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Awayofunderstandingdiffusion:RandomWalkSpreadofmoleculesfromonespotisproportionaltosquarerootoftimeforrandomwalk.Therefore,togo2Xasfartakes4Xaslong.Awayofunderstandingdiffusi1Awayofunderstandingdiffusion:Fick’sLaw
Jisflux
Disdiffusionconstant
isconcentrationAwayofunderstandingdiffusi2
DiffusionConstant:Whatcontrolsit?Randomthermalmotions:D=kTv/ffdependsonsizeofparticleandviscosityofsolution.Spheres:scaleasm1/3(radiusscaling)DiffusionConstant:Whatcont3FRAP-FluorescenceRecoveryAfterPhotobleachingFRAP-FluorescenceRecoveryA4CartoonofFRAPBleachcreates“hole”offluorophores,Diffusionismeasuredby“holefillingin”BleachhighpowerMonitorlowpowerCartoonofFRAPBleachcreates5AnalysisofmembranecompartmentsCellsexpressingVSVG–GFPwereincubatedat40°CtoretainVSVG–GFPintheendoplasmicreticulum(ER)undercontrolconditions(toppanel)orinthepresenceoftunicamycin(bottompanel).Fluorescencerecoveryafterphotobleaching(FRAP)revealedthatVSVG–GFPwashighlymobileinERmembranesat40°Cbutwasimmobilizedinthepresenceoftunicamycin(Nehlsetal,2000NatureCellBiology)Analysisofmembranecompartme6ExperimentalSetupLaserbeamfocusedorthroughsmallfielddiaphragmRapidshuttertoswitchfromhighpoweredbeamforbleachtoattenuatedbeamforrecoverysamepowerwon’twork-Keepbleaching)Detector:PMT,camera?Originalapparatususedstationarylaserspot(stillsometimesused)Laterimprovementincludedscanningmirrortoscanspotoversample.Nowcanbedonewithlaserscanningconfocalinstruments.(forsomecases-e.g.membranes)ExperimentalSetupLaserbeamf7IdealizedphotobleachingdataYX=mobilefractionD=w2/4DIdealizedphotobleachingdataY8RealFRAPdataRealFRAPdata9MoreDiffusiontypesImportantforLargemacromolecules:Collisions,obstacles,bindingFullyrecoversMoreDiffusiontypesImportant10ABBothAandBwillhavesimilarDinMembranealthoughVerydifferentsizesBindingtoimmobilizedmatrixwillreducefractionofmoleculesdiffusingintraextracellularABBothAandBwillBindingto11DiffusionofmembranecomponentscanbeseenasatwodimensionaldiffusionproblemMembraneismodeledasinfiniteplaneViscosityofthelipidbilayeris~2ordersofmagnitudehigherthanwaterAsshownbySaffmanandDelbruck,thetranslationaldiffusioncoefficientformembranecomponentsdependsonlyonthesizeofthemembranespanningdomainDiffusionofmembranecomponen12SpotPhotobleachingBleachandmonitorsinglediffractionlimitedspotAssumesinfinitereservoiroffluorescentmolecules(holecanfillbackin)UseD=w2/4DtoobtainDDeterminew=nominalwidthofGaussianspotbyotheropticalmethod1/e2pointFitfluorescencerecoverycurvetoobtainD
Axelrodetal.,1976SpotPhotobleachingBleachand13PSFandBeamWaistImagingsub-resolution100nmfluorescentbeadsUse1/e2pointstogetωbeamwaist(87%)D=w2/4DPSFandBeamWaistImagingsub-14DifferentbleachinggeometriesyielddifferenttypesofinformationLinephotobleachinggeneratesaone-dimensionaldiffusionproblem
Allowscollectionofmorefluorescence,averagingFxNotethatbeamisstillGaussianLinescanofsinglepointsDifferentbleachinggeometries15ScanningoverbleachspotimprovesabilitytocharacterizerecoverycurvesAllowsaccuratecharacterizationofthebleachgeometryandsizeforeachindividualexperimentSimplifiesfitsofrecoverycurvesto:wherea
isaconstantreflectingextentofbleaching.Koppel,1979Biophys.J.281Allowscompensationforphotobleachingduringmonitoringandsampledrift.Scanningoverbleachspotimpr16NorecoveryRecoveryPre-bleachimagePhotobleachPost-bleachimageDifferentbleachinggeometriesyielddifferenttypesofinformationNorecoveryRecoveryPre-bleachP17FRAPofGFPinMitochondriaSuggestsbarriers(cristae)needtobelargeOcclude90%spaceVerkman,TIBS,2019Fastlimit:cytoplasmSlowlimit:membraneboundFRAPofGFPinMitochondriaSug18Sizedependenceofdextrans(polysaccharides)diffusioninsolutionNotsimplespheres:RandomcoilsNosimplem1/3scalingVerkman,J.CellBiology2019Sizedependenceofdextrans(19DiffusionofFITCDextrans,FicollsinMDCKCellCytoplasmHeavydextransveryslowMobilefractionlow:bindingMorepolarizableVerkman,J.CellBiology2019DiffusionofFITCDextrans,Fi20Problemismuchmorecomplicatedbecauseofthreedimensionalfreelydiffusinggeometry.FRAPinCytoplasmProblemismuchmorecomplicat21ProblemswithFRAPofcytoplasmiccomponents(2ordersofmagnitudefaster
thanmembranes)1. DiffusionisfastcomparedtobleachingandmonitoringrateD=ms:cannottrulyscan2 Ifusesmallbleachregions,redistributionmayoccurduringbleaching.Infact,oftencannotobservebleachofsmallregionatall.3. Byenlargingthesizeofthebleachregion,canovercomethisproblem:butloselocalizationProblemswithFRAPofcytoplas22Onesolutionistomeasurecytoplasmicdiffusionbycomparingtocharacteristictimesofknownsamplesinsolutionsofknownviscosity.
e.g.Luby-Phelpsetal.,1994.SekSeketal.2019.D=kT/fNotreliable,cytoplasmcomplicatedcollectionoffluid,cytoskeletalcomponents,endosome,etc:simpleviscositynotsufficientPhotobleachingofcytoplasmiccomponentsD=w2/4DOnesolutionistomeasurecyt23AnothersolutionistousegeometrysuchdepthoffieldiscomparabletothicknessofcellHighNAlensLowNAlensGeometryapproximatescylinderbleachedthroughZDiffusionbecomes2Dproblem:easierPhotobleachingofcytoplasmiccomponentsRecoveryisconvolvedWithdepthoffieldAnothersolutionistousegeo24MultiphotonbleachingNeed3DtreatmentMultiphotonbleachingNeed3Dt25DeterminationofPointSpreadFunctionofMicroscope175nmBeadSub-resolutionVolumeisEllipsoidAxial~NA2DeterminationofPointSpread26Typical2-photonPhotobleachingsetup(PointBleach)1-pwouldneedpinholeBleachhighpowerMonitorlowpower~20%for2-pControlspowerTypical2-photonPhotobleachin27FluorescenceLossinPhotobleaching“FLIP”
continuousbleachingmeasureofmobilityFigure3
|
Fluorescencelossinphotobleaching.
Proteinfluorescenceinasmallareaofthecell(box)isbleachedrepetitively.Lossoffluorescenceinareasoutsidetheboxindicatesthatthefluorescentproteindiffusesbetweenthebleachedandunbleachedareas.Repetitivephotobleachingofanendoplasmicreticulum(ER)GFP-taggedmembraneproteinrevealsthecontinuityoftheERinaCOS-7cell.Imagetimesareindicatedinthelowerrightcorners.Thepostbleachimagewasobtainedimmediatelyafterthefirstphotobleach.Thecellwasrepeatedlyphotobleachedinthesameboxevery40s.After18min,theentireERfluorescencewasdepleted,indicatingthatalloftheGFP-taggedproteinwashighlymobileandthattheentireERwascontinuouswiththeregioninthebleachbox.(Nehlsetal,2000NatureCellBiology)FluorescenceLossinPhotoblea28PhotobleachingexperimentsObtaindiffusioncoefficientBinding/mobilefractionDefineactivetransport/directedflowmechanismsDefinetraffickingratesthroughintracellularcompartments(includingcytoplasm,fast)PhotobleachingexperimentsObta29Fluctuation(fluorescence)CorrelationSpectroscopy(FCS)FluctuationsinexcitationvolumeduetoDiffusion,reactionsFluctuation(fluorescence)Cor30Comparesprobabilityofdetectingphotonattimetwithsomelattertimet+τComparesprobabilityofdetect31Fluorescence-Recovery-Af教學(xué)講解課件32FormfortranslationaldiffusionN=concentrationofmoleculesinfocalvolumeτD=diffusiontime,R=ωz/ωxyofobservationvolumeFormfortranslationaldiffusi33FCSofRhodamineinSucroseSolutionHigherconcentrationsShortercorrelationtimeswebbFCSofRhodamineinSucroseSo34Fluorescence-Recovery-Af教學(xué)講解課件35APPLICATIONS
–peptidesboundtosolublereceptors,–ligandsboundtomembrane-anchoredreceptors,–virusesboundtocells,–antibodiesboundtocells,–primersboundtotargetnucleicacids,–regulatoryproteins/protein-complexesininteraction withtargetDNAorRNA–enzymaticproducts.Ifthediffusionpropertiesofthereactantsaretoosimilar,bothreactantshavetobelabeledwithfluorescentdyeswithdifferentexcitationandemissionspectra.APPLICATIONS36MathematicalmodelforautocorrelationTwocomponentautocorrelationcurveMathematicalmodelforautocor37BindingtomobilereceptorBindingtoimmobilereceptorMotilityalongmicrotubuleConcentrationDiffusionofreceptorConcentrationKdOnrate(M-1sec-1)Offrate(sec-1)Mobile/immobileMeansquareddisplacementTheslowcomponentinlivingcellsBindingtomobilereceptorBind38fluorescentmoleculesCross-correlationspectroscopy3DGaussianconfocaldetectionvolume~1femtoliterdiffusiontrajectoriesIndividualfluorescentmoleculesaredetectedassinglechannelphotoncountfluctuations.Boundmoleculesaredetectedascoincidentdualchannelfluctuations.
Cross-correlationanalysisprovidesameasureofthenumberandrateofdiffusionofboundmolecules.Cross-correlationfunctionGrg(t)=<Ig(t).Ir(t+t)>11.021.041.061.081.110100100010000microsecondsAlexa488RNASyto61cross-correlationDualchannelfluctuation
100001500020000250003000035000400004500050000012345678910secondsAlexa488RNASyto61CountratefluorescentCross-correlations39謝謝你的閱讀知識就是財富豐富你的人生謝謝你的閱讀知識就是財富40謝謝!謝謝!41Awayofunderstandingdiffusion:RandomWalkSpreadofmoleculesfromonespotisproportionaltosquarerootoftimeforrandomwalk.Therefore,togo2Xasfartakes4Xaslong.Awayofunderstandingdiffusi42Awayofunderstandingdiffusion:Fick’sLaw
Jisflux
Disdiffusionconstant
isconcentrationAwayofunderstandingdiffusi43
DiffusionConstant:Whatcontrolsit?Randomthermalmotions:D=kTv/ffdependsonsizeofparticleandviscosityofsolution.Spheres:scaleasm1/3(radiusscaling)DiffusionConstant:Whatcont44FRAP-FluorescenceRecoveryAfterPhotobleachingFRAP-FluorescenceRecoveryA45CartoonofFRAPBleachcreates“hole”offluorophores,Diffusionismeasuredby“holefillingin”BleachhighpowerMonitorlowpowerCartoonofFRAPBleachcreates46AnalysisofmembranecompartmentsCellsexpressingVSVG–GFPwereincubatedat40°CtoretainVSVG–GFPintheendoplasmicreticulum(ER)undercontrolconditions(toppanel)orinthepresenceoftunicamycin(bottompanel).Fluorescencerecoveryafterphotobleaching(FRAP)revealedthatVSVG–GFPwashighlymobileinERmembranesat40°Cbutwasimmobilizedinthepresenceoftunicamycin(Nehlsetal,2000NatureCellBiology)Analysisofmembranecompartme47ExperimentalSetupLaserbeamfocusedorthroughsmallfielddiaphragmRapidshuttertoswitchfromhighpoweredbeamforbleachtoattenuatedbeamforrecoverysamepowerwon’twork-Keepbleaching)Detector:PMT,camera?Originalapparatususedstationarylaserspot(stillsometimesused)Laterimprovementincludedscanningmirrortoscanspotoversample.Nowcanbedonewithlaserscanningconfocalinstruments.(forsomecases-e.g.membranes)ExperimentalSetupLaserbeamf48IdealizedphotobleachingdataYX=mobilefractionD=w2/4DIdealizedphotobleachingdataY49RealFRAPdataRealFRAPdata50MoreDiffusiontypesImportantforLargemacromolecules:Collisions,obstacles,bindingFullyrecoversMoreDiffusiontypesImportant51ABBothAandBwillhavesimilarDinMembranealthoughVerydifferentsizesBindingtoimmobilizedmatrixwillreducefractionofmoleculesdiffusingintraextracellularABBothAandBwillBindingto52DiffusionofmembranecomponentscanbeseenasatwodimensionaldiffusionproblemMembraneismodeledasinfiniteplaneViscosityofthelipidbilayeris~2ordersofmagnitudehigherthanwaterAsshownbySaffmanandDelbruck,thetranslationaldiffusioncoefficientformembranecomponentsdependsonlyonthesizeofthemembranespanningdomainDiffusionofmembranecomponen53SpotPhotobleachingBleachandmonitorsinglediffractionlimitedspotAssumesinfinitereservoiroffluorescentmolecules(holecanfillbackin)UseD=w2/4DtoobtainDDeterminew=nominalwidthofGaussianspotbyotheropticalmethod1/e2pointFitfluorescencerecoverycurvetoobtainD
Axelrodetal.,1976SpotPhotobleachingBleachand54PSFandBeamWaistImagingsub-resolution100nmfluorescentbeadsUse1/e2pointstogetωbeamwaist(87%)D=w2/4DPSFandBeamWaistImagingsub-55DifferentbleachinggeometriesyielddifferenttypesofinformationLinephotobleachinggeneratesaone-dimensionaldiffusionproblem
Allowscollectionofmorefluorescence,averagingFxNotethatbeamisstillGaussianLinescanofsinglepointsDifferentbleachinggeometries56ScanningoverbleachspotimprovesabilitytocharacterizerecoverycurvesAllowsaccuratecharacterizationofthebleachgeometryandsizeforeachindividualexperimentSimplifiesfitsofrecoverycurvesto:wherea
isaconstantreflectingextentofbleaching.Koppel,1979Biophys.J.281Allowscompensationforphotobleachingduringmonitoringandsampledrift.Scanningoverbleachspotimpr57NorecoveryRecoveryPre-bleachimagePhotobleachPost-bleachimageDifferentbleachinggeometriesyielddifferenttypesofinformationNorecoveryRecoveryPre-bleachP58FRAPofGFPinMitochondriaSuggestsbarriers(cristae)needtobelargeOcclude90%spaceVerkman,TIBS,2019Fastlimit:cytoplasmSlowlimit:membraneboundFRAPofGFPinMitochondriaSug59Sizedependenceofdextrans(polysaccharides)diffusioninsolutionNotsimplespheres:RandomcoilsNosimplem1/3scalingVerkman,J.CellBiology2019Sizedependenceofdextrans(60DiffusionofFITCDextrans,FicollsinMDCKCellCytoplasmHeavydextransveryslowMobilefractionlow:bindingMorepolarizableVerkman,J.CellBiology2019DiffusionofFITCDextrans,Fi61Problemismuchmorecomplicatedbecauseofthreedimensionalfreelydiffusinggeometry.FRAPinCytoplasmProblemismuchmorecomplicat62ProblemswithFRAPofcytoplasmiccomponents(2ordersofmagnitudefaster
thanmembranes)1. DiffusionisfastcomparedtobleachingandmonitoringrateD=ms:cannottrulyscan2 Ifusesmallbleachregions,redistributionmayoccurduringbleaching.Infact,oftencannotobservebleachofsmallregionatall.3. Byenlargingthesizeofthebleachregion,canovercomethisproblem:butloselocalizationProblemswithFRAPofcytoplas63Onesolutionistomeasurecytoplasmicdiffusionbycomparingtocharacteristictimesofknownsamplesinsolutionsofknownviscosity.
e.g.Luby-Phelpsetal.,1994.SekSeketal.2019.D=kT/fNotreliable,cytoplasmcomplicatedcollectionoffluid,cytoskeletalcomponents,endosome,etc:simpleviscositynotsufficientPhotobleachingofcytoplasmiccomponentsD=w2/4DOnesolutionistomeasurecyt64AnothersolutionistousegeometrysuchdepthoffieldiscomparabletothicknessofcellHighNAlensLowNAlensGeometryapproximatescylinderbleachedthroughZDiffusionbecomes2Dproblem:easierPhotobleachingofcytoplasmiccomponentsRecoveryisconvolvedWithdepthoffieldAnothersolutionistousegeo65MultiphotonbleachingNeed3DtreatmentMultiphotonbleachingNeed3Dt66DeterminationofPointSpreadFunctionofMicroscope175nmBeadSub-resolutionVolumeisEllipsoidAxial~NA2DeterminationofPointSpread67Typical2-photonPhotobleachingsetup(PointBleach)1-pwouldneedpinholeBleachhighpowerMonitorlowpower~20%for2-pControlspowerTypical2-photonPhotobleachin68FluorescenceLossinPhotobleaching“FLIP”
continuousbleachingmeasureofmobilityFigure3
|
Fluorescencelossinphotobleaching.
Proteinfluorescenceinasmallareaofthecell(box)isbleachedrepetitively.Lossoffluorescenceinareasoutsidetheboxindicatesthatthefluorescentproteindiffusesbetweenthebleachedandunbleachedareas.Repetitivephotobleachingofanendoplasmicreticulum(ER)GFP-taggedmembraneproteinrevealsthecontinuityoftheERinaCOS-7cell.Imagetimesareindicatedinthelowerrightcorners.Thepostbleachimagewasobtainedimmediatelyafterthefirstphotobleach.Thecellwasrepeatedlyphotobleachedinthesameboxevery40s.After18min,theentireERfluorescencewasdepleted,indicatingthatalloftheGFP-taggedproteinwashighlymobileandthattheentireERwascontinuouswiththeregioninthebleachbox.(Nehlsetal,2000NatureCellBiology)FluorescenceLossinPhotoblea69PhotobleachingexperimentsObtaindiffusioncoefficientBinding/mobilefractionDefineactivetransport/directedflowmechanismsDefinetraffickingratesthroughintracellularcompartments(includingcytoplasm,fast)PhotobleachingexperimentsObta70Fluctuation(fluorescence)CorrelationSpectroscopy(FCS)FluctuationsinexcitationvolumeduetoDiffusion,reactionsFluctuation(fluorescence)Cor71Comparesprobabilityofdetectingphotonattimetwithsomelattertimet+τComparesprobabilityofdetect72Fluorescence-Recovery-Af教學(xué)講解課件73FormfortranslationaldiffusionN=conc
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