Excited-state annihilation reduces power dependence of single-molecule FRET experiments

12 Pages·2015·4.62 MB·English

by  Daniel Nettels

PCCP
PAPER View Article Online
View Journal | View Issue
Excited-state annihilation reduces power
e.
c dependence of single-molecule FRET
M. en
c
13:59 Aorted Li C20it1e5t,h1i7s,:P32h3ys0.4Chem.Chem.Phys., experiments†
3 1:Unp Daniel Nettels,*a Dominik Haenni,‡a Sacha Maillot,b Moussa Gueye,b Anders Barth,c
19/202on 3.0 VBeernejanmaiHnirSscchhufeleldr*,caChristian G. Hu¨bner,c Je´re´mie Le´onardb and
ed on 1/Attributi Single-molecule Fo¨rster resonance energy transfer (FRET) experiments are an important method for
oadns probingbiomolecularstructureanddynamics.Theresultsfromsuchexperimentsappeartobesurprisingly
ownlmmo independentoftheexcitationpowerused,incontradictiontothesimplephotophysicalmechanismusually
ber 2015. DCreative Co ibtnyevphoeakveeinoder.rfogSyrinFtgrRlaeEntT–sf.seiHrngeblreeettwwaeneennishhtiwloatwoiofntluho(aStrSoAepx)hciositreeads-mwstehactilheeanathnisenmyihaiolrafetifoblunoothrpersoincceetnhsceseeirsqfiarusretenecaxhnciinteegsdsiensndintuigaclleetdcasbutaysteeFso¨o(rfSst1teSh1ri)-s,
Novemnder a wjuhstiicfihedisinustuhaellylimnietgolefclotewdeinxctihtaetioinnterraptreest.aWtioendoefmFoRnEsTtraetxepethriamteSnStAs.isHoevwideevnetr,inthfisluaoprepsrcoexnimceaticoonrrieslaotinolny
05 d u measurementsforthecommonlyusedFRETpairAlexa488/Alexa594,witharatecomparabletotherateof
blished on e is license efFrRnoEemrTgAyelxetprxaeanri4smf8ee8rntbtose.tATwlreeaxenansi5et9nh4te.aEdbxosconitoraprttiioeonxnc-ipstpeodewcestrtroadtseecpoaepnnyddsethhnoetwmascictchreoapstteoScrSoAgnrdooccuconurdrresslateatxitocelnu(sSei1vxSep0le)yrtivmhiaaetneitnsseesrgxupyplpotoriatrentdstfheiner
e. Puarticl conclusion based on previously reported absorption spectra of triplet states that singlet–triplet annihilation
cls Received6thSeptember2015, (STA)analogouslymediatesenergytransferiftheacceptorisinthetripletstate.Theresultsindicatethatboth
ArtiThi Accepted1stNovember2015 SSAandSTAhaveapronouncedeffectontheoverallFRETprocessandreducethepowerdependenceof
s
es DOI:10.1039/c5cp05321h theobservedFRETefficiencies.Theexistenceofannihilationprocessesthusseemstobeessentialforusing
c
Ac FRET as a reliable spectroscopic ruler at the high excitation rates commonly employed in single-molecule
en www.rsc.org/pccp spectroscopy.
p
O
Introduction rates,n and n , ofdonor andacceptor fluorescencephotons,
D A
respectively,accordingto
The quantitative observation of inter- and intramolecular
E=n 0/(n 0 +gn ), (1)
F¨orsterresonanceenergytransfer(FRET)isatechniquewidely A A D
usedinfluorescence-basedsingle-moleculespectroscopy,espe-
where g = Q x /Q x corrects for differences in fluorescence
ciallyfortheinvestigationofbiomolecularsystems.1,2Typically, quantumyielAdsA(QD,QD )anddetectionefficiencies(x ,x ).n 0 is
D A D A A
themacromoleculesofinterestarelabeledatspecificlocations
corrected for photons emitted following direct excitation of the
withadonor–acceptordyepair,andthetransferefficiencyEis a
acceptoraccordington 0 ¼n (cid:2) ðn þgn Þ (seebelowfor
most commonly determined from the measured detection A A 1þa A D
thedefinitionoftheacceptordirectexcitationcoefficienta).Eqn(1)
is strictly true for the simple photophysical model depicted in
aDepartmentofBiochemistry,UniversityofZurich,Winterthurerstrasse190,
the Jablonski diagram of Fig. 1a. It contains three states of the
8057Zurich,Switzerland.E-mail:[email protected],[email protected]
bInstitutdePhysiqueetChimiedesMat´eriauxdeStrasbourg&LabexNIE, combinedsystemofdyes,S0S0, S1S0,andS0S1(whereSiSjdenotes
Universit´edeStrasbourg,CNRSUMR7504,67034StrasbourgCedex2,France donorandacceptorbeingintheSiandSjsingletstates,respectively).
cInstituteofPhysics,UniversityofLu¨beck,RatzeburgerAllee160,23562Lu¨beck, Startingfromthegroundstate,SS,thedonorisexcitedwitharate
0 0
Germany coefficientk ,whichistoagoodapproximationproportionaltothe
ex
†Electronic supplementary information (ESI) available. See DOI: 10.1039/
intensityoftheincidentradiationusedforexcitingthedonor.From
c5cp05321h
thenewstate,SS,thesystemmaynoweitherdecaybackdirectlyto
‡Current address: Center for Microscopy and Image Analysis, University of 1 0
Zurich,Winterthurerstrasse190,8057Zurich,Switzerland S0S0byspontaneousemissionwithratecoefficientkD;alternatively,
32304 | Phys.Chem.Chem.Phys.,2015,17,32304--32315 Thisjournalis©theOwnerSocieties2015
View Article Online
Paper PCCP
e.
c
M. en
c
ALi
13:59 orted
3 1:Unp
020
9/2n 3.
1o
ed on 1/Attributi
oadns
wnlmo
om
Do
November 2015. nder a Creative C Fassttniargditc.et1isltysSari(aapadpnaildanictdSiaojb,bnlr)leeeJ.ssa(pscbe)dlcoEetnapivpsoepkp(liryu)d.lai(aaantg)idorSanirmmapdppsu(lroief)ifectoadaldcsdiouinalnggaoltreeart–dm–asfcrfionocgrmelwpettthohairecnhFpnRheihEoqiTlntaodt(pi1oyh)enhypso(SiaclSdiarAs.l.)Sm(wibSo)jitdAdheemlrnadooteetrepecsicroetteheafedlfiisccitniioec(nmbdt)sbiafigknoSrerSadAtmhasr,tneaaedtdedlkimiSitnSioAitw0ni.nahFgliolcycrhaitnsdhceoelsun:sdoncirnhogea,nmitndhteeearicndmco(eebudp)b,italoeetrq-een,axar(ecn1i)dtineissdttnhrsooetansltgoeinnSSggS1leeSAr1t.
05 d u TherelativestrengthofSSAischaracterizedbytheinter-dye-distance-independentparameterso=kSSA/kTando0=kSSA0/kT.Theirvaluesarechosenas
on nse indicatedinthepanels,orzerootherwise.EappiscalculatedfromEapp=nA0/(nA0+gnD),andrappfromsolvingEapp=R06/(rapp6+R06),whereR0istheFo¨rster
blished e is lice (ryaedliluoswo).fTthheeSfu1Sll0li-nesS0wSe1rteracnaslictiuolna.teEdacwhitohfathcceetphtroeredciaresecsteaxrecistahtoiownnafo=r0th.0re5eadnidffetrheendtaesxhceitdatlioinnesraftoers:ak=ex0-.F0ur(tbhleurei)t,kweaxs=a0ss.1ukmDe(pdutrhpalet)k,Dan=dkkAe.x=kD
e. Puarticl
ArticlThis theenergyistransferredwithrateconstantkTtotheacceptor,and efficiencies on the excitation rate might be expected, e.g.,
s stateS0S1isreached.Subsequently,thesystemdecaysbacktothe if surface-immobilized single molecules are investigated in
s
cce groundstateS0S0withtheratecoefficientkA.Thetransferefficiency different regimes of irradiance, or if they are compared to
A Eisdefinedbythefirstequalityin measurementsonmoleculesfreelydiffusinginsolution,where
n
Ope k R 6 typically much higher irradiance is used. However, observed
E(cid:3) T ¼ 0 : (2) transfer efficiencies are often remarkably independent of
k þk r6þR 6
D T 0
excitation rate, raising the question of how nonlinear photo-
Thesecondequalityfollowsfromk =k (R/r)6,asshownbyF¨orster,3 physicalbehavioroutsidetheweakexcitationlimitisprevented.
T D 0
where R and r are the Fo¨rster radius and the inter-dye distance, Potential candidates for counteracting mechanisms are
0
respectively.Alsoincludedinthemodel(Fig.1a)istheoff-resonance, excited-state annihilation processes. The population of S S ,
1 1
directexcitationoftheacceptordescribedbytherateconstantak , forinstance,canleadtosinglet–singletannihilation(SSA)(see
ex
withatypicallybeingintherangeofafewpercent. Fig.1b),atwo-stepprocessoftheformS1S1 k(cid:2)S!SA S0Sn (cid:2)I!C S0S1,
ThesimpleschemeofFig.1a,however,neglectsthepopula-
whereenergyistransferredfromthedonortotheacceptorina
tion of the state S1S1, in which both fluorophores are in the Fo¨rster-typemechanism.Inthisprocess,thedonorreturnstothe
excited state simultaneously (Fig. 1b). (Also neglected are the groundstatewhiletheacceptorisraisedtoahighersingletstate
triplet states of the chromophores, which we will discuss S ,fromwhereitrapidlyreturnstotheS stateviaradiationless
n41 1
below.) The S1S1 state can be populated via S0S1 - S1S1 and internal conversion (IC). Kinetically, the population of the inter-
S1S0-S1S1withtheratecoefficientskexandakex,respectively. mediatestateS0Sncanhencebeneglected.Inthedouble-excited
The omission of the S1S1 state is justified at low excitation state,donorandacceptorcanalsochangetheirroles,i.e.,transfer
iinntteennssiittiieess,,wwhheicrhekaerxe{oftkeAnadnedsiarakebxle{fokrDo+btkaTi.nHinogwheivgehr,eartflhuiogrheesr- in the opposite direction (cid:3)S1S1 k(cid:2)(cid:2)SS!A0 Sn0S0 (cid:2)I!C S1S0(cid:4) may be
cence detection rates, especially in single-molecule experiments, possible4 and is thus included in the model of Fig. 1b. An
the population of the double-excited state S1S1 may become analogousenergytransferprocesscanoccurbetweensingletand
significant,anditsfluorescencedecaybacktoS S orS S leads triplet states, i.e., S T - S T , with subsequent non-radiative
0 1 1 0 1 1 0 n
to conditions where eqn (1) becomes incorrect. As a result, a internal conversion, S T - S T , resulting in singlet–triplet
0 n 0 1
pronounced dependence of experimentally observed transfer annihilation(STA).
Thisjournalis©theOwnerSocieties2015 Phys.Chem.Chem.Phys.,2015,17,32304--32315 | 32305
View Article Online
PCCP Paper
Onthesingle-moleculelevel,SSAandSTAwerefirststudied where R , R , and R0 are the F¨orster radii of the corres-
0 SSA SSA
by Hu¨bner et al.5 and Hofkens et al.6 by measuring fluorescence pondingenergytransferprocesses.Weintroducetheinter-dye
trajectories of single polymer-embedded, bichromophoric mole- distance-independentparameterso=k /k ando0 ¼k0 =k
SSA T SSA T
cules with two peryleneimides as chromophores that act both as to characterize the relative strength of SSA present in the
donorandacceptor(homo-transfer).STAwasevidencedbycollec- system, resulting in the following relation between E and E
app
tive‘‘on-and-off’’eventsoccurringintherecordedemission,which forthephotophysicalsystemdepictedinFig.1b:
were explained by STA and thus quenching of one chromophore
while the other is in the triplet state. The occurrence of SSA was 1 ¼ 1þ kex½1þo0þaf1ðEÞ(cid:4)kD=kA :
e. verifiedfromtheamplitudeofthephotonantibunchingcomponent Eapp E kAþkDþkexþ½oþo0þaf2ðEÞ(cid:4)kDE=ð1(cid:2)EÞ
c
M. en ininter-photonarrivaltimedistributions.Inaddition,Hofkensetal. (4)
c
ALi quantifiedtheFo¨rsterradiiofthethreecompetingresonanceenergy
3 1:13:59 Unported tarnadns‘nfeorrmpaathl’wenayesr.gyThtreaynfsofeurn(d5.4venryms)i,mwihlaerrevaasluthesefFo¨orrsStSeArr(a5d.9iunsmof) Twhheichdedreivsacrtiiobnetohfeienqfnlue(4n)ceanofdacthceepftuonrcdtiiroenctsefx1c(Eit)ataionnd(af2)(oEn),
020 STAturnedouttobesignificantlygreater(8.7nm).Morerecently, Eapp,aregiveninMaterialsandmethods.Notethatinthelimit
9/2n 3. Fu¨ckel et al. quantified SSA of terrylene diimide by photon coin- kex-0, Eapp = E, as expected. By modifying the depopulation
Downloaded on 1/1ommons Attributio caweiffindhdeiHccnihieectrnesewcmqyew,ueeEaeresanfpuficeprrhsre=timntndoegAins0ib/tcn(synuwAstS0hsiSt+ehAthgpfneoouDnllils)no,etwfhtdlouienleadgrnsiiescgrtaehisnetox-gthcfuhiatiteanshthdieaopinSstp.i1f7daSrreo1emnpotoftphetureqaln‘anttrsi(ufo1een)r,’ Ss(rkoateSrxtAae=-t(e0oodfa0=nit,nhdfNoeForidgw0oo.=rhu10iobcc)lh0,(eui=-nEepNxatpepcepri)rtm.=epTdeEahdn.seiTteaablthstelee)uS,foeSoStArlShiAtne(horeristne=wecf1loouliroecmrroneiolsctopei0rnoss=gnEc1dcao)ap,rtspraoe(enrsst)d:hpaneossotnlriidoSmllnStuiAogt-
ber 2015. Creative C dEis,udreeetdfoiuntcehedediSni1nSe1qthnpeo(2pp)ur.elWasteeinoscnheoeonwfhtsahtnaroctentdhgebSdySeAlva.iraWgteieornethxocefintEaadtpiepotnferrormamtienEse,, Hehffiiegrcheieerwnelcayso(ebbrsluepreovwleiensreisgs:)n,kieefxiscp=aen0ct.i1adklleDyvii(naptuitorhpnelsea)bfrasoenmndcektheoxef=tSrkSuDAe.(tTyrehalenlosuwfse)er.
05 Novemd under a tcbhoioemmrmaotoleencolufylSeuSsAs.2e,b8d–e1t6iwneFeosnirnAgthlleeixs-map4ou8ler8pcauonlseed,AFwRleeExTala5bm9e4el,eadasudtryheeempetaenirrtmsveinoryfi ofwrfooumEladpthpreeisntursultteeairnd(Faoipfgp.Ea1rcef,onlrtowdcaeisrlctapunalancteeisnls,g).ratTphphe,etifhnuatletlrl-cidnleyeaesrlidynisdFteaigvni.ca1etecs
blished on e is license pnofearnafoo2sr0me-creeodsniddfuluteiompreoeslcyrpeenrsoocleliuntceioo(rnPr.erolWa2t0ieo)nsphesoppwteidcttehr1oa4s,t1c7oewsppiytehc(FitaChlleSys)etwhdieytheasssayunmbd-- wdviaerstruheaecldalyllciiunnledasetepfdoernwdaiteh=nta0co.cfFeaop.rtoTrrhodisiriResc0,tbeethcxaceiutssahetaiotphneeaoef=nte0hr.eg0y5ctuarnravdnesstfheiesr
e. Puarticl metric shape of the donor–acceptor intensity cross-correlation in rate,kT,isverylarge,andthereforeexcitingdonororacceptor
s Articl This tohbetaninanaoqseucaonntidtartaivnegemiesahsiugrhelyfosretnhseitriavetetooftShSeAstfrreonmgtahgolofbSaSlAf.iWtoef deffiireccietlnyciysoebssseernvteiadllyfoerqruiovaleRn0t.anTdheoap{par1enist ldouweertotradnosnfoerr
cces theFCScurvesusingadetailedphoton-statisticalmodelbasedon photons emitted in S1S1 - S0S1 transitions. For o c 1, the
A the scheme presented in Fig. 1b. To complement and further emission of fluorescence photons by the S S state is instead
n 1 1
Ope validate this result, we use transient absorption spectroscopy to quenched by non-radiative SSA also leading to S0S1, such that
determine the extinction coefficient of the S state of both dyes. E morecloselyapproachesEevenwithlargeexcitationrates.
1 app
Thisallowsustodeterminethenatureoftheenergytransferinthe For large dye separation, r 4 R , the apparent transfer effi-
0
double-excited state and to predict the corresponding SSA rate, ciencyisalmostindependentofo(butnowdependentona)as
which is seen to agree very well with the result of the FCS we have a low energy transfer rate (k E 0); S S is hence
T 1 1
experiment.Finally,weexpandourphotophysicalmodelbyinclud- predominantly populated via acceptor direct excitation from
ingtripletblinkingtodiscusstheimpactofSTAonsingle-molecule S S . In this regime, the acceptor photons emitted from the
1 0
FRETmeasurements.BycomparingwithFRETdatameasuredon double-excited state lead to an overestimation of the transfer
terminally labeled polyproline 14 (Pro14), we conclude that both efficiency,henceanunderestimationoftheapparentinter-dye
SSAandSTAmustbetakenintoaccounttoexplainthelowpower- distance, unless strong non-radiative SSA0 produces S S by
1 0
dependenceoftheapparenttransferefficiencyinthissystem. quenchingtheacceptoremission.
For single-molecule spectroscopy, the case of strong SSA
Results and discussion with kSDS-AA = N would be most desirable, since for small and
intermediate distances, even at high excitation rates, no sub-
According to F¨orster’s theory, the transfer rate coefficients k , stantial deviation from the ideal E(r) dependence would be
T
k ,andk 0(seeFig.1b)dependontheinter-dyedistanceras observed. For larger inter-dye distances, however, a deviation
SSA SSA
due to acceptor direct excitation would remain, albeit small if
kT¼ kDðR0=rÞ6 thelaserpowerismoderate(k =0.1k ).
ex D
From the previous section, it is clear that a quantitative
kSSA¼ kDðRSSA=rÞ6 (3) knowledge of the strength of SSA (and thus o) is required for
(cid:5) (cid:6)6 interpreting single-molecule FRET data accurately. Hence, we
k0 ¼ k R0 =r ;
SSA A SSA usedFCSwithpicosecondtimeresolutiontostudySSAbetween
32306 | Phys.Chem.Chem.Phys.,2015,17,32304--32315 Thisjournalis©theOwnerSocieties2015
View Article Online
Paper PCCP
e.
c
M. en
c
ALi
13:59 orted
3 1:Unp
020
9/2n 3.
1o
ownloaded on 1/mmons Attributi Fdtoboiolbginntt.ahko2iiennr,egdGdF)aCD,atcaDnSo(datdrn)ra,tedhatsaectphcmoaeenneptcdatiboosinuurrgr–rneetdcsdohopioanonnnongrdSP,aiSrnGmAogA2pFDr0lo¨(eittrs(u)sb,iddtaleaeunrcadorklasfapdc(touihcuipeenspptodsetfoorinRnrp–oS0laSoarnA-wceo=celnser0)lp.yp.9tBaop9enros,e(cid:6)piGldsuReA;l0aAst.(tthtiTro)ur,oencce,dtoucearrarmmabel,loparoneltinitspoultyrnrdeaoesftuees,n=ntactha(itejR,itoiS(sodnSenAesn/,poRsreife0tni)stv6hdpiteiweynclagoatsifbvotaeenhnlleeypd.afaSditrphjttueiioncspwgltetainpdbcrelaooeroncefcneitaedtlpnsuooatrprrea)ma.tom(iooaned–note,ce,lb)rwc.Rauoceerkpvr=geererps0osef.eur9aonnt5etmdd(cid:5)t,haate0hnged.dl0oog6tbrnloiawpolblraefa–isttl
Do fitwhilekeepingofixedtoatentimeslargervalue(o=9.5,dashedlines)oratentimessmallervalue(o=0.095,dashed-dottedlines).Thesevalues
ber 2015. Creative C correspondtoRS0SA=1.45(cid:6)R0andRS0SA=0.68(cid:6)R0,respectively.
Novemnder a tahtteacFhRedETbypfaleixribAlleelxiank4e8rs8to(dtohneotre)rmanindioAflPexroa205,9w4h(iacchceseprtvoers) tPrraon2s0fecroenffistcruiecntcwieesrebedtewteeermniAnleedxafr4o8m8 sainndgleA-lmexoale5c9u4leinFRtEhTe
05 d u asarelativelyrigidspacerbetweenthedyesandpositionsthem efficiency histograms.§17 We thus know k and can substitute
blished on e is license scaaotmnafnpolceaavloesrfaintghgeeled-cmiostnoaslnetcrcueuclcetlowinsaesstrtomumtehaeesnutFr¨oeedqrsutiienprpfreradedeiwudisti.ffh14u,t1sw7iooAnd1oonnnoMar ckfioStSnApta=raroasmtkTteoatenordsakbnSeSdsAi0do=e0so,oh0kaTavniendotohnel0yamrlieottdfloeeulironfaflFmTuiegpn.li1ctebu.doTensh,etwhoehnilacyhsfy,rmeine-
e. Puarticl and two acceptor detection channels (Hanbury-Brown & Twiss metric shape of the crosscorrelation function GAD(t) and its
n Access Articl This cPltiiohmmnoiefttioegodnufraba6rytr6iiovtnhahle1o8tu)ijmirttsote.esrcFiwrorocefumrtemhretvehecdenoestretdetehcddteaowtrdasie,,tahftdohBreti5mad0eotposnstooatrlfimmtaheneedraedssuaeotcrleecucmettpioeotrnonsrt., veoaxrcluiSte1eSda1tsk(cid:2)tt(cid:2)SaS!=Ate00oS.cnA0cSsu0sr,usmwineinofgintttehedadtirteehnceteiroFgnCySotrnadlnays,tafeeiritnhfreotrwmSo1tSwh1eak(cid:2)ySd!sSAo,uwSb0ilStehn-
Ope autocorrelations, GDD(t) and GAA(t), as well as the cross- o0 =0andoasafreefitparameter,andviceversa.
correlation GAD(t) were obtained for lag times t ranging from Fig. 2 shows the resulting fits (full lines) and the residuals
(cid:2)10 to 10 ns (Fig. 2). The autocorrelations show a symmetric foro0 =0,yieldingthebestagreementwiththemeasureddata
minimum at t = 0 due to photon anti-bunching,5,19,20 since a for o = 0.95 (cid:5) 0.06.¶ To demonstrate the impact of o on the
single quantum emitter (donor or acceptor) can only emit one modelcurves,wealsoshowfitswhereowasfixedtovaluesten
photonatatime.Notethattheautocorrelationsdecreasetoone timeshigherandtentimeslower,i.e.too=9.5(dashedlines)
insteadofzeroatt=0,asexpectedforafree-diffusionexperiment, ando=0.095(dashed-dottedlines).Importantly,theeffectofo
wheretwophotonscanbeemittedsimultaneouslyandindepen- on the crosscorrelation curve is substantial and cannot be
dently if two (or more) fluorophores are present in the confocal compensated by the other fit parameters, illustrating the sen-
observationvolumeatthesametime.Ofparticularinterestisthe sitivity of the method for quantifying SSA. Varying o0 while
crosscorrelation,GAD(t)(Fig. 2b),withitsasymmetricshapeand o = 0 results in an equally good fit to the data and a value of
GAD(t=0)41.Thelatterisaclearindicationforapopulationof o0 = 0.93 (cid:5) 0.05, identical within error to the result for o.
the double-exited state, because only from this state can donor On the basis of the FCS data, we can hence unequivocally
andacceptorphotonsbeemittedsimultaneously. demonstratetheoccurrenceofSSAbetweenAlexa488and594,
We fitted the three FCS data sets of Fig. 2 globally with
functions corresponding to the photophysical model depicted
§Fluorescenceanisotropymeasurementsindicatethatdiffusionalrotationofthe
in Fig. 1b, using the elegant formalism introduced by Gopich fluorophores,attachedviaflexiblelinkerstotheendsofthepolypeptide,occurs
andSzabo21(fordetails,seeMaterialsandmethods).Wenote on a timescale of 0.1–0.5 ns.23 We conclude that rotation of the dyes has a
that most of the parameters of the model were determined negligibleeffectontheshapeofthecorrelationfunctionsanddonotincludeitin
themodel.
from independent experiments: k and k are known from
D A ¶FCSdatawereindependentlymeasuredintwolaboratories.Theresultsfrom
fluorescence lifetime measurements,22 k from antibunching
ex thesecondlaboratoryareshownintheESI†(Fig.S3).Theyagreewithintheerror
measurements of donor only-labeled polyproline,9 and mean margins.
Thisjournalis©theOwnerSocieties2015 Phys.Chem.Chem.Phys.,2015,17,32304--32315 | 32307
View Article Online
PCCP Paper
but the directionality of the transfer process remains S S -S S andS S -S S ,respectively,determinedfromthe
1 0 0 1 1 1 0 n
indistinguishable. spectrarepresentedinFig.3.FromtheratioJ /J,weobtaino=
SSA
To address this question, we used transient absorption 0.92(cid:5)0.05,inverygoodagreementwiththevalueofo=0.95(cid:5)
spectroscopy for obtaining the excited state absorption (ESA) 0.06fromthefittotheFCSdata.(SeeinMaterialsandmethods
spectra of Alexa 488 and Alexa 594. Fo¨rster3 showed that the the discussion about the effect of a possible systematic error
sixthpoweroftheF¨orsterradiusisproportionaltotheoverlap onthedyes’groundstateextinctioncoefficients).Similarly,within
integralJdefinedby theuncertaintyofthedeterminationoftheextinctioncoefficient
ð oftheS1stateofAlexa488(seeFig.3b),wecanestimatetheratio
e. J ¼ fDðnÞeAðnÞn(cid:2)4dn; (5) JSSA0/Jandobtaino0=0.05(cid:5)0.05,compatiblewiththeabsenceof
c
M. en SSAbyenergytransferfromAlexa594toAlexa488.
c
023 1:13:59 A0 Unported Li wÐpthfuhDemeðranpecÞ–dcpfenDrp(o¼tnbo)re1i,2ast4setcahahnendfuidqenouAc(netnio)otroniseomtmhfeeitsahssmeiuoornwelaarstvhpeeenexctuittmnrraucbnmtiesorine,nnnoct.romWeaffibaeslciouzireespndettdioaonasf ArSa1letSeFx0arvo-e4mr8y8tsShi0ameSns1ide.lar5rAe9cts4ocuoltorthcsda,citunwrogeslfyctw,ahineSthS‘tA‘huausiFsuno¨acrlo’ts’hnteeecnrlueirdnragetdeyitruthmrsaaetnadnSsifSdaeAtrethbpuerreotswgcaieemtsesnae,
9/2n 3. spectrum of the two fluorophores 100 ps after impulsive (Fig. 1) needs to be taken into account for a fully quantitative
1o
oaded on 1/ns Attributi trehexocisirtgaadtnieolianzay,tiinoftnaosattrheienctSoe1mrnspatalletteveid(bs,resaeuticMohnaatthelarirtaetllhaaexnaodtbiosmnerevtaehndoddtrsas).nolsAvifeetnnertt trtrhaeteaetsnm,aaennnodtseofcofornFtRdhEerTqanuegaxenp.te2ir2tiamAtinevnetiimsn,tpeeorsrpptreaecntiatatlicloyonnastoefhqFiugCehnScerexecsoiutflattsSioSinnA
wnlmo spectrum characterizes the relaxed S1 state. The recorded isthatdeviationsintheobservedtransferefficiencycausedby
Doom transient spectrum is a superposition of three contributions: the population of the S1S1 state are mitigated by the resulting
ber 2015. Creative C g(sSirgEon,uannled).gsaBttyaivtmeebseilagesnaucarhli)n,(gGanSindBd,enexpeceigtnaetddivesentatsltiygentahabels),ogsrrptoitmuionundla(sEtetSadAtee,mpaobissssiotiriovpne- nSfiSonAnd-vrtiaoadiebaneteivpregryedfeterpraronepdsuf,elarretfisrouonlmtsofAintlhexeaads4om8u8ablltleoe-reAxdlceeixtvaeiad5ti9sot4na,tewf.rhoIinmchfatwhctee,
Novemnder a tiniotno a(GccSoAu)natntdhefluexoprelisccitenrceelatsitoenadbye-sttwaeteenspGeScAtr,aG, SaBn,dStEakainndg iwdoeualldw(eFaikg-.e1xcc)it.ationlimitthanthereversedirectionoftransfer
05 d u fluorescence(seeMaterialandmethods),theESAspectrumcan Although our results indicate an important role of SSA for
blished on e is license Ttboehgereetthrreeiseruvweltdsitahfcoctrhuerbaogtetrlhoyuancnhddrosqmtuaatoenpthaitobarsteoisvreplatyiro(einnd(uiGsnpSiAtlas)yoeofdfMAi(cid:2)lne1xcaFmig5(cid:2).914)3.. tephffreoeccoetbssssae,rnvsdepdepcFhiRfoitEcoaTpllheyffiystcriciipeanllecstytasattteahsteimgsha(yeTxcc)o,itnawttrhiiobincuhrteaatteroes,taphdoedpoiutvileoartnaealdll
e. Puarticl Interestingly,thereisstrongspectraloverlapbetweentheESAof significantly by most fluorophores u1sed for single-molecule
s Articl This Athleexcaa5s9e4baentwdetehnetfhlueoEreSsAceonfcAeleoxfaAl4e8x8aa4n8d8,twhheefrleuaosrethsciesniscenootf tsitguadtieeds.t2h5eInroalereocfetnritptlheetobrleintikcainlganaanldystihs,eCSa1mS1lestyaetetaoln.26F¨oinrvsetesr-
s
ce Alexa594.WecanthusconcludethatAlexa488isthedonorand transferoutsidetheweak-excitationlimitbutintheabsenceof
c
A Alexa594theacceptorintheobservedSSAprocess.Inaddition, annihilation effects. They assumed that the donor cannot
n
Ope wecanusetheextinctioncoefficientsdeterminedherefortheS1 transfer its energy to the acceptor when the latter is in the T1
states of both chromophores (Fig. 3a) to quantify o. Indeed, state. Since triplet state lifetimes are typically in the micro-
fromR 6pJandeqn(3),itfollowsthato=J /J,whereJand second range (i.e. much longer than the excited singlet state
0 SSA
J are the overlap integrals of the energy transfer processes lifetimes), this scenario leads to an increased emission of
SSA
Fig.3 (a)Extinctioncoefficients(in104M(cid:2)1cm(cid:2)1)ofS (green)andS (red)statesoftheacceptorA(Alexa594),superimposedwiththenormalized
0 1
fluorescencespectrum(blue,in10(cid:2)4cm)ofthedonorD(Alexa488).TheoverlapofthelatterwiththeabsorptionspectrafrombothS andS statesofA
0 1
ispronounced,indicatingefficientenergytransferfromDtoAviaSS -S S (‘normal’FRET)orSS -S S (firststepoftheSSAmechanism).(b)
1 0 0 1 1 1 0 n
ExtinctioncoefficientoftheS state(red)ofD,superimposedwiththefluorescencespectrumofA(blue):heretheoverlapisnegligible,indicatingthatno
1
annihilationoccursbyenergytransferfromAtoD(SSA0mechanism).
32308 | Phys.Chem.Chem.Phys.,2015,17,32304--32315 Thisjournalis©theOwnerSocieties2015
View Article Online
Paper PCCP
e.
c
M. en
c
ALi
13:59 orted
3 1:Unp
020
9/2n 3.
1o
ed on 1/Attributi
oadns
wnlmo
om
Do
ber 2015. Creative C
Novemnder a
05 d u
on nse
cle. Published s article is lice FsceQtirfgrufooe.escn4sntgicnohSgf(iTanS(A)ggTJ.rAeoaFybofolrtanohrenreEaosackSpwhip1Ssdic)1si.aasFdgstleearuamtoaemgroebanosyinscftSeartSanhdAtcreoeeadennpoiddnhri–of(tfbhteao)erc,necwSnse1htpTeeet1mroxseicrtt,aitFtaetaRnedtEaiobfTlornyopgSmraoaTiutrASesi1nrcStecoo1dl,ueFuSdfi1fcgiTince.1g1i,etchant,rnetEispdadlwpeTeptev1(rSiTra)e11ta(iasnogtsdrnase.turee(amFnspopeoa(rrdfn)c:bdwlkaoreertexirhtdey-d,acytrah0erloecs(uwbtThllsa1uaT)tete1a)da,rserktfeaeortxepre=sotpihsp0orure.n1eleaksptiDlbreimeld(epsieautfinonnrptdrgelteddch)ea,etspwaednoisecdp:veunkialieoantxti,oe=tinhndtkeevoDidrfam(iyEaienegapltdrlepaoiarmwfstreyo).).s,mtkTaeSnhmSEdeA.
ArtiThi wassettokTinallcalculations.TheratecoefficientsofISCfordonorandacceptordyeweredeterminedfromFCSmeasurementstobeforAlexa488:
ccess kuSn1c-eTr1ta=in0t.y9in(cid:5)k0e.x4.)mTsh(cid:2)e1aTn1Sd1ksTt1a-teS,0w=h0ic.2h(cid:5)ca0n.1emmsi(cid:2)t1aacncdepfotorrAflleuxoare5s9c4e:nkcSe1-pTh1o=to1.n0s,(cid:5)is0n.5otmsq(cid:2)u1eanncdhekdT1-inSt0h=is0m.3o(cid:5)de0l.c1amlcs(cid:2)u1la.t(iTohne.Ietrirso,rhsorweseuvletrf,roomnlythweehaikglhy
A repopulatedfromTS (lightbluearrow)withak ,whiletheST stateisrepopulatedfromS T withk (darkblue).Fulllineswerecalculatedwith
pen acceptordirectexci1ta0tion,a=0.05,dashedlinesewxitha=0.Fu1rth1eritwasassumedthatkD=0kA1. ex
O
donor photons until the acceptor returns to the singlet mani- Hofkens et al., who determined the Fo¨rster radii for homo-
fold, resulting in a decreased E .26 However, energy transfer transfer in perylene diimide.6 They found an S S - S S
app 1 0 0 1
ofthetypeS T kS!TA S T withsubsequentradiationlessinternal F¨orster radius of 5.4 nm, an SSA F¨orster radius of 5.9 nm,
1 1 (cid:2)(cid:2) 0 n
conversion,S T -S T , i.e.,singlet–tripletannihilation(STA), and a significantly larger STA Fo¨rster radius of 8.7 nm, i.e.,
can occur in0mnultich0ro1mophoric systems.27 Analogous to the kSTA E 17(cid:6)kT in this case. We are not aware of any triplet
absorption spectra reported for Alexa 488 and Alexa 594 that
caseofSSA,sufficientlystrongSTAwouldleadtothequenching
could be used to quantify the strength of STA for this specific
of donor fluorescence in the S T state, and the deviation
1 1
dye pair. However, microsecond FCS experiments using Pro20
between E and E would become less pronounced or even
app
negligible,asillustratedinFig.4. with variable direct excitation of the acceptor in addition to
Transient absorption spectra of the T state have been donorexcitationareindicativeoftheexistenceofSTA(Fig.5).
1
measuredwithflashphotolysis andradiolysisexperiments for We observe, as expected, a significant increase in the triplet
severalorganicdyes,includingrhodamines.28–32Inthesecases, componentofgAA(t)withincreasingacceptordirectexcitation,
the absorption spectra of the T state are blue-shifted with indicativeofanincreasingtripletpopulationoftheacceptor.In
1
respecttoS absorption,andtheT absorptioncross-sectionis the absence of STA, we would expect the donor to increase in
1 1
of similar magnitude, often even greater, than the S absorp- brightnesswhiletheacceptorisinthetriplet.Hence,onewould
1
tion.TheresultinglargeroverlapofthedonorS1emissionand alsoexpectanincreasingtripletcomponentingDD(t).Instead,
theacceptorT absorptionsuggeststhattheF¨orsterradiusfor virtually no change in the triplet component of the donor
1
theS T -S T energytransfertendstobelargerthantheone autocorrelation is observed (Fig. 5a). From this observation
1 1 0 n
oftheS S -S S transfer.Asimilarobservationwasmadeby we conclude that k is of similar magnitude as k . With the
1 0 0 1 STA T
Thisjournalis©theOwnerSocieties2015 Phys.Chem.Chem.Phys.,2015,17,32304--32315 | 32309
View Article Online
PCCP Paper
e.
c
M. en
c
ALi
3 1:13:59 Unported Faanuigtd.o5(cbo)rrFreeCplSaretdisoaentnaftumtnheceatdsiouonrneso,drr–oesndpo1enncotMirv,eoglfDyP.DrT(toh)2,e0adnfodrenaeoclyrcewdpiafftsouers–ixncagciticenedspoattolu4rt,8iog8AnA.n((tma)), Flaibge.l6edAwpitpharAelenxtat4ra8n8safenrdAeffilexcaie5n9c4y,mhiestaosgurraemdsatdoifffePreron1t4la,seterrpmoiwnaelrlys
19/202on 3.0 wobitjhecativlea)s.eTrhpeowarerorwofin2d0icamtWes(amdedaitsiuorneadl daitretchteabcaccekptaopreertxucrietatoiofnthaet (tsheeetcraonlosfrelregeeffincdi;e2n0cypMofitnh5e01m00MmsWodmiuemaspuhroemspehnatteasbuaffreerf,epreHn7c)e.T(abklaincgk
oaded on 1/ns Attributi 5FcCo94mSpncuomrnvewensitth.ariencnroeramsianlgizepdowweitrh(0re,s2p0e,c4t0to,6t0he,8a0m,p10lit0u,daenodf1t1h0emdWiff)u.sTiohne bavcenalarldcctiukkclacaltuelr=ivnEeekas)p)p:(ai(nna1ts)deaarbamssfuseeunndmcciaetitinoeognsflSotohSpfaAetth)a;uen(3ndl)daSoseTerA=rtph(1laoiasrwngcdeeorskntfdnoiertig=ofoan3tuikvrkeec(xssalmso=epas0ell().ss;0le(o52ekp)Deion,);s=w(e4te1),
wnlmo sameSaTsAcaseT2,butwithanadditionaltransitionSSTTA-STS duetoreverse
om 1 1 0 1
ber 2015. DCreative Co tareesnmsuthaminopsftikvoeDnraytnchdlaotkseAkSt(ToFAiEgE.a4skblT)o,,nmagroaedsgeikmlexceaisltchnuaoltattigisorernaasrteeslrhytohewxacnteheaadbteoEduatipnap IaamSrlsCreooawwsiunistrd)heaicdanardFtaeRctdeEaTscbeoypntehasarrtekraoenswtm(tosoefpia0nrs.s1ethto(cid:6)eoukfthTadis(rudrtooeagswthrosae)m.dpAhsltionhfetoio)gr.bhCcleeaaraslcceeuhxlocianinttgeaedtoi(ofEbnaotphptpteoovwamacleucrseeses,pttathooreerf
blished on 05 Noveme is licensed under a seElEaixaanscppeTgppitr,loaaewtn-ptimeoedosnwotmEleer.o2reacus6atureslsuuepsrrwieFenodRdguiEctlTrdtaaionleFensxaRsfpdeEeorTrtnioe-mlffitaphebrceneoitleinesnn.odfculWyunceohicntneihcsdsotetourdogutefrcvaStSimTaSftAAsoio,raanentswvdedhbniSieffcTthtewAhreeewoensnneet (ctt(oshhoebeamestnaepminav6aeraii0dslnuo0eftnresmox((mWtce)o.rr,TlGooharareesubdsmawsripseai)oant.hsi-nuptreisen)ad.kcWrmfeieteasas)enisantEnigmadpapeatxraeecreiartneagpitvuireoennsnceebnrryttaeattidhneet,iynptheothafeke(cid:5)tpir0noa.ss0nei3ttsioffoenonrsr
e. Puarticl expect a pronounced potential dependence of Eapp on laser efficiencypeaksmearsouttowardsmallervalues;thiseffectis
ArticlThis powerandondifferentstrengthsofSSAandSTA.Tothisend, noticeable alreadyatpowers 4200mWand most likelydueto
s wechosea14-residuepolyprolinepeptide(Pro14,labeledwith increased photobleaching of the acceptor during the diffusive
s
ce Alexa 488 and Alexa 594 at its termini, as for Pro20), which is passageoflabeledPro14throughthelaserfocus.Notethatthe
c
A expected to have a transfer efficiency of B0.8 (Fig. 6). Besides excitationwavelengthof485nm(correspondingto20600cm(cid:2)1)
n
pe the smaller inter-dye distance, Pro14 has the advantage of isclosetoaresonanceintheESAspectrumofAlexa594(Fig.3a),
O
exhibiting a narrower transfer efficiency peak than Pro20.17 andexcitedstateabsorptionofAlexa594mostlikelyaccelerates
We measured Pro14 at different laser powers that roughly photobleaching.33
correspondtok valuesof0.05,0.1,0.2,and0.3timesk .On Both SSA and STA thus contribute to a low dependence of
ex D
the one hand, we observe, as expected, an increase in the theobservedtransferefficiencyonexcitationpower.Toaccount
number of detected bursts with increasing laser power until for the residual deviation of the calculated power dependence
saturation is approached. (The threshold for burst identifi- of E from the experimental data (Fig. 6), additional photo-
app
cationwasheldconstantataminimumofeightyphotonsper physical processes may contribute. For instance, it has been
burst.) On the other hand, there is no significant shift in the suggested5,34thattheSTAprocesshastwonon-radiativerelaxa-
apparenttransferefficiencytowardslowervalueswithincreas- tionchannels,asdepictedinthefollowingreactionscheme:
inglaserpower.IntheinsetofFig.6,wedepictforcomparison
S T
three different scenarios of the changes in E expected 0 1
app
%
theoretically assuming the photophysical model of Fig. 4a
(with kSSA = kT). As discussed above, the greatest shift in Eapp S1T1 k(cid:2)(cid:2)S!TA S0Tn
&
would be expected in the case of complete absence of STA
S S
(line with largest negative slope). The shift is, however, much 0 1
lesspronouncedforthecaseofintermediatestrongSTA(k =k ). ThetripletstateT oftheacceptorcaneitherdecaybacktoT
STA T n 1
If we assume stronger STA with k = 3k , the dependence of (as discussed above), or the higher density of states near T
STA T n
E onlaserpowerapproachestheexperimentalobservationof causesacceleratedreverseISC(ReISC)34–49thatfinallyleadstoa
app
an apparent transfer efficiency that is essentially constant conversiontothelowestexcitedsingletstateS .Anaccelerated
1
(curve with smallest slope). Unfortunately, we do not observe depopulationoftheacceptortripletstateinducedbythisprocess
histograms of suitable quality at laser powers much greater would lead to an increase in the apparent transfer efficiency.
32310 | Phys.Chem.Chem.Phys.,2015,17,32304--32315 Thisjournalis©theOwnerSocieties2015
View Article Online
Paper PCCP
To illustrate this effect, we added a transition S T - S S to wave, 488 nm solid-state laser (FCD488-010, JDSU) and an
1 1 0 1
the model in Fig. 4a, with a rate coefficient of 0.1 (cid:6) k , and OlympusUplanSApo60x/1.20Wobjective.Afterpassagethrough
T
calculated the dependence of the apparent transfer efficiency atriple-bandmirrorthatseparatesexcitationandemissionlight
onexcitationrate(assumingk =k ,dashedlineintheinset (BS R405/488/594, Chroma Technology), fluorescence emission
STA T
of Fig. 6). Although this contribution to the very low power passedthrougha100mmpinhole.FornsFCSmeasurements,the
dependence of the apparent transfer efficiency observed for photon signal was then divided randomly by a 50–50-beam
Pro14atelevatedexcitationpowersisspeculative,itillustrates splitter cube. Each fraction was further separated into donor
that effects in addition to the dominant contributions of SSA and acceptor fluorescence by a dichroic mirror (585DCXR,
e. andSTAidentifiedabovecouldfurthermodulatetheobserved ChromaTechnology).Donorfluorescenceineachchannelthen
c
M. en transfer efficiencies. More quantitative studies of the triplet passed a filter (ET525/50m, Chroma Technology) before being
c
ALi states of Alexa488 and Alexa594 will be needed to refine our focused onto a single-photon avalanche diode (MPD 100ct,
13:59 orted understanding of the detailed mechanisms of STA in single MicroPhotonDevices).Similarly,acceptorfluorescenceineach
3 1:Unp moleculeFRETexperiments.Furtheraspectsthatmighthaveto channel passed a filter (HQ650/100m, Chroma Technology)
020 be considered are saturation effects in an inhomogeneous before being focused onto an MPD. Since the QT650/100 filter
9/2n 3. irradianceprofile50andstimulatedemission,whichisapossible does not provide sufficient blocking in the infrared range, an
1o
05 November 2015. Downloaded on 1/d under a Creative Commons Attributi s5metFtianartfl%RaitfktomeinEoIecdrnoTsniunSeeifl0leancpaTknitoocrtnei1tfeovnix)tede.cFoc(saIeslimnbugesesases.mhsetcoih4cocoFoiraheowsupingsauptnht,i.nsinoraoaiSeiitndsnsnn4smeevnfSFionistnir1ihhprfttgouteeic(cid:2).rlhaScaa!a4wEettsltbrlhqeieyaEo,eSauaSnnhk0andtIoohn†depeowe)tcexrf.i6aefcotIf.ayvirAcnetaetelacocitersvttelf,xiuseowoaSedcn1nseuiSo4ncnt1lee8higavfd8mifneinetidchitaraqteoisit,peunstnSapaa4tpn0tlnan8ySrrdd8to1ekinifcSnt(nyneeEhotgesmfrertsdfyrooooaimfmtrtnfnooSsatttt1fhhhhbbkTeeeeeeee1r awwPiWpfamfnrlcdeaaeeoucerrdsrrtmekethheeidupdtieenieratdoscetoral.eneaceE5rsrtlod1aliemddrmdblcWd(eirefitbreteanieseeeulrdtdcetcciterdootOtwirlibbnboopegi(ytetwn7xtah=dmoc2eiaine0r1ttnpelowea/.etarS0fdtiocesamPi5touvvdc,rianaeraoooSevenlnrutreaamodreeimnslecfcsalecbcstyonrnaoht).oli1c=tureoc7whs=stkn0..iei5Tpo).t0I20hrfhnn.waa60poP)cnath5thfehatssooiopsogifwnrrisetthncsiaortcdoeshsdngaeremeiisfrsco=fqetpasdidec,ucaal0edociaiamro.enuc5entdn(clfd3poStaieeculgPtypteasemuoCsnutdhbroMptdarirwhepstfe-ifrebpteAraofoorehikQMnmcg=esodi.RrsPetoa0pTo-nDttm1w.rhhh0nc4esn4eeesys-.,
blished on e is license ampnreeiasmesunprcoeermtoaefnnSttScsAoo,nnwtrheibixcuchittilaoetnaiodtnsotrroeadtaeun.cOeinffiugrctirheenestuddletesppeconlpedauerlnlayctiesohonofowFfRttEhhTee ecoxtriTrnehcleatitoaendrr,icvosaeilnfftgiiclmeie-epnhtosoftoeofvneArlcyeoxpauhn5ot9ti4nonganwmdaosAdlreuexlceaor4(dH8e8yddartwa4iHt8ha8rapnmti4m.00e-,
e. Puarticl dinoduibcalytioenxscitthedatsSiTnAglaeltsostoactec.urIsninadoduirtiFoRnE,Tthpearier aanrdefsutrrtohnegr PicoQuant). All measurements were performed with a laser
s Articl This cFoRnEtTribeuffitecsientocierse.dEuxccinitgedthsetatpeoawnenrihdielapteinondecnacne tohfusobesxeprlvaeind opbojweecrtivoef(b1e0a0mmWwa,ismteBas8urmedma)tutnhleessbainckdicaapteerdtuoretheorfwitshee.
s
cce whyFRETefficienciesobservedexperimentally,e.g.,onsurface- FortheFCSmeasurements,therelativetimingofthedetection
A channels was synchronized by recording on all four MPDs
n immobilized single molecules, are usually quite robust with
Ope respect to the irradiance used. Likewise, in the absence of photons of picosecond laser pulses from a supercontinuum
laser (Fianium, Sc-450-6-PP-01) with the repetition rate set to
excited-state annihilation, the distribution of excitation inten-
20 MHz reflected from a cover slide (filters removed). The
sityacrosstheconfocalvolumewouldbeexpectedtoleadtoa
wavelength of the laser pulses was selected by a band pass
broadening of the FRET efficiency histograms observed for
filter (z582/15, Chroma Technology). Photon detection times
molecules freely diffusing in solution. For the most common
weremeasuredrelativetoasynchronizationsignalfromafast
applications of FRET, SSA and STA thus lead to the wide
photodiode onto which a fraction of the laser light was
applicabilityoftheapproximationstakenfromtheweakexcita-
diverted. Photon arrival time histograms (1 ps binning) were
tion limit and do not need to be considered in detail. For a
integratedovertenminutesatphotoncountratesofabout104
rigorousanalysisofrapidcorrelationexperimentsinthenano-
per second on each detector. The recorded distributions have
secondrangeandbelow,however,annihilationprocessesneed
tobetakenintoaccountexplicitly.22Giventhatproblemswith full width at half maximum of about 100 ps. They can be
overlaid with a residual jitter of about 3 ps for repeated
deviationsinFRETefficienciesoutsidetheweakexcitationlimit
measurements. Finally, we adjusted the timing offset settings
have rarely been reported, it seems likely that the processes
of the HydraHarp 400 such that all four normalized pulse
described here affect other commonly used single-molecule
distributionswereinagreementtowithin3ps.
FRETpairsinasimilarfashion.
For FCS measurements, the arrival times of the output
signals of the MPDs were recorded and stored to hard disk
Materials and methods with respect to the internal clock of the HydraHarp with 1
picosecondresolution(T measurementmode).TheMPDsare
2
Single-moleculefluorescencespectroscopy specified to have a timing jitter of B50 ps. The correlation
Observationsofsingle-moleculefluorescenceweremadeusinga curves were calculated for equidistant lag times with 20 ps
custom-built confocal microscope equipped with a continuous binning. To avoid the dead times of the individual detectors
Thisjournalis©theOwnerSocieties2015 Phys.Chem.Chem.Phys.,2015,17,32304--32315 | 32311
View Article Online
PCCP Paper
and the effect of afterpulsing, only crosscorrelations between K, V , and V were extended to 9 (cid:6) 9 matrices to calculate
D A
detectorsignalswerecalculated:53,54forG (t)betweenthetwo E according to the photophysical model shown in Fig. 4a,
DD app
donordetectionchannels,forG (t)betweenthetwoacceptor which includes (in addition to the model above) inter-system
AA
detection channels, and for G (t) between the combined crossing transitions and STA. The obtained algebraic form of
AD
signals of the two acceptor and donor detection channels, E iscomplicated,butcaneasilybereproducedwithsuitable
app
respectively. computeralgebrasoftware.
Calculationof E Calculationof G (s)
app ij
ce. We define p as the normalized vector whose elements are the The fluorescence intensity correlation function, gij(t), between
M. en populationsofthefourphotophysicalstatesintheorderS S , detector channels i and j (i = D, A) of a single molecule with
c 0 0
13:59 Aorted Li Sgo1Sv0e,rnS0eSd1,bayntdheS1rSat1e(seeqeuaFtiigo.n12b1). The time evolution of p(t) is pgihvoetnonby9e,m21,i5s5sion kinetics described by the rate matrix K is
19/2023 1:on 3.0 Unp withtheratematrix: dp/dt=Kp (5) gijðtÞ¼ð1T1VTiVpsjseÞK(cid:7)t1VTiVpsjspss(cid:8)¼(cid:7)1T1V~TiV~psjse(cid:8)K(cid:7)t1V~TiV~psjspss(cid:8); (8)
ed on 1/Attributi 0(cid:2)ð1þaÞkex kD kA 0 1
wnloadmons K¼BBBB kex (cid:2)kD(cid:2)kT(cid:2)akex 0 kAþkSSA0 CCCC: (6)
November 2015. Donder a Creative Com VFuAr=thQeArxwAkeAV˜dAefwinieththe detectiBB@on maatk0reicxes VD = QDxaDkkkTeDxV˜D and (cid:2)wkAhkee(cid:2)xrekexeKt(cid:2)kisD(cid:2)thkekADm(cid:2)þakktSSrSSiAxA(cid:2)exkpSSoAn0eCCAntial of Kt. The second
05 d u 00 1 0 01 00 0 1 01 equality results from the cancellation of the common Qkxkkk
ccess Article. Published on This article is license aonkdDEw/V~(e1Dm¼(cid:2)akBBBBBB@Ee)000,thae000nrdep000klSaSc010AeCCCCCCA0m¼enoat0nskdTkT¼V=~oAk0Dk¼ED/EBBBBBB@(1=000ð(cid:2)1(cid:2)E000)E, kÞ000.SSAW100=CCCCCCAithoktTh=e wpVfsdcamraeAicotCtrthaseaoslc=mlrttstaeVebhldtAkueient+riisnesnnbxitcogVitonehnmDpeiafiattniicnhcaocaacdenotncoueVt~rlnopaAffttsarC,otanorc¼VdttAediVoa~dremnnaAetendnþcodotofimobgofkkdV˜0niAD,oAneV~nqatcDhhtonho,aerarvrn.(fee8vlnsuTa)petolyoulepra.ceeritscFsbeiacvoeeleorklnlyfrnycte.oaetaphNkwlllpaieonnrchtmegeeodftortitosohdhnbmaeiasystl
n A definitions above, the mean fluorescence photon detection independent measurements. kD = 0.25 (cid:5) 0.01 ns(cid:2)1 and
Ope ratescanbecalculatedas kA = 0.25 (cid:5) 0.01 ns(cid:2)1 have been determined previously from
fluorescence lifetime measurements.22 k = 0.02 (cid:5) 0.01 ns(cid:2)1
n =1TVp with i=D,A, (7) ex
i i ss was determined from antibunching measurements of donor-
where 1T = (1,1,1,1) is the transposed unity vector and p is onlylabeledpolyproline.9
ss
the normalized steady state solution of eqn (5), i.e. Kp = 0 Polyproline samples exhibit a significant population of cis-
ss
and 1Tp = 1. Inserting the rates into eqn (1), we obtain the isomerswithinall-transpolyprolinehelices,whichleadstothe
ss
general formula for E (eqn (4)) with the functions f and asymmetric broadening of single-molecule FRET efficiency
app 1
f givenby histograms observed for longer polyproline peptides14,17
2
(Fig. S1, ESI†). The high transfer efficiency peak in the FRET
f (E)=(2+a)(1+o0)+k (cid:2)1(1+a)[k (1+a)+k (2(cid:2)o)
1 D ex A histogramofPro20canbewellfittedbytwoGaussiancurvesof
+k (2+o0)](1(cid:2)E)/E(cid:2)k (cid:2)2(k (cid:2)ak ) different positions E and E , different amplitudes, but iden-
D D A D 1 2
(cid:6)[k +k +(1+a)k ](1(cid:2)E)2/E2 ticalwidths(seeFig.S1,ESI†).ForobtainingmorerealisticFCS
A D ex
curves, we hence treat the Pro20 sample as a mixture of two
and species(labeled1and2)withmeantransferefficienciesE and
1
f (E)=o+o0 +k (cid:2)1k (cid:2)1[k 2+k k +k k (1+(1+a)o) E2.AthirdspeciesofPro20moleculeslackinganactiveaccep-
2 D A A A D A ex
tordye(‘‘donor-only’’)alsohastobetakenintoaccount.Hence,
(cid:2)k k (1+a)(1+o0)](1(cid:2)E)/E(cid:2)k (cid:2)2k (cid:2)1(k (cid:2)ak )
D ex D A A D the overall correlation function used for fitting the experi-
(cid:6)[k +k +(1+a)k ](1(cid:2)E)2/E2. mentaldataisgivenby
A D ex
c B B g ðtÞþc B B g ðtÞþc B B g ðtÞ
GijðtÞ¼1þaij (cid:7)1 1;i 1;j 1;ij 2 2;i 2;j 2;i(cid:8)j(cid:7) donly donly;i donly;j donly (cid:8) : (9)
c B þc B þc B c B þc B þc B
1 1;i 2 2;i donly donly;i 1 1;j 2 2;j donly donly;j
32312 | Phys.Chem.Chem.Phys.,2015,17,32304--32315 Thisjournalis©theOwnerSocieties2015
View Article Online
Paper PCCP
Here we used the FCS formula for a mixture of species freely about the values given above assuming normal distributions.
diffusingtroughtheconfocalvolume56forthecasethatthelag k wasalsovaried,butwithastandarddeviationof50%owing
ex
time t is much shorter than the mean diffusion time through toitslargeruncertainty.Thedistributionofovaluesobtained
theconfocalvolumeaswellasthecharacteristictripletblinking bythisprocedureisessentiallysymmetricaroundo=0.95with
ofthefluorophores,i.e.t{1ms.Theamplitudesa dependon astandarddeviationof0.06.
ij
the mean number of labeled particles present in the confocal
Excitedstateextinctioncoefficients
volumeandontripletblinking.c =0.59,c =0.30,andc =
1 2 donly
0.11aretherelativeconcentrationsofthesubpopulationswith Weusedacustom-madepump–probesetup.AnamplifiedTi:Sa
e. transferefficienciesE1=0.57andE2=0.77,andofthe‘donor- laser system (800 nm; 40 fs pulse duration; 5 kHz repetition
c
M. en only’population,asobtainedfrompeakfunctionsfittedtothe rate) is used to inject a TOPAS (optical parametric amplifier,
c
13:59 Aorted Li tthraenrsefleartievffiecmieonlecycuhlaisrtobgrrigahmtn(eFsigs.vSa1lu,eEsSIo†f).spBes,ciiaensdsB=d1o,nl2y,iaanrde l4i9g0htncmonoverr6s0io0nn).mThtoeelaxcttieterAprleoxdau4c8e8stohreApleuxmap59b4e,armes,pteucntievdeltyo.
3 1:Unp thedonor-onlyspeciesasseenbydetectori: A white-light supercontinuum was produced by focusing a
9/202n 3.0 Bs,D=1(cid:2)Es, Bs,A=g(Es+a)+b(1(cid:2)Es), scmrysatlallf,raanctdiounseodf tahsethfuenpdraombee.nTtahle8s0a0mnpmlepsoullusetioinntsowaitChaaFn2
oaded on 1/1ns Attributio Wspeecidesesbcyribe tBhdeonlcy,oDrr=el1a,tioanndfunBcdtoinolny,Do=fb.the dono(r1-o0n)ly bdopuimtfifceeatrhlpydlHens7us.il2tfyoixonidfteBh,e30p.c0rm2e%s(cid:2)e1n2icn-em1oe0fr0c0am.p1t%Moeptshooadtaniusosmli,umwazeirpdeheo,fsi0lpt.2ehr5ae%tde
wnlmo witha0.22mmfilterandcirculatedina 1mmthickflow cell,
om g (t)=1(cid:2)c e(cid:2)kD|t|. (11) using a peristaltic pump. Pump and probe pulses were over-
Do donly ab
ber 2015. Creative C dTuhee taontaibsumncahllinfrgacatmiopnlitoufdPeroca2b0dmevoilaetceuslefrsolmabuelneidtywpiothssitbwloy lwTahiptehpeitnrdatnihnsemsildiitneteeadthrperreofglboimewescpoeeflcl.terxuTcmhiteatwisoaansmdbpeyleteascptweuedlrsewedietxhlcaisateesrdpbetecoatrmSo1-.
05 Novemd under a dGolonboarldfiyteso.ftheFCSdata gbwreiatahpmha,ntehdqeuwtiripathpneosdmutiwtetixetcdhitpianrogCbtCehDsepsecacamtmrupemlrea.w.AaBsydmifcfheeaorespunprtieinadlgsautbhcsceoerspbsuaivnmeclpey
blished on e is license goWlfoetbhafriletltyeedtcoortthrheeespmmoenoaddseiunlrgeFdwC2dSfauctnaucritvnieosFn,isgG,.eD3aDbc(thy),mbeGiniAniDmg(toi)z,fintahgnedthfoeGrmAsAu(mt) tashidgejnutasrltae(nDdsAibe)ynistmtshetuaantsescso.omfThapeudtteeilmdaytehliadnteerlaetyvoeba1el0st0wthepeeicnsopsteheccetortnawldossi.gpnualstuesrewsaosf
Article. PuThis articl wij2¼wijXm (cid:7)FCSi;jðtmÞ(cid:2)GijðtmÞ(cid:8)2: tribTuhtieonress,uwlthinicghtraarnestiehnetEsSpAecwtreaaairme tahterseutrmievoinfgt,htrheee cGoSnB-
s The weights are the reciprocal variances for each data point, which is the opposite of GSA, and the SE. Exactly as GSA, SE
cces wij=1/sij2(weassumeuniformvariancesforalldatapointsin may be described by a (negative) extinction coefficient eSE(n)
n A oneFCScurve).Koppel57showedthatthesignal-to-noiseratio (in units of M(cid:2)1 cm(cid:2)1), since both processes result from the
pe of an FCS curve of a single species is proportional to its samelight–matterinteraction,asrevealedbytheequalityofboth
O
molecular brightness B if B(cid:7)D { 1, where D is the binning corresponding Einstein coefficients B.58 In molecular systems,
interval of the experimental FCS data. In our case with a however, since equilibrium ground and excited states corre-
molecularbrightnessofB0.1ms(cid:2)1andD=20ps,thisrequire- spond to different nuclear configurations, the spectral shapes
ment is clearly met. As the amplitude of the FCS curve itself forGSA,SEandfluorescencearedifferent.24Still,wheneverthe
does not depend on the brightness, we conclude that the molecular transition dipole moment is weakly affected by the
varianceofthesignalisproportionaltos2p1/B2.Generalizing nucleardegreesoffreedom,asimplerelation,derivedbyStrickler
thisresulttodual-colorFCS,weobtains 2p1/(BB).Therefore &Berg,59relatestheextinctioncoefficientforGSAtothatofSEor
ij i j
we weight the w2 functions with w = B B , w = B B , and tothefluorescencespectrum,asfollows:
AA A A AA A A
wc1ABD1,i=+4c2BBA2B,iD+, cwdhonelryBedoBnilyi,si.TthheefmacetaonrfroeulartiisvejusbtriifgiehdtnseinssceBtih=e ðeSEnðnÞdn¼(cid:2)ðeGSAnðnÞdn; with eSEðnÞ¼(cid:2)fðnÞ(cid:9)n2:
crosscorrelationwasobtainedfromtwodonorandtwoacceptor
detectionchannelsandtheeffectivemolecularbrightness‘seen’ Hereweusethesecondrelationtocomputethespectralshapeof
by a detector pair is twice as large as for a single detector. Our the SE from that of the measured steady-state fluorescence
choiceofrelativeweightsisempiricallyconfirmedbycomparison spectrum f(n) (measured in a specrofluorometer, Fluorolog,
tothevariancescalculatedfromtheresidualsshowninFig.3. Jobin Yvon), and the first one to scale the absolute magnitude
The total of the three w 2 functions was minimized by (in M(cid:2)1 cm(cid:2)1) of e (n) with respect to the measured (steady-
i,j SE
varying o and the four amplitudes a , a , a , and c . The state)e (n).Themaximume (n)isscaledtotheknownvalues
DD AD AA ab GSA GSA
bestfitvalueswerefoundtobeo=0.95,a =0.59,a =0.41, of90000M(cid:2)1cm(cid:2)1forAlexa594and71000M(cid:2)1cm(cid:2)1forAlexa
DD AD
a = 0.70, and c = 0.91. For estimating the error on o, we 488(Invitrogen).
AA ab
minimizedw2repeatedly(10000times)byrandomlyvaryingthe The ESA extinction coefficient e (n) is retrieved by sub-
ESA
‘‘fixed’’modelparametersa,b,g,k ,k ,E ,E ,c ,andc by5% tractingthespectrum(e (n)(cid:2)e (n))fromthescaledtransient
D A 1 2 1 2 SE GSA
Thisjournalis©theOwnerSocieties2015 Phys.Chem.Chem.Phys.,2015,17,32304--32315 | 32313