Association of nanodiamond rotation dynamics with cell activities by translation-rotation tracking - Feng et al. - Unknown - Unknown

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SupplymentaryInformationforAssociationofnanodiamondrotationdynamicswithcellactivitiesbytranslation-rotationtrackingXiFeng1+,Weng-HangLeong1+,KangweiXia1+,Chu-FengLiu1,Gang-QinLiu1,TorstenRendler4,JoergWrachtrup4,Ren-BaoLiu1,2,3*,QuanLi1,2,3*1.DepartmentofPhysics,TheChineseUniversityofHongKong,Shatin,NewTerritories,HongKong,China2.CentreforQuantumCoherence,TheChineseUniversityofHongKong,Shatin,NewTerritories,HongKong,China.3.TheHongKongInstituteofQuantumInformationScienceandTechnology,TheChineseUniversityofHongKong,Shatin,NewTerritories,HongKong,China.4.3rdInstituteofPhysicsandCenterforAppliedQuantumTechnologies,UniversityofStuttgart,70569Stuttgart,Germany.+Theseauthorscontributedequally:XiFeng,Weng-HangLeong,KangweiXia.*CorrespondenceandrequestsformaterialsshouldbeaddressedtoR.-B.L.(email:rbliu@cuhk.edu.hk)ortoQ.L.(email:liquan@phy.cuhk.edu.hk)

1MethodsTrackingNDorientationbyODMRmeasurementTheNVcentersinadiamondcrystalhavefourinequivalentcrystallographicdirections.InaweakexternalmagneticfieldB(<100Gauss),theangle?betweentheNVaxisandthemagneticfielddeterminesthefrequencies?േൎ?േ??cos?ofthetransitionsbetweenthe?ௌൌ0spinstateandthe?ௌൌേ1states,where?ൎ2870MHzisthezero-fieldsplittingand?ൎ28MHzmTିଵistheelectrongyromagneticratio1.SincearotationofthediamondaboutthemagneticfielddoesnotchangetheanglesbetweentheNVaxesandthefield,weemploythemeasurementundertwomagneticfieldsthatarenotparallel.Thisway,therotationofthediamondisunambiguouslydeterminedbyfittingthetwoODMRspectra୼௙మ୼௙మ?ሺ?ሻൌ?െ∑௜?௜൤శమమ൅షమమ൨ሺ1ሻସ൫௙ି௙೔൯ା୼௙ସ൫௙ି௙೔൯ା୼௙where?isthebaseline,?௜representstheODMRcontrastoftheNVcentersalongേthe?thcrystallographicdirection,Δ?isthelinewidth(FWHM),and?௜arethetwotransitionfrequenciesoftheNVcentersalongthei-thdirection.Intheleast-squarefitting,thefittingparametersaretheEuleranglesሺ?,?,?ሻ(seeSINote2-3fordefinationofthediamond’sorientation),thebaselines,thecontrasts,theFWHM,andthezero-fieldsplitting?(slightlydifferentamongdifferentNDsandatdifferenttemperature).GenerationofGPMVGPMVisgeneratedfromHelacellbasedonreportedprotocols2.Briefly,Helacellsareseededoncoverglasstoreach70%confluency.Thesampleiswashedwith1mlofGPMVbuffer(10mMHEPES,150mMNaCl,2mMCaCl2,pH7.4)twicebefore1mLGPMVbuffercontainingPFA/DTT(25mMPFA/2mMDTT)isadded.Thesampleisincubatedat37°Cfor1htoallowGPMVformation.SurfacemodificationofmicrodiamondsThemicrodiamondsarepurchasedfromAdámasNanotechnologies.Wemodifythesurfaceofmicrodiamondswithpolyethyleneimine(PEI,Mn~1,200,fromSigma-Aldrich).Briefly,3mg/mlPEIisdissolvedindeionizedwater(DI-H2O)and

21MHClisaddedtoadjustpHtoaround7.0.MDsarethendispersedinthesolutionataconcentrationabout0.25mg/mlandthemixtureisstirredovernight.ThedispersionisthencentrifugedandwashedwithDI-H2Oforthreetimes.Preparationoffibronectin-coatednanodiamondsFibronectiniscoatedontonanodiamondsviaphysicaladsorption3.Briefly,100ug/mLfibronectin(purchasedfromSigma-Aldrich)and100ug/mlNDsaremixedandincubatedovernight.TheNDsarethencentrifugatedandwashedforthreetimesanddispersedinPBSforfurtherexperiments.CultureofHelacellsandincubationwithNDsHelacells(fromATCC)areseededinculturedishwithDulbecco’smodifiedEagle’smedium(DMEM,Gibco),supplementedwith10%FetalBovineSerum(FBS),0.1g/Lstreptomycinsulfate,and0.06g/LpenicillinG.Thecellsareincubatedat37℃foradaywithhumidityandCO2levelcontrolled.BeforeintroducingNDs,thecellsareserumstarvedfor1day.TheNDs(fromAdámasNanotechnologies,NDNV140nm)aredispersedinDMEMandincubatedwithcellfor30min.at4℃toallowattachmentbeforeperformingthe6Dtrackingat37℃.PlasmamembranesofthecellsarelabelledwithCellMask™GreenPlasmaMembraneStainaccordingtotheproductmanual.ATPdepletionandrecoverySodiumazide(Sigma-Aldrich)and2-Deoxy-D-glucose(DG,ALADDINReagent)areusedtodepletetheintracellularATP.TheATPdepletionregentispreparedbydissolvingsodiumazideandDGwithPBStodesiredconcentration.TodeterminetheconcentrationofthesodiumazideandDGforATP-depletionexperiments,thecellsaretreatedwithATP-depletionagentofvariousconcentrationfordifferenttime,andtheATPlevelofthecellsaremeasuredwithluminescentATPassaykit(abcam)accordingtotheproductmanual(seeFigureS20forresults).Toperform6DtrackingonATP-depletedcells,theNDsareaddedintheculturemediumtoallowattachmentontocells.Aftertheexperimentsoncellsatnormalstateareperformed,thesampleiswashedwithPBSforthreetimesandtheATP-depletingagentcontaining10mMsodiumazideand50mMDGisaddedtotheculturedish.

3TheNDtrackingisperformedabout20minutesafteradditionoftheinhibitors.Forexperimentsoncellsintherecoverystate,thecellsarewashedwithPBSforthreetimes,suppliedwithfreshmediumandwaitedforaperiodofabout10minutesbeforetracking.FixcellwithPFATheNDsareaddedtothesampletoallowadheretothecell,thenthemediumiswashedwithPBSforthreetimesand4%PFAinPBSisadded.Thesampleisincubatedforabout0.5hbeforethetrackingexperiment.Killcellwithalaserwavelengthat473nmTheviabilityofthecellistestedwiththeBCECF,AM(Invitrogen™)accordingtotheproductmanual.TotriggercellnecrosisandtrackthedynamicsofNDduringthisprocess,wefirstfindanNDoncellmembraneandperformtrackingforafewhundredsofsecond,thenfocusthe473nmlaserofabout5μWonthecellandcontinuetracking.Thelaserilluminationeventuallyleadstocellnecrosisduetophoto-damage,aselaboratedinSINote5.

4SINote1.SetupFigureS1illustratesthesetup.Trackingofdiamondparticlesandimagingofthesamplesareperformedonahomebuiltconfocalmicroscopewithtwoindependentchannels.A594-nmlaserisusedfortheexcitationofNVcenterswitha1.4numericalapertureoilimmersionobjectivelens.Thefluorescencesignaliscollectedwiththesameobjectivelensandfilteredbeforebeingdetectedwithanavalanchephotodiode(APD,SPCM-AQRH-15-FC,Excelitas).ThesignalfromtheAPDiscollectedbyaNIDAQcard(PCIe-6363,NationalInstruments).Thescanningisachievedbymovingthesamplewitha3-axispiezoscanner(P-517.3CD).A473-nmlaserisusedfortheexcitationofdyesforfluorescenceimaging.ThesignalisdetectedwiththesecondAPD.Imagesareobtainedbyscanningtheexcitationlaserwithagalvomirror.Themicrowaveisgeneratedbyanarbitrarywaveformgenerator(AWG,AWG70002A,Tektronix)andamplifiedwithanamplifier(ZHL-16W-43-S+,Mini-Circuit)beforebeingdeliveredtothesampleviaanΩ-shapedco-planerwaveguide.FigureS1.Schematicofthesetup.APD:avalanchephotodiode,MW:microwave,BS:beamsplitter.Theexternalmagneticfieldisappliedbyplacingapermanentmagnetnearthesample.Thepositionofthemagnetiscontrolledbyastepmotortochangetheamplitudeanddirectionofthe

5magneticfieldsappliedtothesample.SINote2.Methodoftranslationandorientationtracking(1)TimingoflaserfocusscanningandmicrowavefrequencysweepingThetranslationalandorientationalinformationofthediamondisencodedinthephotoncountsuponpositionscanningandMWfrequencysweepingsimultaneously.FigureS2showsthetimesequenceoflaserfocusscanningandmicrowavefrequencysweeping.Thelaseriskeptonduringthewholeprocess,andtheAPDdetectsphotonscontinuously.Fortranslationtracking,thelaserfocusisscannedthrougheightdifferentpositionsinthevicinityofthetarget(from1to8)andthephotons?௜ሺiൌ1,2,…,8ሻineachfocuspositionarecountedbytheCounter1.Theperiodofpositionscanningis?୮ൎ0.16s.Thetranslationtrackingbasedon?௜willbeelaboratedinthenextsection.FigureS2.Sequenceforthesignalcollection.Fororientationtracking,thefrequencyoftheMWissweptthrough?ଵ,?ଶ,..,and?௡withaperiodof?ୱ୵୮ൎ7ms.ThephotonsforeachMWfrequency?௜arecountedbytheCounter2as?௜toobtaintheODMRspectra.Tohaveasufficientsignal-to-noiseratio(SNR),theODMRspectrumiscontinuouslycollectedinonemagneticfieldforatimeof?୦୭୪ൎ0.3s.Thenthemagneticfieldisswitchedbyrotatingthemagnet.Adurationof?ୱ୵୧୲ୡ୦ൎ0.1siswaitedforthestabilizationofthemagneticfieldbeforethenextODMRspectrumismeasured.Themagneticfieldswitchingtimeisnotthelimitingfactorofourpresenttimeresolution.However,whenhighertemporalresoutionisneeded,fasterfieldswitchingwouldbeneeded,whichcanberealized

6byusinganelectromagnet(~1kHz).(2)TranslationtrackingThetranslationtrackingmethodisadaptedfromthepreviouslydeveloppedtechniques4–6.TheprotocolisillustratedinFigureS3.Theprocessstartswithaninitialcenter?଴thatisclosetothetargetattime?ൌ0.Thelaserfocusisthenscannedthrough?ଵto?଼,eachwithanoffsetof??௜ൌሺേ??,േ??,േ??ሻwithrespectto?଴,asillustratedinFigS3aandFig.1b.Thephotoncounts?௜isobtainedforeachposition,andtheanisotropyineachofthethreedirectionsiscalculatedasଵ??ఓൌ஼̅ቀ∑ఋ௉೔,ഋவ଴?௜െ∑ఋ௉೔,ഋழ଴?௜ቁሺ1ሻwhere?ൌ?,?,?.TheanisotropyofphotoncountsisusedastheinputforthethreeindependentPIDcontrollers,andthemovementineachdirectionisobtainedas௧ௗ൫ఋ஼ഋ൯??ఓൌ???൫??ఓ൯ൌቂ?୔??ఓ൅?୍׬௧ିఋ௧??ఓ??′൅?ୈௗ௧ቃሺ2ሻwhere?୮,?୍,?ୈand??arethePIDcontrolparameters.Thecenterofthenexttracking-roundissettobeሺ?଴൅??).Thisway,thecenterofeverymovement?଴followsthetargetandthusthetranslationofthetargetisrecorded.The3DtrajectoryofanNDonthecoverglassisshowninFigureS3cwiththemeasurementtimeofeachpositionabout?୮ൎ0.16s.Theprecisionofpositionmeasurementforthisstaticsampleis~10nminthex-yplaneand~40nminthezdirection.FigureS3.Protocolfortranslationtracking.a.Thesamplingpositionsofthelaserfocusrelativetothetarget.b.flowchartfortranslationtracking.c.TrajectoryofanNDoncoverglass.

7(3)DiamondorientationandrotationFigureS4.a.TheorientationofthediamondisdescribedwiththreeEuleranglesሺ?,?,?ሻ.b.TherotationbetweentwoEuleranglesistherotationvector??,whichcanbedecomposedtothreecomponents??௫,??௬and??௭.TheorientationofadiamondparticleisobtainedbyfittingthetwoODMRspectraintwomagneticfieldsofdifferentdirections,bythemethodinRef.7.Therotationofthediamondparticleisrepresentedbyitsorientationchange.Anyorientationcanbedescriptedbythez-y-zproperEuleranglesሺ?,?,?ሻ(seeFig.S4a),whicharetheanglesofthreesequentialrotationswithrespecttothelaboratorycoordinates.Theseoperationcanbedefinedbytherotationmatrix?ሺ?,?,?ሻ8.TheangulardisplacementofadiamondparticlecanberepresentedbytherotationvectorΔ?asshowninFigureS4b,wherethedirectionofthevectorisalongtherotationaxisandthemagnitude??ൌ|Δ?|istherotationangle.TherotationvectorΔ?isobtaiendbycomparingtheEuleranglesሺ?,?,?ሻandሺ?ᇱ,?ᇱ,?ᇱሻbeforeandaftertherotation,thatis,?ሺΔ?ሻൌ?ሺ?ᇱ,?ᇱ,?ᇱሻ?ି?ሺ?,?,?ሻ.Whentherotationangle??issmall(??≪1rad.),therotationcanbedecomposedintothreecomponentsሺ??௫,??௬,??௭ሻbyprojectingΔ?toaorthgonalbasis(suchasthex,y,andzaxes)8,where??,??,??representsthemagnitudeofrotationalongthethree௫௬௭respectiveaxes.Errorsraisedinthedecompositionareestimatedtobeclosetoሺ??ሻଶ.(4)CalculationofmeansquareangulardisplacementThemeansquareangulardisplacement(MSAD)isusedfortheanalysisofdiamondrotation.AsdescribedinthelastSection,therotationofthediamondfromtime?to?൅?isdescribedbyΔ?ሺ?ሻ,definedby?ሺΔ?ሻൌ?ሺ?,?,?ሻ?ି?ሺ?,?,?ሻ.Thusthemeansquareangular௧ାఛ௧ାఛ௧ାఛ௧௧௧displacementisMSADሺτሻൌ〈|Δ?ሺτሻ|ଶ〉௧ሺ3ሻ

8SINote3.ValidationoforientationtrackingTovalidatethemethodoforientationtrackingandtoevaluatetheangularsensitivityofthemeasurement,wemanuallyrotateabulkdiamondsampleandperformtheODMRmeasurementtodetermineitsorientation.AsillustratedinFigureS5a,weputabulkdiamondcrystalonaflatsurfacewith(001)planefacingup.Thediamondisrotatedaboutitsz-axisforhalfacircleatastepof~5°(?ൌ0°,5°,⋯180°).FigureS5bshowstheODMRspectraundertwomagneticfieldsasfunctionsoftherotationangle?overlappedwiththefittingresults(solidlines).Thefrequencyofthemicrowaveappliedisplottedasthey-axis.ThecontrastoftheODMRspectraisencodedinthecolorscale.ResonancefrequenciesinthefittingresultsforNVcentersoffourdifferentcrystallographicorientationsareplotindifferentcolors.FigureS5.Demonstrationoforientationtrackingwithabulkdiamond.a.Illustrationoftheexperimentconfiguration.b.TheODMRspectraobtainedofdifferentrotationanglesoverlappedwithfittingresults.c.TheEuleranglesobtainedfromthefittingresults.d.Therotationaltrajectoryofthediamond.e.Therotationaxisshownasunitvectorswiththeirprojectionsinx-yplaneshownonthebottom.f.Therotationcomponentineachaxisforeachrotationstep.TheorientationofthebulkdiamondisextractedandshownasthreeEuleranglesሺ?,?,?ሻinFigureS5c.?increaseslinearlywiththerotationangle?,whilethevariationrangefor?and?isabout10°.FigureS5dillustaresthediamondrotationinarotationaltrajectory,inwhich

9theredtetrahedrondenotestheinitialorientation,andthetrajectoriesofthefourNVaxes(colorencodingisthesameasinFigS5c)showtherotation.Itisclearthatthesamplerotatesby180°.ThetrajectoriesoftheNVaxesformaplanethatisnotexactlyparalleltothex-yplane,suggestingaslightmisalignmentofthe[111]directionofthecrystalfromthezaxis.SuchmisalignmentisalsoseeninFigureS5e,wherethechangeoftherotationaxisisplotted(thesamecolorencodingapplies).ThecalculatedrotationanglesineachdirectionareshowninFigS5f.Therotationanglesinthexandydirecitonsnearzerowithinerrors,butthatinthezdirecitonisabout5°ineachstep,whichisconsistentwiththerotationweapplied.Todeterminethesensitivityoftheangularmeasurement,wefixthediamondsampleatapositionandmeasuretheODMRspectracontinuouslyforvraiousdataacquisitiontimes.Sincethediamonddoesnotrotateduringthemeasurement,thevariationsoftheEuleranglescomefromFigureS6.Estimationofangularsensitivity.a.Typicaltime-dependentODMRspectraundertwomagneticfields.b.EuleranglesobtainedbyfittingtheODMRspectrameasuredwithvariousdataacqusitiontime(~3,6,12,24,48,96s,fromtoptobottom).Thecurvesareoffsetverticallyforthesakeofclarity.c.StandarderrorsoftheEuleranglesasfunctionsofthedataacqusitiontime.Theangularsensitivity?isestimatedas2−3°Hzିଵ/ଶ.d.Dependenceofangularsensitivityontheorientationofthediamond.noises.TheODMRspectraareshowninFigureS6aasfunctionsoftime.Theresonance

10frequenciesdonotchangewithtime.TheevolutionsoftheEuleranglesasfunctionsoftimeareplottedfordifferentdataacqusititiontimeT,asshowninFigureS6b.ThestanddeviationsoftheଵEulerangles(?ఈ,?ఉ,?ఊ)decreasewiththeintegrationtimebyalinearfunctionof(Figure√்S6c),whichindicatesthatthemeasurementisshotnoiselimited.Byfittingthedatato?ሺ?ሻൌଵିଵ/ଶ?ൈ,theangularsensitivity?isestimatedas2−3°Hz.Theanalysisisalsoperformedfor√்diamondplacedatotherorientations(?ሻ,andtheobtainedangularsensitivity(histogramsshowninFigureS6d)isintherangeof1−5°Hzିଵ/ଶwithoutsignificantdependenceontheactualorientationofthediamond.Theuseoftwomagneticfieldsinoursetupmitigatesthepotentialissueoftheorientationdependenceofthesensitivity.

11FigureS7Characterizationofthemicrodiamondsample.a-dTEMimagesofthemicrodiamonds.Scalebaris1μmina-cand2μmind.eZetapotentialofpristineandPEI-modifiedmicrodiamonds.ThepristinemicrodiamondsdonotattachtoGPMVs(negativelycharged9)possiblyduetolowerconcentrationofproteinsonGPMV10aswellaselectrostaticrepulsion.ThepositivelychargedPEImodifiedmicrodiamonscaneasilybindwithGPMVsduetoelectrostaticinteraction.

12FigureS8ExpeirmentconfigurationfortrackingMDsonGPMVs.Asubmergedmetaltubeconnectingtocooling/heatingcirculatingbaths(Cole-Parmer®Polystat®)worksastheheatexchangertocontrolthetemperatureofthebuffersolution.Thetemperatureismeasuredbyathermalcouple.

13FigureS9TrackingofanMDonaGPMV.a.FluorescenceimageoftheGPMVinx-y,x-z,andy-zplanes.Thescalebaris5μm.TheGPMVisconnectedtoacell,whichismarkedbythereddashedline.ThereforetheGPMVremainsstaticintheliquidbufferenvironment.b.Time-dependentpositionoftheMDfromtranslationtracking.Thepositionsarefittedtoasphericalsurface.Briefly,thecentered?଴andradiusRofthespherearesearchedtominimize∑௜ሺ|?଴െ??|െ?ሻଶforallposition??.Theresultisaspherecenteredat?଴ൌሺ0.67,െ0.88,െ1.08ሻwithradius?ൌ8.6μmasshownbywhitedashlinesina.Theinsetshowsthehistogramofthedistancebetweeneachpositiontothecenterofthesphere,andthesinglepeaksuggeststhatthefittingresultisreliable.c.SpeedoftheMDcalculatedfromitstime-dependentposition.Insetshowsthehistogramofthespeed.d.EuleranglesobtainedbyfittingtheODMRspectrainFigure2binthemaintext.e.AngularspeedoftheMD.Insetshowsthecorrespondinghistogram.

14SINote4.RotationofMDinthemotionalcoordinateToanalysistherotationoftheMDmovingontheGPMVsphere,wefirstlyobtaintherotationoftheMDateachtimestep?௜to?௜ାଵby?ሾΔ?ሺ?௜ሻሿൌ?ሺ?ᇱ,?ᇱ,?ᇱሻ?ି?ሺ?,?,?ሻ(seeSINote1),whereΔ?istherotationvectoroftheangulardisplacement,andሺ?,?,?ሻandሺ?ᇱ,?ᇱ,?ᇱሻisthemeasuredEuleranglesattime?௜and?௜ାଵ,respectively(theEuleranglesaresmoothedbyGaussianfuntionwithlinewidth1.6s).Therotationvectorisdecomposedonthetime-dependentFigureS10ProjectionofMDrotationalongdirectionsparallelandperpendiculartotheGPMVlocalsurface.a.Schematicofthedefinitionof??∥,??,??௡and?௣,inwhich??௡isalongthelocalplanenormal,??∥and??areperpendicularto??௡withrotationaxesparallelandperpendiculartothetranslationaldisplacementΔ?,respectively.?௣istherotationinducedbyparalleltransportonthecurvedsurfaceoftheGPMV.b.Time-dependentangulardisplacement(colored)oftheMDforeachtimestepcalculatedfromtheODMRspectraandtherotrationinducedbyparalleltransport(black)decomposinginthreedirections.c.Tait-Bryanangles(theZ-X-YproperEulerangles)oftheMDinthemotionalcorrdinate.Theoff-planeandin-planerotationsarelabeledby1and2.dande,Theangulartrajectoriesoftheoff-planeሺ?ൌ60െ100sሻandin-planeሺ?ൌ110െ130sሻrotations.ThethreecoloredbasisvectorsillustratetheinitialorientationoftheMD.Thedotsshowthetrajectoriesoftwoaxesonthe

15orthogonalbasisሺ?∥,?,?௡ሻtobeΔ?ൌሺ??∥,??,??௡ሻasshowninFig.S10a,where?௡isalongthenormalofthelocalsurface,and?∥and?areparallelandperpendiculartothetranslationaldisplacementonthesurface,respectively.Meanwhile,therotationoftheMDinducedbythetranslationonthesphereisalwaysalong?(seeFig.S10a)andisdeducedbythepositionoftheMDonthesphereas??௣ሺ?௡ሻ൧.FigureS10bshowsthetime-dependentangulardisplacementoftheMDforeachtimestep(colorlines)andtherotationinducedbytranslation(black)decomposinginthethreedirections.Theerrorsinducedbythedecompositionoftherotationvectorareestimatedtobeሺ??ሻଶൎ0.4°,whichismuchsmallerthan??ൎ5°..ThenetrotationoftheMDinrelativetotheGPMVsurfaceiscalculatedbysubtractingtherotationinducedbytranslationfromtherotationobtainedfromtheODMRspectraas?ሺΔ?′ሻൌିଵ?ሺΔ?ሻ?൫?൯൧.Theerrorinducedbythesubtractionisalsointheorderofሺ??ሻଶandis௣neglected.TovisualizetherotationoftheMDinrelativetotheGPMVsurface,wedefinethemotionalcoordinateoftheMDas?ሺ?ሻൌሾ?୫ሺ?ሻ,?୫ሺ?ሻ,?୫ሺ?ሻሿ.Thetime-dependentmotionalcoordinateiscalculatedas?ሺ?௡ାଵሻൌ??௣ሺ?௡ሻ൧?ሺ?௡ሻ,wherewefix?ൌሺ?∥,?,?௡ሻat?ൌ46s.TheorientationoftheMDinthemotionalframeisdescribedbytheTait-Bryanangles(thez-x-yproperEulerangles),whichisdefinedbysequentiallyrotatingtheMDattime?ൌ0withtheangles?௬,?௫and?௭alongthe?୫,?୫and?୫axes.Thetime-dependentTait-BryananglesareplottedinFig.S10c.Theoff-planeandin-planerotationillustratedinFig.2cinthemaintextarelabeledwith1and2inthefigurewithlargeincreaseof?௬and?௭.ThetrajectoriesofthetworotationsareshowninFig.S10dሺ?ൌ60െ100sሻandeሺ?ൌ110െ130sሻ,whichshowtheoff-planerotationof~98°along?୫ൎ?,followedbythein-planerotationof~76°along?୫.

16FigureS11Long-termtanslationtrackingofanMDonaGPMV.a.Time-dependnetpositionofthesameMDasinFigureS9.Thetrajectoryisfittedtoasphericalsurfacecenteredatሺ0.57,െ1.12,െ0.16ሻwitharadius8.5μm.Theinsetshowsthehistogramofthedistancefromeachpositiontothecenterofthesphere.b.Translationaltrajectoryin3D.Thecolorsofthedotsencodethetimeandthecolorbarisshownontheright.c.Themeansquaredisplacementcalculatedfromthetrajectory.TheresultsarefittedtoMSDൌ6??൅ሺ??ሻଶ,withdiffusioncoefficient?ൌሺ1.2േ0.2ሻൈ10ିଶμm2/sandspeed?ൌሺ0.21േ0.01ሻμm/s.

17FigureS12Long-termorientationtrackingofanMDonaGPMV.a.Time-dependnetODMRspectracollectedtogetherwiththetranslationtrackinginFigureS11withfittingresultsoverlaid.b.EuleranglesdeducedfromtheODMRfittingresults.c.Time-dependentangulardisplacement(colored)oftheMDcalculatedfromtheODMRspectraandtherotationinducedbyparalleltransportonthecurvedsurface(black)inthreedirectionsdefinedinFigureS10a.Thehistogramofeachcomponentisshownontheright,whichfollowstheGaussiandistribuition(markedbytheblackdashedline).Theerrorsinducedbythedecompositionoftherotationrvectorareestimatedtobeabout10%oftheangulardisplacement.d.MSADalongthreedirections.TheresultssuggestthattherotationoftheMDisnotrestrictedtoin-planerotation(?௡),butratherfree.

18FigureS13Characterizationofthenanodiamondsample.a-b.TEMimagesofnanodiamonds.Scalebaris100nminaand200nminbandc.Thenanodimondsareirregularinshapewithsizerangingfromabout100nmto250nm.c.DistributionofhydrodynamicdiametersofnanodiamondsmeasuredbyDLS.ThesizedistributionisconsistentwiththeTEMmeasurement.d.Zetapotentialmeasurementsuggeststhatthenanodiamondsarenegativelycharged.e.RamamspectrumoftheNDs.Thestrongdiamondpeakataround1330cm-1andthenegligibleG-bandataround1330cm-1suggestthatthesampleiswellpurifiedwithverylowcontentofnon-diamondcarbon11,12.f.Fouriertransforminfraredspectraofthenanodiamondsample.Theabsorptionat1700-1850cm-111,13,whichsuggeststhatisassignedtoC=Ostretchingmodesfrom-COOHgroupthesurfacesofthenanodiamondsarerichedwithcarboxylgroups.

19FigureS14TrackingofanNDonaHelacellplasmamembrane.a,Time-dependentdisplacementoftheNDprojectedalongthelabcoordiate(x,y,z).b.InstantspeedoftheNDcalculatedfromthetrajectory.Thehistogramshownintheinsetrevealsthemostprobablespeed.c.Time-dependentEuleranglesdeducedbyfittingtheODMRspectra.ThedashedrectangularmarksthesegmentcorrespondingtotherotationaltrajectoryshowninFig.3dinthemaintext.d.AngularspeedcalculatedfromtheEulerangles.Insetshowsthecorrespondinghistogram.

20FigureS15TranslationandrotationtrackingofanNDonaPFA-fixedcell.a,FluorescenceimageoftheNDonthePFAfixedHelacell.b,TranslationaltrajectoryoftheNDshownina.c,translationalspeedoftheND.Insetshowsthehistogram.d,Time-dependentODMRspectrawithfittingresults.ThetwoleftpanelsshowtheunbinnedODMRspectra.Therotationiswithinnoiselevel.Thesignal-to-noiseratioofthedataisimprovedbybiningafewODMRspectraintoone.ThetwopanelsontherightshowstheODMRspectrabinnedevery16spectra.e,EuleranglesdeducedbyfittingtheunbinnedODMRspectra(graylines)andthosebinnedevery16spectra(colored).f,ThestandarddeviationofthethreeEulerangles(?ఈ,?ఉ,?ఊ)obtainedfordifferentଵdataacquisitintimeT(binningvalues).Thelineardependenceof?ఈ,?ఉ,?ఊonsuggeststhat√்thesensitivityoftheEuleranglemeasurementisshotnoiselimited.Scalebarinais10μm.

21FigureS16InteractionofNDswithcellplasmamembranes.a.FluorescenceimageofNDsonHelacellsstainedwithCellMaskGreenafterfiation.b.Fluorescenceimageofthesameareaasinaafterpermeabilization,wherethefluorescencesignalvanishesduetotheremovaloflipidswhilethepositionsoftheNDsdonotchange.Sincethepermeabilizationprocessremovesthelipidmoleculesfromtheplasmamembranes,theretentionoftheNDsonthecellssuggeststhattheNDsareanchoredontheproteinsonthecellmembranes.Scalebarsare10μm.

22SINote5.TrackingNDsonplasmamembranesduringandaftercellnecrosisNecrosisofcellunderilluminationbya473nmlaserisconfirmedusingtheviabilityassayBCECFAM(ThermoFisher).Accordingtotheproductmanual,theunchargedBCECFAMmoleculescanpermeatecellmembranesanddiffusepassivelyintocells.Onceinsidecell,thenon-fluorescentBCECFAMmoleculesarecleavedbynon-specificintracellularesterasestoformfluorescentBCECFwithnegativecharges,withtheirmembranepermeabilitylost.Thus,thefluorescencesignalfromBCECFworksasanindicatorofenzymaticactivityandmembraneintegrity,whicharevitalforcellviability.ThefluorescenceimagesofHelacellsstainedwiththeBCECFAMbeforeandafterilluminationbya473-nmlaseratpowerwith5wfor5minareshowninFigureS16.Thephotoluminescencecountsareencodedincolorscale.Blackcrossesmarkthelaserfocuses.Thefluorescenceintensityofthethreecellsilluminatedwiththe473-nmlaserissignificantlyreduced,whilethatofuntreatedcellshaslittlechange.Theseresultssuggestthatthemembraneintegrityisdisruptedbytheilluminationofthe473-nmlaser,indicatingthecelldeath.FigureS17.Effectoftheilluminationofa473-nmlaseroncellviability.a,FluorescenceimageofHelacellsstainedwiththeviabilityassayBCECF.b,Fluorescenceimageofthecellsafterilluminationbya473-nmlaserwith5wpowerfor5min.Thelaserisfocusedonpositionmarkedwithcrossesina.Scalebarsare10μm.AnNDonthesurfaceofacellistrackedforabout5h,duringwhicha473-nmlaserof5wpoweriscontinuouslyscanningacrossthearea,whicheventuallyleadstocellnecrosis.Duringthenecrosisprocess,thecellularactivitiesgraduallyslowdown14,15,asindicatedbytherotationoftheNDslowingdown(FigureS17).Therelativelylargerrangeoftranslationaltrajectorymaybe

23FigureS18.TrackinganNDonacellduringnecrosis.a,TranslationaltrajectoryoftheND.b,Translationalspeedcalculatedfromthetrajectoryina.c-d,Time-dependentODMRspectraundertwomagneticfieldscollectedtogetherwithtranslationtracking.Thefittingresultsareoverlappedwiththerawdata.e-g,EuleranglesobtainedbyfittingtheODMRspectra.h,AngularspeedoftheNDcalcualtedfromtheEulerangles.explainedbythemorphologicalchangeofthecellunderlaserirradiation,and/orsystemdriftduetothelongdatarecordingduration.Inthe5hoursofrecording,theNDhasasmalltranslationalspeed(<200nm/s),whichisnotsignificantlychangedduringthewholeprocess.TherotationoftheND,however,changessignificantlywhenthelaserirradiationaccumulates.Fromthetime-dependentODMRspectrainFigureS17candd,oneobservesthatthefrequencyshifttakesplaceatahighrateinthefirst10000s.Theshiftgraduallyslowsdownandfinallystopsatabout17500s.SimilartrendsareseenintheevolutionofEulerangles,asshowninFigureS17e-g.Gradualslowdownoftheangularspeedisalsoseen(FigureS17h).ThebehaviorsofNDsoncellsafternecrosisarefurtherchecked.AtypicalresultisshowninFigureS18.ThefluorescenceimagesofthecellandtheNDbeforenecrosisareshownina.The

24FigureS19.AnalysisoftheNDmotiononadeadcell(photo-inducednecrosis).a,FluorescenceimageoftheNDandtheHelacell.b,TranslationaltrajectoryoftheND.c,translationalspeedoftheND.Insetshowsthehistogram.d,Time-dependentODMRspectraunbinned(twoleftpanels)andbinnedevery16spectra(tworightpanels)withfittingresultsoverlappedontherawdata.e,EuleranglesobtainedfromfittingtherawODMRspectra(gray)andthebinnedODMRspectra(colored).f,ThestandarddeviationofthethreeEulerangles(?ఈ,?ఉ,?ఊ)fordifferentintegrationtimeT(binningvalues).Scalebarinais10μm.cellisthenscannedwitha473-nmlaserforlongenoughtimeuntiltheODMRspectrumstopchaning.Theresultsinthelast500sareshown.ThetranslationaltrajectoryinbandthespeedincareslightlylargerthanthosemeasuredinPFA-fixedcellsasshowninFigureS14,butarestillquiteconfined.Thisisprobablybecausethenecrosedcellissofterduetothelackofproteincross-linking.ThefittingresultstotherawODMRspectraarenoisy,duetotheverysmallrotationangle(ifany)oftheNDandthelimitedangularsensitivityofourcurrenttechnique.Toimprovetheprecisionoftherotationanglemeasurement,theODMRspectraareintegratedoveraperiodT(binnedforevery16spectra)andtheresultsareplottedinthetworightpanelsind.TheEuleranglesobtainedbyfittingtherawandbinnedODMRspectraareshownineasgreyandcoloredlines,respectively.Asmallrotationbyaboutseveraldeg.canbefound.ThestandarddeviationoftheEulerangles(?ఈ,?ఉ,?ఊ)obtainedbyfittingtheODMRspectraofdifferentintegrationtimeT(binningvalues)isshowninf.ThedecreasingstandarddeviationwithincreasingTsuggeststhatshotnoisehasasignicicantcontributiontotheuncertaintyofEulerangledetermination,especiallyforsmallintegrationtimeT.

25TherotationoftheNDstopsafternecrosis.Thisphenonenon,consistentwiththeobservationsinPFA-fixedcells,suggeststhatexternalenvironmentfactorsmakelittlecontributiontotherotationoftheND.Thatistosay,theNDrotationiscausedbylivecellactivities,suchasactivefluctuationoftheplasmamembranes(asaresultofvariousmetabolicprocess).Inaddition,theangularspeeddecareasingduringthelaserirradiationsuggeststheslowdownofactiveplasmamembranefluctuationbythelaserirradiation.

26FigureS20.EffectofDG/AzideontheATPlevelofcellsmeasuredbyluminescentATPdetectionkit.a,TheATPlevelofcellstreatedwithvariousconcentrationsofsodiumazide(bottomx-axis)andDG(topx-axis)for30min.TheATPleveldropsdramaticallytobelow20%withtheintroductionofazide/DGevenatlowconcentrationsof0.3mM/1.5mM(azide/DG).TheATPconcentrationlevelsoffat~10%athigherconcentrationofazide/DG.b,EvolutionoftheATPlevelincellstreatedwith10mMsodiumazideand50mMDG(black)anditsrecoveryafter30mintreatmentwiththeinhibitorsofthesameconcentration(red).TheATPleveldropstobelow20%afterbeingtreatedwithazide/DGfor5minthenlevelsoffafter15min,andgraduallydecreasestobelow5%after60min.Fortherecoveryprocess,thecellsarepretreatedwith10mM/50mM(azide/DG)for30min,thensuppliedwithfreshmedium.Therecoveryprocessisslowascomparedwithdepletion.Itregainsa~20%normalATPlevelin5minaftertheinhibitorsarewashedaway,butincreasesonlyto45%thenormalATPlevelafter80min,probablyduetosomedamageaccumulatedduringtheATPdepletion.Theerrorbarineachgraphisthestandarddeviationfromthreeindependentmeasurements.

27FigureS21.TranslationofanNDonacellinthenormal,ATP-depeleted,orATP-recoveringstate.a-c,Time-dependenttranslationaldisplacementmeasuredinthenormal,ATP-depletedandATP-recoveringstates.d-f,thecorrespondingtranslationaltrajectoriesforthreedifferentcellstates.g-i,thecorrespondingtranslationalvelocitiesestimatedfromthetrajectoriesshownind-f.Thehistogramofspeedisshownintheinsets.ThetranslationoftheNDonthecellatthreedifferentstatesisnotsignificantlydifferent.Thetrajectoriesarewithina1μmcube,andthevelocitiesarebelow1μmsିଵ.

28FigureS22.RotationofanNDonacellinthenormal,ATPdepeleted,orATP-recoveringstate.a-c,Euleranglesobtainedbyfittingthetime-dependentODMRspectra(Fig.4ainthemaintext)oftheNDonthecellinthreedifferentstates.TherangeofEuleranglesoftheNDonthecellintheATP-depletedstate(within5°)issignificantlysmallerthanthoseinthetwootherstates(uptoabout100°).d-f,RotationaltrajectoriesoftheNDonthecellinthreedifferentstates.TherotationoftheNDisrepresentedbytheevolutionoftwoofthefourNVaxes.TherotationoftheNDonthecellinthenormalandtheATP-recoveringstatesissignificant,whilethatintheATP-depletedstateisnegligible.

29FigureS23.Rotationoffibronectin-coatednanodiamondsoncellmembranes.a,Fourier-transforminfraredspectraofthefibronectin-coatednanodiamonds.Theabsorptionpeaksat~1650cm-1-116ofand~1540cmareascribedtothecharacteristicamideIandamideIIbandsproteins.b,Distributionofhydrodynamicdiameteroffibronectin-coatednanodiamondsmeasuredbyDLS.Thehydrodynamicdiameterisabout200nm.c,OnetypicalsetofODMRspectracollectedfromafibronectin-coatednanodiamondonaplasmamembraneatnormal,ATP-depleted,andrecoverystates.d.Meanofsquaredangulardisplacementsfortimeintervalof30sfromafewmorefibronectin-coatedNDsoncells.ThedatapointsofthesamecoloraretheresultsfromthesameNDsandcells,whiletheblackdatapointsaretheresultsfromindependentcells.Theresultsarefrom16trajectoriesof9NDson9cells.

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