97751.97761.97771.9778Figure2ThexaxisrepresentsfractaldimensionandtheyaxisrepresentsShannondinucleotideentropy.DiamondTambunstrain,CrossMalaysiastrain,SquareUM0128strainandSungaiBulohstrain,TriangleUMMC2strain,Serembanstrain,UMMC1strain,andCDCstrain.ThefractaldimensionofthesequencesisfoundtobeassociatedwiththeGCdinucleotidepaircontent.TheclassificationofthestrainsintothreeclustersasdisplayedinFig1showsupinFig3aswell.ThefractaldimensionandGCcontentclassificationnotonlyproducesthreeclusters,butalsosuggestsacorrelationwithR2ofabout0.9withN10.ItwasreportedthattheNipahviruscanusethemonocytestocrossthebloodbrainbarriercausingfatalencephalitis.TheeffectivenessofattachmenttothemonocytescoulddependontheGCcontentandproduceevolutionarypressure.y0.2708x0.5025R20.89230.03150.0320.03250.0330.03350.0340.03450.0350.03550.0360.03650.0371.9751.981.9851.991.995Figure3ThexaxisrepresentsfractaldimensionandtheyaxisrepresentsGCcontentN10B.NucleproteinsequencenucleotidefluctuationThefractaldimensionandShannondinucleotideentropyofthenucleoproteinsequencesoftheNipahvirusstrainsaredisplayedinFig.4.Thedataclustersintotwogroups.TheBangladeshstrainhasthehighestentropywiththerestoftheninestrainsneareachotheratlowerentropyvalues.TraditionalphylogenyanalysisputtheBangladeshstrainhavingthelargestdistance,andCambodiastrainasthenearbyneighboringsequence.TheFigure4distancebetweenBangladeshstrainDiamondandtheCambodiastrainSquareisalsothesmallest,consistentwiththetraditionphylogenyanalysisresultinFigure1AofReference1.TheclosenessoftheMalaysiastrainCrosswiththeothersequencesStarinFig.4isalsoconsistentwiththeresultofReference1.asthetopthreestrainshavingthelargestdistancesrespectively,andputtheremainingstrainstogetherhavingtheleastdistance.OuranalysissplitstheTambunstrainTriangleinFig.4fromtheremainingstrainsasthestrainhavingthelowestfractaldimension.Aregressionanalysisofthe9strainsexcludingtheBangladeshstrainshowscorrelationwithR2at0.9Fig.5.Theevolutionarymechanismofthenucleoproteinsequenceisdifferentfromthatoftheglycoproteinsequence.ItwasreportedthattheTambunstrainhavecausedthehighestfatality2,andtheassociationwithlowfractaldimensionalitywouldbeaninterestingissue.AnextensiontoincludeothervirusnucleoproteinsequenceswasperformedandtheresultisdisplayedinFigure6.3.9053.9063.9073.9083.9093.913.9113.9123.9133.9143.9151.9961.99822.002Figure4ThexaxisrepresentsfractaldimensionandtheyaxisrepresentsShannondinucleotideentropy.DiamondBangladeshstrain,TriangleTambunstrain,SquareCambodiastrain,CrossMalaysiastrain,StarUM0128strain,SungaiBulohstrain,UMMC2strain,Serembanstrain,UMMC1strain,andCDCstrain.y0.3998x4.7048R20.88063.90543.90563.90583.9063.90623.90643.90663.90681.9961.9971.9981.999Figure5ThexaxisrepresentsfractaldimensionandtheyaxisrepresentsentropyN93.8653.873.8753.883.8853.893.8953.93.9053.913.9153.921.941.961.9822.02Figure6ThexaxisrepresentsfractaldimensionofthenucleoproteinsequenceandtheyaxisrepresentsShannondinucleotideentropy.DiamondNiphavirusCrossSARSCoVSquareSwineflu,Avianflu,Spanishflu,andH2N2NetherlandsfluTriangleH2N2Koreaflu,H3N2CheongJuflu,andH3N2NewYorkfluCross16SrRNAgorilla,chimp,neanderthals,andhumanCircle12SrRNAgorilla,chimp,neanderthals,andhuman.TherelatedHendravirusnucleoproteinsequencehasfractaldimension1.991andentropy3.915bits,notshownUsingthe16SrRNAand12SrRNAsequencespreadsasguides,theevolutionarypressureexperiencedbythestudiedvirusnucleoproteinsequenceswouldbeofthesameorderofmagnitudeasthestudiedribosomalRNAsequences.AmongtheSwineflu,Avianflu,Spanishflu,andH2N2Netherlandsflucluster,thehighestfatalitySpanishflu13,14alsohasthelowestfractaldimension1.97,similartothehighestfatalityassociatedwiththelowestfractaldimensionNipahvirusTambunstrain2.TheSARSCoVclosenesstotheNipahclustercouldbeindicativeofitsbatorigin15.Futurestudycanincludethosevirusesthathaveinternalribosomeentrysites,forexample,therhinovirus16.IV.CONCLUSIONThefractaldimensionandShannonentropywereusedtoanalyzethenucleotidefluctuationoftheglycoproteinandnucleoproteinsequencesintheNipahvirus.Theclassificationrecapsthemainresultsoftraditionalphylogenyanalysis,butwithbetterresolution.ThefractaldimensioncorrelationwiththeGCpaircontentintheglycoproteinsequenceanddinucleotideentropyinthenucleoproteinsuggestsdifferentevolutionarymechanismsorstrategies.ExtensiontootherfluvirussuggeststhatlowfractaldimensionalityinthenucleoproteinsequencecouldbeavirulentmarkerfortheNipahandSpanishflulikeviruses.REFERENCES1LiYenChang,SazalyAbuBakar,NipahvirusPhylogenyandreplication,NeurologyAsia1463–66,2009.2AbuBakarS,ChangLY,MohdAliAR,SharifahSH,YusoffK,ZamrodZ.IsolationandmolecularidentificationofNipahvirusstrainsfrompigs.EmergInfectDis10222830,20043N.N.OiwaandJ.A.Glazier,Thefractalstructureofthemitochondrialgenomes,PhysicaA,vol311,pp221–230,2002.4Z.G.Yu,A.Vo,Z.M.GongandS.C.Long,FractalsinDNAsequenceanalysis,ChinesePhysics,vol11,pp13131318,2002.5H.D.Liu,Z.H.Liu,X.Sun,StudiesofHurstIndexforDifferentRegionsofGenes,ICBBE2007,pp238240,2007.6C.Y.Lee,MassFractalDimensionoftheRibosomeandImplicationofitsDynamicCharacteristics,PhysicalReviewE,vol73,0429013pages,2006.7K.S.Pollard,S.R.Salama,N.Lambert,S.Coppens,J.S.Pedersen,etal.AnRNAgeneexpressedduringcorticaldevelopmentevolvedrapidlyinhumans.Nature,vol443,pp167172,2006.8T.Holden,R.Subramaniam,R.Sullivan,E.Cheung,C.Schneider,G.Tremberger,Jr.,A.Flamholz,D.H.Lieberman,andT.D.Cheung,ATCGnucleotidefluctuationofDeinococcusradioduransradiationgenes,Proc.SPIE,vol6694,669417,10pages,2007.9PollardKS,SalamaSR,KingB,KernAD,DreszerT,etal.Forcesshapingthefastestevolvingregionsinthehumangenome,PLoSGenet210e168.DOI10.1371/journal.pgen.0020168,200610M.J.Berryman,A.Allison,andD.Abbott,MutualInformationforexaminingcorrelationsinDNA,FluctuationNoiseLetters,vol4,ppL237L246,2004.11T.Higuchi,Approachtoanirregulartimeseriesonthebasisoffractaltheory,PhysicaD,vol31,277283,1998.12Parkhomchuk,DV,DinucleotideEntropyasaMeasureofGenomicSequenceFunctionality,arXivqbio/0611059,200613NelsonMI,ViboudC,SimonsenL,BennettRT,GriesemerSB,MultipleReassortmentEventsintheEvolutionaryHistoryofH1N1InfluenzaAVirusSince1918.PLoSPathog42e1000012.doi10.1371/journal.ppat.1000012,200814TokikoWatanabea,ShinjiWatanabea,KyokoShinyab,JinHyunKima,MasatoHattaa,andYoshihiroKawaokaa,ViralRNApolymerasecomplexpromotesoptimalgrowthof1918virusinthelowerrespiratorytractofferrets,PNAS,vol.106,588–592,200915JieCui,NaijianHan,DanielStreicker,etal,EvolutionaryRelationshipsbetweenBatCoronavirusesandTheirHosts,EmergInfectDis13152632,200716AnnC.Palmenberg,etal.EvolutionRhinovirusGenomesRevealStructureandSequencingandAnalysesofAllKnownHuman,ScienceVol324,5559,2009
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