Biophysical Journal Volume 68 March 1995 1110-1119

Photophysics of the Fluorescent Ca2+ Indicator Fura-2

Viviane Van den Bergh,* Noel Boens,* Frans C. De Schryver,* Marcel Ameloot,* Paul Steels,*Jacques Gallay,§ Michel Vincent,§ and Andrzej Kowalczyk$*Department of Chemistry, Katholieke Universiteit Leuven, B-3001 Heverlee, Belgium; tLimburgs Universitair Centrum,B-3590 Diepenbeek, Belgium; Laboratoire pour 'Utilisation du Rayonnement Electromagn6tique, Centre Universitaire Paris-Sud,91405 Orsay, France; and Nicholas Copernicus University, 87-100 Torun, Poland

ABSTRACT The photophysics of the complex forming reaction of Ca2+ and Fura-2 are investigated using steady-state andtime-resolved fluorescence measurements. The fluorescence decay traces were analyzed with global compartmental analysisyielding the following values for the rate constants at room temperature in aqueous solution with BAPTA as Ca2+ buffer:ko, = 1.2 x 109 s-', k2l = 1.0 x 10" M-1 s-1,k02 = 5.5 x 108 s-1, k12 = 2.2 x 107 s-1, and with EGTA as Ca2+ buffer: ko1 = 1.4 x 109-1, = 5.0 x 1010 M1 s', = 5.5 x 1 8 s-', = 3.2 x 107 s-1. kcl and k2 denote the respective deactivation rate constants

of the Ca2+ free and bound forms of Fura-2 in the excited state. k, represents the second-order rate constant of binding of Ca2+and Fura-2 in the excited state, whereas k12 is the first-order rate constant of dissociation of the excited Ca2+:Fura-2 complex.The ionic strength of the solution was shown not to influence the recovered values of the rate constants. From the estimatedvalues of k12 and k,, the dissociation constant K* in the excited state was calculated. It was found that in EGTA Ca2+ bufferpKl* (3.2) is smaller than pKd (6.9) and that there is negligible interference of the excited-state reaction with the determinationof Kd and [Ca2+] from fluorimetric titration curves. Hence, Fura-2 can be safely used as an Ca2+ indicator. From the obtainedfluorescence decay parameters and the steady-state excitation spectra, the species-associated excitation spectra of the Ca2+free and bound forms of Fura-2 were calculated at intermediate Ca2+ concentrations.

INTRODUCTION

The fluorescent indicator for Ca", Fura-2, developed byR. Y. Tsien and associates was a significant step forwardin the determination of intracellular Ca>2 concentrations(Grynkiewicz et al., 1985; Cobbold and Rink, 1987;Tsien, 1991). Fura-2 is now the most popular Ca>2 probe,particularly in measurements of Ca21 in single cells(Iaizzo et al., 1989; Bush and Jones, 1990; Moore et al.,1990). In comparison with previously developed Ca>2 in-dicators, Fura-2 has a higher quantum yield of fluores-cence and higher molar extinction coefficients. There-fore, a good signal-to-noise ratio can be obtained at lowprobe concentration resulting in less disturbance of bio-logical systems. The ground-state dissociation constant,Kd, for the Ca2+/Fura-2 complex is around 200 nM, avalue close to levels of cytoplasmic Ca>2 concentrationsin cells. Ca>2 binds to Fura-2 with a simple 1:1 stoichio-metry and causes the fluorescence excitation spectrum toshift to lower wavelength. The fluorescence emissionspectrum of Fura-2 is virtually insensitive to [Ca>2]. Themagnitude of the fluorescence signal depends on [Ca>2].The ratio of the fluorescence signals at dual excitationwavelengths is independent of the actual amount of in-

Receivedfor publication 21 April 1994 and infinalform 12 October 1994.Address reprint requests to Dr. Noel Boens, Department of Chemistry,Katholieke Universiteit Leuven, B-3001 Heverlee, Belgium. Tel.:32-16-200656; Fax: 32-16-201215; E-mail: Noel@mds.chem.Kuleuven.ac.be.A preliminary account of this research was presented at the SPIE meeting"Time-Resolved Laser Spectroscopy in Biochemistry IV" Los Angeles,California, 24-26 January 1994.X 1995 by the Biophysical Society0006-3495/95/03/1110/10 $2.00

dicator in the cell and can be used to determine intra-cellular Ca" concentrations (Grynkiewicz et al., 1985;Tsien et al., 1985). When the indicator concentration can-not be held constant in different samples due to photo-bleaching or leakage, the ratio method is the method ofchoice. The ratio of the fluorescence intensities at 340 and380 nm as excitation wavelengths and 510 nm as emissionwavelength are generally used to determine the intracel-lular [Ca"] with Fura-2 as fluorescent indicator. Fromthis ratio, the level of intracellular [Ca>2] can be esti-mated by comparison with calibration curves obtained invitro or in vivo (Grynkiewicz et al., 1985; Cobbold andRink, 1987; Tsien, 1991).

It is not generally acknowledged that the binding re-action of Ca>2 and Fura-2 in the excited state and thecorresponding dissociation of the formed excited-statecomplex could severely distort the results derived fromfluorescence measurements. The degree of interference ofthe excited-state reaction with the determination of Kd and[Ca>2] depends on the values of the four rate constantsdefining the excited-state reaction. These values can beassessed by the analysis of time-resolved fluorescenceexperiments. So far, only one study (Keating and Wenzel,1991) has been published describing time-resolved fluo-rescence measurements of Fura-2. The obtained fluores-cence decays were analyzed in terms of a biexponentialdecay law. However, this study did not provide any in-formation about the rates of interconversion of the Ca2+free and bound forms of Fura-2 in the excited state.

Time-resolved fluorimetry is an ideal technique to un-ravel the often complex kinetics of excited-state pro-cesses (O'Connor and Phillips, 1984; Boens, 1991). Fluo-rescence decay curves can be collected under various

1110

Photophysics of Fura-2

experimental conditions and with high accuracy allowinga detailed data analysis. All related experimental fluo-rescence decay traces can be analyzed simultaneously toenhance the capacity to distinguish between competingmodels and to obtain the most reliable parameter esti-mates. To benefit the most of the merits of this globalanalysis approach, one has to fit directly for the rate con-stants, the relative absorbances of the species in theground state and the spectral emission weighting factors.This implementation has been called the global compart-mental analysis and was presented in a series of articlesfrom this laboratory (Ameloot et al., 1991, 1992; Van denBerg et al., 1992).

Before any new fluorescent molecule is proposed as afluorescent indicator for biologically important ions ormolecules, time-resolved fluorescence measurementsshould be performed to estimate values of the four rateconstants defining the excited-state reaction. Using thesevalues and the theory developed in this paper allows oneto predict if the determination of the ground-state dis-sociation constant Kd from fluorimetric titration is un-disturbed by the excited-state reaction. This general ap-proach is exemplified here for Fura-2. Therefore, thephotophysics of the reversible complex formation ofFura-2 and Ca21 is studied in detail, using the globalcompartmental analysis approach. Application of the ana-lytical expressions for the fluorescence signal in the ab-sence and presence of an excited-state reaction indicatesthat the determination of Kd and/or [Ca21] is not influ-enced by the excited-state complex formation and dis-sociation. Hence, Fura-2 can be safely used as a Ca21indicator.

THEORYKineticsConsider a causal, linear, time-invariant, intermolecularsystem consisting of two distinct types of ground-statespecies and two corresponding excited-state species as isdepicted in Scheme 1. Ground-state species 1 can revers-ibly react with M to form ground-state species 2. Exci-tation by light creates the excited-state species 1* and 2*,which can decay by fluorescence (F) and nonradiative(NR) processes (internal conversion (IC) and intersystemcrossing (ISC)). The composite rate constants for theseprocesses are denoted by ko1 (=kFl + kNR1 = kFl + kici+ k1scl) and ko2 (=kF2 + kNR2 = kF2 + kIC2 + k,sC2). Thesecond-order rate constant describing the transformation1* + M -* 2* is represented by k21. The first-order rateconstant for the dissociation of 2* into 1* and M is de-noted by k12. In the case of Fura-2, species 1 representsthe ground state of the free form of the indicator, species2 the ground state of the complex between Ca2+ andFura-2, and M denotes the Ca2+ ion. 1* and 2* are theircorresponding excited-state species. If the system de-picted in Scheme 1 is excited by a 8-pulse that does notsignificantly alter the concentrations of the ground-state

k2l1 + M ' 2

hv |kol h)4ko2

[g+ M ' E

Scheme 1

species, the fluorescence 8-response function, JAem, Aex,t), at emission wavelength Xem due to excitation at Ae, isgiven by (Ameloot et al., 1991)

J(Aem, Aex, t) = c(Xem)Uexp(tF)U-lb(Cex), t 2 0(1)

U = [U1, U2] is the matrix of the two eigenvectors of thecompartmental matrix A (Eq. 2) and U-' the inverse ofU. y1 and 72 are the eigenvalues ofA corresponding to theeigenvectors U1 and U2, and exp(tF) = diag{exp(Qylt),exp(y2t)}.

A =[ -(kol + k2l[M])k2l[M]

k12 1

-(kO2+k+2) (2)

b(ACX) is the 2 X 1 vector of the excited-state concen-trations at time zero,

[ub2u [2[*](0)Note that b is dependent on the excitation wavelength Aexand [M].

C(Xer) is the 1 X 2 vector of the spectral emission weight-ing factors ci(Aem),

c (Aenm) = kFi Pi (Aem) dAem.A,k

(4)

kFi is the fluorescence rate constant of species i*; AXem is theemission wavelength interval where the fluorescence ismonitored; pi(Aenm) is the spectral emission density of speciesi* at ACm defined by

Pi(Aem) =F. (Aem)

p.Ar)=f F1(Aem) dAem (5)

where the integration extends over the whole steady-statefluorescence spectrum Fi of species i*. Defining the nor-malized elements Xi and ji,

gi = bi/(b1 + b2)

ji = ci/(cl + C2)

Equation 1 can be written as

for i = 1, 2

for i = 1, 2.

(6a)

(6b)

f(Arem, Aex, t) = Kc(Aem)U exp(tF)U-1 f(Aex), t 2 0 (7)with K a proportionality constant. b(ACX) can be linked overdecay curves collected at the same excitation wavelength and

Van den Bergh et al. 1111

(3)

(5)

Volume 68 March 1995

[M], whereas Z(AXe) can be linked over decay curves obtainedat the same emission wavelength.

Equation 7 can be written as a sum of two exponentialterms:

f(AXem, Aex, t) = a,G(Aem, Xex)exp(-ylt) + a2(Aem, AeX)exp(,yt)2t 0 (8)

The exponential factors y1,2 are given by

,= -½{X + X2 ± [(X1-X2)2 + 4 k21k12[M]]2} (9)

and are related to the decay times T2 according to

(10)F(Aem, Aex, [M])with

wavelength XCX impinging on the sample, and Ei(Xex) is themolar extinction coefficient of species i at excitationwavelength AX.

In the absence of an excited-state reaction

Without an excited-state reaction the compartmental matrixA is given by

(16)A [-kol o0]L -ko2 '

If the absorbance of the solution is low, then Eq. 14 isexplicitly given by

(17)

X1 =k1 +k21[M]

X2 = kW2 + kl2

(lla)

(llb)

For clarity, we shall not use the notation T1 and T2 but we shallrefer to TL (L for long) and Ts (S for short) with TL > TS.The contribution of species i to the steady-state excitation

spectrum E(Xem, Aex, [M]) at [M], recorded at eAem due to ex-citation at Aex is called the species-associated excitation spec-trum of species i, SAEXSi(Xer, Aex), and is given by(Ameloot et al., 1991)

SAEXSi(Aem, Aex, [M])

(z(Aem)A-l)jii(Aex, [M]) E(Xe, Aex [M])z(Aem)A-lfi(ex, [MI) '

= 2.3dI (Aex)g(Aem){a, (Aem))E1 (AeX)[1] + a2(Aem)E2(kex)[2]},a1(Anm) and a2(Ae,m) are defined by

al (Aem) Cc e(Aem)

a2(Aem) = C2(em)0o2

(18a)

(18b)

Expressing the ground-state dissociation constant Kd in theform of molar concentrations

[1][M]Kd=(12)

The contribution of species i* to the steady-state emissionspectrum F(kem, Aex, [M]) at [M], recorded at X'm due to ex-citation at Aex is called the species-associated emission spec-trum of species i*, SAEMSi(XCm,, Aex), and is given by(Ameloot et al., 1991):

SAEMSi(kem, Akex, [M]) (13)

C(Aem)(A-lb(Aex, [M]))i F(Aemrn Aex, [M]).

z(Aem)A-1fb(Aex, [M])

Fluorimetric titration

For the compartmental system depicted in Scheme 1, themeasured steady-state fluorescence signal F(Xem, Aex, [M])due to excitation at Aex and observed at xem is given by(Ameloot et al., 1991)

F(Aem, Aex, [M]) =-((Aem)c(Aem)A-lb(Aex, [M]), (14)

where K(kem) is an instrumental factor. If Beer's law is obeyedand if the absorbance of the solution is low (<0.1), then theelements bi(Aex, [M]) of b can be approximated as

b(Aex, [M]) 2 3eiAx)[i]joAx^(5

where d denotes the excitation light path, 1o(XeX) repre-sents the concentration (in mol/l) of excitation photons of

(19)

and using the total analytical concentration, CT = [1] + [2]of the fluorescent probe allows us to rewrite Eq. 17 as

F(Aem Aex, [M])

= 2.3dIO(Aex)(Aem) allKd + a2e2[M] CT

(20)

with al,2 defined by Eq. 18. The plot of F vs. -log[M] ex-hibits a unique inflection point at [M] = Kd. Equation 20 canbe rewritten in the form of a Hill plot:

log(F Fman) = log[M] - logKd. (21)

Equation 20 indicates that the measured fluorescence sig-nal F depends on CT, IO, and (. Most modem fluorimetershave the capability to correct for fluctuations of F due to Ioby measuring simultaneously F and Io and computing/displaying the ratio F/Io. If CT, IO, and ( are constant duringthe measurement of samples with different [M], Eq. 20 con-stitutes the basis for fluorimetric titrations. In all other cases,the ratio method has to be used.The ratio method can be performed in two ways. For

each concentration ofM one can either measure the ratioR(em, xex//ex, [M]) = F(xem,xe, [M])/F(emn, 2Xe, [M]) attwo different excitation wavelengths and at a commonemission wavelength, or the ratio R(Aem/e2m, XeX, [M]) -F(Aem',Aex, [M])/F(km', Aex, [M]) at two different emissionwavelengths due to excitation at a single wavelength.

Biophysical Journal1112

'Yl,2 = -1/Tl,2'

Photophysics of Fura-2

The ratio R obtained from dual excitation wavelengths ata common observation wavelength is given by Eq. 22

R(Aem, Aex/Aex, [M]) (22)

(S1(Aem AeX)Kd + S2(Aem, Xex)[M] Ae(I0(Xex)AVS (Xem, xex)Kd + S2(Xem, Xe)[M] io( ex)

where

S1(eem,AIeX) = aj(Xem)Ei(Xkx). (23)

Equation 22 indicates that R is independent of the totalconcentration CT. The dependence on Io can be eliminated bymeasuring directly F/IO.The plot of R as a function of -log[M] has a unique in-

flection point at [M] = KdSl(Aem, A2x)/S2(xem,,X2x). It must beemphasized that the ratio S1(Aem, AXx)/S2(Aem, AeX) must beknown in order to determine Kd. This ratio is determinedby fluorescence measurements of the same system at theindicated wavelengths using extreme values of [M]: Fmin(Xem, AXe, [M] 0) 2 x3dI0(AX)W(Xem)S,(XemX) CT andF(Ae2e =Mm)2.3dIo(A2)(A )2( s 2 )CT.anFma(X em, xex, [M] __> 00) 2.dI(ex~)~(Xem)S2(emn, xex)CT.If the observation wavelength is set at the iso-emissivepoint, the ratio S,(Aem, Xex)/S2(Aem, AXx) simplifies to El(A e2x)/E (A eX) .

An inappropriate choice of excitation and observationwavelengths can make R invariant with [M], thus inhibitingthe determination of Kd. The ratio R(Aemr, Aex/X2x, [M]) is in-dependent of [M] if

a1(Aem)a (Aem)[El(Aex)E2(Aex) - El(ex)E2( ex)] = 0. (24)

This is the case when (i) one of the excited-state species doesnot emit at the observation wavelength xem (al(Aem) = 0 ora2(Xem) = 0) or when (ii) El(AXex)/E2(Aex) = E1(AXx)/E2(Xx), i.e.,when the absorption spectra ofground-state species 1 and 2 haveidentical shapes.

Equation 22 can be rearranged to yield [M]

/ Sl(Xem,vxe)Io(xex)[M] = Kd

RS(Xem,eXx)io(Xe(x)J( (e, Ax)

d (R em e(x)iot( ex)ex) / S (Xem, ex)

S2(Xem, Xe)I0( ex) R(25)

which can be written as

R__R ~tje,kxX)[M] = Kd(R -R) (SA X))' (26)

with Rmax = E(Xeex)I(Xex)/E e(x)IO(Aex) for [M] >> Kd and= E1 (XxI()/El()0(AXex) for [M] «< K.

Note that Eq. 26 is the same as the calibration equationdeveloped by Grynkiewicz et al. (1985) with

5f1 = 2.3dIo(AeX)((Aem)Sl(Aem, AeX)CT = Fmin(Aem, AeX)and

Equation 26 is often rearranged in the form of a Hill plot:

log___ = log[M] - log(Kd S2(A"', X)l(R -RJ Sd( em, A ex)j (7

The expression of the left side of Eq. 27 plotted vs. log[M]should give a straight line that intersects the abscissa at thevalue corresponding to log (KdSl(erem, AXk)/S2(Xrem, Xe)).Most often this plot is used to determine Kd providedS,(Xem, AXe)/S2(Xemr, Xe) is known.The ratio R at dual emission wavelengths due to a common

excitation wavelength is expressed by

(28)R(Aem/Aem Aex []

(1S (Aelm, xeX)Kd + S2(X em, kex)[M] A ((Xem)=S1(AeXm, xex)Kd + S2(xe,m XeX)[M])\ (Aem)JI

with

Si(AXm, AeX) = a;(AXm)Ei(Aex). (29)

The plot of R vs. -log[M] has an inflection point at [M] =KdSl(Xem, XeX)/S2(Xkmr, Xex). The ratio R(Xejm/Xm,eex, [M]) be-comes independent of [M] when

E1(Aex) E2(Xex)[aj(Aem) a2(e"m) - al(Ae(m) a2(Aem)] = 0. (30)This situation occurs when (i) one of the ground-state speciesdoes not absorb at the excitation wavelength V (E1(Xex) = 0,E2(Xex) = 0) or when (ii) c1(AXlm)/c2(Xetm) = cl(A2m)/c2(A'),i.e., when the fluorescence spectra ofexcited-state species 1 * and2* have identical shapes.

Equation 28 can be transformed to give [M]

[M] = KdR-( R) (Aem,m exj)) (31)

with Rmax = C2(Ak I 1 Yc2 2 2 for [M] >>Kd andRmen= c m)(Aelm)/Cl(Aem)((Aem) for [M] << Kd.Equation 31 also can be written in the form of a Hill plot

log(R = log[M] -lo Kd(KXem2 exR - R d (A em, Aex)'~k~ (32)

This Hill plot intersects the abscissa at the value correspond-ing to log(KdS1(AXem, xeX)/S2(Xkem, XeX)).

In the presence of an excited-state reaction

In this case (Scheme 1) the compartmental matrix A is givenby Eq. 2. The excited-state reaction will cause redistributionof excited states and consequently the fluorescence signaloriginating from each excited-state species will no longer beproportional to the number of photons absorbed by the corre-sponding ground-state species. In this case F(Aem, XCk, [M]) isgiven by Eq. 17 or 20 with the coefficients alA(Xem) defined by

a(Aem) = c (Xe)(k02 + k12) + C2(Aem)k2l[M]k1l (kO2 + kl2) + kO2k21[M]

( em) = Cl(Aem)kl2 + C2(Xem)(k., + k2l[M])-k1(kO2 + k12) + k0k2j[M]

(33a)

(33b)5b2 = 2.3dIO(AeX)((Aem)S2(Aem Xex)CT = Fmax(Aem, AXe).

Van den Bergh et al. 1113

Volume 68 March 1995

Whether or not there is excited-state reaction, F is formallydescribed by Eq. 17 or 20 but with one significant difference.Indeed, the coefficients a12 do not depend on [M] when thereis no excited-state reaction (Eq. 18), whereas they do whenthere is an excited-state reaction (Eq. 33).

It has been shown (Kowalczyk et al., 1994) that the co-

efficients al,2 given by Eq. 33 are virtually independent of[M] except in the concentration range around [M] given byEq. 34

[M] = k0o(k02 + k12) ()

If [M] given by Eq. 34 is quite different from Kd, theinflection point in the fluorimetric titration due to theground-state equilibrium will occur at [M] = Kd. This impliesthat the excited-state reaction does not interfere with the de-termination of [M] and that Eq. 26 can be used.The ratio of the fluorescence signals at two different ex-

citation wavelengths and a common emission wavelength,R(Xemn,Xx/AXe,[M]) in the presence of an excited-state reac-

tion is given by Eqs. 22 and 23 with ai(Aenm) given by Eq. 33.At dual emission wavelengths and a common excitationwavelength the ratio R(Aem/'IAm, Aex, [M]) of the fluorescencesignals is given by Eqs. 28 and 29 with ai(Aem) given byEq. 33. In general, the functional dependence of R(Aem, Ax/A2x, [M]) and R(Aelm/Aem, Ax, [M]) on -log[M] isvery complicated and cannot be used to determine Kd. Theratios Rmin and Rmax, however, remain independent of thepresence or absence of an excited-state reaction. Theknowledge of all rate constants enables one to calculateai according to Eq. 33 and, consequently, to determine theconcentration range of M where the interference of theexcited-state reaction is insignificant.

the single photon timing technique using the synchrotron radiation machineSUPER-ACO (Anneau de Collision d'Orsay at LURE, France) as describedelsewhere (Kuipers et al., 1991). The polarization of the excitation beam wasvertical with respect to the excitation-emission plane. The total fluorescencedecay was constructed from the polarized fluorescence intensity decayscollected with the polarizer in the emission path set parallel and perpen-dicular with respect to the excitation polarization and taking into accountthe polarization bias of the instrument. The storage ring provides a lightpulse with a full width at half maximum of -500 ps at a frequency of 8.33MHz in double-bunch mode. A Hamamatsu microchannel plate R1564U-06was used to detect the fluorescence photons. The instrument response func-tion was determined by measuring the light scattered by glycogen in aqueoussolution at the emission wavelength and was collected alternately with theparallel and perpendicular components of the polarized fluorescence decay.All decay traces were collected in 1/2K channels of a multichannel analyzerand contained approximately 5 X 103 peak counts. The time increment perchannel was 12 ps.

Data analysisThe global compartmental analysis of the fluorescence decay surface ofspecies undergoing excited-state processes was implemented in the existinggeneral global analysis program (Boens et al., 1989) based on Marquardt's(1963) algorithm. Our implementation of global compartmental analysis,which is an extension of that described by Beechem et al. (1985), allowsunnormalized decay curves to be used. The global fitting parameters are kolk21, kI2, k,2, 5,, and 4l. The rate constants kol, k2l, k02, and kl2 are the same

for all decays. In contrast, the coefficients 4l are expected to be identical onlyfor those decays observed at the same emission wavelength. The normalizedground-state absorbances E, are identical for the decays at the same exci-tation wavelength and Ca21 concentration. This knowledge about internallinks between the fitting parameters of the decay curves constituting thefluorescence decay surface is presented graphically in Scheme 2. In thatscheme boxed parameters represent linked parameters, and X denote localscaling factors.

Specifying the Ca21 concentration and assigning initial guesses to the rateconstants kol, k2l, k02, and k,2 allows one to construct the compartmental

MATERIALS AND METHODS

Materials

Fura-2, pentapotassium salt was obtained from Molecular Probes (Eugene,OR). EGTA (ethylene glycol-bis(,B-aminoethyl ether) N,N,N',N'-tetraaceticacid), BAPTA (1,2-bis(2-aminophenoxy)ethane-N,N,N',N'-tetraaceticacid), and MOPS (3-(N-morpholino)propanesulfonic acid) Free Acid were

purchased from Sigma Chemie (Bornem, Belgium). KCl and CaCl2 were

obtained from Janssen Chimica (Geel, Belgium). All of these products wereused without further purification. Milli-Q water was used to prepare theaqueous solutions according to the procedure described by Grynkiewicz etal (1991). Free [Ca21] levels were controlled either by Ca2+/BAPTA buffersassuming a dissociation constant of 130 nM for the Ca2+/BAPTA complexor by Ca2+/EGTA buffers assuming a dissociation constant of 151 nM forthe Ca2+/EGTA complex both at pH 7.2 in 100 mM KCI aqueous solutionat room temperature. The dissociation constants of the Ca2+/BAPTA andCa2+/EGTA complexes calculated according to Marks and Maxfield (1991)were used to determine the free [Ca21]. The ionic strength of these solutionsvaried from 0.1 to 0.3. In a second set of experiments, KCI was used to adjustthe ionic strength of each solution to a constant value of 0.3.

(MH] X

x

x

(MJ2 x

x

x

(M]i x

x

Instrumentationx

Fully corrected steady-state excitation and emission spectra were recordedon a SPEX Fluorolog 212. The fluorescence decay traces were measured by

k21 ko2 k12

III

I

I

Scheme 2

c1 (X1 ) |

6 2

cl(em).(

Li

c7em)

Co (2m) -

Icl(4m) |

l 1

- Nem)

1III

iI

II

II

iI

I I1.1

J

1114 Biophysical Joumal

Photophysics of Fura-2

matrix A (Eq. 2) for each decay trace. The eigenvalues y and the associatedeigenvectors U of this matrix are determined using routines from EISPACK,Matrix Eigensystem Routines (Smith et al., 1974). The eigenvectors are thenscaled to the initial conditions 5. The preexponential factors a are computedfrom the rate constants, [Ca2"], 5, and e, allowing the calculation of thefluorescence decay of the sample. Using this approach, all decay tracescollected at different excitation/emission wavelengths, at multiple timingcalibrations, and at different Ca21 concentrations are linked by all rate con-

stants defining the system and can therefore be analyzed simultaneously bythe model given by Eq. 7.

The fitting parameters were determined by minimizing the global re-

duced chi-square X2:

q

X2 wli(yo - yj)2IV, (35)

I i

where the index 1 sums over q experiments, and the index i sums over theappropriate channel limits for each individual experiment. y' and y' denoterespectively the observed (experimentally measured) and fitted values cor-

responding to the ith channel of the Ith experiment. wli is the correspondingstatistical weight taking into account the construction of yoj from the po-

larized intensity decays (Boens, 1991). v represents the number of degreesof freedom for the entire multidimensional fluorescence decay surface. Thestatistical criteria to judge the quality of the fit comprised both graphical andnumerical tests. The graphical methods included plots of surfaces ("car-pets") of the autocorrelation function values versus experiment number, andof the weighted residuals versus channel number versus experiment number.The global reduced chi-square statistic x2 and its corresponding ZX2 providednumerical goodness-of-fit criteria for the entire fluorescence decay surface.

2 = (X2 - 1)<;N /2V(36)

Using ZX2 the goodness-of-fit of analyses with different v can be readilycompared. Moreover, the goodness-of-fit was examined for the individualdecay curves by the calculation of the ordinary runs test, the Durbin-Watsonstatistic, the local x2 value x2 and its normal deviate ZX2 (Boens, 1991). SEestimates were obtained from the parameter covariance matrix availablefrom the analysis. All quoted errors are one standard deviation. All analyseswere done on an IBM RISC System/6000 computer.

RESULTS

The ground-state dissociation constant Kd of the Ca2+/Fura-2complex was determined from a Hill plot using absorptionmeasurements at AeX = 340 nm, at 20°C, pH 7.2, and 100 mMKCI in aqueous solution with EGTA as Ca2' buffer. The Hillplot yielded a value of 134 (± 11) nM for Kd (correspondingto pKd = 6.87) and indicated a 1:1 stoichiometry for theCa2+/Fura-2 complex. The dissociation constant in theexcited-state, K*, can be calculated according to the Forstercycle (Weller, 1961):

pK*= pd-AE2 AE1

dK 2.303RT

where AE1 is the 0-0 transition energy of the free formand AE2 the corresponding 0-0 transition energy of thebound form of the indicator. Because of the broad ab-sorption and emission spectra, it is impossible to deter-mine the 0-0 transitions. To overcome this difficulty, thedifference (AE2 -AE1) was calculated by averaging thefrequencies of absorption and fluorescence maxima ofboth the Ca2+ free and bound forms of the indicator. Thisresulted in a pK* of 4.

To determine the excited-state parameters, time-resolved fluorescence measurements were performed.With BAPTA as Ca2" buffer decay curves of Fura-2 atdifferent concentrations of Ca2' ranging from 101 nM to0.1 M were measured at two different excitation wave-lengths (kXe = 350 nm, 370 nm) and two different emis-sion wavelengths (Xem = 490 nm, 510 nm). When EGTAwas used as Ca2' buffer, the two excitation wavelengthswere 340 and 370 nm, whereas the other experimentalconditions were identical. In both cases no extra salt wasadded to keep the ionic strength constant.The decays arising from solutions with identical Ca2+ con-

centrations were analyzed globally as biexponential func-tions in terms of preexponential factors and decay times (Eq.8) with the latter being linked over the emission and exci-tation wavelengths at each concentration of Ca2+. Biexpo-nential global analysis gave good fits over the whole con-centration range even at Ca2+ concentrations of 5 X 10-5 Mor higher, when the indicator is saturated in the ground state.The estimated decay times are shown in Table 1. From thistable it is clear that for increasing [Ca21] the shorter decaytime decreases whereas the longer decay time increases. Theonly detailed information on the rate constants that can bederived from this observations is that ko2 <Ikol.

In global compartmental analysis, all the decays were ana-lyzed simultaneously according to linking Scheme 2. Theresulting rate constants are shown in Table 2. It is noteworthythat good fits were only obtained when Ca21 concentrationsand not activities were entered into the program. It must beemphasized that all solutions-even those at high Ca2+concentration-had to contain BAPTA orEGTA to obtain anacceptable fit for the global compartmental analysis. It wasonly when all solutions were prepared with the same totalBAPTA or EGTA concentration that an acceptable fit wasobtained for all the decays at all Ca2+ concentrations. Theresults of Table 2 indicate that kol and ko2 are independent ofthe Ca2+ buffer used. The values of k12 and k2j, however, areclearly dependent on the Ca2' buffer: they are apparent rateconstant values. Beside the interconversion of the Ca2+ free

TABLE 1 Globally estimated decay times of Fura-2 atdifferent ionic strength as a function of Ca2+ concentration

[Ca2+] TL (ns) Ts (ns) #* X2 ZxA. BAPTA as Ca2+ buffer

101 nM 1.691 (±0.004) 0.777 (±0.004) 3 1.08 2.48604 nM 1.755 (±0.003) 0.799 (±0.004) 4 1.10 4.355 X 10-5M 1.804 (±0.003) 0.807 (t0.005) 4 1.05 2.135 X 10-4 M 1.795 (±0.009) 0.807 (±0.007) 4 1.09 2.3810-3 M 1.794 (±0.008) 0.691 (±0.006) 4 1.12 3.2110-2 M 1.822 (±0.001) 0.44 (±0.02) 4 1.05 2.040.1 M 1.867 (±0.004) 0.30 (±0.02) 4 1.08 2.41

B. EGTA as Ca2+ buffer101 nM 1.717 (±0.003) 0.684 (±0.003) 4 1.10 4.82604 nM 1.683 (±0.003) 0.684 (±0.003) 4 1.10 4.125 X 10-5M 1.722 (±0.003) 0.713 (±0.004) 4 1.11 3.305 X 10-4 M 1.784 (±0.002) 0.691 (±0.003) 4 1.08 3.3810-3 M 1.801 (±0.006) 0.631 (±0.002) 4 1.06 3.2110-2 M 1.819 (±0.003) 0.50 (±0.01) 4 1.05 2.440.1 M 1.870 (±0.002) 0.41 (±0.01) 4 1.14 5.21

*Number of decays analyzed simultaneously.

Van den Bergh et al. 1115

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Volume 68 March 1995

TABLE 2 Rate constant values of Fura-2 estimated by globalcompartmental analysis from decay traces at different ionicstrength

Rate constant BAPIA as Ca2" buffer EGTA as Ca2" buffer

kol (ns)-' 1.239 (±0.004) 1.424 (±0.003)k2l (M ns)-1 103 (±7) 50 (±4)k02 (ns)-1 0.5509 (±0.0008) 0.549 (±0.001)k12 (ns)-1 0.022 (±0.003) 0.032 (±0.001)

and bound forms of Fura-2 in the excited state (Scheme 1,Eq. 38a), reactions of excited Fura-2 with Ca2+:EGTA (Eqs.38b-c) and Ca2+:BAPTA (Eq. 38d) complexes must beincluded in the reaction scheme (Marks and Maxfield, 1991).

Fura-2* + Ca2+ ± [Ca:Fura-2*]2> (38a)

Fura-2* + CaEGTA2 (38b)

¢ [Ca:Fura-2*]2+ + EGTA4-

Fura-2* + CaHEGTA- (38c)

[Ca:Fura-2*]2+ 3HEGTA

Fura-2* + CaBAPTA> (38d)

i± [Ca:Fura-2*]2+ + BAPTA4

Therefore, k21 and kl2 describe not only the process of Eq 38abut all the above excited-state processes. The different valuesobtained for k2l and kl2 with EGTA and BAPTA buffersreflect the different values of the individual rate constants.The occurrence of the excited-state processes given by Eqs.38b-d may account for the fact that the same concentrationof Ca2+ buffer had to be present in all solutions to obtain an

acceptable fit in global compartmental analysis. From theobtained rate constants the decay times can be calculated as

a function of [Ca>2] according to Eqs. 9-11. For BAPTA as

Ca>2 buffer these decay times are plotted in Fig. 1 as a func-tion of -log[Ca21] together with the decay times estimateddirectly from global biexponential analysis. It is clear that

there is a good agreement between the decay times estimateddirectly from standard global biexponential analysis andthose calculated using the rate constant values from globalcompartmental analysis. Similar results were obtained forEGTA as Ca" buffer (results not shown).

For the estimation of the rate constants of Table 2, solu-tions of Fura-2 with high Ca>2 concentrations (up to 0.1 M)were used. Obviously, the ionic strength of the solutions withhigh [Ca2] is much higher than that of solutions with lowCa>2 concentration. To check whether the decay times are

sensitive to the change in ionic strength, decay curves ofsolutions with the same ionic strength (I = 0.3) were meas-

ured with BAPTA as Ca>2 buffer. As in the previous ex-

periments, the Ca2+ concentration was varied from 101 nMto 0.1 M. The decays arising from solutions with identicalCa2+ concentrations were analyzed globally as biexponen-tials as before. Biexponential global analysis gave good fitsfor all Ca>2 concentrations. The estimated decay times (Fig.2) as a function of -log[Ca2+] are virtually the same as inFig. 1. Therefore, the ionic strength can be excluded as an

experimental variable influencing the decay times and therate constant values. The normalized preexponential factorsat Aex = 350 nm and Aem = 490 nm corresponding to the longdecay time aL/(aS + aD as a function of -log[Ca2+] are

shown in Fig. 3. It is clear that the ionic strength has a minoreffect on the preexponential factors. Similar plots were ob-tained at other excitation and/or emission wavelengths.Therefore, the ionic strength influences minimally the bind-ing of Ca2+ by Fura-2.From the values for kol, kO2, and the quantum yields of

fluorescence, Q for the Ca2+ free and bound forms of Fura-2,the respective radiative deactivation rate constants can becalculated. According to Grynkiewicz et al. (1991) the valuesfor Q are 0.23 and 0.49 for the Ca2+ free and bound formsof Fura-2, respectively. Because koi comprises both radiativeand nonradiative rate processes, the rate constants of non-

radiative decay can also be calculated. Table 3 gives the rate

2

U,

0

0 2 4 6 8 10 12

-log [Ca2"]

FIGURE 1 Decay times ( ) of Fura-2 as a function of -log[Ca2+]calculated according to Eqs. 9-11 with the rate constant values obtainedfrom global compartmental analysis using BAPTA as Ca2' buffer (Table 2).The symbols * and * represent the decay times estimated from standardglobal biexponential analysis of solutions with unequal ionic strength.

1.5

U,

0.5

0

0 2 4 6 8 10 12

-log [Ca2+]

FIGURE 2 Decay times ( ) of Fura-2 as a function of -log[Ca2"]calculated according to Eqs. 9-11 with the rate constant values obtainedfrom global compartmental analysis using BAPTA as Ca2+ buffer (Table 2).The symbols * and * represent the decay times estimated from standardglobal biexponential analysis of solutions with high constant ionic strength(I = 0.3).

2

__.p

!.5

1

U~~ ~ ~

0O I.

* _ 4 ,*

1116 Biophysical Journal

1.

I

Photophysics of Fura-2

I

0.8- +08* **+4t ;

+z% 0.4_

0.2

0 ...............0 1 2 3 4 5 6 7 8

-log [Ca21340 360wavelength (nm)

FIGURE 3 Normalized preexponential aL/(aS + aD obtained at AX" =350 nm and Acr = 490 nm as a function of -log[Ca2"]. aL (respectivelyas) is the preexponential factor corresponding to TL (respectively Ts). Thesymbols * and * depict measurements at variable and constant ionicstrength, respectively. BAPTA was used as Ca2" buffer.

constant values for fluorescence and nonradiative decay forthe Ca" free and bound forms of Fura-2. The radiative rateconstant is almost the same for both species, whereas thenonradiative processes are less important in the bound form.This accounts for the increase in the fluorescence intensitywhen the Ca2 concentration is increased.To construct the species-associated excitation spectra

(SAEXS), decay curves of solutions with [Ca2] = 226 nMand EGTA as Ca>2 buffer were collected at two differentemission wavelengths (xem = 470 nm, 490 nm) due to ex-citation at different excitation wavelengths between 320 and390 nm. BAPTA could not be used because it absorbs atwavelengths under 350 nm. Sixteen decays were included inone global compartmental analysis yielding a x2 value of1.03 (Zx2 = 3.01). The SAEXS calculated according to Eq. 12at Xem = 490 nm are shown in Fig. 4. The SAEXS correspondvery well with the excitation spectra of the Ca>2 free andbound forms of Fura-2 recorded separately (Grynkiewiczet al., 1985). Note that the pseudo-isosbestic point is at370 nm (fig. 4) for detection at 490 nm. The usuallyreported wavelength for the pseudo-isosbestic point is360 nm for detection at 510 nm (Grynkiewicz et al.,1991).From k,2/k2l the dissociation constant K* in the excited

state can be calculated. This yields values for pK* of 3.7 with

TABLE 3 Radiative (kF) and nonradiative (kNR) deactivationrate constant values of the Ca2+ free and bound forms ofFura-2

Species Q* kF (ns)-1 kNR (ns)-1

A. BAPTA as Ca2' bufferFree (1) 0.23 0.28 0.96Bound (2) 0.49 0.27 0.28

B. EGTA as Ca2' bufferFree (1) 0.23 0.32 1.10Bound (2) 0.49 0.27 0.28

*Values taken from Grynkiewicz et al. (1985).

FIGURE 4 Decomposition of the measured steady-state excitation spec-trum E ( ) of Fura-2 into the SAEXS of the Ca21 free form (--) andCa2' bound form (-U-) at [Ca21] = 226 nM and A"m = 490 nm. EGTA wasused as Ca2' buffer.

BAPTA and 3.2 with EGTA as Ca>2 buffers. These valuesare in fair agreement with the result of the Forster cycle. Thisindicates that the excited state is more dissociative than theground state.

0

0

-log [Ca2+l

-log [Ca2+]

FIGURE 5 Fluorimetric titration curves F computed in the absence ( )and presence (-------) of an excited-state reaction at AWM = 510 nm with ACX =340 nm (a) and Ae' = 380 nm (b). The rate constants of Table 2 for BAPTAas Ca2+ buffer were used together with the following experimentally determinedvalues of Kd = 130 nM; cl = 13,300 M` cm-', e2 = 29,900 M` cm-' at A"'= 340 nm; el = 18300 M` cm-',e2 = 1700 M` cm-' at A'= 380 nm; cl/(c,+ c2) = 0.43, c,/(cl + c2) = 0.57 at A"m = 510 nm.

1117Van den Bergh et al.

Volume 68 March 1995

0 S 10

-log [Ca2+]

FIGURE 6 Fluorimetric titration curves R = F(510 nm, 340 nm)/F(510nm, 380 nm) computed according to Eqs. 22 and 23 with ai given by Eq.18 (without excited-state reaction) and Eq. 33 (with excited-state reaction)using the rate constants of Table 2 for BAPTA as Ca2' buffer at A" = 340nm (e, = 13300 M- cm-l, E2 = 29900 M` cm-) and 380 nm (El = 18300M-l cm-%, E2 = 1700 M` cm-'), observed at A'tm = 510 nm(c,/(c, + c2)= 0.43, c2/(cl + c2) = 0.57), Kd = 130 nM.

0 s 10

-log [Ca2l

FIGURE 8 Experimental (*) fluorimetric titration curve F(510 nm, 340nm) for Fura-2 at pH 7.2 with EGTA as Ca2' buffer in aqueous solution atroom temperature. The solid line represents the F(510 nm, 340 nm) valuescalculated with Kd = 130 nM, E, = 13300 M` cm-' and e2 = 29,900 M`cm-l at Aex = 340 nm; cl/(c, + c2) = 0.43, c21(c, + c2) = 0.57 at Ae" =

510 nm. The used rate constants are those of Table 2 for EGTA as Ca2"buffer.

o00

0.8

0.6 -

0.4 -

0.2 -

0

-0.2-

-0.4-

-0.6 ; -

-0.8 ,- ,-_7K -7 _71 _7 -A -AK -A A _A -a

log [Ca'+]

FIGURE 7 Hill plot (Eq. 21) of F for Fura-2 measured at A"X = 340 nmand observed at A'em = 510 nm at pH 7.2 with EGTA as Ca2' buffer inaqueous solution at room temperature.

The determined values for kol kO2, k12, and k2l allow us tocheck whether the excited-state reaction interferes with thefluorimetric determination of the ground-state dissociationconstant Kd. It is not generally acknowledged that theexcited-state reaction can severely distort the values of Kdand/or [Ca2+] obtained from fluorimetric titrations. To in-vestigate the interference of the excited-state reaction withthe recovered value of Kd, fluorimetric titration curves F were

computer-generated at two excitation wavelengths (340 and380 nm) and a common observation wavelength (510 nm)assuming the presence or absence of an excited-state reac-

tion. The rate constants for BAPTA as Ca>2 buffer (Table 2)were used together with the following experimentally de-termined values of Kd = 130 nM, E1 = 13300 M- cm-1, andE2 = 29900 M1 cm-' at Aex = 340 nm; El = 18300 M1cm-l, E = 1700 M-1 cm-' at Ae, = 380 nm; cl/(Cl + C2) =0.43, c2/(c1 + C2) = 0.57 at A'tm = 510 nm. The resultingfluorimetric titration curves F vs. -log[Ca2+] are shown in

Fig. 5, indicating that the inflection points are practicallyindependent of the presence of an excited-state reaction.Note that the inflection points due to ground-state reactionoccur at [Ca"] = Kd. Calculation of the Ca" concentrationwhere the inflection point due to the excited-state reactionoccurs (Eq. 34) also shows the negligible interference of theexcited-state reaction on the determination of Kd. Indeed,according to Eq. 34, -log[Ca2"] = 1.90 when BAPTA isused as Ca> buffer and -log[Ca2"] = 1.52 when EGTA isused. As these inflection points are far removed from pKd(6.87), the excited-state reaction does not influence the fluo-rimetric titrations. Therefore, fluorimetric titrations can besafely used to determine Kd and/or Ca>2 concentration.The titration curves of Fig. 5 were used to calculate R in

the absence and presence of an excited-state reaction. Thecalculated titration curves R = F(510 nm, 340 nm)/F(510nm, 380 nm) in the presence or absence of an excited-statereaction are shown in Fig. 6 and are indistinguishable. It mustbe emphasized that the inflection point occurs at a Ca2+ con-centration different from Kd. Indeed, the titration curve R hasan inflection point at [Ca2+] = KdS (Aem, Aex)/S2(Aem, Axe) = Kd[El (Aex)C, (Aem)k02[2(Aex)c2(Aem)ko1] =478 nM. Using the values of E1(380 nm) = 18300 M-1 cm-',e2(380 nm) = 1700 M` cm-', c1/(c, + c2) at 510 nm = 0.43,C21(Cl + C2) at 510 nm = 0.57, kol = 1.239 X 109 s-5 andko2= 0.5509 X 109 s-1, the ground-state dissociation con-stant Kd was calculated and found to be 132 nM. This valueagrees excellently with the simulation value.From the fluorimetric titration of Fura-2 in aqueous so-

lution at pH 7.2 in the form of a Hill plot (Eq. 21) with EGTAas Ca2+ buffer (Fig. 7), a value of 129 (±5) nM was foundfor Kd in excellent agreement with the value of 134 (± 11)nM obtained from absorbance measurements. These resultsconfirm that the excited-state reaction does not interfere withthe determination of Kd. The slope (0.99 ± 0.04) of the Hillplot indicates that Ca>2 binds to Fura-2 with a 1:1 stoichiom-etry. In Fig. 8 the experimental fluorimetric titration curve F

Biophysical Journal1118

-/.0 -1.4 -/.Z -/ 0.6 -0.0 -0.4 -0. ; -0K

Van den Bergh et al. Photophysics of Fura-2 1119

(340 nm, 510 nm) at pH 7.2 with EGTA as Ca2' buffer isshown as a function of -log[Ca2+] with [Ca21] ranging from38 nM to 0.1 M. The solid line represents the fluorescencesignal calculated with Kd = 130 nM, E1 = 13300 M1 cm-1and E2 = 29900 M- cm-' at Aex = 340 nm; cll(Cl + C2) =0.43, c2/(cl + c2) = 0.57 at Xem = 510 nm. The used rateconstants are those of Table 2 for EGTA as Ca2' buffer.There is an excellent agreement between the experimentaland calculated fluorimetric titration curves. The inflectionpoint due to the excited-state processes is hardly visible. Notethat the calculated fluorimetric titration curves in the pres-ence and absence of an excited-state binding reaction havean inflection point at Kd.

CONCLUSION

In this paper, we have investigated the reversible excited-state complex forming reaction of Ca2+ by Fura-2. Usingglobal compartmental analysis, it was possible to determineall the rate constants of the excited-state reaction only when(i) Ca2+ concentrations and not activities were entered intothe program and when (ii) the total Ca2+ buffer concentrationwas the same in all samples. The ionic strength of the solutionwas shown not to influence the recovered values of the rateconstants. From the estimated values of k12 and k2l the dis-sociation constant K d was calculated. It was found thatpK dis smaller than pKd by more than three units. There is neg-ligible interference of the excited-state reaction with the de-termination of Kd and [Ca21] from fluorimetric titrations.Using the results from global compartmental analysis, thesteady-state excitation spectrum could be decomposed intothe excitation spectra associated with the Ca2+ free andbound forms of Fura-2.

V. Van den Bergh is a predoctoral fellow of the Belgian Instituut tot Aan-moediging van het Wetenschappelijk Onderzoek in de Nijverheid en deLandbouw (IWONL). N. Boens is an Onderezoeksleider of the BelgianFonds voor Geneeskundig Wetenschappelijk Onderzoek (FGWO). The con-tinuing support of the Ministry of Scientific Programming through IUAP-II-16 is gratefully acknowledged. A. Kowalczyk had an Individual E. C.Fellowship under the Community mobility action for Cooperation in Sci-ence and Technology with Central and Eastern European Countries whichenabled him to stay at the K.U. Leuven. He also thanks the K.U. Leuvenfor the hospitality during his stay there.

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