Ligand Rebinding Self-consistent Mean-field Theory

1LigandRebinding:Self-consistentMean-fieldTheoryandNumericalSimulationsAppliedtoSPRStudiesManojGopalakrishnan¶1,KimberlyForsten-Williams§*,TheresaR.Cassino§,LuzPadro§,ThomasE.Ryan†andUweC.Täuber¶¶DepartmentofPhysics,VirginiaPolytechnicInstituteandStateUniversity,Blacksburg,VA24061-0435,USA.§DepartmentofChemicalEngineeringandVirginiaTech-WakeForestUniversitySchoolofBiomedicalEngineeringandSciences,VirginiaPolytechnicInstituteandStateUniversity,Blacksburg,VA24061-0211,USA.†Reichert,Inc.,3374WaldenAvenue,Depew,NY14043,USA.*CorrespondingAuthorKimberlyForsten-WilliamsDepartmentofChemicalEngineeringandVirginiaTech-WakeForestUniversitySchoolofBiomedicalEngineeringandSciencesVirginiaPolytechnicInstituteandStateUniversityBlacksburg,VA24061-0211,USA.540-231-4851(tel),540-231-5022(fax),[e-mail]ssociatedligandsfromcellsurfaceproteinscanconfoundquantitativemeasurementsofdissociationratesimportantforcharacterizingtheaffinityofbindinginteractions.Thiscanbetruealsoforinvitrotechniquessuchassurfaceplasmonresonance(SPR).WepresentexperimentalresultsusingSPRfortheinteractionofinsulin-likegrowthfactor-I(IGF-I)withoneofitsbindingproteins,IGFbindingprotein-3(IGFBP-3),andshowthatthedissociation,evenwiththeadditionofsolubleheparininthedissociationphase,doesnotexhibittheexpectedexponentialdecaycharacteristicofa1:1bindingreaction.Wethusconsidertheeffectof(multiple)rebindingeventsand,withinaself-consistentmean-fieldapproximation,wederivethecompletemathematicalformforthefractionofboundligandsasafunctionoftime.Weshowthat,exceptforverylowassociationrateandsurfacecoverage,thisfunctionisnon-exponentialatalltimes,indicatingthatmultiplerebindingeventsstronglyinfluencedissociationevenatearlytimes.Wecomparethemean-fieldresultswithnumericalsimulationsandfindgoodagreement,althoughdeviationsaremeasurableincertaincases.OuranalysisoftheIGF-I-IGFBP-3dataindicatesthatrebindingisprominentforthissystemandthatthetheoreticalpredictionsfittheexperimentaldatawell.OurresultsprovideameansforanalyzingSPRbiosensordatawhererebindingisproblematicandamethodologytodosoispresented.1PresentAddress:MaxPlanckInstitutfürPhysikkomplexerSysteme,NöthnitzerStrae38,01187Dresden,Germany.2(i)IntroductionSignaltransductionviatransmembranereceptorproteinsisinitiatedbyextracellularbindingwithspecificproteinsknownasgrowthfactors.Theseinteractionstendtobeofhighaffinityand,inmanysystems,areregulatedbybindingproteinspresentintheextracellularenvironment.Insulin-likegrowthfactor-I(IGF-I)constitutesoneprominentexampleofsuchagrowthfactor.CellsignalingistransmittedbydirectinteractionwiththeIGF-Ireceptorbutthisbindingcanbeimpactedbysolutionandcell-associatedIGFbindingproteins(IGFBPs),ofwhichthereareatleastsix.QuantificationoftheinteractionsofIGF-IwithIGFBPsiscriticalifoneistounderstandhowchangesinexpressionandsecretionwillimpactIGF-Isignaling.Surfaceplasmonresonance(SPR)isonetechniqueamenabletosuchmeasurements.SPRisanopticalsensortechniquethathastheadvantageofbeingabletotakereal-timemeasurementsusinglowconcentrationsofunlabeledbiologicals[reviewedinCooper2003].QuantificationofIGF-IinteractionswithbothcellsurfacereceptorsandIGFBPsusingSPRhasbeenperformedasameansofevaluatingandpredictingthecompetitionbetweenthesemoleculesforIGF-I.StudieshaveusedimmobilizedIGF-I[Wongetal.1999;DubaquieandLowman1999;Galanisetal.2001;Fongetal.2002;Vorwerketal.2002],IGF-Ireceptor[Janssonetal.1997],orIGFBPs[Hedingetal.1996;Janssonetal.1997;Marinaroetal.1999;Fongetal.2002;Vorwerketal.2002]usingaminechemistrytolinktheproteinstoacarboxymethyldextran(CMD)layerontheSPRchip.Deviationsfromasinglereversiblebindingmodelhavebeennotedandattributedprimarilytonon-uniformcouplingoftheligandtothegel.Fongetal.(2002)comparedkineticparametersforIGF-IandIGFBP-1usingbothaCMDandaselfassembledmonolayer(SAM)chipandsawsignificantdifferencesinderivedbindingaffinitiesthattheyattributedtopossiblesterichindranceeffectsandtransportissues.Vorwerketal.(2002)usedaCMDchipwithcoupledIGFBP-3andmeasuredvaluesthatdifferedfrompreviouswork[Hedingetal.1996;Wongetal.1999;Galanisetal.2001;Fongetal.2002]thattheyattributedtotheuseofincreasedflowratetoassistincombatingmasstransportandrebindingeffects.However,regardlessofflowrate,fittingofdissociationdataforthissystemhasbeenproblematic.Aphenomenonofparticularinterestinthequantificationofligandinteractionsisrebinding:aligand,followingdissociationfromaboundproteinonthesurface,maydiffuseintheextracellularfluidenvironmentforsometimeandmaybereabsorbedlateratoneofthefreebindingsites.Rebindingisbelievedtobeanimportantmechanisminproducingcellularresponse,especiallywithdiluteligandconcentrations,byassistingreceptorproteinstostayintheactivestateforlongerperiodsoftime.Rebindingalsomaypromoteco-operativebehavioramongclusteredreceptorsbyreducingtheoverallliganddissociation,aphenomenonobservedrecentlyinexperimentsaddressingtheroleofclusteringinlipidrafts[Chuetal.2004].Fromamoregeneralperspective,aquantitativecharacterizationoftheeffectsofrebindingisimportantinexperimentslikeSPR,whendissociationrate