538BiochemicalSocietyTransactions(2013)Volume41,part2 - PDF document

538BiochemicalSocietyTransactions(2013)Volume41,part2 KnotlocalizationinproteinsEricJ.Rawdon*,KennethC.Millett,JoannaI.Su›kowska‚§andAndrzejStasiak*DepartmentofMathematics,UniversityofSt.Thomas,2115SummitAvenue,St.Paul,MN55105,U.S.A.,DepartmentofMathematics,UniversityofCaliforniaSantaBarbara,552UniversityRoad,SantaBarbara,CA93106,U.S.A.,CenterforTheoreticalBiologicalPhysics,UniversityofCaliforniaSanDiego,9500GilmanDrive,SanDiego,CA92037,U.S.A.,FacultyofChemistry,UniversityofWarsaw,Pasteura1,02-093Warsaw,Polandand Thebackbonesofproteinsformlinearchains.Inthecaseofsomeproteins,thesechainscanbecharacterizedasforminglinearopenknots.Theknottypeofthefullchainrevealsonlylimitedinformationabouttheentanglementofthechainsince,forexample,subchainsofanunknottedproteincanformknotsandsubchainsofaknottedproteincanformdifferenttypesofknotsthantheentireprotein.Tounderstandfullytheentanglementwithinthebackboneofagivenprotein,acompleteanalysisoftheknottingwithinallof Fromthefirstdiscoveryofknotsinthebackbonesofproteins TopologicalAspectsofDNAFunctionandProteinFolding539 Figure1 MatrixpresentationsfortheproteinswithPDBcodes3FR8(left)and2WSX(right)Eachsquarecellinthematrixshowstheknottypeofonesubchainoftheprotein.TheN-terminalaminoacidpositionofthatsubchainisindicatedonthe-axis,anditsC-terminalaminoacidpositionisindicatedonthe-axis.Thusthelower-left-handcornershowstheknottypeoftheentirechainandcellsnearthediagonalcorrespondtoveryshortsubchainsoftheprotein.Theintensityofthecolourwithineachcellcorrespondstothepercentageofclosuresformingthegivendominantknottypeforthesubchain.Thecolourbarontherightshowstheknottypesobtainedfortheproteinaswellasagradientforthecolouringintensitybystepsof10%.Forchiralknottypes,thesignsindicatetheright-andleft-handedforms CharacterizingtheknottinginproteinsBeforewediscusstheknottingpatterns,wemustbeclearabouthowweclassifyknottinginanopenchain.Indeed,definingtheknottypeofanopenchainisaninterestingprobleminitselfanddifferentalgorithmsarediscussedinanotherarticleinthisissueofBiochemicalSocietyTransactions[8].Inthatarticle,wepresenttheuniformclosuremethod[9–11],wherebytheknottingofanopenchainisclassifiedasadistributionofknottypesobtainedbyconnectingthefreeendsoftheopenchaintopointsuniformlychosenonalargesphereenvelopingthechain.Thedominantknottypeisthenlabelledastheknottypeofthechain.Fortheremainderofthepresentarticle,weusethatstrategytoclassifythetypesofknotsinopenchains.Oncewehaveagreedonhowtodefinetheknottingofanopenchain,wecancomputetheknottypeoftheentireproteinchainandofallofitssubchains.Kingetal.[7]definedamatriximagepresentationforencodingtheknottingofallsubchainsofagivenprotein.In[11],webuiltonthispresentationusingtheuniformclosuremethod[8–10].Figure1explainshowtoidentifytheknottingwithinthesubchainsofaproteinfromitsmatrixpresentation.Knottedproteins,suchasketol-acidreductoisomerasefromrice(PDBcode3FR8)havethelower-left-handcornerofthematrixpresentation(correspondingtotheknottypeoftheentireproteinchain)coloured,whereasslipknottedproteins,suchasthecarnitinetransporterfromEscherichiacoli(PDBcode2WSX),containcolouredregionselsewhereinthematrix,buthaveagreylower-left-handcorner(signifyinganunknottedarc).Inadditiontoknotsandslipknots,wesometimesobserveisolatedregionsinthematrixpresentationcontainingthesameknottype,asinthetwotrefoilregionsfor2WSX.Knotting“ngerprintsForagivenprotein,weusethetermknottingfingerprinttodenotetheentiretyoftheknottinginformationpresentinthematrixpresentation,includingtypesofknotspresentandtheregions’sizesandshapes.Forknottedorslipknottedproteins,oneseesatleastoneroughlyrectangularregionofknotting.Eachsuchregioncorrespondstoanestedsetofsubchainswithaparticularknottype.Theshortestsubchainwithintheregion(thesubchaincorrespondingtothecellclosesttothediagonal)oftheparticularknottypedefinestheknottedorslipknottedcore.Theroughlyrectangularknottingregionsarenotalwaysfullyfilledin,sincetheboundariesaretransitionareaswhereonecanhavetwoormoreknottypeswithsimilarprobabilities.Becauseofthenearlyconstantdistancebetweensequentialcarbonsandthestericexclusionofpolypeptidechains,proteinsbehaveessentiallyassmooththicktubes[12].Forthisreason,theknottingfingerprintsofproteinsarerathertame,i.e.changingasubchainlengthbyoneaminoacidcanresultinachangeofknottypethatcouldbeproducedbyatmostoneintersegmentalpassage[13].Suchabehaviourwouldnotbeexpectedforrandomchains,forexample,whereshorteningasubchainbyonesegmentcanresultinachangeofknottypethatwouldrequiremorethanoneintersegmentalpassage.Byobservingsomeknottingfingerprints,wecanseewhythesearchfortheknottedcoresometimesgivesadifferentresultwhenitiscarriedoutusingatop-downapproachincontrastwithabottom-upapproach[14].Inthetop-downapproach,oneremovesterminalverticesuntiltheknottypedetectedfortheentireproteinisnolongerpresent,whereasinthebottom-upapproach,onesearchesfortheshortestsequenceofaminoacidsformingthesameknotastheentireprotein.TheknottingfingerprintoftheDehIprotein(PDBcode3BJX)(Figure2A)showsthatthetop-downapproachwouldgivea6coresizethatisapproximately40aminoacidslargerthanthe6coresizedetectedusingthebottom-upapproach.Alsonotethattheprecisepatternintheknottingfingerprintdependsonthealgorithmusedtodeterminetheknottypeofanopenchain.WhentheterminiofanopenTheAuthorsJournalcompilation2013BiochemicalSociety 540BiochemicalSocietyTransactions(2013)Volume41,part2 Figure2 MatrixpresentationsfortheproteinswithPDBcodes3BJX(left)and2AXC(right)Left:thedeterminationoftheknottedcorefortheDehIprotein(PDBcode3BJX)variesbyapproximately40aminoacidsdependingonwhetheroneusesatop-downorbottom-upapproachsincetherearetwodistinctregionsformingthe6knot.Right:theN-terminaltranslocationdomainforcolicinE7inE.coli(PDBcode2AXC)showsfourdifferenttrefoilregions. Figure3 TheubiquitinC-terminalhydrolasesfrom(PDBcode2WDT)(left)andhumans(PDBcode3IRT)(right)havealmostidenticalknotting“ngerprintsdespiteonly32%sequencesimilarity chainareonthe‘outside’ofachain(whichistypicallythecasefortheentireproteinchain),thedifferentalgorithmsgenerallyagreeinassigningaknottypetothechain.However,whentheterminiare‘nearthecentre’ofachain(whichhappensextensivelywhenanalysingsubchainsofproteins),thealgorithmscandisagreeinassigningaknottypetothechain.Thesingleclosurealgorithms(suchaschainsimplification)[8]oftenrequiresome‘choices’tobemadeinordertoassignanappropriateclosure,andthusknottype,forthechain.Thestochasticalgorithms,suchastheuniformclosureprocedureusedhere,requireno‘choices’intheseambiguoussituationssincetheyuniformlysamplefrompotentialknottedstatesandthusremainunbiased.Forexample,in[11],wefoundthattheLeuT(Aa)protein(PDBcode2A65),containssubchainsforming3and4knots.Kingetal.[7]found3and5knotsfor2A65.The‘choices’one,inevitably,isforcedtomakewhenusingsingleclosurealgorithmsisaseriousdeficiencyintheapproach,andthuswebelievethatthestochasticalgorithmsprovideamoresolidcharacterizationoftheknottingwithinsubchains.However,notethat,despitethedifferencesinknotdetectionalgorithms,generallythereisonlyasmallfractionofsubchainsforwhichthedifferentalgorithmsdisagree.Wethencandefineanotationfortheknottingregionspresentintheprotein.WebeginwithaKorS,representingthattheproteiniseitherknottedorslipknottedrespectively.Thisisfollowedbyalistoftheknottypescorrespondingtotheregions(withmultiplicityifthereismorethanoneregionwithagivenknottype)indecreasingorderofknottedcorelengthwithintheregions.Forexample,inFigure1,theprotein3FR8isoftypeK4andprotein2WSXisS3Thisnamingisnotsensitivetothesize,shapeorplacementoftheregionsintheknottingfingerprint.Inparticular,therearemanyproteinsthataredescribedsimplyasK3orS3butwhosematrixpresentationslookmuchdifferent.Onemightassumethattheknottingfingerprintsareuniquetoeachprotein.However,wefoundthatmanyknottingfingerprintmotifsreappearthroughoutourcalculations.Furthermore,wefoundthatproteinswiththesamefunctionindifferentorganismsshowedsimilarknottingfingerprintsdespitelargedifferencesintheaminoacidsequences.Forexample,thematrixpresentationfortheubiquitinC-terminalhydrolases3IRT(human),1CMX(yeast)and2WDT)arenearlyidentical(Figure3)despiteverylowsequenceidentities(rangingfrom25%to32%).ThisknottingfingerprintmotifhaspersistedthroughhundredsofTheAuthorsJournalcompilation2013BiochemicalSociety TopologicalAspectsofDNAFunctionandProteinFolding541 millionsofyearsofevolutionaryseparation,suggestingthattheknottingisindeedcriticaltothefunctionoftheprotein.Wepresentseveralsimilarcasesin[11].Althoughtheexactfunctionoftheknottingisnotyetestablished,thecaseofcloacinsandS-pyocinsprovidespossiblecluestothismystery.CloacinsandS-pyocinsaretoxinswhicharereleasedbysomebacteria.Theyenterotherbacterialcellsviamembranetranslocation.TheknottingfingerprintinFigure2(B)fortheN-terminaltranslocationdomainforcolicinE7inE.coli(PDBcode2AXC)showsfourisolatedregionsof3knots(seetheschematicdrawinginFigure2Btoseehowtheseregionsarecreated).Theproteinformsalargeloopstrappingtogetherseveral-strands.Infollowingthechain,onealternatesbetweenbeingondifferentsidesofthestrappingloop.Ifasubchainterminatesononesideoftheloop,itformsatrefoilknot,butifitterminatesontheothersideoftheloop,anunknotisformed.Sincethelargeloopembracesasignificantportionoftheprotein,oneistemptedtoconjecturethatthisembracingstabilizestherelevantpartsoftheproteins.Thisisconsistentwithresultsofmanyresearchers(see,e.g.,[15–19]).Today,basicinformationaboutknottedproteinsiseasilyaccessiblethroughmanywebpages[20–23]thatallowresearcherstodeterminetheknottypeofaproteinaswellastolocateknottedpositionsalongthebackbone.Furthermore,theentiretyoftheknottingandslipknottingwithintheproteinscannowbevisualizedusingthematrixpresentation.Thefutureanalysisoftheknottingfingerprintmotifswithinthematrixpresentationswillyieldnewcluesintothecriticallinkbetweenthegeometricalconfigurationandthefunctionofproteins. WethanktheIsaacNewtonInstituteforMathematicalSciencesforsponsoringtheTopologicalAspectsofDNAFunctionandProteinFoldingworkshopandforhostingourstaysattheInstitute. 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