E ff ect of Loading on the Adhesion and Frictional Characteristics of Top Layer Articular Cartilage Nanoscale Contact A Molecular Dynami

《E ff ect of Loading on the Adhesion and Frictional Characteristics of Top Layer Articular Cartilage Nanoscale Contact A Molecular Dynami》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

pubs.acs.org/LangmuirArticleEffectofLoadingontheAdhesionandFrictionalCharacteristicsofTopLayerArticularCartilageNanoscaleContact:AMolecularDynamicsStudyAbhinavaChatterjee,DevendraK.Dubey,*andSujeetK.SinhaCiteThis:Langmuir2021,37,46−62ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Articularcartilageisawater-lubricatednaturallyoccurringbiologicalinterfaceimpartinguniquemechanicalandultralowfrictionalpropertiesinbonejoints.Althoughthematerialofcartilage,synovialfluidcomposition,andtheirlubricatingmodesandpropertieshavebeenextensivelyinvestigatedatvariousscalesexperimentally,thereisstillalackofunderstandingofloadbearing,adhesion,andfrictionmechanismsofthecartilage−cartilageinterfacefromanatomisticperspectiveunderheavyloads.Inthisstudy,theeffectofloadingonadhesionandfrictionalbehaviorinarticularcartilageisinvestigatedwithaproposedatomisticmodelfortoplayercartilage−cartilagecontactinunhydratedconditionsusingmoleculardynamics(MD)simulations.Pull-offtestsrevealthatcohesiveinteractionsoccurattheinterfaceduetoformationofheavilyinterpenetratedatomisticsitesleadingtostretchingandlocalizedpullingoffragmentsduringsliding.Slidingtestsshowthatfrictionisload-anddirection-dependentwiththecoefficientoffriction(COF)obtainedintherangeof0.20−0.75attheinterfaceforslidinginparallelandperpendiculardirectionstothecollagenaxis.Thesevaluesareingoodagreementwithearliernanoscaleexperimentalresultsreportedforthetoplayercartilage−cartilageinterface.TheCOFreduceswithanincreaseinloadandtendstobehigherfortheparallelslidingcasethanfortheperpendicularcaseowingtothepresenceoftheconstantnumberofH-bonds.Overall,thisworkcontributestowardunderstandingslidinginunhydratedbiointerfaces,whichistheprecursorofwear,andprovidesinsightsintoimplantresearch.13■INTRODUCTIONpresenceofwater.ThismechanismofboundarylubricationleadstoswellingupandpressurizationresultinginaverylowArticularcartilage(AC)isanaturallyoccurringhierarchicalfrictionalforceandwearlessconditionatthecartilagebiologicalmaterial,whichiswater-filledporousconnective14interface.Incontrasttothis,cartilagesdofail,i.e.,deformtissue,separatedfromopposingcartilagebysynovialfluid,andDownloadedviaUNIVOFPRINCEEDWARDISLANDonMay16,2021at12:23:15(UTC).orwearout,duetocontinuousslidingledbyasetofcascadingofferssuperiorbiomechanicalandlubricatingpropertiesoveraSeehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.mechanisms,i.e.,removalofthefilmandruptureofcollagenlifetimeatthecartilagesynovialinterfaceforthehealthyfibersoccurringatthecartilage−cartilageinterfacialcontactoperationofjoints.ACpossessesvariousmodesoflubricationduetolubricantscarcity.Therefore,theinitiationofwearisunderseveralbiomechanicalconditionslikehigherload,lowmajorlyamechanicalprocessbasedonthenanostructureofvelocitytoimpartsuperiorload-bearingcharacteristics,lowertheporoustissue.adhesion,andcoefficientoffriction(COF=0.0005−0.04)at1−3Thearrangementandtangentialorientationofcollagentypethesynovialjointinterfaces.AmongtheseverallubricationIIfibersatthetopmostsuperficialamorphouslayer(SAL)ofmechanismsproposedtilldate,themixedandtheboundarycartilageareassumedtoprovideresistanceagainstshearwhenlubricationsaredominantwhenjointsareheavilyloaded,and15cartilagesslideagainsteachother.Thefibrillarynetworkofthecartilagesarenotcapableofsupportingafluidfilmin4−8collagenbindsmacromoleculestoprovidenecessaryload-betweenthesolidsurfaces.Athigherloads,theboundarylubricantslikealbumins,phospholipidswithcollagen,andwateratthemolecularasperitylevelcontactsreduceadhesionReceived:August3,2020andprovidelowstaticandkineticfrictionathighlyconfinedRevised:December10,2020geometriesbearinghighcontactstress(1.9−6MPa).9−12Published:December31,2020Aqueouslubricationoccurringatthecartilageinterfaceisassumedtobeduetotherepulsiveinteractioninbetweennegativelychargedpolymerbrushlikeproteoglycansinthe©2020AmericanChemicalSocietyhttps://dx.doi.org/10.1021/acs.langmuir.0c0228346Langmuir2021,37,46−62

1Langmuirpubs.acs.org/LangmuirArticleFigure1.Hierarchicalstructureoftoplayercartilage−cartilagecontactwiththeproposedthree-dimensionalatomisticmodelforMDsimulations.(a)Schematicoftoplayercartilage−cartilagecontactatthekneejoint.(b)TopmostlayeroftheSALintheextracellularmatrix(ECM)madeupofcollagenfibersarrangedtangentiallytotheslidingdirection.(c)SEMimageofcollagenfiberattheknee.Imageobtainedunderthetermsofthe2626CreativeCommonsAttributionLicense.(d)Schematicofprototypicfiber,whichmakesupthecollagenfiber.(e)Representationofcollagen26heterofibril.(f)Atomisticmodelofcartilageintheformofasliderusingarepresentativefragment.(g)CollagentypeIIfragmentchosenforthestudy.(h)Theatomisticrepresentationoftheportionhighlightedwhereoxygen,nitrogen,sulfur,carbon,andhydrogenarerepresentedinred,blue,yellow,gray,andwhitespheres.9,16,17bearingduringcompressionandshearing.Thehydrationaddressthisfundamentalissue,effortshavebeenmadetostateofthecollagenfibersisassociatedwiththemechanicalbridgethegapbetweenthecontinuum-scaleunderstandingpropertiesofthefibers.Atthenanoscale,thesecollagenfibersandtheatomicscaleusingexperimentaltechniqueslikeatomicandhydratedproteoglycansduringheavyloadingareassumedforcemicroscopy(AFM)andsurfaceforceapparatusmicros-18,19tooffermolecular-levelefficientlubricatingproperties.Thecopy(SFA).Despitethesenanotribologicalinvestigations,thetensilebehaviorofcartilageisimpartedbythenetworkofgenesisoflowadhesionandultralowCOFisstillnot20collagenattheinterface.completelyunderstoodfromstructuralandatomicperspec-9Lubricationatthecartilageinterfaceisascale-andtime-tives.Therefore,amoleculardynamics(MD)studyofthetopdependentprocess,andthemechanicalpropertiesarealsointerlayercartilageunhydratedinterfaceissuitableandinfluencedbythetissue-levelpropertieslikemorphologyandrequiredtounderstandhowthemolecular-levelstructural20thestructuralorientationofthecartilage.Tounderstandandpropertiesofthecartilageinterfacecontributetotheload-47https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

2Langmuirpubs.acs.org/LangmuirArticle9bearing,antiadhesive,andlow-frictionalcapabilitiesoftheinfluencestheasperity-leveltribologicalproperties.Thecartilageusinganatomistic-levelanalysis.However,thedepletionofproteoglycansandbreakdownofthecollagenknowledgeofthecompositionofthetoplayercartilagefibrillarnetworkleadtoanincreaseinadhesion,changeintheextracellularmatrix(ECM),surfacemorphology,anditsroleatroughness,degradationofcartilage,andthusleadtoosteo-28theinterfacialcontactisimportant.arthritissequentially.Itisfoundthatthecontentof29Tounderstandthestructure−functionrelationofload-proteoglycanattheSALisveryscarce.Torelatethistobearingcartilageatthenanoscale,thehierarchyofthecartilagetheinitiationofwear,thereisaneedtounderstandthetoplayerandtheinterfacialcontactzoneformedbetweencollagenmolecular-levelactivitieswiththephysiologicalopposingcartilageisillustratedinFigure1.Followingatop-to-loadingofthecartilageinterface.Thiswillalsoprovideinsightsdownapproachofatoplayercartilage−cartilagecontact,theintoin-depthinformationontheloweringoffrictionandload-toplayeroftheextracellularmatrix(ECM)comprisesthreebearingandrevealfailuremechanismsthatwillprovideuniquezones,top,middle,anddeep,whereonlythetopsuperficialsolutionsforimplantresearchusingMDsimulations.amorphouslayer(SAL)isshowninFigure1b.ThetoplayerofThemeasurementofforceanditscorrelationwiththetheSALoftheECMconsistsoftangentiallyarrangedcollagenpolymerstructurestillremainachallengeattheslidingfibers,whichcontributemajorlytothesurfacemechanicalandinterfacesinnanotribologicalexperiments.MoleculardynamicstribologicalpropertiesandareshowninFigure1c.Collagen(MD)studieshavebecomeapotentialtoolforstudyingfibershaveadiameterof200nmandplacedalmost10nmatomic-scalefrictionandconductingslidinganalysisforapart.Basedontheirlocation,thecollagenfibersarestraightpolymers.PreviousMDstudiesreportthefactorsaffectingandhelical-shapedtwinnedproteotypicfibersforhipandkneefriction,i.e.,load,slidingvelocity,slidingdirection,and30joints,respectively,asshowninFigure1d,andaremadeupoftemperatureofmaterials.Thesestudiesalsocomplimentmanycollagenheterofibrils.HeterofibrilsasshowninFigure1emissingunderstandingofthephenomenonsuchasstick−slip,arecircularinthecrosssection,comprisingcollagentypeXIwhichisnotprovidedthroughsmall-scaleexperiments.andcollagentypeIImoleculeswiththelatterinabundance.FrictionstudiesofpolymersrevealinformationonmechanismsThemostabundantproteininthedrystateofcartilageislikeinterfacialbrushing,combing,andchainscissionfor2131collagentypeIIfibrils(20−30%).ThecollagentypeIIpolymer-on-polymersliding.FewMDstudieshavealsomonomeris300nmlongandhasadiameterof1.6nm,whichobservedthedependenceofatomic-scalefrictionofpolymerscomprisesatriplehelixpolypeptidechain,eachchainofwhichonthesurfacechemistrylikethenumberofatomsinteracting32,33isasequenceofthousandaminoacidsmostlyGly-X-Y.Glyacrossthesurfaceandthestructureofthepolymers.representsglycine,andX-Ycanbeanyaminoacid.TheHowever,similarstudiesarepresent,whichhighlighttheatomisticmodeloftoplayercartilageusingarepresentativefactorsaffectingfriction,butamechanicalandfrictionalfragmentofthecollagentypeIImoleculeanalysisonjointproteinsattheatomisticscalerelatingtothe(GPMGPMGPRGPP)ischosenforconstructingthesliderinitiationoffailureinunhydratedcartilagesisrare.Fewstudies22modelinFigure1f.Thecompleteproposedatomisticmodelarepresent,whichproposedasynovialfluidinterlayercartilage34oftoplayercartilage−cartilageunhydratedcontactcomprisesamodelconsideringthemesoscalenatureoftheproblem.sliderandsubstratewithaninterfacialgapinbetweenforAnotherMDstudyonthefrictionalbehaviorinbetweentribologicalstudies.Itisknownthatunderhigh-loadhyaluronicacidandphospholipidsatthecartilageinterfaceis35conditions,somenanoscopiclocalizedcontactzonesinperformed.TheeffectofbreakageofH-bondsandtheroleofsynovialjointscanbecomeunhydratedduetofluidsqueezingdifferentlipidsarealsoinvestigatedtogainmoreinsightinto2336,37outcompletely.Suchzonescanbecomefriction/wearthecartilagetribologyusingmoleculardynamics.Althoughhotspotsandmaystartinfluencingoveralltribologicalbehaviorseveralmechanismsincludingthepolymericbrushtypeofandthereforeareofinterestforfurtherinvestigations.Thisboundarylubricationatthecartilageinterfacearepredicted,simplifiedunhydratedcontactmodelishelpfulinthetheroleofsuperficialtoplayercollagensintheadhesionandincrementalstudyoftheunderlyingloading,adhesion,andload-bearingattheinterfaceintheabsenceofsynovialfluid,shearmechanismsonatoplayercartilage−cartilagecontactwhichcouldleadtowearatveryhighcontactstresses(orderofinterfaceintheabsenceofmolecularconstituentspresentinMPa),requiresin-depthinvestigation.Also,theload-bearingaqueousconditions.Thethreeα1-polypeptidechainsofthezoneisfoundtocontinuouslymigrateattheslidinginterfacescollagentypeIIfragmentchosenasshowninFigure1gareforcartilages.Thus,astudyofthetopcartilagelayermodelidenticalandformedofthesameaminoacidsequenceintheinsteadofpolymer-graftedbrushlubricationissuitableforearliermentionedaminoacidsequence,whereastherearetwounderstandingtheinitializationoffailureinunhydratedα1(I)chainsandoneα2(I)chainforthecollagentypeIconditions.Therefore,ananoscaleMDanalysisofadhesion24molecule.TheatomisticrepresentationofaportionoftheandfrictionisrequiredtostudyfrictionalbehaviorpredictionfragmentanditselementalconstituentsareshowninFigureundertheinfluenceofexternalloadinunhydratedconditions.1h.Accordingtoapreviouscomputationalstudy,aInthisstudy,atopsuperficiallayercartilage−cartilagerepresentativefragmentcanbeanindicatorofitschemicalunhydratedcontactsimplifiedatomisticmodelisdevelopedin25andmechanicalproperties.Thus,theproposedatomistictheformofasliderandsubstratetounderstandtheatomistic-modelisthentestedforitsadhesiveandfrictionalbehavior.levelbehaviorofthemechanismofadherenceattheinter-andTheloadingandslidingbehavioratthecartilagehavebeenintracartilageinterfaceintheunhydratedstateandpredictreportedtomodulatethestiffnessofthestructureoftheECMfrictionalbehaviorduringslidingofthoseinterfaces.Forthethatleadstotailoredbiomechanicalandlubricatingproperties.above,three-dimensionalmoleculardynamicssimulationsonThechangeinthestructure,size,shape,andorientationoftheatomisticcontactmodelareconductedtounderstandthemacromolecules,therefore,affectsthenanoscalemechanicaleffectofexternalloadontheload-bearing,adhesive,and27andshearingpropertiesofthecartilage.Theadhesionfrictionmechanismattheinterfacesusinglarge-scaleatomic/betweenthesemacromoleculesatthetoplayerhighlymolecularmassivelyparallelsimulator(LAMMPS)atthe48https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

3Langmuirpubs.acs.org/LangmuirArticleFigure2.Three-dimensionalproposedatomisticmodelofatoplayercartilage−cartilageunhydratedcontact.(a)Asinglerepresentativefragmentischosenforthedevelopmentofamodelconsistingofthreeidenticalhelicalchainsoftheaminoacidsequence(GPMGPMGPRGPP).Asinglegreenchainhasbeendemarkedwithitsaminoacidconstituents(glycine,proline,andmethionine)ofwhichtheatomicstructureofglycineisexplicitlyshown.(b)Isometricviewoftheproposedatomisticmodelintheformofthesliderandsubstratedepictingonlytwofragmentsbothinitsatomisticandhelicalrepresentations.Eachcylinderrepresentsasinglecollagenfragment.(c)Frontviewoftheproposedatomisticmodeloftoplayercartilage−cartilageunhydratedcontactwiththecollagenfragmentarrangedintotheplanealongitsaxis.(d)Right-handsideviewofthe44proposedatomisticmodel.RenderedusingVMD.atomicscale,whichisnotcompletelyaddressedthroughparameterslikeload,velocity,anddirectionforanunhydrated38experiments.orsparselylubricatedcontact(boundarylubrication).OneofDuetohighcomputationaltimeandcost,fullcollagenthestudiespredictsthatfrictionforcenotonlydependsonthe41microfibrilcontactisnotconsidered.Thisstudyalsoprovidesnormalforcebutalsoontheadhesionofthepolymers.ToinsightintothecontributionofexternalloadingontheCOFobtainnanoscalefrictionbetweensurfaces,theinterfacemustandtheslidingdirectionoftheinterfaces.Furthermore,thisbeclean,atomicallysmooth,andfreeofdefects.Inthestudyisabletopredicttheoverallfrictionalbehaviorofthepresenceofinhomogeneities,theunderstandingoftheunhydratedcartilagecontact.Moreover,onlyafewstudiesfrictionalcontributionscannotbeunderstoodduetostronghavetriedtounderstandthebehavioroftheunhydrateddeviationsowingtothesefactors.cartilage,whichcanbeaprecursorofhighercohesionandmayToconductNEMDsimulationsforcapturingtheadhesiveleadtowearandfailureofthecartilageandadversejointandfrictionalbehaviorofthetoplayercartilage−cartilageconditions.Thepresentstudyalsopredictstheevolutionoftheunhydratedinterface,threestepshavebeenfollowed:first,frictionmechanismfromthenanoscaleduetothearrangementdevelopingtheatomisticmodelofthetoplayercartilage−ofmoleculesandintheabsenceofthelubricantinbetweencartilagecontactinunhydratedconditions,thereafterimposingfibrils.thecomputationalmethodology,andfinallyconductingtheclassicalmoleculardynamicstestforbothadhesiveand■METHODOLOGYANDFRAMEWORKfrictionalpropertiesseparately.ApreviousMDstudyoncollagenadhesionpredictsthatAtomisticModelforTopLayerIntercartilageNano-adhesionforceanddeformationbehaviorofcollagenincreasescaleContact.Toconstructtheatomisticmodelofthetop39layercartilage−cartilageunhydratednanoscalecontact,thewiththedegreeofroughnessofthecollagensurface.Thereisalackofstudytounderstandthecartilage−cartilage(inter)orabovementionedrepresentativecollagentypeIIfragment24intralayercartilageadhesioninbetweenmolecularsurfacesat(GPMGPMGPRGPP)ischosenfromthePDBDatabank.cartilageinterfacesinbiotribology.NonequilibriummolecularThewholecollagentypeIImoleculecontainsthreeidenticaldynamics(NEMD)haslongbeenusedasapotentialα1-polypeptidechainsof1060aminoacidresidues.Thistechniqueforsimulatingnanoscalecontactsandtoobtainfragmentisrepetitiveinnature,inthefibrillarportionofthe40insightsattheatomisticbehaviorofshearing.Mostofthecollagenmolecule,andthuscanbesuitableforamolecularMDstudiesonfrictionaimtofindtheeffectoffundamentaldynamicsstudy.Thischosenfragmentsequenceisusedto49https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

4Langmuirpubs.acs.org/LangmuirArticle46−48generatetheatomisticmodelofacollagenfragmentusingthebehaviorattheinterfaceofmaterialsandisapreferred42gencollagenpackageasshowninFigure2a.Thefragmentchoiceforlarge-scaleMDsimulationswithaccuracyin31,49hasthreehelicalchainsrepresentedinred,blue,andgreen.measurementofforces.All-atomsimulationsarecon-Eachofthesechainsconsistsofaminoacidslikeglycine,ductedusingtheCHARMM27potentialfunctionconsideringproline,andmethionineasdepictedinFigure2a.Theatomicanonbondedforcecutoffof13ÅforvanderWaalsandstructuresofafewofthoseaminoacidsarealsoshowninCoulombicinteractionstomodeltheforceinteractionbetween50Figure2a.Eachofthosehelical-shapedchainsisaddedwithHtheatoms.TheCHARMM27potentialfunctionusedtoatomsusingthepsfgenmoduleoftheNAMDpackagetosimulatetheintraandinteratomicforcescomprisestwo43generatetheatomisticfragment.Therepresentativeatomisticcomponents:UINTERfornonbondedinteractionsandcollagenfragmentisplacedsidebysideatadistanceof15ÅtoUINTRAforsimulatingthebondedinteractions.The44expressionforthepotentialenergyfunctionisshownineq1formalayerinVisualMolecularDynamics(VMD).Threelayersofthechosenfragmentplacedatadistanceof15ÅU=+UUINTERINTRA(1a)(centertocenter)generatedthesliderasshowninFigure1fandsimilarlythesubstrateasshowninFigure2b.EachÄÅÅ126ÉÑÑcylinderrepresentsthecollagentypeIIfragmentsandarrangedÅÅÅÅijjRminijyzzijjRminijyzzÑÑÑÑ1qqijkeepinginviewthetangentialorientationofthecollagenfibrilsUINTER=−∑∑εijÅÅÅÅjjjjzzzzjjjjzzzzÑÑÑÑ+LJÅÅkrij{krij{ÑÑCoul4πεorijatthetopsurfaceofthecartilageineachoftheslidersandtheÅÇÑÖsubstrates.Theatomisticmodelofthesliderandthesubstrate(1b)isplacedataninterfacialgapof15ÅalongtheY-axistoobtain∑∑22aflat-on-flatconfigurationatomisticmodelofthetopUKINTRA=−b()bbK0+−θ()θθ0intercartilageinterfaceforinvestigatingnanoscaleadhesionbaandfrictionasshowninFigure2c.Thisisasimplified+[∑Knφ1c+−os(φδ)]nanoscalemodelandrepresentslocalizednanoscopiccontactdzonesofinterestattheintercartilageinterface.Theatomistic∑∑22modelalsorepresentstwocollagenfragmentsbothinthe+−KKω()ωω0+−UB()uiku0iUBatomisticandribbonrepresentationsofVMD.Thesideviewof(1c)thesameatomisticmodelispresentedinFigure2d.MolecularSimulationSetup.Theconstructedthree-whereKb,Kθ,Kφ,KωandKUB,arethebond,angle,dihedraldimensionalatomisticmodel(86Å×98Å×42Å)oftheangle,improperdihedralangle,andUrey−Bradley(UB)forceunhydratedtopintercartilagecontactmodelconsistsof36constants,respectively.b,θ,ω,φ,anduikarethebondlength,collagenfragments,eachcontaining477atoms,thusresultingbondangle,dihedralangle,impropertorsionangle,andin17,172atoms.Tostudytheeffectofloading,thetopmostdistancebetweeniandkatoms,respectively,withthesubscriptlayeroftheatomisticmodelissubjectedtovariousloads.zerofortheequilibriumvalues.ThesearethecomponentsofBasedonthepreviousexperimentalstudies,thecontactbondedinteractions.Meanwhile,thenonbondedinteractionspressurerangechosenforAFMexperimentsis1.9−6MPa.9compriseLennardJonesandCoulombicinteractions.FortheMoreover,incomparisontoAFMexperiments,MDoffrictionLennardJones(LJ)potential,εijisthepotentialwelldepthforstudiescansimulatethefrictionalprocessbetteraccountingatomsiandj,andRministhedistanceatwhichthepotentialijeachparametersystematicallyintheformofanincrementalreachesitsminimumvalue,andrijisthedistancebetweenthestudytorevealatomic-levelinformationofthephenomenonatatomsiandj.FortheelectrostaticCoulombicinteractions,qi,thehiddeninterface.Highercontactstresscanaccuratelyqjarethechargesoftheatomsiandjwithεobeingthe45predictthefrictionbehaviorofanatomicsystem.Therefore,dielectricconstantofvacuum.tosimulateaclosenanoscaleinterfacialcontact,arangeofPeriodicboundaryconditionsareimposedinthex-andz-highercontactstressesinincreasingorderhasbeensimulatedaxes,i.e.,perpendicularandparalleltothecollagenaxes,(96.25,192.5,385,770MPa)byapplyingdifferentloads(3.5,whereasshrink-wrappedconditionsinthey-directionnormal7,14,28nN)ontheatomisticmodel.Toascertaintheeffectoftothecollagenbedformedareimposedtosimulateaninfiniteloadonadhesionandfriction,differentloadsareappliedonflat-on-flatinterfacialcontact.Thetimestepischosentobe1thetopmostlayerconsistingof2850atomsafterpre-fsforallequilibrationsimulations.Theatomisticmodelequilibration.Afterloading,foreachcase,post-equilibrationconsistsofsixlayersintheformofthesliderandsubstrate.isperformedfor0.1ns.Thereafter,foreachcaseusingtheTherefore,theload-bearing,adhesion,andfrictionalbehaviorpotentialfunctions,thedynamicpropertiesareobtainedforwhileslidingareobtainedandanalyzedlayerbylayer.ThetheiradhesiveandfrictionalbehaviorusingLAMMPS.Forthestepsfollowedforallthesimulationsareminimizationandpre-adhesivetest,thesecaseswillbereferredtoasL3.5,L7,L14,equilibrationfollowedbyloadingandpost-equilibration.andL28,whereasforthefrictiontestalongtheperpendicularFinally,thepost-equilibratedloadcasesaretestedfordynamicdirection(X-axis),thesecaseswillbereferredtoasL3.5X,propertiesowingtoadhesionandfriction.L7X,L14X,andL28X.ForthefrictiontestalongtheparallelTheatomisticmodelforeachcaseisminimizedusingthedirection(Z-axis),thecasesarenomenclatureasL3.5Z,L7Z,ConjugateGradientalgorithmfor10ps.TheinitialatomicL14Z,andL28Z,respectively.velocitiesareassignedusingGaussiandistributioncorrespond-Three-dimensionalmoleculardynamicssimulationshaveingto310K.Pre-equilibrationofallthecasesisperformedbeenconductedonthetoplayercartilage−cartilageatomisticusingaconstanttemperaturemaintainedbyaNose−HoovermodelusingLAMMPS,anopen-sourceMDcodedevelopedthermostat,andtheconstantpressureisalsomaintainedbya38bytheSandiaNationalLaboratory.LAMMPSisapotentialNose−Hooverbarostat(NPT)ensembleatapressureof1atmtoolforconductingmolecular-scalesimulationsformetal,andtemperatureof310K(forinducingthermodynamicpolymers,andbiomoleculesandinvestigatingfrictionalproperties)for0.1ns.Thereafter,theabovementionedloads50https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

5Langmuirpubs.acs.org/LangmuirArticleFigure3.(a)Schematicrepresentationofthesimulationmethodologyforthepull-offtestofthetoplayercartilage−cartilageinterfaceatomisticmodel.Thetopblockisbeingpulled,whereasthedynamicsisstudiedonthedeformableatomsbothatthetopintracartilageinterfaceandtheintercartilageinterface.(b)Three-dimensionalrepresentationofthedifferentlayersconsideredandtheirroleinobtainingthenormalandfrictionalforcesforbothpull-offandfrictiontests.Forceiscalculatedonallthegreenatomsduetoallthepinkatomstoobtainthenormalandfrictionalforcesattheinterface.Theorangelayerrepresentsthethermostattedlayerwherethetemperatureisscaledastheslidingtakesplace.areappliedonthetopmostlayer(contactstressinMPa)tocartilage).Thenormalforcecalculatedalongthey-directionbringthesliderandsubstrateincontactwiththesubstrate.representstheforceofadhesion.AsfrictionforceistheAfterloading,foreachcase,postequilibrationisperformedresistancetoslidingmotion,similarly,theadhesivebehaviorisusingaconstantpressureof1atmandtemperatureat310KtheresistivepropertyofamaterialduringapullconductedusingaNose−Hooverbarostatandthermostatfor0.11ns.ThenormallyintheY-direction.loadedcasesareequilibrateduntilthetotalenergyandSlidingTest.Slidingsimulationsarecarriedoutforallthepressuregetstabilized.Thereafter,pull-offandslidingfourloadsL3.5,L7,L14,andL28forobtainingthefrictionalsimulationsareconductedforeachloadcase.ThedetailsofbehaviorofthetoplayerintercartilageatomisticmodelasthosetestsareasfollowsdependingonthephenomenontheyshowninFigure4a,c.Thetimestepchosenforslidingbehaviorsimulate.is0.5fs.PeriodicboundaryconditionshavebeenappliedalongPull-OffTest.Thepull-offtestsforallthefourloadcasestheXZ-planeandthenonperiodicalongtheY-axistosimulateareperformedasshownintheschematicinFigure3a.Theinfinitecontact.Thebottommostboundarylayerconsistingofobtainedre-equilibratedatomisticsystemsafterapplicationof2862atomsisfixedalongthey-direction.Thetopmostlayerofloadhavebeentestedfortheiradhesivenature.Thetopmostcollagenfragments(2850atoms)isappliedwithavelocityof1layerconsistingof2850atomsissubjectedtoapull-offvelocitym/stosimulateaslidingprocessbothperpendicularand(1m/s)inthey-directiontosimulatetheadhesivebehaviorofparalleltothecollagenaxesasshowninFigure4b.Figure4btheinterfaceduringthepull-off.Atlowervelocities,i.e.,0.1andpresentsboththelayerofthesliderandsubstrateatthe0.01m/s,considerablepullanddynamicshavenotbeeninterfaceinactualcontactduringloadingandsliding.Theobtainedduetolongerinteractiontimeleadingtoanelongatedshearrate(γ̇)is109s−1correspondingtothechosenstaticzoneandlongercomputationaltime.Thedistanceofsimulationvelocityissignificantlyhigherincomparisonbyseparationiscomputedasthedistanceofthecenterofmassordersofmagnitudetotheexperimentalvalues(γ̇<107s−1).(c.o.m)ofthetopmostmovinglayertothec.o.moftheinitialHighershearratesensurecalculationoffrictionforcesatthepositionoftheunderneathlayeritisdetachingfrom.Thesteadystate.Attemptingtoexactlysimulatethenanoscopicmaximumdistanceofseparationforthetopmostlayeris15Å.processforthespecifictimeperiodbecomescomputationallyThetimestepchosenforthesesimulationsis0.5fs.Theresource-intensive(severalnanoseconds).Therefore,thebottommostlayeriskeptfixedduringallthesimulations.choiceofslidingvelocityintherangeof1m/sorhigherbyThedeformableatomsareequilibratedwithacanonicalanorderresultsinacceleratedMDleadingtoovercomingof(NVT)ensembletosimulatethedynamicsoftheseatomsatTenergybarrierslikethetransitionfromthestatictodynamic=310K.Theinterfacialforcesarecomputedasthesummationregimequicklymakingitconvenienttobecomparablewithofforcesonthedeformableatomsofthetopsliderblockdueexperimentallyobtainedparametersutilizingcomputation51tothedeformableatomsofthesubstrateateachtimestepasoptimally.Theshearratescorrespondingtothesesimu-representedinFigure3b.Thegreenatomsrepresentthetoplationsarealsofoundtobehigher(γ̇>108s−1),butaprevioussurfaceofthecounterface(uppercartilage),whereasthepinkstudysuggeststhatdespitethedifferenceintime-andlength-atomsrepresentthetopmostlayerofthesubstrate(lowerscalecoefficientsoffrictionobtainedinexperimental51https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

6Langmuirpubs.acs.org/LangmuirArticleFigure4.Schematicandthree-dimensionalmodelforconductingnonequilibriummoleculardynamics.(a)Representationofthefrictionsimulationmethodologyasnormalforceisappliedonthetopmostlayerwiththemiddlelayerkeptataconstanttemperatureusingathermostatandinterfacialforcesarebeingobtainedonthebottommostlayeroftheslider.(b)SchematicforconductingfrictionsimulationsperpendicularalongtheX-axisandparallelalongtheZ-axis.Uppersliderblockmarkedindottedblueisslidagainstthelowersubstratebothparallelandperpendiculartothecollagenaxes.(c)Simulationmethodologyanddistributionofthelayerforconductingfrictionsimulationsintheformofasliderandsubstrateintheatomisticmodelastherepresentationshowninpanel(a).Eachofthecirclesrepresentsacollagenfragmentchosen.Thenormalandshearforcesarecomputedasthesummationofforcesobtainedateachtimestepalongthey-andx-directionsonthetopNewtonianatomsofthesliderduetotheNewtonianatomsofthesubstrate.Frictionalforcesareresolvedoppositetothemotionandequalinmagnitudeofshearforcesobtained.TheNewtonianatomsofthesliderarerepresentedingreenandthatofthesubstrateinpinkasshownintheforcemethodologydepictedinFigure3b.conditions,theycouldbecomparedtotheacceleratedMDbehavior.CHARMM27doesnotcapturebond-breaking52simulationresults.Fewstudiesalsosuggestfrictionbehavior,sochemicalreactivitycannotbemodeledinthissimulationresultstobeinsensitivetoslidingspeedsrangingstudy.overordersofmagnitudeforsystemsunderheavyload-InitialResultsandValidation.Accordingtopreviousing.47,53−55Inadditiontothis,thenanoscalemodeldevelopedmacroscalestudies,itisassumedthatinthepresenceofinthisstudyisforalocalizedcontactzone.Therefore,theadhesion,thefrictionforce−loadrelationtobeusedislocalizednanoscalecontactzonemodeledneartotheinterfaceFFN=+0μ(2)willbehavingshearratesthatareveryhighdespiteanaveragelowshearratevalueduringamacroscaleslidingprocess.ThewhereFisthecalculatedfrictionforce,F0isthepull-offinterimlayerofcollagenfragmentsofboththesliderandtheobtainedattheintercartilageinterface,μstandsfortheaveragesubstrateisthermostattedbycontrollingthetemperatureatfrictioncoefficient(COF),andNistheappliednormalforce.310K(bodytemperature)usingaLangevinthermostatforItisbeingobservedthatthepull-offobtainedatthestabilizingthesystem.Thechoiceofthermostatparametersisintercartilageinterfaceisnegligibleincomparisontohigherbasedoninitialsimulationsperformedtoobtainastablevalueappliednormalload(14,28nN),whereasduringapplicationofnormalforce,approximatetotheappliedload.Theoflowerloads(i.e.,3.5nN),thefrictionforceisequaltotheNewtonianatomsaretheatomsclosetotheinterfaceonadhesive/cohesivestrength.Thus,thisfrictionrelationreducesboththesliderandthesubstrate,andastheycontact,normal56totheAmontonslawaspredictedinapreviousMDstudy.andfrictionalforcesarecomputedonthoseatomsastheyareTherefore,forourcurrentsimulationsofcohesioncoupledcloserduringcontact.Theseatomsaresimulatedusingafriction,theAmontonslawissuitableforpredictionofthemicrocanonicalensemble(NVE)tomodelthefrictionalappropriateCOF.52https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

7Langmuirpubs.acs.org/LangmuirArticleF=μN(3)agreementwiththisavailableexperimentalfrictionstudyresultsdespitethecontrastinthetimeandlengthscales.whereFisthefrictionforcethatincludesthetangentialpull-offanddeformationcomponentandNisthenormalforce■obtainedatthelocalizedmolecular-scaleinterfaceateverytimeRESULTSANDDISCUSSIONMoleculardynamicssimulationsforpull-offandslidingstep.Therefore,computedCOFvaluestakeintoaccountthebehaviorusingthetoplayercartilage−cartilageunhydratedambientconditions(unhydratedinterfaces),atomspresentonatomisticmodelareemployedtostudytheadhesiveandeithersideoftheinterfaceandtheirattractiveorrepulsivefrictionalphenomenawithincreasingloadattheintercartilageinteraction,thedirectionofsliding,contactpressureapplied,interface.Moleculardynamicssimulationsforallfourloadandthepull-offgeneratedattheintercartilagesurfacecasesareperformedtopredicttheinteractionbothatthetoprepresentedintheatomisticmodel.interface(intracartilage)andlowerinterface(intercartilage)Alltheresultsanddiscussionsinthisstudyarebasedontheanddevelopanunderstandingofthecontactphenomenoninconsiderationthatthefrictionalforceoccurringatthetheabsenceoflubricantmolecules.Basedonthestudyofunhydratedinterfaceisdirectlyproportionaltothenormalinteractions,theeffectofslidingonthefrictionalbehavioratforceapplied.Thecurrentsimulationsaidinunderstandingthetheintercartilageinterfaceisobtainedinthedirectionsparallelunderlyingslidingphenomenonattheinterfaceofthecartilageandperpendiculartothecollagenaxes.withinaverylocalizedzoneunderunhydratedconditions.AdhesionBehaviorofArticularCartilageinUnhy-Therefore,itisdifficulttofindastudytovalidatethesameasdratedConditions.MDsimulationsareperformedonthemostofthestudiesareeitherconductedatthenanoscaleorunhydratedtoplayercartilageatomisticmodelforunder-havingstructuralhydration.AnotherimportantthingisthatstandingtheadhesivebehavioroftheintercartilageinterfaceasthemajorityoftheexperimentalstudiesareconductedinshowninFigure3.Normalforcesarecalculatedattwoenvironmentalconditions,whereasallthesemolecularinterfaces,intra-(topinterface)andintercartilageinterfacedynamicssimulationsareconductedinvacuum.Experiment-(whereblueandredatomscontact),tounderstandthebasedfrictionstudiesarefoundforcollagentypeI,whichisadhesionphenomenonwithincreasingload.Theatomsofthepresentinmostofthetissuesandplaysavitalbiomechanicaltopmostlayerofthemodelarepulledwithavelocityof1m/sroleinthebody.topredictthebehavioroftheremainingunhydratedinterfaceInanearlierexperimentalstudy,fibrillar,amorphous,andatthesteadystate.Thepullofthetopmostlayertowardthey-denaturedcollagentypeIIcoatedonmicagluedtoanAFMdirectionleadsthefreeatomsunderneathittodeformthebluemicrospheretipwithanothersimilarcollagentypeIIcoatedatomsandisusedtopredictthepull-offbehavioroftheintra-micasheetonasubstratearetestedfortheiradhesiveandandintercartilageinterfacesasshowninFigure5.frictionalpropertiesseparatelyinanunhydratedaswellaslubricinenvironment.10ThereportedvalueofthefrictionFigure5ashowsthevariationofnormalforceasafunctionofthedistanceofseparationofthetopmostlayerforthecoefficient(COF)underunhydratedconditionsforthisstudyintercartilageinterfaceatdifferentexternalloads(3.5,7,14,is0.25.Thestudyclaimsthatthefrictionalforceislessforand28nN),whereanegativeforceisindicativeofthepull-offfibrillarthanforamorphousanddenaturedcollagen.Theforce.Attheintercartilageinterface,withanincreaseinthepullcollagensurfacesexhibitahigherforceofadhesionofthetopmostlayer,thenormalforceontheblueatomsduecorrespondingtolongerpull-offdistancesintheabsenceoftotheredatomsreducesinitially.Tworegionsdemarked,i.e.,lubricinattheinterfaces.Acomparisonofourfrictionaltherelaxationzone(0−5Å)andthentheadherencezonesimulationsresultswiththepreviousexperimentbyChang’sgroup10isshowninTable1.(10−15Å),arerepresentedinblueandgolden,respectively.Duringrelaxation,forallfourcases(L3.5,L7,L14,L28),thenormalforceattheintercartilageinterfacedecreasesandtheTable1.ComparisonofCurrentMDStudieswithPreviouscollagenfragmentsreorienttheirtriplehelixstructure(thus,ExperimentalStudiestotalinteractionenergyreduces)toregaintoitspreviousmaterialpairCOFtypeofstudygeometrydimensionsbeforeloadingasshowninFigure5b.Thepullcollagen-on-collagen0.20−currentMDflatonflatactingatthetopmostlayerhasaweakereffectattheunhydratedatomistic0.75study(atomistic)intercartilageinterfacethantheresistiveforcegeneratedatthemodel(fibrillar)interfaceoppositetothepullduetotheheavyintermolecularunhydratedfibrillar0.25earliermicrosphereonflatlocking(cohesivesites)formedduetotheinterpenetratedcollagen−fibrillarexperimentalusingAFM(flat10collagenatomsinunhydratedconditions.Themainbackbonecollagenstudyonflat)chainofcollagensegmentsusedinthestudyisnotentangledwitheachother;instead,thesidegroups(fromaminoacidAll-atommolecularsimulationshavebeenconductedtogainresiduesformingthechain)areeithercreatingstronganunderstandingoftheunderlyingsurfacephenomenon,nonbondedinteractionsorgettinglockedintothesurfacewhereastheexperimentalstudiesconductedatthemacroscalenanocavitysitesformedattheinterfaceduetoappliedloadcapturethefrictionalbehavioronthescaleofcollagenfibers.Itconditions.Suchload-inducedintermolecularlockinghasalso57isconcludedthatthepresentstudyisveryspecifictoalocalbeenreportedinanearliernanotribologicalstudy.Thereareportionoffibrillarcollagen-to-collagencontactattheinterfacenointerchainorintrachainentanglementsconsideredintheofcartilage.Thespeed/shear-rateschoseninthecurrentpresentmodelasthismodelisofnanoscopiclengthscaleandsimulationsarehigherthanthoseintheexperimentalworkrepresentslocalizedcontactzones.referred,anditisdifficulttofindanexactcomparisonduetoTheL28caserequiresmoretime(correspondstothethelackofexperimentsatthelengthscaleofthesimulationsdistanceofseparation)fortherelaxationprocess,whereastheconducted.Therefore,itisbelievedthattherangeofCOFsL3.5caserequireslesstime.TheL3.5caseexhibitsslightpull-obtainedinthiscomputationalfrictionstudyresultsisinoffduetofewintermolecularlockings(interpenetration)53https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

8Langmuirpubs.acs.org/LangmuirArticleFigure5.(a)Variationcurveofnormalforceobtainedattheintercartilageinterfacevsdistanceofseparationofthetopblock.Thetopmostlayerispulledasshownintheschematic,andforceismeasuredontheblueatomsduetotheredatomstopredicttheadhesivebehavioroftheintercartilage.(b)Variationoftotalinteractionenergywiththedistanceofseparationatthetoplayerintercartilageinterface.Higherloadleadstohigherattractionduetoadecreaseinenergy,indicativeofcohesiveinteractionsandincreasedpull.(c)Pull-offtesttrajectoryvisualizationforvariousloadsduringthepull-offtest.Aminoacidshowninyellow(MET)ofthesliderisinterpenetrateddeeplyintothesubstrateandactsasacohesivesiteforlocalizedpullathigherloads,i.e.,theL28case.Moviesofthepull-offtestfor3.5and28nNloadsareprovidedintheSupportingInformation(MoviesS1andS2,respectively).formedbydiffusingattheinterfacialcontactzoneandthusisinterface,itislessenergeticfortheatomstointerlockeachattractedeasily.Intheadherencezone,theblueatomspossessotherthroughvanderWaalsinteractionattheintercartilageaminimumnormalforce,i.e.,residualforceneededtodetachinterfaceandformcohesivesitestoresistthedeformationtheblueatomsfromtheredatomsofthesubstrate.generatedbythepull.IntermolecularinteractionishighlyattractiveforhigherloadsAttheintracartilageinterface,thepull-offforceisfoundtoof14and28nN,incomparisontolowerloadsof3.5and7bemorepronouncedasitisnearesttothepulledtopmostnN.Thedifferenceintotalinteractionenergyforloadsof3.5layer.Thestudyofthebehavioroftheintracartilagehelpsinaand28nNispresentedinFigure5b.Asthetotalinteractionmoreaccurateunderstandingoftheadhesivebehavioroftheenergyattheinterfacedecreaseswithincreasingloadunhydratedcartilageattheatomisticscaleastheforcecutoffisindicatingthatathigherloads,theinteractionbetweenblue13Å.Thevariationofthetotalinteractionenergyandnormalatomsandlowersubstrateatomsishighlycohesive(attractive)forceexperiencedatthetopmostlayerduetotheunderneathinsteadofadhesiveinteraction.Inadditiontothis,thehigherlayerwiththedistanceofseparationwithanincreaseinloadistheloadapplied,thehighertheresidualforceactingnormallypresentedinFigure6.TheprocessoftheintracartilageduetotheformationofthisintermolecularlockingasshowninadhesionmechanismcanbecategorizedintosimilarthreeFigure5c.distinctregions,i.e.,relaxation,pull-offorstretching,andFigure5cshowsthecontactconfigurationattheatomicfracturezones,representedinblue,golden,andwhite.scaleattheintercartilageinterface.TheatomsoftheaminoThedistancesofseparation,whichisacharacteristicoftheacidsofthesliderarecompletelyinterpenetratedathighertime,arefoundtobe1,2,3,and4Å,correspondingtoanloads.Theseatomisticallylockedsitesorintermolecularincreaseinloadfrom3.5,7,14,to28nNtorelaxtotheirlockingsoccuracrossthesurfaceinbetweenthechainpreviousconfigurationsduringpullingasshowninFigure6a.segmentsofthesliderandthesubstrate.Inadditiontothis,Inthestretchingzone,forallthecases,pull-offisexperiencedathigherloads,theseyellow-coloredintermolecularlockingsatthetopinterface.Theeffectofthepullatthetopmostlayeractasanchorsresistingthepull-offandthuspreventthereducessomeforceattheintercartilageinterfaceformedbybreakingofthenonbondedinteractionattheintercartilageheavyintermolecularlocking.Theseinterlockedcohesivesitesinterface.Contrarytothis,atlowerloads,theatomsoftheleadtounfoldingandstretchingofthecollagenfragmentsupperbedhavelessinterpenetratedatoms,andthus,theyarelaterallyperpendiculartothecollagenaxisandfinallyattractedtowardthesubstrateresultinginaverylowpull-offdetachment.Thetypicaldynamicsofcollagenfragmentsinforce.Moreover,forallthecases,norelativeseparationatthetheL28caseattheintracartilageinterfaceduringthepull-offinterface(blueandred)isobserved.Therefore,itisclaimedtestispresentedinFigure6c.Thetoplayerisobservedtothatathigherload,intheabsenceofanylubricantattheundergobendingfromtheinitiationoffracturetothefinal54https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

9Langmuirpubs.acs.org/LangmuirArticleFigure6.(a)Variationcurveofnormalforceobtainedattheintracartilageinterfacevsdistanceofseparationofthetopblock.(b)Variationoftotalinteractionenergyatthetopsliderbedsurfaceatomsduetothesubstrateatoms.Theincreaseinloadleadstoheavyintermolecularlockingandlongerstretchinglengthofcollagenfragments.(c)Pull-offtesttrajectoryatvariousstagesoftheadhesiontest.Highcohesionattheintercartilage44interfaceleadstodetachmentofthetopmostlayerattheintracartilageinterface.RenderedusingVMD.separation.Usually,thetoplayerceasestohaveaneffectonregionoftheplotexplainshowthetopmostcollagenfragmenttherestofthemodelfromd=15Åbutcompletelygetslayerisdetachedfromthewholeatomisticmodelsignifyingthedetachedatd=17Å.fractureofthemodelduetopull-off.Duetolimitation(cutoffItisfoundthatthereisastronginfluenceofadherenceofdistance)ofcalculationinmoleculardynamics,onlyasmalltheintercartilageinterfaceontheintracartilageinterface.rangeofstretchingofthecollagenfragmentcouldbecapturedDependingonthenormalforceapplied,thechangeintheseinthesesimulations.Moreover,itisclearthatintheabsenceofload-inducedintermolecularlockingattheinterfaceleadstoanylubricantorwatermoleculesinbetween,theunhydratedincreasedlocalizedstretchingandthepull-offforceaslistedincollagenfragmentsdoresultinveryhighstretchinglengths.Table2.Thehighertheload,theatomsattheinterfaceandThiscohesivebehaviorisattributedtotheheavyintermo-lecularlockingsitesandclosepresenceofatomsduringloadingTable2.DependenceofPull-offForcesontheLoadAppliedinanunhydratedenvironment.Thisisinagreementwithpreviouspull-offexperimentalstudiesperformedonunhy-casesstretchingzone(Å)pull-offforceobtained(nN)dratedcollagen−collagentypeIIsurfacescoatedontheAFML3.53−65microspheretipandmicasubstrate.L74−86EffectofLoadontheFrictionalBehaviorofL147.1−146UnhydratedArticularCartilage.MDsimulationstocaptureL287−156thefrictionalbehaviorareperformedasshowninFigure4cforalltheloadcases.Althoughthearrangementofthecollagenwithinthechainsofthesliderandsubstratearemorefragmentattheintercartilageinterfaceistangential,thefrictioninterpenetratedordiffusedandrequirehigherstretchingtimesimulationmustensurethatslidinginbothperpendicularand(length).Thestretchingzoneliesintherangeof3−18Å,parallel,i.e.,thex-andz-directions,respectively,topredictthecorrespondingtoanincreaseintheloadfrom3.5to28nN.overallfrictionalbehaviorofthetoplayercartilage−cartilageThepull-offforcesexperiencedinthecasesare5,6,6,and6unhydratedinterfacialcontactasshowninFigure4b.InallthenN,respectively,fortheL3.5,L7,L14,andL28cases.Thefinalcases(L3.5,L7,L14,L28),themaximumdisplacementofthe55https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

10Langmuirpubs.acs.org/LangmuirArticleFigure7.(a)Nanoscalefrictionforcevariationwithtimeinpicosecondsatthetoplayerintercartilageinterfacewhileslidingperpendiculartothecollagenaxis.(b)Normalforcevariationwithtimeforperpendicularsliding.(c)Nanoscalefrictionforcevariationagainsttimewhileslidingparalleltothecollagenaxis.(d)Normalforcevariationwithtimeforparallelsliding.Threezonesofthefrictionalprocess,staticzone,geometry-dependent,anddeformationzone,showninblue,golden,andwhite,respectively.Averagefrictioncoefficient(COF)calculatedinthegolden-coloredzone.topslideriskeptatd=15Å(t=1.5ns)inboththedirectionsinterlockingsdevelop,whichresistthemovementatthetopredicttheoverallsurfacefrictionalbehavioroftheinterface.Thenormalforceobtainedattheintercartilageunhydratedintercartilageinterfaceandobtainacomprehensiveinterfaceisalmostequaltotheappliednormalforceobtainedunderstandingoftheatomisticmechanismoccurring.AchoicefromthereactionforceatthecohesivesitesasshowninFigureofahighershearrate(γ̇>108s−1)ensuresthefrictional7b,d.Theanalysisoftheslidingsimulationtrajectoriespredictspropertytobecalculatedinthesteady-statedynamicregionthatthefrictionalprocessexistsinthreezonesforboth58comparabletotheorderofexperiments.perpendicularandparallelslidings,i.e.,initiallystaticzone,theThefrictionalforceandnormalforcebehaviorsofthegeometry-dependentsliding,andfinallytheadhesion-depend-collagenfragmentsslidperpendicularattheintercartilageentdeformationzone,asshowninblue,golden,andwhite,interfaceareillustratedinFigure7a,bandforparallelslidinginrespectively.ThefrictionforceincreaseslinearlyforalltheloadFigure7c,d.AsperthesimulationmethodologyinFigure4c,casesirrespectiveofthedirectioninthestaticzone.Thereafter,slidingisconductedintheformofasliderandsubstratemadethefrictionforceisrelativelyconstantforhigher-loadcases(14upofcollagenfragments.Thefrictionalforceandnormaland28nN),whereasitvariesslightlyforthelowest-loadcaseforcesarecomputedbysummingupalltheforcesinthex-and(3.5nN)accordingtothemolecularsurfacemorphologytheyy-directions,respectively,onthecollagenfragmentsrepre-slideupon.Therefore,thiszoneistermedasthegeometry-sentedusingblueatomsduetothatofredatomsateachtimedependentzone.Finally,thefrictionforcecorrespondingtostep.Theobtainedfrictionalforcevariationswithslidingthehigher-loadcasesincreasesdrastically,anddeformationdistanceforcasesundergoingperpendicularmovementL3.5X,takesplacewithintheslidingloadedcasesinthedeformationL7X,L14X,andL28XareshowninFigure7a.zone.First,theinitiationofslidingenhancesfrictionalforceFrictionalforcesincreasewithariseintheappliednormallinearly,andalthoughthetopmostportionofthesliderstartsforceonthebluelayerinbothperpendicularandparalleltomove,therestofthefreeatomsarenotabletomoveduetoslidingsasshowninFigure7a,c.Frictionforcecorrespondingtheintermolecularlockingattheintercartilageinterface.ThetotheL28XandL28Zcasesarehigherthantheotherloadsfrictionforceincreasescorrespondingtoamovementfortimetduetointermolecularlylockedsitesattheinterface.The=400psinperpendicularanduptot=500pswhileslidingfrictionforcefortheloadcasesvariesintheorderofL28>L14paralleltothecollagenaxis.Thereafter,frictionforcegradually>L7>L3.5suchthatathigherload,moreload-inducedbecomesconstantforbothdirections.56https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

11Langmuirpubs.acs.org/LangmuirArticleFigure8.(a)Schematicrepresentinggeometry-dependentmovementandfrictioninperpendicularsliding.Thebluearrowrepresentsthedirectionofthemotionoftheupperslidercollagenlayeronthesubstratecollagenlayer.(b)Geometry-dependentmovementandfrictioninparallelsliding.(c)Stagesofslidingofthetoplayercartilage−cartilageunhydratedatomisticmodelperpendiculartothecollagenaxesindicatingthethreezonesofthefrictionprocess,i.e.,initialzone,geometry-dependentzone,anddeformationzone.Thereddottedboxshowsthemovementofthetopmostlayerinthex-direction,andthebottommostreddottedboxshowsthefixedregionofthesubstrateforfrictionalsimulations.(d)Stagesofslidingoftheunhydratedatomisticmodelparalleltothecollagenaxes.AllthecollagenfragmentsareshownintuberepresentationofVMD,andtheblueand44redtubesrepresentthetopmostportionsofthesliderandthesubstrate,whileotherportionsaremarkedingray.Thegeometry-dependentzonet=(400−1000ps)formovementofthetopmostlayerkeepingtheinterfaceintact.perpendicularandt=(500−1000ps)correspondstotheCohesivezonesactasanchoragesexhibitinglocalizedpullforvariationoffrictionalforcesduetothegeometryofthesurfacedisengagementthroughtheselockedfeaturesfromthepassingthroughasshowninFigure8.Thecollagenfragmentssubstratewhilesliding,thusincreasesfrictionasshowninattheintercartilageinterfaceexperienceastick−slipbehaviorFigure9b.Asdiscussedearlier,theseintermolecularlockingsofbasedontheclosenessofatoms.ItisevidentfromFigure7ctheblueatomsofthetopsliderinsidethesubstrateareload-thatparallelslidingleadstoaslippingeffect,whichexhibitsadependentandincreasewithanincrementinload.Itissmoothernaturethantheperpendicularsliding.ThedifferenceobservedthatfortheL28Xcase,thebluecohesivesitesexertinfrictionalforcecorrespondingtotheincrementinload(14resistancetomovementbychangingtheirorientationduringto28nN)ishigherintheparallelcasethaninperpendicularslidingfrom(t=500to1000ps)incomparisontotheL3.5Xsliding.Thisisattributedtothedifferenceinmorphologyandcase.ThestagesofslidingforbothperpendicularandparallelnumberofH-bondsformedatthemolecularinterfaceasslidingsareillustratedinFigure8c,d,respectively.TheshownlaterinFigure11b.Themacroscopiccontactareaisadhesion-dependent/deformation/interlayerslidingzone(t=estimatedtobealmostthesameforbothparalleland1000−1500ps)forbothperpendicularandparalleldepictstheperpendicularcasesandhencecannotbeusedforunder-deformationbehaviorofthesliderandsubstratewithmotion.standingthefrictionbehavior.TheloadingattheinterfaceTheunhydratedcohesivecontactattheinterfaceleadstoleadstothreetypesofphysicalinteractionshowninFigure9a,almostnomotionattheinterface(blueandredportions),andTypeAinwhichatomsacrosstheboundaryarefar,TypeBfurtherslidingleadstofracture/interlayerslidingmoresuitablewherethesliderandsubstrateatomsarenear,andTypeCforaparallelcaseasshowninFigure8d.Inthecurrentwheretheatomsoftheslidercrosstheboundaryanddiffusesimulationstudy,theinterfacialcontactandfrictionprocessintothesubstrate.TheloadcaseofL3.5mostlyhasTypeAcomprisephysicalnonbondedinteractions.Thereisainteraction,TypesA,B,andCarefoundinL7andL14,contributioninfrictionfromboththeH-bondsandthevanwhereasL28ismostlyTypeC.Therefore,theatomisticderWaalsforces.However,theH-bondformationandmorphologyofthecontactafterloadingsuggeststhatthesebreakage(Coulombicinteraction)areobservedtocontributeintermolecularlockingsitesactascohesivezonesandfacilitatesignificantlytothefrictionprocessincomparisontovander57https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

12Langmuirpubs.acs.org/LangmuirArticleFigure9.(a)Typeofinteractionattheintercartilageinterface.Theblueatomsaretheatomsofthebottommostlayerofthetopslider,whichisunderpull,andtheredatomsarethoseofthelowersubstrate.Loadbearinghappensatsuchdiscretesites,whichconsistofTypesA,B,andCinteractions.(b)Snapshotsoftheintercartilageinterfaceduringthefrictionphenomenonslidingperpendicularly(x-direction).Athigherload,the44cohesivesitesrepresentedinbluearestretchedandofferlocalizedpulltoresistthedeformationduetosliding.RenderedusingVMD.Figure10.Interlayerslidingandinitiationofslidingwithload.(a)Interlayerslidingdeformationinslidingparallel.(b)Variationofinterlayerslidinginitiationwithload.Athigherload,thisdeformationisearlier.Moviesofinterlayerslidingfor3.5and28nNloadsindiferrentdirectionsareprovidedintheSupportingInformation(MoviesS3,S4,S5,andS6,respectively).Waalsinteractionduetoitshigherstrength.AsignificantforboththecasesasshowninFigure7a,c.ThisisanalogoustodifferenceinthefrictionalforceisobservedduetotheH-theslidingmechanismproposedinpreviousworkonvarying59bondsinboththeslidingdirectionsasshowninFigures7a,blateraldistancesbetweencollagen.Interlayerslidingismoreand11b.InparallelslidingasshowninFigures8dand10a,theprevalentathigherloadsof14and28nN,i.e.,atalowerinterimlayerjustabovethebluetubesdetachesduetoweakerslidingdistance,andtheinitiationofinterlayerdeformationvanderWaalsinteractionandthereisareductioninthecommencesearlier,asshowninFigure10b.ThenumberofH-numberofH-bondsincomparisontoperpendicularslidingatbondsformedbeforetimet<1000psisalmostconstant;thus,theintercartilageinterfacewherecohesionispredominantandalltheloadcasesslidingparallelexperiencehigherfrictionalinterlayerslidinginitiatesasindicatedinFigure11b.TheforcethanperpendicularslidingasshowninFigure11b.deformationintheformofinterlayerslidingleadstoreductionEffectofLoadontheAverageFrictionCoefficientinthecorrespondingloadduetothenumberofatomsinthe(COF).Averagefrictioncoefficient(COF)foralltheloadcasescontactzoneattheinterface;thus,frictionalforcedecreases.Iniscomputed,consideringthefrictionandnormalforcescurrentsimulations,duetothelesslateraldistancebetweentheobtainedineachcaseintheirgeometry-dependentzones.Thecollagenfragments,atomsareverycloseintheL28XandL28Znormalloadappliedisnotdirectlyattheinterface;thus,thecases;thus,deformationishighercorrespondingtot>1000psnormalforceobtainedattheslidingintercartilageinterfaceis58https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

13Langmuirpubs.acs.org/LangmuirArticleFigure11.Comparisonoftheaveragefrictioncoefficient(COF)obtainedinparallelandperpendicularsliding.(a)VariationoftheCOFwithloadandslidingorientation.COFhigherintheparallelcaseduetotheconstantnumberofH-bondsattheinterface.(b)NumberofH-bondswithrespecttoslidingdistance(ford=1Å,timet=100ps).Atd=7Å,thenumberofH-bondsdipsandinterlayerslidinginitiates.usedinordertocalculatetheCOF.AlineardependenceofnumberofH-bondsasshowninFigure11b.COFvaluesfrictionalforcewiththenormalforceisconsidered,andtheobtainedarelowerinthecaseofperpendicularthaninparallelAmontonslawisusedforCOFcalculation.TherangeofCOFsmotionduetothegeometryoftheatomisticinterfaceandalsoobtainedfortheintercartilageinterfaceatomisticmodelforvariationinthenumberofH-bondsduetodeformationasslidingmotioninbothperpendicularandparalleldirectionsisshowninFigure11a,b.TheCOFdecreaseswithincreasing0.20−0.75.ThevaluesobtainedineachcasewiththeloadareloadasthenumberofatomsinteractingattheinterfaceshowninTable3whereper-andpar-representperpendicularincreaseswithloadasshowninTable3.Withanincreaseinload,interlayerslidingisalsoresponsibleforadecreaseintheTable3.ComparisonofCOFsObtainedinPerpendicularasfrictionalforceincomparisontootherloads.wellastheParallelMovementoftheSliderInunhydratedconditions,intercartilageinterfacialcohesionispredominantoverintralayerinteractionsleadingtoload(nN)COF(μ)perCOF(μ)pardeformation(interlayersliding)andfailure.Athigherloads,3.50.610.75thepull-offforcesincreaseduetoTypeCintermolecular70.420.45lockingattheintralayerinterfacesleadingtohigherstretching140.230.34lengthandfracture.Interlayercohesionleadstomolecular280.200.26stretchinganddeformationattheunhydratedinterface.ThestretchingdistancefollowstheorderL28>L14>L7>L3.5andparallelslidings,respectively.TheCOFforallthecasesfortheloadcases.NanoscaleadhesionattheintercartilagevariesintheorderofL28

14Langmuirpubs.acs.org/LangmuirArticlehydration,andlengthscale.Thus,theacquiredresultsinthetopullandstretchingofcollagenfragments.Theoverallcurrentstudyshouldbeconsideredtogetherwiththeaveragecoefficientoffriction(COF)obtainedatthecomputationalandgeometricassumptionsmadeintheseintercartilageatomisticinterfaceisintherangeof0.20−0.75MDsimulations.First,allthesimulationshavebeenconductedforalltheslidingtests.TheCOFreducedwithanincreaseininacompletelyunhydratedandvacuumenvironment.Second,loadduetovariationintheintermolecularlockingformedattheatomisticmodelisaverysmallnanocontactbetweenthetheintercartilageinterface.TheseCOFvalueslieintherangemicrofibrilsandsimulatesalocalizedcohesion,friction,andofvaluesavailableintheliterature.Forparallelsliding,thedeformationmechanism.AschematicrepresentingthediscreteCOFisfoundtobehigherateachloadcaseduetothenanoscalecontactandcomparisonofscaleonanasperityofconstantnumberofH-bondsthanthatforperpendiculartoplayercartilage−cartilagecontactandthemechanismofslidingwherethenumberdecreases.Thefrictionalbehavioratnanoscaleadhesionandfrictionmechanismareshowninthistoplayercartilage−cartilageinterfaceisfoundtoexistinFigure12.thethreezoneswhilesliding,i.e.,initiallystaticzone,thegeometry-dependentsliding,andfinallythedeformationzone.Athigherload,underunhydratedconditions,theatomisticinteractionattheintercartilageinterfacealterssignificantlyleadingtocohesion,stick−slipattheintercartilageinterfaceduringinitialandgeometry-dependentzones,andinterlayerslidingoftheintermediatelayerduringthedeformationzone.Interlayerslidingspecificallyoccursintheparallelslidingcaseduringthedeformationzone.ItisalsoobservedthatH-bondsplayamajorrolecomparedtovanderWaalsforcesintheoriginsoffrictionalforcesinthecurrentunhydratedsystem.Thispredictsthattheadhesiveandfrictionalpropertiesaredependentontheatomisticinteractionattheinterfaceandstructuralhierarchyofthetissue.Overall,analysissuggeststhatthesimulationmethodologyandatomisticmodeldevelopedforthecartilage−cartilagebiotribologicalstudyareappropriateforunderstandingtheeffectofloadonthecollagenfragmentsandtheirroleintheloaddistributionandprovidesinsightsintotheatomisticcontactphenomenonattheunhydratedcartilageinterface.Figure12.Comparisonofscaleandlocalizedcontactmechanism.Furthermore,thisinvestigationrevealsnanomechanicalunder-Theredandtheblackcirclesdenotetheasperity−asperitycontactatstandingoftheoriginsofadhesionandfrictioninpeptidethetoplayer.Amagnifiedviewoftheareaofinterestpresentsagroupsattheunhydratedcartilage−cartilageinterfaceatthedifferenceinscaleofthesurfaceandtheMDmodeldevelopedinthepresentstudy.nanoscaleandcontributestowarddevelopmentofalternative■approachesinartificialimplantresearch.ASSOCIATEDCONTENT■CONCLUSIONS*sıSupportingInformationInpresentstudy,atoplayercartilage−cartilagecontactTheSupportingInformationisavailablefreeofchargeatatomisticmodelisproposedandNEMDsimulationsarehttps://pubs.acs.org/doi/10.1021/acs.langmuir.0c02283.performedforinvestigationsontheadhesiveandfrictionalCalculationofinterfacialforcesinthreedirections;behaviorofjointsuponloadinginunhydratedconditions.Tocalculationofequivalentcontactstress;MDsimulationunderstandtherelevantmechanismsofloading,contact,anddetailsintableformat(PDF)shearingattheinterfacefromanatomisticperspective,thePull-offtrajectoryoftheintercartilagemodelat3.5nNatomisticmodelwasappliedwitharangeofloadssimulatingload.Shortdurationstretchingobservedattheintra-thestressattheintercartilageinterface.Duringpull-offandcartilageinterfacebeforefracture(MPG)frictionaltests,thetoplayersoftheloadedcasesweremovedPull-offtrajectoryoftheintercartilagemodelat28nNequaltothediameterofthecollagenfragmentsinthey-andx-load.Heavyentanglementleadstoformationofcohesivedirections,respectively.Thepull-offtestindicatedthepresencesitesandlargestretchingattheintracartilageinterfaceofseveralcohesivesitesattheintercartilageinterfaceinthebeforefracture(MPG)formofload-dependentintermolecularlockingintheabsenceofafluidfilm,whichresultedinhigherstretchinglength(bySlidingdynamicsoftheintercartilagemodelat3.5nNanchoring)whenpulledathigherloads,i.e.,theL14andL28loadwhenslidinthedirectionperpendiculartothecases.Thepull-offforceattheintracartilageinterfaceincreasedcollagenaxis.Lessdeformationforfewcohesivesitesfrom5to6nNwithloadduetoincreasedintermolecularformed(MPG)lockingatthesesitesoftheinterface.ThesecohesivesitesSlidingdynamicsoftheintercartilagemodelat28nNhighlydeformthetissuewhileshearingduetolocalizedpullloadwhenslidinthedirectionperpendiculartothethroughtheseintermolecularlockingsattheinterfacesatcollagenaxis.Heavycompressionandslidingleadtohigherloads,whichcouldleadtowear.heavydeformationasmanycohesivesitesexertlocalizedTheslidingtestconductedinbothparallelandperpendic-pullonthecollagenfragments(MPG)ularcasesrevealedhigherfrictionalforcesthanreportedvaluesSlidingdynamicsoftheintercartilagemodelat3.5nNforcartilageduetointermolecularlockingofresiduesleadingloadwhenslidinthedirectionparalleltothecollagen60https://dx.doi.org/10.1021/acs.langmuir.0c02283Langmuir2021,37,46−62

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