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Awayofunderstandingdiffusion:RandomWalkSpreadofmoleculesfromonespotisproportionaltosquarerootoftimeforrandomwalk.Therefore,togo2Xasfartakes4Xaslong.Awayofunderstandingdiffusion:Fick’sLaw

Jisflux

Disdiffusionconstant

isconcentration

DiffusionConstant:Whatcontrolsit?Randomthermalmotions:D=kTv/ffdependsonsizeofparticleandviscosityofsolution.Spheres:scaleasm1/3(radiusscaling)FRAP-FluorescenceRecoveryAfterPhotobleachingCartoonofFRAPBleachcreates“hole”offluorophores,Diffusionismeasuredby“holefillingin”BleachhighpowerMonitorlowpowerAnalysisofmembranecompartmentsCellsexpressingVSVG–GFPwereincubatedat40°CtoretainVSVG–GFPintheendoplasmicreticulum(ER)undercontrolconditions(toppanel)orinthepresenceoftunicamycin(bottompanel).Fluorescencerecoveryafterphotobleaching(FRAP)revealedthatVSVG–GFPwashighlymobileinERmembranesat40°Cbutwasimmobilizedinthepresenceoftunicamycin(Nehlsetal,2000NatureCellBiology)ExperimentalSetupLaserbeamfocusedorthroughsmallfielddiaphragmRapidshuttertoswitchfromhighpoweredbeamforbleachtoattenuatedbeamforrecoverysamepowerwon’twork-Keepbleaching)Detector:PMT,camera?Originalapparatususedstationarylaserspot(stillsometimesused)Laterimprovementincludedscanningmirrortoscanspotoversample.Nowcanbedonewithlaserscanningconfocalinstruments.(forsomecases-e.g.membranes)IdealizedphotobleachingdataYX=mobilefractionD=w2/4DRealFRAPdataMoreDiffusiontypesImportantforLargemacromolecules:Collisions,obstacles,bindingFullyrecoversABBothAandBwillhavesimilarDinMembranealthoughVerydifferentsizesBindingtoimmobilizedmatrixwillreducefractionofmoleculesdiffusingintraextracellularDiffusionofmembranecomponentscanbeseenasatwodimensionaldiffusionproblemMembraneismodeledasinfiniteplaneViscosityofthelipidbilayeris~2ordersofmagnitudehigherthanwaterAsshownbySaffmanandDelbruck,thetranslationaldiffusioncoefficientformembranecomponentsdependsonlyonthesizeofthemembranespanningdomainSpotPhotobleachingBleachandmonitorsinglediffractionlimitedspotAssumesinfinitereservoiroffluorescentmolecules(holecanfillbackin)UseD=w2/4DtoobtainDDeterminew=nominalwidthofGaussianspotbyotheropticalmethod1/e2pointFitfluorescencerecoverycurvetoobtainD

Axelrodetal.,1976PSFandBeamWaistImagingsub-resolution100nmfluorescentbeadsUse1/e2pointstogetωbeamwaist(87%)D=w2/4DDifferentbleachinggeometriesyielddifferenttypesofinformationLinephotobleachinggeneratesaone-dimensionaldiffusionproblem

Allowscollectionofmorefluorescence,averagingFxNotethatbeamisstillGaussianLinescanofsinglepointsScanningoverbleachspotimprovesabilitytocharacterizerecoverycurvesAllowsaccuratecharacterizationofthebleachgeometryandsizeforeachindividualexperimentSimplifiesfitsofrecoverycurvesto:wherea

isaconstantreflectingextentofbleaching.Koppel,1979Biophys.J.281Allowscompensationforphotobleachingduringmonitoringandsampledrift.NorecoveryRecoveryPre-bleachimagePhotobleachPost-bleachimageDifferentbleachinggeometriesyielddifferenttypesofinformationFRAPofGFPinMitochondriaSuggestsbarriers(cristae)needtobelargeOcclude90%spaceVerkman,TIBS,2019Fastlimit:cytoplasmSlowlimit:membraneboundSizedependenceofdextrans(polysaccharides)diffusioninsolutionNotsimplespheres:RandomcoilsNosimplem1/3scalingVerkman,J.CellBiology2019DiffusionofFITCDextrans,FicollsinMDCKCellCytoplasmHeavydextransveryslowMobilefractionlow:bindingMorepolarizableVerkman,J.CellBiology2019Problemismuchmorecomplicatedbecauseofthreedimensionalfreelydiffusinggeometry.FRAPinCytoplasmProblemswithFRAPofcytoplasmiccomponents(2ordersofmagnitudefaster

thanmembranes)1. DiffusionisfastcomparedtobleachingandmonitoringrateD=ms:cannottrulyscan2 Ifusesmallbleachregions,redistributionmayoccurduringbleaching.Infact,oftencannotobservebleachofsmallregionatall.3. Byenlargingthesizeofthebleachregion,canovercomethisproblem:butloselocalizationOnesolutionistomeasurecytoplasmicdiffusionbycomparingtocharacteristictimesofknownsamplesinsolutionsofknownviscosity.

e.g.Luby-Phelpsetal.,1994.SekSeketal.2019.D=kT/fNotreliable,cytoplasmcomplicatedcollectionoffluid,cytoskeletalcomponents,endosome,etc:simpleviscositynotsufficientPhotobleachingofcytoplasmiccomponentsD=w2/4DAnothersolutionistousegeometrysuchdepthoffieldiscomparabletothicknessofcellHighNAlensLowNAlensGeometryapproximatescylinderbleachedthroughZDiffusionbecomes2Dproblem:easierPhotobleachingofcytoplasmiccomponentsRecoveryisconvolvedWithdepthoffieldMultiphotonbleachingNeed3DtreatmentDeterminationofPointSpreadFunctionofMicroscope175nmBeadSub-resolutionVolumeisEllipsoidAxial~NA2Typical2-photonPhotobleachingsetup(PointBleach)1-pwouldneedpinholeBleachhighpowerMonitorlowpower~20%for2-pControlspowerFluorescenceLossinPhotobleaching“FLIP”

continuousbleachingmeasureofmobilityFigure3

|

Fluorescencelossinphotobleaching.

Proteinfluorescenceinasmallareaofthecell(box)isbleachedrepetitively.Lossoffluorescenceinareasoutsidetheboxindicatesthatthefluorescentproteindiffusesbetweenthebleachedandunbleachedareas.Repetitivephotobleachingofanendoplasmicreticulum(ER)GFP-taggedmembraneproteinrevealsthecontinuityoftheERinaCOS-7cell.Imagetimesareindicatedinthelowerrightcorners.Thepostbleachimagewasobtainedimmediatelyafterthefirstphotobleach.Thecellwasrepeatedlyphotobleachedinthesameboxevery40s.After18min,theentireERfluorescencewasdepleted,indicatingthatalloftheGFP-taggedproteinwashighlymobileandthattheentireERwascontinuouswiththeregioninthebleachbox.(Nehlsetal,2000NatureCellBiology)PhotobleachingexperimentsObtaindiffusioncoefficientBinding/mobilefractionDefineactivetransport/directedflowmechanismsDefinetraffickingratesthroughintracellularcompartments(includingcytoplasm,fast)Fluctuation(fluorescence)CorrelationSpectroscopy(FCS)FluctuationsinexcitationvolumeduetoDiffusion,reactionsComparesprobabilityofdetectingphotonattimetwithsomelattertimet+τFormfortranslationaldiffusionN=concentrationofmoleculesinfocalvolumeτD=diffusiontime,R=ωz/ωxyofobservationvolumeFCSofRhodamineinSucroseSolutionHigherconcentrationsShortercorrelationtimeswebbAPPLICATIONS

–peptidesboundtosolublereceptors,–ligandsboundtomembrane-anchoredreceptors,–virusesboundtocells,–antibodiesboundtocells,–primersboundtotargetnucleicacids,–regulatoryproteins/protein-complexesininteraction withtargetDNAorRNA–enzymaticproducts.Ifthediffusionpropertiesofthereactantsaretoosimilar,bothreactantshavetobelabeledwithfluorescentdyeswithdifferentexcitationandemissionspectra.MathematicalmodelforautocorrelationTwocomponentautocorrelationcurveBindingtomobilereceptorBindingtoimmobilereceptorMotilityalongmicrotubuleConcentrationDiffusionofreceptorConcen

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