Theoretical aspects and expressions for appare

ContentslistsavailableatScienceDirect

Journal of Photochemistry and Photobiology A:

Chemistry

jou rn a l h o m e pa g e:w w w. e l s e v i e r . c o m / l o c a t e / j p h o t o c h e m

Acid–base equilibrium of drugs in time-resolved fluorescence measurements:

Theoretical aspects and expressions for apparent pK _a shifts

Fabricio Casarejos Lopes Luiz, Sonia Renaux Wanderley Louro

DepartmentofPhysics,PontificalCatholicUniversityofRiodeJaneiro,RiodeJaneiro,Brazil

a r t i c l e i n f o

Articlehistory:

Received28May2010

Receivedinrevisedform3March2011 Accepted13March2011

Available online 21 March 2011

Keywords:

Acid–baseequilibrium pKshift

Time-resolvedfluorescence Fluorescencelifetime Dibucaine

Levofloxacin

a b s t r a c t

Spectroscopicpropertiesofmoleculeswhichundergoacid–baseequilibriumaregreatlyinfluencedby thelocalpH.Theiracid–baseequilibriumconstantscanbeexperimentally obtainedunderdifferent environmentsbymeasuringspectroscopicparameterssuchasabsorbance,fluorescenceintensityand fluorescencelifetimesasafunctionofpH.ThepKavaluesareobtainedfittingthedatawiththewell knownHenderson–Hasselbalchequation.Decaycurvesobtainedwithtime-resolvedpulsefluorometry areusuallyanalyzedintermsofmulti-exponentialfunctionscharacterizedbythepre-exponentialfac- torsorbytheintegratedfractionalfluorescenceintensitiesassociatedwitheachlifetime,thislastbeing analogoustothesteadystatefluorescencecontributions.Inthispaperweshowthatundernormalcondi- tionsformanyfluorescentdrugs,atwo-exponentialanalysisisadequate.Wedevelopexpressionsforthe pHdependenceofpre-exponentialfactorsandfractionalfluorescenceintensitiesintime-resolvedpulse fluorometryofafluorophoreundergoingacid–basetransition.WeshowthattheobtainedpKavalues areapparentlyshifted,andgivetheexpressionsforthepK-shifts.Theexpressionsweretestedusingthe fluorescencedecaypropertiesoftwocompounds:thewellcharacterizedlocalanestheticdibucaineand theantibioticlevofloxacin.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Acid–base equilibrium ofvarious substrates,drugsand indi- catorsareofteninvestigatedinhomogeneousandheterogeneous solutions[1–14].Spectroscopicpropertiesaregreatlyaffectedby theionizationstateofmolecules,which canserveasindicators for local pH [1,2,14–19], and local electric potential [2,3,6,20].

Drugsactivityandtoxicityalsofrequentlydependontheionization state.Evaluationofequilibriumconstantsisthereforeimportantfor analyticalapplications,andfortheinvestigationoftheirpharma- cologicalproperties[1,2].

During the past decades time resolved fluorescence experi- mentshasbeenincreasinglyusedinmultidisciplinaryscience[2].

Fluorescent drugs and dyes are known to be useful molecular probes forexamination of interfacialregions and bindingreac- tions[4,6–12].Manyofthemundergoacid–basetransitionswith environment-dependent equilibrium constantspKa. Their spec- troscopic parameters provide important means to observe the acid–baseequilibrium.Themostimportantcharacteristicsofaflu-

∗Correspondingauthorat:DepartmentofPhysics,PUC-Rio,RuaMarquesdeSao Vicente225,RiodeJaneiro22451900,RJ,Brazil.Tel.:+552135271260;

fax:+552135271269.

E-mailaddress:sonia@fis.puc-rio.br(S.R.W.Louro).

orescentdrugarethefluorescencequantumyieldsandlifetimes.

Thequantumyieldsareassessedbysteadystatemeasurements.

Thelifetimes,whichdeterminethetimethattheexciteddrughas tointeractordiffuseintheenvironmentbeforereturningtothe groundstate,ismeasuredusingphase-modulationorpulsefluo- rometry.

In general,whena fluorescent drugundergoesanacid–base transition,thefluorescencepropertiesofthetwospeciesaredif- ferent. Bothsteadystateandtime-resolvedfluorometryprovide importantparametersthatallowobtainingtheapparentpKaunder differentconditions.Inthecaseofsteadystatefluorescence,the expressionforthefluorescenceintensityatasinglewavelength, orfortheintensityratioattwodifferentwavelengths,asafunc- tionofpHiswellknownandappearsinChapter10,AppendixAof [1].Ontheotherhand,theacid–basepropertiesofamoleculethat absorbslightcanchangewhenthemoleculeisintheexcitedstate.

Theexcitedstateequilibriumconstant,Ka^∗,canbedifferentfrom thatofthegroundstate,Ka.Severalmethodshavebeendescribed toobtainKa^∗usingbothsteady-stateandtimeresolvedfluorescence [1,21].

Valeur treatsthe case of a selective excitation of theacidic forminChapter4of[1].Ingeneral,itisnotpossibletoselectively excite oneformbecausemanydrugspresent onlyminordiffer- encesbetweentheacidicandbasicUV–visibleabsorptionspectra.

ExpressionsbasedontheHenderson–Hasselbalchequationareno 1010-6030/$–seefrontmatter© 2011 Elsevier B.V. All rights reserved.

doi:10.1016/j.jphotochem.2011.03.006

curvesobtainedwiththeseparametersgiveshiftedpKavalues.The apparentpKashiftswerefoundasfunctionsofthequantumyields andlifetimesoftheinvolvedspecies.Theexpressionsweretested using thefluorescence ofthe localanesthetic dibucaine and of thefluoroquinoloneantibioticlevofloxacin.Thefluorescencedecay curveswereobtainedbyTCSPCpulsefluorometry.Pre-exponential factorsand fractionalcontributions wereobtained usingglobal analysis.ApparentpKashiftsobtainedfromtheexperimentaltitra- tionplotswerecomparedwiththecalculatedvalues.

2. Theory

Let us consider a molecule undergoing a protonation–deprotonation reaction in aqueous solution. The usualequationforanalyzingpHtitrationcurvesofasingleioniza- tionequilibriuminthegroundstate(Scheme1)isthewellknown Henderson–HasselbalchEq. (1),whereristhemolarfractionof thebasicform,r=[A]/([A]+[AH]),andKaistheapparentacid–base equilibrium constant, Ka=[A].[H]/[AH] (electric charges were omitted).

(Scheme1) pH=pKa+log r

1−r (1)

Ingeneral,themolarfractionrcanbeexpressedasafunctionof spectroscopicparametersoftheacidicandbasicforms.Theacidic andbasicforms ofa drugaredifferently charged.Thedifferent chargedistributionsleadtodifferentphysico-chemicalcharacter- istics.ConsideringaspectroscopicparameterP,

P=(1−r)P^AH+rP^A (2)

withP^AHandP^AbeingthevaluesofPwhenallthemoleculesarein theacidicandbasicforms,respectively,Eq.(1)becomes:

pH=pKa+log P−P^AH

P^A−P (3)

ParameterPisobtainedfromEq.(3)asafunctionofthepH:

P=P^AH10^pKa+P^A10^pH

10^pKa+10^pH (4)

Insteadystatefluorescence,forexample,parameterPisthefluo- rescenceintensityatagivenwavelength,I_␭[1].

TheexcitedstateequilibriumconstantK˛^∗canbedifferentfrom thatofthegroundstate.Theeventsfollowingtheexcitationofboth theacidicandbasicformsofamoleculearedescribedby(Scheme 2).o^AHando^Aaretheexcitedstatelifetimesoftheacidic(AH*)and basic(A*)forms(electricchargeomitted),respectively,andk^∗₁and k^∗₋₁aretherateconstantsfortheexcitedstatedeprotonationand reprotonation,respectively.Theexcitedstateequilibriumconstant isKa^∗=k^∗₁/k^∗₋₁.Valeurtreatsthecaseofaselectiveexcitationofthe acidicforminChapter4of[1],butingeneralthisisnotpossible

(Scheme2) Taking into account that H⁺ is in fact H₃O⁺,the differential equationsexpressingtheevolutionofthespeciesaftera␦-pulse excitationofbothAHandAarewrittenaccordingto(Scheme2):

d[AH^∗]

dt =−(k^∗₁+1/^AH_o )[AH^∗]+k₋₁^∗ [H₃O][A^∗] d[A^∗]

dt =k^∗1[AH^∗]−(k^∗₋1[H3O]+1/o^A)[A^∗]

(5)

In generaltheexcitedstateback-protonationreaction needsto betakenintoaccountonlyifpH≤2or3,becausethisreactionis diffusion-controlled(k^∗₋₁≈5×10¹⁰ L mol⁻¹ s⁻¹)andatpH≈3 thepH-dependentrateisk^∗₋₁[H₃O]≈5×10⁷ s⁻¹.Thereciprocal ofthisvalueismuchgreaterthantheexcited-statelifetimesofmost organicbases[1].Eq.(5)become:

d[AH^∗]

dt =−(k^∗1+1/^AHo )[AH^∗] d[A^∗]

dt =k^∗₁[AH^∗]−(1/o^A)[A^∗]

(6)

The solutions of Eq. (6) when both AH and A are excited, undertheinitialconditionsthat att=0, [AH^∗]=[AH^∗]₀; [A^∗]= [A^∗]₀;d[AH^∗]/dt=−k^∗1+1/_o^AH[AH^∗]₀;andd[A^∗]/dt=k^∗₁[AH^∗]₀− 1/o^A[A^∗]₀,leadstothefollowingexpressionsforthefluorescence intensitiesafterthe␦-pulse:

iAH^∗(t)=kr^AH[AH^∗](t)=k^AH_r [AH^∗]₀e^−ˇ1t

iA^∗(t)=k^Ar[A^∗](t)=−k^Ar

k^∗₁ ˇ1−ˇ2

[AH^∗]₀e^−ˇ1t

+k^Ar

[AH^∗]₀+[A^∗]₀

e^−ˇ2t

(7)

InEq.(7),k^AHr andkr^Aaretherateconstantforradiativede-excitation of AH*and A*,respectively,andˇ1=k^∗₁+1/^AHo andˇ2=1/o^A. Thetotalfluorescenceintensityisthesumofthecontributionsin Eq.(7),havinginmindthatk^AHr andk^Ar mustbetheradiativerate constantsatagivenemissionwavelengthandbandwidth.

i(t)=

kr^AH−k^Ar

k^∗₁ ˇ1−ˇ2

[AH^∗]₀e^−ˇ1t

+k^Ar

[AH^∗]₀+[A^∗]₀

e^−ˇ2t (8)

Eq.(8)tellsthatthedecayisfrequentlybiexponential,withdecay ratesgivenbyˇ1andˇ2.Inthecasethatk^∗₁<<1/o^AH,thedecay rates correspondtothose of theacidic and basicspecies: ˇ1= 1/o^AHandˇ2=1/o^A.

ThedecayofthetwospecieswillbeindependentandEq.(8) willreducetoEq.(9)inthecaseoftheadditionalrestrictionk^∗₁<<

(1/o^AH−1/o^A).

i(t)=kr^AH[AH^∗]₀e^−ˇ1t+k^Ar[A^∗]₀e^−ˇ2t (9)

Fig.1. Chemicalstructuresofdibucaine(a)andlevofloxacin(b).ThepKaofcircledgroupsare8.8and8.2,respectively.

Inordertoanalyzewhenthiswilloccur,itisworthrecallingthatEq.

(8)isvalidonlyfordiffusion-controlledreprotonation,k^∗₋₁≈5× 10¹⁰ L mol⁻¹ s⁻¹.Therefore,itispossibletoestimatek₁^∗=Ka^∗k^∗₋₁ fromthevaluesofpKa^∗.Forexample,alifetimeo^AH≈2×10⁻⁹ s givesk^∗₁o^AH<0.1forpKa^∗>3.Infact,manyfluorescentmolecules satisfythiscondition.Intensitydecaysaretypicallyfittothemulti- exponentialmodel:

I(t)=C+

i

˛iexp−t i

(10)

whereCisaconstantassociatedwiththenoise,iarethelifetimes oftheindividualspeciespresentinthesampleand˛iarethepre- exponentialfactors.Eachlifetimecontributeswithafractionf_ito thetotalnumberofemittedphotons,f_ibeingproportionalto˛ii, theareaunderthedecaycurveforeachdecaytime.Itisdemon- strated[1]thatthefractionalcontributionsf_irepresentthesteady statefractionalintensitiesofeachfluorophoreattheobservation wavelength.

f_i=

˛_jj

(11)

WhenEq.(9)isvalid,therewillbenoexcited-stateprotontransfer duringtheexcited-statelifetime,and thedeconvolutedfluores- cencedecayI_␭(t)inpulsefluorometrywillbefittedbyadouble exponentialfunctionandthetime-resolvedspectroscopicparam- eterswillreflectthepresenceofthetwospecies.

TheproportionalityconstantbetweenEqs.(9)and(10)depends onlyontheinstrumentalsetup.Theinitialconcentrationofexcited moleculesinEq.(9),ontheotherhand,dependsontheground stateconcentrations [AH]and [A], and onthemolarabsorption coefficients ε^AH and ε^A atthe excitationwavelength. Then, the pre-exponentialfactorsinEq.(9)areproportionalto:

˛^AH∝[AH]ε^AHk^AHr and ˛^A∝[A]ε^Ak^Ar (12) TheratiobetweenexpressionsinEq.(12)gives:

r

1−r= [A] [AH] = ˛^A

˛^AH ε^AH

ε^A kr^AH

k^Ar

(13)

whichcanbeusedinEq.(1)toexpresstheHenderson–Hasselbalch equationintermsofthepre-exponentialfactors˛^AHand˛^A. pH=pKa+logε^AHk^AHr

ε^Ak^Ar

+log ˛^A

˛^AH (14)

Eq.(14)indicatesthat,whenusingthepre-exponentialfactorsas spectroscopicparametersinapHtitrationexperiment,thepK_awill beapparentlyshiftedtopKa,with

pKa =pKa+logε^AHk^AHr

ε^Ak^Ar

(15)

TheradiativerateconstantsKr^AHandk^Ar canbewrittenintermsof thefluorescencequantumyields,^AH_f and^A_f,andlifetimes^AHand ^A.

k^AHr = ^AH_f

^AH and kr^A=_f^A

^A (16)

where^AH_f and^A_f arethequantumyieldscomputedonlyforthe measuredpartoftheemissionband.UsingexpressionsEq.(16)in Eq.(15),thepKashiftofbecomes:

pKa^˛=pKa−pKa=logε^AH_f^AHA

ε^AA_f^AH (17)

The normalizedpre-exponential factorsasa functionof pHare obtainedfromEq.(14):

˛^AH

(˛^A+˛^AH)= 10^pKa

10^pH+10^pKa and ˛^A

(˛^A+˛^AH)= 10^pH 10^pH+10^pKa

(18) TheseequationsareequaltoEq.(4),withparameterPgivenbythe normalizedpre-exponentialfactorsandP^AH=1,P^A=0andP^AH=0 and P^A=1, respectively. The shifted pKa given by Eq. (17) are obtainedwhenfittingthenormalizedpre-exponentialfactorsas afunctionofpHwiththeHenderson–HasselbalchEq.(4).

Thetime-resolvedparametersassociatedwiththecontributions ofeachspeciesinasteady-statefluorescenceexperimentarethe fractionalintensitiesf_i(Eq.(11))[1,2].Equation13canbeexpressed asafunctionofthefractionalintensitiesusingEq.(16):

r

1−r = [A] [AH]= f^A

f^AH ε^AHAH

ε^AA (19)

Hence,theHenderson–HasselbalchEq.(4)intermsofthefractional intensitiesbecomes:

pH=pKa+logε^AHAH

ε^AA +log f^A

f^AH (20)

Eq.(20)indicatesthat,whenthefractionalintensitiesareusedas spectroscopicparametersinapHtitrationexperiment,therewill beanapparentpKashift,givenby:

pKa^f=pKa−pKa=logε^AHAH

ε^AA (21)

The equations used to fit the fractional intensities versus pH obtainedfromEq.(20)are:

f^AH

f^AH+f^A = 10^pK

10^pH+10^pK and f^A

f^AH+f^A = 10^pH

10^pH+10^pK (22) Eq.(22)areequaltoEq.(4),withparameterPgivenbythefractional intensitiesandwithP^AH=1,P^A=0andP^AH=0,P^A=1,respectively.

Itisworthnotingthat,althoughthefractionalintensitiesina TCSPCexperimentareequivalenttothesteadystatefluorescence intensities,theygiveshiftedpKavalues,accordingtoEq.(21).This maylookstrange,butitcanbeexplainedbythefactthatinthe steady-stateexperimentthefluorescenceintensityI_␭isthecontri- butionofbothspeciesduringafixedpre-determinedtimeinterval,

3.1. Materials

Highpuritydibucainehydrochlorideandlevofloxacin(Fig.1) werepurchasedfromSigmaandusedwithoutfurtherpurification.

Concentratedstock solutions(1mM)were preparedin ethanol.

Analyticalgradechemicalswereusedforthepreparationofbuffers andfortheadjustmentofpH.Milli-Qwaterqualitywasusedforall thepreparations.

3.2. Methods

Dibucaineand levofloxacinsolutions(10␮M)atdifferentpH werepreparedinbuffers.Appropriateamountsofthe1mMethanol stocksolutionswerepartiallydriedanddilutedinthebuffersolu- tionssothatthefinalethanolconcentrationswerelessthan0.1%.

The buffers stock solution contained 33mM citric acid, 50mM phosphoric acid, 50mM boric acid and 330mM NaOH. After a 1:15dilution(20mMNa)anddissolutionofthedrug,thepHwas adjustedwithsmallamountsofconcentratedsolutionsofHCland measuredusingaCole-ParmerChemcadet5986–25pHmeterwith anAg/AgClsemimicrocombinationelectrode.pHmeasurements wereperformed immediatelybeforeand after thefluorescence measurements.Spectrophotometric measurementswerecarried outatambienttemperature(24–26^◦C).Opticalabsorptionspectra intherangeof220–800nmwereobtainedwithaHP8452ADiode Arrayspectrophotometer.Fluorescencemeasurementswereper- formedonaPTI–QM1FluorescenceSystemequippedwithatem- peraturecontrollerandmagneticstirrer.Lifetimemeasurements wereperformedonaHoriba–JobinIvon–IBHTCSPCfluorom- eter.Thelightsourceusedfortheexcitationofdibucainewasa 330nmnanoLEDN-16,1.0nsnominalpulseduration,1MHzrepe- titionrate.ComputerprogramssuppliedbyHoribaJobinIvonIBH wereemployedintheprocessingofthetimeresolvedfluorescence data.Fluorescenceintensitydecaycurveswerefittedusingtwo-or three-exponentialexpressions,withaglobalanalysisprocedure.

4. Resultsanddiscussion

Thefluorescenceoftwodrugs,e.g.thelocalanestheticdibucaine andtheantibioticlevofloxacin,are usedtotest theexpressions obtainedinthesection“TheoreticalSurvey”.Steady-stateandtime resolvedfluorescence measurements were performedfor dibu- caine(threepHtitrationseries)offorlevofloxacin(twopHtitration series).Thetitrationseriesforeachdruggavesimilarresultswith differencesinpK_avaluesoftheorderof0.1,atmost.Theerrors presentedbelowarethestandarderrorsgivenbytheleastsquares fittingprocedure.

SteadystatefluorescencespectraofdibucaineatdifferentpH arepresentedinFig.2.Theinsetdepictsthefluorescenceat405nm (peakatpH7)asafunctionofthepH.ThedatawasfittedusingEq.

(4),withapKa=8.78±0.02.

TCSPCfluorescencedecaycurvesofdibucainewereobtainedfor eachpH.Fig.3showstypicalresults.Foreachtitrationsequence, allthecurvesatdifferentpHweresubmittedtoaglobalanalysis usingthemulti-exponentialexpressionofEq.(10).

Since the data was not conveniently fitted using a two- exponential function,a three-exponentialexpression wasused.

Usingglobalanalysis,itwaspossibletofindasetofthreelifetimes (1=3.14ns,2=0.67nsand3=0.23ns)tofitallthefluorescence

Fig.2.Steadystatefluorescencespectraofdibucaine(excitationat330nm)atdif- ferentpH(6.2,6.9,7.5,8.0,8.6,8.8,9.0,9.3,9.7,10.0,10.4,10.9,12.1,fromtopto bottomasindicatedbythearrow).Theinsetshowsthefluorescenceat405nmasa functionofpH;thesolidlineistheleast-squaresfitobtainedusingEq.(4),withP^AH, P^AandpKaasfittingparameters.ThepKawas8.78±0.02.

decaycurvesinthealkalinepHrange,from7.3to12.1.Theglobal ²valuewas∼1.2andthesetoflifetimeswasconsistentwiththe individualanalysisinitiallyperformed.

Thefractionalcontributionsf₁,f₂ andf₃,calculatedfromthe pre-exponentialfactors˛1,˛2and˛3andcorrespondinglifetimes accordingtoEq.(11),appearin theinsetofFig.3asafunction ofpH.Itcanbeobservedthatthelargestlifetime1=3.14nsis duetoprotonateddibucaine,since both˛1andf₁ decreasewith increasingpH.Thelifetime2=0.67nsisduetotheneutral,unpro- tonateddrug,andthesmalllifetime,3,isusuallyintroducedin amulti-exponentialanalysistoaccountforsomescattering.Since f₃displayedthesamepatternasthefractionalintensityf₂dueto unprotonateddibucaine,itwasattributedtoaggregationofneu- traldibucainemolecules,developedintheabsenceofelectrostatic repulsion.Accordingtothisinterpretation,f₂plusf₃intheinsetof Fig.3isthetotalcontributionofneutralmolecules.

Thefractionalintensitiesf₁,andf₂+f₃fittedusingEq.(4)gavea pKaof9.8±0.1,whichgivesapositivepKaof1.0relativetothe

Fig.3. DibucainefluorescencedecaycurvesatdifferentpH(7.5,8.8,9.4,10.0,10.6, 10.9,11.4,fromtoptobottom).Excitationat330nm,emissionat405nm.The solidlinesrepresentthe3-exponentialfitsobtainedfromtheglobalanalysiswith 1=3.14ns,2=0.67nsand3=0.23ns.Theinsetshowsthecorrespondingfrac- tionalintensities:(䊉)f1,attributedtoprotonateddibucaine,(+)f2;(×)f3,and( ) f2+f3,attributedtoneutraldibucaine.

Fig.4. Typicalsteadystate fluorescencespectra oflevofloxacin (excitation at 330nm)atdifferentpH(7.1,7.5,7.9,8.4,9.1,9.4,10.0,10.6,fromtoptobottom asindicatedbythearrow).Theinsetshowsthefluorescenceintensityasafunction ofpHfortwodifferentseriesofmeasurements:(䊉)at457nm,and( )at448nm.

Thesolidanddottedlinesaretheleast-squaresfitsusingEq.(4),withP^AH,P^AandpKa

asfittingparameters.TheobtainedpKavalueswere8.25±0.02( )and8.32±0.03 (䊉).

steadystatefluorescence.Thenormalizedpre-exponentialfactor

˛1/(˛1+˛2+˛3)plottedasafunctionofthepH(resultsnotshown) gaveapKaof9.0±0.1,withpKa=0.2relativetothatobtainedby steadystatefluorescence.

Fordibucaine,themolarabsorptioncoefficientsfortheneutral andprotonatedspeciesaresimilar(ε^AH=ε^A);thequantumyields are˚^A=0.04and ^AH=0.27[2]andthelifetimes^A=0.67nsand ^AH=3.14nswerefoundinthis work.Using thesevalues inEq.

(21)andEq.(17),theexpectedapparentpKshiftsare:pKa^f=0.83 andpKa^˛=0.16,forthefractionalintensityandpre-exponential factor,whichareverysimilartothevaluesobtainedfromthefits oftheexperimentalresults.

Vanderkooi[3]alsoobtainedexperimentalpKashiftsfordibu- caineinplotsoftheapparentphaseandmodulationlifetimesasa functionofpHobtainedfromphase-modulationfluorometry,and performedtheoreticalcomputationsforthedifferentcurvesfound uponusingthelifetimes_P^appand^app_M ,obtainedfromphasedelays andrelativemodulations,respectively.

InthecaseoflevofloxacintheexperimentalpKashiftsobtained usingthefluorescencedecayparameterswerealsoexplainedby Eqs.(17)and(21).Typicalsteadystatefluorescencespectraoflev- ofloxacinatdifferentpHarepresentedinFig.4.Theinsetpresents thefluorescenceintensity(at457nm,meanwavelengthbetween peaksatpH7and11,foroneoftheexperimentalseries,andat 448nm,peakatpH7,fortheotherseries)asafunctionofthepH.

TheleastsquaresfitofthedatausingEq.(4)gaveapKa=8.32±0.03 and8.25±0.02.Thedifferencebetweenthetwovaluesshowsthat theexperimentalerrorsaresmall.

Typicalfluorescencedecaycurvesoflevofloxacinarepresented in Fig.5for severalpHvalues. Foreach titration sequence, the curvesatdifferentpHweresubmittedtoaglobalanalysisusing atwo-exponentialexpression(Eq.(10),withi=1,2).Foronetitra- tionsequence,thetwolifetimesthatfittedthefluorescencedecay curvesinthealkalinepHrangewere1=6.1ns(zwiterioniclev- ofloxacin)and2=0.7ns(anioniclevofloxacin).Thesevalueswere differentfortheothertitrationsequence(1=5.4nsand2=0.6ns), probablybecauseofthedifferentambienttemperaturesduringthe measurements.Nevertheless,theobtainedpK_awereverysimilar forbothtitrationsequences.

Fig.5.TypicalfluorescencedecaycurvesoflevofloxacinatdifferentpH(7.5,8.8,9.4, 10.0,10.6,10.9,11.4,fromtoptobottom).Excitationat330nm,emissionat448nm.

Thesolidlinesrepresentthe2-exponentialfitsobtainedfromtheglobalanalysis with1=5.4ns(zwiterionic)and2=0.6ns(anionic).Theinsetshowsthenormal- izedpre-exponentialfactor˛1(䊉)andthefractionalintensityf1()ofzwiterionic levofloxacinasafunctionofthepH.Thedottedandsolidlinesaretheleast-squares fitsusingEq.(4),withpKavalues8.39±0.02and9.26±0.03,respectively.

The inset of Fig. 5 shows the plots of the normalized pre- exponentialfactor˛1/(˛1+˛2)andofthefractionalcontributions f1asafunctionofpH.Thefractionalintensityf1fittedusingEq.(4) gaveapKaof9.26±0.03,whichgivesapositivepKaof∼1.0rel- ativetothatobtainedwiththesteadystatefluorescence.Theplot ofthenormalizedpre-exponentialfactorgaveapKaof8.39±0.02, withalmostnopKshiftrelativetothesteadystatefluorescence.

ThepKshiftspredictedbyEqs.(17)and(21)arecalculatedas follows:forlevofloxacin,themolarabsorptioncoefficientsforthe anionicand zwitterionicspeciesaresimilar(␧^AH=␧^A);theratio of thequantum yields are obtainedfrom the steady state flu- orescence results ^AH/ ^A=11, and thelifetimes ␶^A=0.7nsand

␶^AH=6.1nswereobtained.UsingthesevaluesinEqs.(21)and(17), theexpectedapparentpKshiftsare:pKa^f=1.0andpKa^˛=0.1.

Theyarealsoverysimilartotheobtainedexperimentalvalues.

It is worth calling attentionto thefact that, in general,the pre-exponentialfactorsgivesmallerpKashiftsthanthefractional intensities.Inconclusion,thisworkconcernstocorrectionsthat havetobemadewhenusingtime-resolvedfluorometryparame- tersinanalyticalapplications.Expressionstocorrecttheacid–base equilibriumconstantsobtainedwithpre-exponentialfactorsand fractional intensitieswereobtained, and theirlimits ofvalidity werediscussed.Theexpressionswereshowntoexplaintheexper- imentallyobtainedpKashiftsoftwodifferentdrugs.

Acknowledgments

ThisworkhasbeenpartiallysupportedbytheBrazilianAgencies FAPERJandCNPq.

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