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THE J O U R N A L OF BlOLOGlCAL CHEMISTRY tc’ 1985 by The American Society of Biologzal Chemists, Inc

Voi. 260, No. 1, issue of January 10, ,g p. . 242-251.1985 . rznted m U.S.A.

Kinetic Studies of Calcium and Magnesium Binding to Troponin C* (Received for publication, November 2, 1983, and in revised form, July 5,1984)

Steven S. Rosenfeld and Edwin W. Taylor From the Department of Biophysics and Theoretical Biology, University of Chicago, Chicago, Illinois 60637

The kinetic mechanism of calcium binding was in- vestigated for the high-af~nity calcium-magn~ium sites of troponin C (TN-C), for the C-terminal fragment containing only the high-af~nity sites (TR2) and for the TN-C:TN-I (where TN-I represents the inhibitory subunit of troponin) complex. Rate constants were measured by the change in fluorescence of the proteins labeled with 4-(N-iodoacetoxyethyl-N-methyl”7-nitrobenz-2-oxa-1,3-diazole at Cys 98. Rate constants for calcium dissociation were also measured using the fluorescent calcium chelating agent quin 2. Calcium binding to TR2 at 4 “C is a two-step process at each binding site.

T + Ca -- T*Ca - TI4a KO kl k-1

A first order transition (k, = 700 s“) follows the formation of a weakly bound collision complex (KO = 2.5 x 10’ M - ~ ) . The two sites of the labeled protein are distinguishable because of a 2-4-fold difference in rate constants of calcium dissociation. The kinetic evidence is consistent with additive changes in structure induced by calcium binding to two identical or nearly identical high-affinity sites. The mechanism for TN-C:TN-I is similar to TR2. TN-C gave complex kinetic behavior for calcium binding but calcium dissociation occurred with the same rate constants found for TR2. Calcium binding to the high-affinity sites of TnC can be interpreted by the same mechanism as for TR2 but an additional reaction possibly arriving from calcium binding to the low-affinity sites leads to a high-fluorescence intermediate state which is detected by the fluorophore. The interactions between the two classes of sites are interpreted by a model in which calcium binding at the high-affinity sites reverses the fluorescence change induced by calcium binding at the low- affinity sites. Magnesium binding to the calcium-magnesium sites of TR2 and TN-C occurs by the same two- step binding mechanism with a smaller value for KO and a &fold larger rate constant of dissociation.

Skeletal muscle troponin C has four homologous domains which correspond to the four calcium binding sites in the molecule (1, 2). These sites have been named I-IV, starting from the N terminus. Sites I and I1 are the so-called “low- affinity” sites which are specific for calcium, and they have an association constant of 5 X lo5 M-’. Sites 111 and IV, the

*This work has been supported by Program Project Grant HL20592 from the National Institutes of Health and by the Muscular Dystrophy Association of America. The costs of publication of this a r M e were defrayed in part by the payment of page charges. This article must therefore be hereby marked “advertisement” in accord- ance with 18 U.S.C. Section 1734 solely to indicate this fact.

“high-affinity” sites, have a binding constant of 2 x lo7 M-’. In addition, these sites also bind m a ~ e s i ~ , with an apparent affinity constant of 3 X lo3 M” (3-5).

Johnson et ai. (6) have studied the kinetics of the reactions with calcium for both classes of binding sites of dansy1aziridine’-labeled TN-C. While both classes exhibited rapid calcium binding, the rate of calcium release from the high-affinity sites was considered to be too slow to allow these sites to participate in the dynamic regulation of contraction. Further studies of the complex of TN-C and fluorescently- labeled TN-I led to the same conclusion (7). However, a kinetic model of calcium binding was not formulated in these studies since measurements were confined to a single calcium concentration. Iio et ai. (8-14) have made a systematic study of the effect of ligand concentration on the rate of structural change in TN-C and troponin, and have proposed complex kinetic models which take into account the biphasic nature of their observed transients. The results presented here are in partial agreement with their more recent experiments.

In this study, we have systematically examined the kinetics of calcium and magnesium binding to TN-C, to a C-terminal fragment of TN-C containing the high-affinity sites (TR2), and to a complex of TN-C and TN-I, by using the fluorescent probe IANBD. The studies show that calcium binding to the high-affinity sites of TR2 is not a simple diffusion limited process. Binding is a two-step reaction in which an initial collision complex is formed followed by a conformational change of the protein to a state in which the calcium is very strongly bound. The kinetic behavior of the high-af~nity sites of TN-C is very similar to TR2 but the fluorescent label detects an additional transition which is attributed to calcium binding at the low-affinity sites. The kinetic evidence and the fluorescence titration data are interpreted by a model in which calcium binding at the high-affinity sites reverses the fluorescence change induced by calcium binding at the low-affinity sites. In a subsequent paper (15) kinetic studies of calcium binding to the low-affinity calcium specific sites of regulatory complexes will be presented.

MATERIALS AND METHODS

Protein Preparation-TN-C, TN-I, and TN-T were prepared by the method of Greaser and Gergely (16). Protein concentrationa were determined by ultraviolet absorbance with the following molecular

The abbreviations used are: dansyl, 5-dimethylaminonaphtha- Iene-I-sulfonyI; EGTA, ethylene glycol his(@-aminoethyl ether)- N,N,N’,N’-tetraacetic acid; IANBD, 4-( N-iodoacetoxyethyl-N- methyl)-7-nitrobenz-2-oxa-l,3-diazole; quin 2, the alkaline hydroly- sate of 2[[2-[bis[(ethoxycarbonyl)-methyl]amino]-5-methylphenoxy] methyl]-6-metboxy-8-[bis[(ethoxycarbonyl)methy1]amino]quinoline; TES, N-tris[hydroxymethyl]methyl-2-amino-ethanesulfonic acid; TN-C, calcium-binding subunit of troponin; TN-I, inhibitory subunit of troponin; TN-T, tropomyosin binding subunit of troponin; TR2, C-terminal tryptic peptide of TN-C, containing residues 89-153; PIPES, 1-4-piperazinediethanesuifonic acid MES, 4-morphoiinepro- panesulfonic acid.

242

Kinetics of ~alc~um and M ~ ~ s i u m ind din^ to TN-C 243

extinction coefficients: TN-C, M, = 17,840, c2T8 = 0.200 cmz/mg; TN-I, M , = 24,000, fZm = 0.596 cm2/mg; TN-T, M, = 37,000, tZ7* = 0.504 cm*/mg. In each case, the absorbances were corrected for light scattering by subtraction of the absorbance at 320 nm.

TR2, the C-terminal tryptic peptide of TN-C, contains residues 89-153 (17). It was prepared by digesting TN-C in 50 mM Tris, 0.1 mM CaCI2, pH 8.0, with 1 mg of trypsin/100 mg of TN-C. The reaction was carried out a t room temperature for 30 min, and stopped by addit.ion of 4 mg of soybean trypsin inhibitor/mg of trypsin. The digest was then added to a suspension of activated thiol-Sepharose 4B (Sigma). TR2, which contains the single cysteine residue of TN- C (position 98), attaches covalently to the resin via the activated thiol groups. After washing the resin several times with buffer to remove the other tryptic peptides, TR2 was eluted by addition of 50 mM Tris, 10 mM dithiothreitol, pH 8.0.

Fhorescerzt Derivat~v~s-La~ling of both TN-C and TR2 with IANBD was accomplished by addition of a IO-fold molar excess of label to the proteins in 25 mM TES, 2 mM EDTA, pH 7.5. The reaction was allowed to proceed for 18 h at 4 "C in the dark, and was terminated by addition of dithiothreitol to a concentration of 10 mM, followed by dialysis. The concentration of IANBD was determined by absorbance using a molar extinction coefficient of 25,000 M" cm" at 480 nm. The IANBD label was attached primarily to cysteine 98 of TN-C since 85% of previously reactive sulfhydryls were no longer reactive with 5,5'-dithiobis(nitrobenzoic acid) when the ratio of bound IANBD to TN-C was 0.75-0.90. However, the uncertainty in the molar extinction of IANBD (reported values for 6480 range from 20,000 to 30,000 M"Cm") raises the possibility that up to 20% of the IANBD label is attached to sites in addition to the one on cysteine 98. Labeling of TN-C with dansylaziridine was carried out. according t.o the procedure of Johnson et ~ l . (18).

Quin 2 was a generous gift of Dr. Michael Field, Department of Pharmacological and Physiological Sciences, The University of Chi- cago.

Analytical Methods-Electrophoresis in polyacrylamide gels containing 0.1% sodium dodecyl sulfate was performed according to Weber and Osborn (19).

Calcium titrations of labeled proteins were carried out by addition of small volumes of CaClz directly to quartz cuvettes containing the test solutions in 25 mM TES or PIPES buffer. The pH was adjusted as required. Steady-state fluorescence measurements were made in a Perkin-Elmer MPF 44a fluorescence spectrophotometer equipped with a thermostatted cell holder. For IANBD, excitation was at 490 nm, and emission was scanned from 500 to 600 nm, using 4 nm excitation and emission slit widths. The absorbance at the exciting wavelength was always less than 0.1. Titrations were also performed by mixing the protein with calcium in the stopped flow apparatus. The titration curves agreed with the results obtained in the fluo- rimeter.

The free calcium concentration was calculated at 4 and 20 "C for solutions containing EDTA, EGTA, and nitrilotriacetic acid by using the published constants for the association of calcium and protons with these chelating agents (20).

Kinetic Methods-Transient-state measurements were carried out in a stopped flow instrument with a dead time of 1.6 ms (21). Most experiments were performed at 4 "C but measurements a t 20 "C are included. In the stopped flow experiments, the incident beam was passed through a 436-nm interference fiiter (5-8 nm half-band width, Omega Optical, Brattleboro, VT). Fluorescence was observed at 90" relative to the incident. beam with a 500-nm cut off filter. In a typical experiment, one drive syringe contained labeled protein in a 2.0 mM solution of chelator, while the other syringe contained 2.0 mM chelator plus smaller concentrations of calcium (0.1-1.8 mM). This arrange- ment prevented transient surges of millimolar free calcium immedi- ately after mixing. A possible source of error is the decrease in the free calcium concentration on mixing by the binding to chelator but this reaction is expected to be nearly complete in 2 ms. A series of experiments in which the protein solution contained 0.1 mM chelator gave the same values for the rate constants. In this case there is only a small change in free calcium concentration on mixing. In order to measure the apparent rate constant of calcium binding over the concentration range from lO-'to IO-* M, EDTA, EGTA, and nitrilotriacetic acid were used as calcium buffers and measurements were made at pH 7.0 and 7.5. Data sets over a more restricted range for both pH values agreed within 30%. Rate constants of dissociation of calcium or m a ~ e s i u m were obtained by mixing with a large excess of EGTA or EDTA. The vaiues were equal at pH 7.5 and 7.0 within

an experimental error of f25%. Kinetic data were fitted to one or two exponential terms by a method of moments program (21,22).

The rate constants of calcium dissociation were measured directly by using the fluorescent calcium chelator quin 2. A 5-6-fold enhancement of fluorescence is obtained in the formation of a complex with calcium. The association constants for calcium and magnesium are 1.7 X IO' M-' and 500 M" according to Tsien (23). An association constant of 1.1 X lo7 at pH 7.5 was obtained by calcium titration. The rate constant €or dissociation is 45 s-l at 20 "C and 30 s" at 5 "C measured by reaction with EDTA. The apparent second order rate constant for calcium binding was approximately 5 X lo8 M" s" at 5 "C. The observed rate constant increased linearly with calcium concentration and exceeded 800 s-'. As predicted by Tsien (23) the rate constants of quin 2 are much larger than t.hose of EGTA. The rate constant of calcium dissociation from EGTA was 0.4 s" at pH 7 and 5 "C measured by reaction with excess quin 2. Based on the binding constant and dissociation constant the second-order rate constant of calcium binding is approximately lo6 M" s-I.

Rate constants for calcium dissociation from TN-C and TR2 were measured by mixing with an excess of quin 2. Measurements over a 3-fold range of quin 2 concentrations gave the same result. Magne- sium ion was present in most experiments to ensure that all of the calcium was released at equilibrium.

Equilibrium and Kinetic Equations-In this study a single fluorescent label is used to monitor occupancy of the two high-affinity sites of TN-C. The sites are arbitrarily assigned the subscripts 1 and 2. The normalized calcium binding curve for two potentially interacting sites is

B = (b + tybz)/(l + 2b + ab') (1)

where b = K[Ca], the binding constants to sites (1) and (2) are Kl and Kz for the occupancy of a single site and the binding constants for the second calcium bound are K12 and K21. Thus K12 is the binding constant to site (2) when site (1) is occupied by calcium. K = (Ih)(K1 + Kz) and CY = 4 KlKI2/( Kt + K2)'.

The two calcium binding sites are not identical since they are in different regions of the protein but the binding constants may be equal. If Kl = K2 then K12 = KZl, K = Kl = Kz, and a = K1/K12. Equilibrium binding studies (3) are consistent with a value of LY 1. Since the fluorophor may distinguish between the binding sites even if they have the same binding constant the most general formulation is given here.

To obtain the fluorescence titration curve we assign fluorescence emissions relative to the value in the absence of calcium of f l , f 2 , and &for the occupancy of site 1, site 2, and sites 1 and 2. The fluorescence titration curve normalized to the change in fluorescence for saturation of the sites (fi2) is

F = (2yb + abz)/(l + 2b + ab2) (2)

where Y = [~I(KI/(KI + Kz)) + fdKd(K1 + Kd)]/flz. In the special case of identical sites, y = ( ' / z ) ( j l + f2)/fiz. Direct measurements of calcium binding and a fluorescence titration will yield the same binding curve if y = %. A value of y = Ih does not require the fluorescence changes to be equal for each transition but only to be additive, f l + f2 = f 1 2 . A similar analysis of binding and fluorescence has been given by Grabarek et al. (24). We are indebted to these authors for providing a preprint of their work prior to publication. The kinetic behavior described under "Results" shows that the transitions induced by calcium binding attain a maximum rate a t high calcium con~entrations, and the hyperbolic dependence of t.he measured rate constant on calcium concentration indicates the initial formation of a relatively weak calcium binding state. If a single binding site were present, the evidence would be consistent with a two-step reaction,

T + Ca .-- T.Ca .-" 7;.Ca KO k, k-1

where the first step is a rapid equilibrium (KO) followed by a change in conformation to yield a state of enhanced fluorescence denoted by Tl.Ca. The association constant K = Ko(l + k l / k I ) . For this model the fluorescence signal for association Fa fits a single exponential term, Fa = 1 - exp(-At) and the apparent first-order rate constant, X = (kif k-1) Ko[Ca]/(l + Ko[Ca]). The maximum rate constant is A M = kt + k-1 and the apparent second-order rate constant for calcium binding obtained from the initial slope of a plot of first-order rate constant versus calcium concentration is k" = Ko(k, + k-,). Disso-

244 Kinetics of Calcium and Magnesium Binding to TN-C ciation of calcium in the presence of a chelator satisfies the equation F d = exp(-k-,t). F d is the normalized fluorescence signal for the dissociation reaction.

The kinetic data in some cases fitted two rate constants for association and dissociation. Analysis of the data requires the rate equations for two potentially interacting sites when each site can undergo a two-step binding reaction. Two mechanisms are considered; nonidentical but noninteracting sites and identical interacting sites.

Nonidentical and noninteracting sites are equivalent to two species of molecules which yield fluorescence enhancementfland f2with first- order rate constants kl and k2, respectively. It is assumed that the enhancements are additive for the two sites hence ji2 = fl + ji. The equilibrium constants are Ko(l + k1/k- , ) and K'o(l + k2/k-2). The rate equations are simply the sum of the equations for each species.

Fa = 1 - a exp(-X,t) - b exp(-h2t) F d = a exp(-kd) + b exp(-k-d)

(3)

where a = f d f 1 2 , b = ~ z / ~ I z , XI = ( k l + k-l)K~[Cal/(l + Ko[CaI). In the case of identical interacting sites, KO is the same for each

site and it is assumed for simplicity that it is unchanged if one site undergoes a transition induced by calcium. The rate constants kl and k2 now refer to the first and second transitions.

The steps in the mechanism are:

The collision intermediate at either site is symbolized by Ca. T and T. Ca. The occurrence of the transition giving fluorescence fl at site (1) is indicated by Tl.Ca. Cooperative interactions occur if k2 # kl and k 2 # k-l. The cooperativity parameter a = (1 + k2/k-2)/(l + kl/

The constituents in the first square bracket are in equilibrium. In the second bracket the pair of states with subscript 1 are in equilibrium, the pair with subscript 2 are in equilibrium, and the concentration of TI .Ca is equal to Ca. T2. The kinetic scheme is therefore equivalent to transitions between three components X - Y - Z and the solution of the rate equations fits two exponential terms. The fluorescence enhancements of components Y and Z are (l/z)(fl + j z ) and flz, respectively. The contribution of Y normalized to the maximum fluorescence change flzis (l/2)(fI + f2) / f1z which is the parameter y defined for the equilibrium titration. To obtain the effective rate constant for the transition from X to Y we note that

k-1).

-dx/dt = kl(Ca.T) + kl(T.Ca) + 2kl(Ca.T.Ca)

Substitution for the concentrations of Ca. T, T. Ca, and Ca. T . Ca using the equilibria among the constituents gives -dx/dt = 2Xlx where AI = k,KolCa]/(l + Ko[Ca]). Similar considerations give X2 = k2Ko[Ca]/(1 + Ko[Ca]) for the effective rate constant for the transition from Y to Z . Dissociation occurs in two steps with effective rate constants 2k-, and k-l, respectively. The kinetic equations assuming irreversible binding or dissociation at each step are

compared to kl or kp is straightforward. It should be noted that The generalization to the case in which k-l or k-2 are not small

Equation 3 and Equation 4 have the same form. If the sites are identical and noninteracting the kinetic behavior can still show two exponential terms if the fluorescence transitions are not additive (y

# 112). In favorable cases, the value of y can be estimated from the shape of the titration curve and the type of kinetic behavior (one exponential term, two exponential terms, presence of a lag phase).

RESULTS

Equilibrium Measurements of Fluorescence-The effects of calcium and magnesium ions on the fluorescence emission of labeled TN-C, TR2, and the TN-C:TN-I complex are listed in Table I and examples of fluorescence titration curves are shown in Fig. 1. The fluorescence enhancement of TN-C is 0.89 for calcium binding and the titration curve (Fig. 1A) has a midpoint of 6 X 1 0 - ' ~ (5 "C, pH 7.5) which agrees with the dissociation constant of the high-affinity sites (3). The enhancement for magnesium binding is 0.35. The titration curve (not shown) yielded a binding constant of 2 X 10' M" based on the midpoint (pH 7.5,20 "C) which is larger than the value obtained by direct binding measurements under somewhat different conditions (3 X lo3 at 4 "C, pH 7.0, and 150 mM KC1). The fluorescence emission of TN-C increased with KC1 concentration to a maximum enhancement of 0.65 in agreement with Mrakovcic et al. (25). The concentration dependence yielded a dissociation constant of 50 mM. However, KC1 had only a small effect on the midpoint of the calcium titration

TR2 which has only the high-affinity sites, gave the same enhancement as TN-C for calcium, magnesium, and KC1. The midpoint of the titration curve at 20 "C was 5 X lo-' M (Fig. 1B). A value of 2 X IO-' M has been obtained from a titration of the intrinsic tyrosine fluorescence (4).

The fluorescence emission of TN-C was increased 1.3-fold by formation of a complex with TN-I. The increase in fluorescence indicated a 1 to 1 stoichiometry for complex formation. The binding of calcium gave a fluorescence enhancement 0.45 relative to TN-C:TN-I in the absence of divalent cations. The titration curve (Fig. 1B) had a midpoint of 2-3 x lo-' M which agrees with the dissociation constant of the high- affinity sites (3).

Direct calcium binding measurements on TN-C and TN- C:TN-I are fitted by simple binding isotherms indicating essentially indistinguishable noninteracting sites (3). The fluorescence titration curve for TN-C:TN-I was fitted by a simple isotherm but the curve for TN-C had a steeper slope and could be fitted by a cooperative binding curve with a of 4-5. The curve for TR2 was slightly flatter than a simple binding curve and the fit was improved by a small negative cooperativity (a = I/=) or two independent sites with a 4-fold ratio of binding constants. As discussed in the next section

TABLE I Fluorescence emission of IANBD-labeled TN-C, TR2, and TN-C:TN-

I, relative to divalent cation-free IANBD-labeled TN-C The conditions were: 20 mM TES, pH 7.50,20 "C. All samples were

diluted to give the identical absorbance at the exciting wavelength

CUNe.

( A ~ W = 0.074). Relative

emission Protein fluorescence

TN-C No divalent cation 1.00 + 5 mM MgCI, 1.36 + 0.1 mM CaCI2 1.89

No divalent cation 1.02 + 5 mM MgCI2 1.38 + 0.1 mM CaC12 1.89

No divalent cation 2.33 + 0.1 m M CaC12 3.39

TR2

TN-C:TN-I

Kinetics of Calcium and Magnesium Binding to TN-C 245

c

CC~+ZILMI

L 10-8 10"

[Ca"] (MI FIG. 1. Fluorescence titration curves of labeled TN-C, TR2,

and Tn-C:TN-I. A, TN-C, 5 "C, 25 mM TES, 2 mM EDTA, pH 7.5. The dashed curue is the binding isotherm for identical sites, the solid curue fitted to the data points corresponds to an apparent cooperativity (Y = 5. 8, T R 2 , 0 , 20 "C, 2 mM EGTA; TN-CTN-I, 0, 20 "C, 2 mM EDTA, other conditions as in A. The solid curves are binding isotherms for identical sites. The data points for TR2 fit a binding isotherm which is slightly less steep, corresponding to a small negative cooperativity (CY = %) or two different sites. C, effect of ionic strength of the shape of the titration curve of TN-C, pH 7.5,20 "C: A, 100 mM KCI; 0, 50 mM KCI; 0, no KC1 added, 2 m M EGTA, 25 mM TES. The fluorescence enhancements of KC1 and CaCL are approximately additive and the curves are normalized to the change in fluorescence produced by 2 X M calcium at each KC1 concentration.

the kinetic evidence is consistent with a small negative cooperativity or a small difference in the binding constants of the two sites. These are small effects and some heterogeneity in the labeled protein preparations is a possible explanation.

The TN-C results present a more serious problem. Rela-

tively steep titration curves have generally been obtained from fluorescence measurements using either intrinsic or extrinsic fluorophores (4 ,5) . If the value of the fluorescence parameter in Equation 2 is not 95 the fluorescence titration curve can appear to show positive cooperativity (24). Calculations indicate that an apparent cooperativity parameter of approximately three could be obtained for noninteracting sites for y = 0 or 1. These extremes for the value of y are not sufficient to account for the apparent cooperativity, and the kinetic evidence described in the next section indicates that y is close to Y2.

The shape of the fluorescence titration curve was investi- gated for a range of conditions. The steepness of the curve increased for an increase in temperature from 5 to 20 "C and for an increase in pH from 7.0 to 7.5. The curve became less steep with increasing KC1 concentrations from 0 to 100 mM. Titration curves at pH 7.5 and 20 "C are shown in Fig. 1C for a range of KC1 concentrations. In 100 mM KC1 the curve is only slightly steeper than a simple titration curve but with decreasing ionic strength the curve becomes steeper and in the absence of KC1 it passes through a maximum at approximately 7 X lo-' M free calcium and decreases as the calcium concentration is raised to approximately 5 X M. The enhancement generally increased slightly as the concentration was raised to 2 X M. At this concentration all of the curves had reached a plateau. Raising the calcium concentration to 2 X M gave a further increase in enhancement of 5-8% of the value at 2 X M.

The titration curve obtained using the tyrosine fluorescence was even steeper than for the labeled TN-C but not dependent on KC1 concentration. Labeling the protein with IANBD decreased the steepness of the curve measured by tyrosine fluorescence without changing the midpoint (data not shown). Thus the apparent cooperativity of the titration curve does not appear to be introduced by labeling the protein since it is observed using an intrinsic fluorophore. A small perturbation of the binding sites may be caused by labeling but analysis of the kinetic evidence shows that if such an effect is present it would lead to a titration curve which is slightly less steep than a simple binding curve. The shape of the binding curve for the labeled protein cannot be explained by a cooperative interaction between the high-affinity sites. A possible explanation is suggested by the kinetic evidence which shows the presence of an additional fluorescent intermediate for TN-C which is not observed for TR2 and which probably arises from calcium binding to the low-affinity sites.

Kinetic Studies of Calcium Binding to TR2"The fragment TR2 contains only the two high-affinity sites and has a simple binding curve. Consequently it provides the best model for examining the mechanism of calcium binding. The fluorescence signal for calcium binding a t 4 "C gave a good fit to a single exponential term over a range of calcium concentrations up to 1 mM (Fig. 2A). No lag was observed at any calcium concentration. The apparent rate constant increased linearly with concentration in the low concentration range and the slope gave a value for k" of 1.5 to 2 x IO6 M-' s". Over the complete range of concentrations the apparent rate constant fitted a hyperbola (Fig. 3) yielding a maximum rate of 700 s" and apparent binding constant KO = 2.5 X lo3 M-'.

The relatively small values of k" and KO and a maximum rate at high calcium concentration are consistent with a two- step mechanism rather than a simple diffusion limited binding of calcium. A collision intermediate T.Ca is converted to a more strongly bound state by a conformational change which is detected by the fluorophore.

T + Ca - T.Ca - Tl.Ca KO kl k-1

246

2.6

2 41 I G r , l I .6 14 12

14 28 42 56 70

Time (msec)

Kinetics of Calcium and Magnesium Binding to TN-C

I , , I 1.2 24 3.6 48 6.6

Timebec)

FIG. 2. Calcium binding to TR2 in the absence and presence of magnesium. A, fluorescence transient for the reaction of TR2 with calcium. The jagged curue depicts the output voltage in arbitrary units uersus time for calcium binding to TR2 and the smooth curue is the computer-generated fit, with apparent rate constant of 65 s-'. The conditions were: 100 mM KC1,25 mM TES, 2 mM nitrilotriacetic acid, 0.9 mM CaClz (final concentration after mixing), pH 7.5, 4 "C. The free calcium concentration after mixing is 37 p ~ . B, Fluorescence of TR2 uersus time for calcium binding to TR2 in the presence of a saturating concentration of magnesium. The conditions were: 100 mM KC1, 25 mM TES, 8 mM MgC12, 0.1 mM EGTA, 1 mM CaClz (final concentration), pH 7.5, 4 "C. The rate parameters for this transition are 5.2 and 1.0 s-'. These rate constants agree with values for release of magnesium from the high-affinity sites of TR2.

6ooi 500-

- - 400-

- 2 'Y 300- Lz

200-

I O 0 i /

. ! . I

100 200 300 400 500 600 700 800 900 1000

[Ca**](pM)

FIG. 3. Plot of the first-order rate constant versus free calcium concentration for the fluorescence change depicted in Fig. 2A. The range of calcium concentration is 1-1000 p ~ . The solid line was drawn to the equation: X = ( k , + k-l)(Ko[CaZ+])/(KO[Ca2+] + l ) , where h is the observed rate constant, KO = 2500 M" and k , + h-, = 714 s-'. The apparent second-order rate constant, k" = K,,(k, + h-') = 1.8 X lo6 M-' s-'.

The dissociation of calcium was measured by the decrease in fluorescence on mixing with a large excess of chelator. An example of the fluorescence signal is given in Fig. 4A. The curve shows no lag phase but it deviates from a fit to a single exponential term. In this instance, the fitting procedure gave rate constants of 0.8 s-' and 0.2 s" with approximately equal amplitudes for the two terms. Measurements on several preparations yielded similar results a t pH 7 and pH 7.5 and in the presence or absence of 100 mM KCl. The amplitude of the step with the larger rate constant varied from 30 to 50% of the total but in all cases the curve deviated from a single exponential. The results indicate that the two calcium binding sites have different rate constants for calcium dissociation either because they are intrinsically different or because of a small interaction.

It is assumed in the kinetic model that the slow transition detected by a change in environment of the fluorophore is followed by a very rapid dissociation of calcium so that the rate constant which refers to an alteration of the protein also measures the effective rate constant of the actual dissociation

2.54 iiiL p 17 , , , , A , i 1.5

13 I I

0 2 4 6 8 IO 12 14 16 18 20

Timebec)

6. I

I '

0 09 18 27 36 45

Time (sec) FIG. 4. Rate of dissociation of calcium from TR2. A , fluores-

cence transient for mixing labeled TR2 plus calcium with a large excess of EDTA. The conditions were: 10 mM TES, 2 mM EDTA, 0.1 mM CaC12, pH 7.5,4 "C. The fluorescence signal fitted two exponential terms with apparent rate constants of 0.75 and 0.17 s-', with the faster phase constituting approximately 65% of the total signal amplitude. Similar results were obtained in 100 mM KCl. B, fluorescence transient produced by mixing 20 p M TR2 plus 40 p M CaClZ with 600 p~ quin 2 plus 5 mM MgC12. This transient directly measures the rate of calcium release from the high-affinity sites of TR2. The conditions were: 100 mM KC1, 25 mM TES, 2.5 mM MgC12, 20 pM CaC12, 10 p M TR2, 300 pM quin 2, pH 7 4 4 "c (final concentrations). The rate parameter for this process, fitted to a single exponential, is 0.83 s-', and is very close to the value of the rate constant for the faster process in A.

of the calcium. This assumption was tested by measuring the rate of calcium dissociation directly by its reaction with a large excess of quin 2. The fluorescence transient is shown in Fig. 4 B for the reaction of 20 pM TR2,40 p~ CaClz with 600 p M quin 2 plus 5 mM MgC12. The transient shows no lag and was fitted by a single exponential term with rate constant of 0.7 k 0.1 s-'. The large ratio of quin 2 to calcium was used to establish the point that the slow transition of the protein is the rate-limiting step in dissociation. The small relative change in fluorescence leads to a high noise to signal ratio and photobleaching of quin 2 can distort the shape of the time dependence. The results for TR2 were identical to those for TN-C and a quantitative comparison of rate constants is presented in the next section.

The results do not distinguish between two intrinsically different sites and two identical and interacting sites. In the first case (Equation 3), k,= h a n d 4h-2= k-,. Thus the binding constants differ by a factor of 4. In the cooperative case (Equation 4 ) k , kt and 2k-z = k-,. Thus the cooperativity parameter is a = I/z . In the cooperative case it is necessary to evaluate the fluorescence parameter. If y were close to 1, the fluorescence signal for dissociation of calcium would show a lag while if y were close to 0 the signal for dissociation would fit a single exponential term and the signal for association would show a lag. These conditions were not fulfilled and the results are consistent with a value of y close to Either interpretation of the mechanism leads to a titration curve which is slightly less steep than a simple binding curve.

Kinetic Studies of Calcium Binding to TN-C-The kinetics of calcium dissociation was measured using labeled TN-C and by the reaction with quin 2 for a range of conditions, pH 7 and 7.5,O and 100 mM KCl, and a range of temperatures from 4 to 30 "C. In all cases the labeled protein gave a biphasic fluorescence signal and the rate constants were not altered by pH and ionic strength within an uncertainty of k 20%. The two apparent rate constants increased from 0.8 k 0.1 s-' and 0.2 k 0.05 s" at 4 "C to 4 k 0.2 s" and 1 k 0.1 s" at 20 "C, respectively. The relative amplitude of the transition with the larger rate constant varied from 25 to 50% but no trend was evident for various conditions.

An example of a fluorescence transient at 20 "C is shown in Fig. 5A. The fitted values of the two rate constants are 4.0 s" and 0.9 s-', respectively. The fluorescence signal obtained


Time (sed Time (sed Tlme (sed FIG. 5. Calcium and magnesium dissociation from TN-C. A , fluorescence transient for calcium dissociation

from labeled TN-C, 20 "C, 25 mM TES, pH 7.5,5 p M TN-C, 4 mM EDTA after mixing. The initial ratio of calcium to high-affinity sites was approximately 1.2 to 1. The solid curve is the experimental record and the computer generated fit to two exponential terms which are superimposable. The rate constants are 4.0 s-' and 1.2 s-' with the faster process contributing 65% of the amplitude. The dashed extension of the curve shows the fit to the slower process. Voltage is expressed in arbitrary units. B, fluorescence transient for calcium dissociation measured by quin 2 for unlabeled TN-C. Conditions as in A except that calcium release was obtained by mixing with a 5-fold excess of quin 2. The voltage gain was adjusted to give nearly equal amplitudes for the signals obtained in A and B. The signal fitted a single exponential term with rate constant of 2.7 s-I. The decrease in signal after 2 s arises from bleaching of quin 2. C, fluorescence transient for magnesium dissociation from labeled TN-C. The conditions were: 5 "C, 25 mM TES, pH 7.5, 5 p~ TN-C, 0.5 mM Mg acetate, 5 mM EDTA after mixing. The transient fitted two exponential terms, with rate constants of 3.9 s-' and 1.0 s-I. The dashed curue illustrates the fit to the slower process.

by reaction with a &fold excess of quin 2 over calcium is shown in Fig. 5B for unlabeled TN-C. The signal fits a single rate process with rate constant of 2.7 s-'. At 20 "C the reaction is faster and the effect of photobleaching is less serious but the estimated loss of signal was 10% at the end of the transient. The same experiment for labeled TN-C was also fitted by a single rate constant of 2.8 f 0.1 s-'. The fluorescence emission maximum of quin 2 is almost equal to the absorption maximum of the labeled protein, consequently the errors are larger. Although the experiment shows that labeling the protein does not have a measurable effect on the rate constant of calcium dissociation obtained from the fluorescence signal of quin 2, there is some doubt that the measurement would resolve two transitions. Simulations showed that two process with rate constants of 4 s" and 1 s-' and a 10% loss of signal during the duration of the transient could be fitted reasonably well by a single rate constant of 2.7 s-l. The experiments do not rule out the possibility that the two rate constants obtained for the labeled protein are the result of a small perturbation of essentially equal rate constants for the native protein.

However, the fluorescence transients obtained for the binding of calcium to TN-C are strikingly different from those obtained with TR2 and may provide an explanation for the apparent cooperativity of the equilibrium titration curves. At low calcium concentrations (less than 0.2 FM) the fluorescence signal fitted a single exponential term (Fig. 6 A ) . As the concentration was increased a second process was observed with a much larger rate constant (Fig. 6, B and C). For calcium concentrations of 10 FM or larger the fluorescence signal passed through a maximum value which corresponded to an enhancement of approximately 1.5 and then decreased to the equilibrium value of 0.9 (Fig. 6D) . At very-high calcium concentrations (1 mM or larger) the increase in fluorescence occurred in the dead time of the apparatus (1.5 ms) and the observed signal consisted of a decrease in fluorescence which fitted a single exponential term.

The apparent rate constant of the slower process is plotted

I I

I 0 4 8 12 1 6 2 0

Time (sed

'i"] 5.4 5.0

4.6

0 1 2 3 4 5 Time (sec)

" I 7 14 21 28 35 40 80 120 160 200

Time(msec) Timdmsec)

FIG. 6. Fluorescence transients for the binding of calcium to TN-C. A, fluorescence transient for the reaction of TN-C with calcium. The conditions were: 10 mM Tris/MES, 2 mM EGTA, 0.2 mM CaC12 (final concentrations); pH 7.0,4 "C. The final free'calcium concentration is 0.18 pM. The rate parameter for this transient is 0.28 8 . B, conditions as in A, except that the final free calcium concentration is 6.3 p ~ . The fluorescence transient consists of a fast initial rise (arrow), followed by a slower phase which fits a rate parameter 5.8 s-'. C, same conditions as in B. The time scale has been shortened to show that the initial fluorescence rise fits a single exponential term with rate constant of 350 s-', and the vertical scale has been expanded to amplify the signal. The arrow indicates zero time at which flow stops. D, same experiment as in A except that the final free calcium concentration is 24 pM. The fluorescence transient now consists of a rapid rising phase (rate parameter of 500 s-'), followed by a falling phase with rate parameter of 14 s-'. The solid curve is the computer fit to the signal beginning at 40 ms. The rising phase has the same apparent second-order rate constant as that for the fast phase of the transient in Fig. 5B; approximately half of the fast signal is lost in the dead time of the apparatus.

248 Kinetics of Calcium and Magnesium Binding to TN-C

[ Ca+*] CpMl

B I C S O O C I '0 9) v)

9)

Q

U

c

a

FIG. 7. Plot of the first-order rate constant versus free calcium concentration for the fluorescence signals illustrated in Fig. 6. A, Plot of the first-order rate constant uersus free calcium concentration for the single exponential term at very-low calcium concentrations or for the slower phase in the fluorescence change as described in Fig. 6B. The range of free calcium concentration is from 0.2 to 6.5 @M, and the slope of the line defines an apparent second- order rate constant, k" = 1.3 X lo6 "' s-'. B, plot of the apparent first-order rate constant for the decreasing phase of the fluorescence signal as described in Fig. 6D. Open circles refer to experiments in which TN-C was titrated with calcium to give 80-90% of the equilibrium fluorescence charge and then reacted with a higher concentration of calcium (for details see text). The curve drawn in the figure is the hyperbola fitted to the kinetic data for TR2, KO = 2500 "I, k , + k-I = 700 s-', to illustrate that the slower transition for TN-C is equivalent to the single transition for TR2.

in Fig. 7 . The points for concentrations less than 6 &M (Fig. 7A) refer to the increase in fluorescence and give a value of k" of 1.4 X lo6 IC'. The points for concentrations greater than 14 WM (Fig. 7 B ) refer to the decrease in fluorescence and are fitted by a hyperbola ( K O = 2-3 X lo3 M-', maximum rate 700 s-'). The value of k" is 1.5 to 2 X lo6 M" s-'. Thus the same process appears to be responsible for the slower increase in fluorescence at low calcium concentrations and for the decrease in fluorescence at higher calcium concentrations. The rate constants describing this process agree with the values obtained for TR2 which suggests that this component of the fluorescence signal is produced by the transition induced by calcium binding at the high-affinity sites.

The apparent rate constant for the faster process increased linearly with calcium concentration and gave a value of k' of approximately 5 X lo7 M" s-'. A maximum rate could not be determined but based on the loss of signal amplitude and the dead time of the apparatus the rate constant exceeds 3000 s-'.

The high-fluorescence state formed in the fast reaction

cannot be an additional transient intermediate on the pathway of calcium binding to the high-affinity sites. In that case, the mechanism for one of the sites becomes

KO k k, 2" + Ca - T.Ca - Tk.Ca - T1.Ca

where 12 >> kl and T,.Ca has a larger enhancement than Tl. Ca. Analysis of a three-step mechanism (26) shows that for low calcium concentrations such that Ko[Ca] k << kl the signal fits a single exponential term. As the concentration increases a second slower rate process is observed but the apparent rate constant is essentially independent of concentration. The actual behavior is opposite to the prediction of this mechanism. A faster transition appears at higher concentration and both rate constants depend on concentration. Also the results are not explained by supposing that after one transition has occurred the second calcium binds with a larger value of k". TN-C was titrated with a calcium/EDTA buffer to give 80-90% of the maximum equilibrium value of the enhancement and then reacted with increasing concentrations of calcium. For these conditions the reaction starts with most TN-C molecules having one calcium bound. The fast transition was still observed and the rate constant of the slower step had the same concentration dependence (open circles in Fig. 7 B ) .

It is probable that the fast reaction is caused by calcium binding at other sites. One possibility is calcium binding to the low-affinity sites which have a value for the apparent second-order rate constant in the range observed for the fast process (6 ) and the sites would begin to be occupied at 0.2 p~ calcium. An estimate of the second-order rate constant for the conditions used in these experiments was obtained from the association constant of 5 X lo5 "' and a measurement of the rate constant of dissociation of 270 s" at 4 "C using dansylaziridine-labeled TN-C prepared by the method of Johnson et al. (6). The calculated rate constant is 1.5 X lo8 M" s-' which is in the required range.

Kinetic Studies of Magnesium Binding to TN-C-The fluorescence transient for the binding of magnesium ion to TN- C fitted a single exponential term over the concentration range up to 200 MM. As the concentration was increased a faster transition was observed whose relative amplitude increased. At concentrations above 2 mM the rate constant became too large to measure and the observed signal consisted of a decrease in fluorescence. Thus the behavior is essentially the same as for calcium binding. The rate constant of the slower transition is plotted in Fig. 8. The apparent second- order rate constant is 5 X lo4 "' s-'. A maximum rate could not be determined accurately because of the weak binding of magnesium ion but it appears to be the order of 500 s-'. Dissociation of magnesium ion from TN-C or TR2 (Fig. 5 0 ) gave clearly biphasic transients with apparent rate constants of 5 s-l and 0.7 s-' and each term contributed approximately equal amplitudes.

Thus magnesium binding at the high-affinity sites appears to produce the same transitions as calcium binding except that the initial complex has a much smaller association constant ( KO = 10' "') and the rate constants of dissociation are five times larger.

Magnesium binding reduces the apparent calcium affinity for the high-affinity sites which was interpreted as a compe-' tition for the same sites (3). A simple test of this proposal is provided by a measurement of the rate constant of calcium binding in the presence of magnesium ion. Fig. 2B shows the fluorescence transient obtained by mixing 1 mM calcium with. a solution of TR2 containing 8 mM MgC12 at 5 "C. The


[ M i 2 1 (mM1 FIG. 8. Plot of the apparent rate constant for the binding of

magnesium to TN-C. The conditions were: 5 "C; pH 7.5, 25 mM TES, 0.5 mM EGTA, 5 M TN-C (final concentrations). The free magnesium ion concentration was corrected for binding to EGTA. For magnesium concentrations greater than 1 mM the data points were obtained from the rate of decrease of the fluorescence signal. The value of k" is approximately 5 X 10' "' s-I.

1.0-

- 0.8- - I u ln Q

0.6- c

LL 0

0.4-

0.02 0.04 0.06 0.08 o.io [ca+'] ( p ~

FIG. 9. Plot of the apparent rate constant for the binding of calcium to the TN-C:TN-I complex. The label is on the TN-C moiety. The conditions were: 4 "C pH 7.5, 25 mM TES, 2 mM EDTA. Data are shown for the low range of calcium concentrations to determine k" which is equal to 1.4 X 10' M" s-'.

transient fits two exponential terms and the apparent rate constants are 4 s-' and 1 s-l which agree with the rate constants for magnesium dissociation. The same result was also obtained with TN-C.

Kinetic Studies of Calcium Binding to the TN-C:TN-I Com- plex-The binding of calcium to TN-C:TN-I gave a fluorescence transient which fitted a single exponential term a t low- calcium concentrations (up to 0.1 pM). A plot of the rate constant uersus calcium concentration in this range is shown in Fig. 9. The slope of the curve gives a value of 12" of 1.2 x lo7 M" s-' which is six times larger than for TN-C. At high calcium concentrations the rate constant obtained a maximum value of approximately 500 s-' (data not shown). Dis- sociation of calcium gave a biphasic signal with rate constants of 0.6 s-' and 0.1 s" which are similar to the values obtained for TN-C. Thus the increase in calcium binding constant of

TN-C:TN-I compared to TN-C is primarily caused by an increase in the apparent second-order rate constant of association.

The kinetic and equilibrium data are summarized in Table 11.

DISCUSSION

The main problem addressed in this work is the kinetic mechanism of calcium binding to the two high-affinity sites of TN-C. The use of a fluorescent probe to monitor a change in environment induced by calcium binding is the most con- venient technique but various problems have to be considered in interpreting the results, whether the probe alters the properties of the protein, how a single probe responds to binding a t two sites, and whether the results are affected by calcium binding to the low-affinity sites.

The kinetic mechanism was analyzed first for the simpler case of TR2 which contains only the high-affinity sites and appears to retain the properties of TN-C associated with those sites (27-29). The fluorescence titration curve is slightly less steep than a simple binding curve (Fig. 2B) and the binding constant obtained from the midpoint of the curve is 2 x lo7 M-' which agrees with the value for the high-affinity sites (3). The kinetic behavior for calcium binding satisfied a simple two-step binding mechanism for either site, thus for site (1).

T + Ca - T.Ca - T,Ca

Calcium first forms a relatively weakly bound collision intermediate T + Ca with association constant KO = 2.5 X lo3 "', A transition to a state TI. Ca with a relative enhancement of fluorescence emission fl occurs at rate kl where kl is approximately 700 s" at 4 "C. The time course fitted a single exponential term thus the rate constants are equal for both sites, kl E k2. A difference of a factor of two in the rate constants would be detected by the curve fitting procedure. The apparent second-order rate constant of calcium binding is 2 x lo6 M" s-l at 4 "C. The dissociation of calcium fitted two exponential terms with rate constants of 0.8 s" and 0.2 s-'. This result indicates that the sites are distinguishable either because of a small interaction and the rate constants k-2 and k-, are 0.4 s" and 0.2 s-', respectively (Equation 4), or because they are intrinsically different and the rate constants differ by a factor of 4 (Equation 3). Either case would produce a titration curve which is slightly less steep than a simple binding curve. The average equilibrium constant calculated from the rate constants is 0.6-0.8 X lo7 M" a t 4 "C. At 20 "C the corresponding value is 1-1.5 X lo7 M" in reasonable agreement with the value obtained from the titration curve.

The steps in calcium dissociation were indistinguishable for TR2 and TN-C and if a perturbation of the binding sites is introduced by the probe it should be equivalent for both molecules. Direct measurements of calcium dissociation by quin 2 yielded a fit to a single rate process and the rate constant was not altered by labeling the protein. Over a range of temperatures the rate constant obtained with quin 2 was roughly equal to the average value obtained for the two transitions of the labeled protein. A consideration of the errors in the quin 2 experiments arising from bleaching occurring during the transient leaves open the possibility that the rate constants are essentially equal in the native protein and the probe introduces a small perturbation which allows the sites to be distinguished. It is of interest to compare these results with a recent report of Wang et al. (29). These authors obtained a single rate constant of calcium dissociation of 2.9 s" a t 20 "C using the intrinsic tyrosine fluorescence which

KO k1

k-1

250 Kinetics of Calcium and Magnesium Binding to TN-C TABLE I1

Equilibrium and kinetic constants for calcium and magnesium reactions with TR2, TN-C, and TN-C:TN-Z The conditions were: 4-5 "C unless indicated, pH 7.5. Rate constants at pH 7.0 and in the presence of 100 m M

KC1 were not distinguishable from values above within experimental error. Association constants from fluorescence titrations refer to the reciprocal of the concentration at the midpoint of the titration curves. Protein labeled with IANl3D on Cys 98 in all cases. Error limits refer to range of values for several preparations. The relationship of rate constants for dissociation and intrinsic rate constants depends on the kinetic model as described in the text.

Protein and ion

Association constant

(fluoreseence titration)

second-order Apparent

rate constant Maximum

rate constant rate constant Dissociation

"1 s-1

TR2, Ca2+ z x 107 M - ~ ( Z O "c) 1.8 f 0.3 X lo6 700 0.8 f 0.1, 0.2 f 0.05 TN-C, Ca2+ z x 107 "1 1.5 f 0.3 X lo6 TN-C:TN-I, Ca*+

-700 0.8 f 0.15,0.2 f 0.05

TR2, M$+ 0.65,0.18 3 X 10' M" (20 "c) 1.4 X 107 -500

ND" 2 x 104 "1 (20 T) 4 f 1 x 104 2500 5 f 1,o.a f 0.2 TN-C, M$+

4 f 1 x 104 2500 5 f 1, 0.9 f 0.2

a ND, not determined.

agrees within experimental error with the value of 2.7 f 0.1 s" obtained from the quin 2 fluorescence. However, substitution of a dansyl group in the NHz-terminal half of the molecule reduced the rate constant measured by tyrosine fluorescence to 1.8 s-l while the dansyl fluorescence gave a rate constant of 0.9 s" in agreement with Johnson et al. (6). Thus modification of the protein introduces a small perturbation and two rate constants for calcium dissociation can now be resolved because the two fluorescent groups located in different regions of the protein each respond to a different transition. In this study, the fluorescent probe on Cys 98 is located in helical region I11 close to a calcium binding site (27) and it appears to sense both transitions. The two rate constants of the modified protein may correspond to transitions induced at site 111 detected by the labe1 on Cys 98 and the intrinsic fluorescence of Tyr 109 and site IV detected by Cys 98 and the dansyl label. Even if labeling the molecule introduces a small perturbation it has the useful consequence that the calcium binding sites become distinguishable and it can be concluded that the transitions at each site produce additive and essential independent alterations in the structure

The association of both calcium and magnesium, with TN- C showed complex kinetic behavior and the titration curves were steeper than simple binding curves as monitored by the fluorescence probe. Since TR2 and TN-C:TN-I showed simple kinetic behavior and simple titration curves the two effects are correlated. The analysis of the kinetic evidence for calcium binding to TN-C suggests that the fluorescent probe responds to two separate processes. One process is the transitions induced by calcium binding to each high-affinity site which has the same kinetic constants (lz", KO, k,) as were found for TR2. The second process is a much faster transition which produces a high fluorescence intermediate state which decays as the reaction at the high-affinity sites reaches completion. A reasonable explanation is that the fast transition is caused by calcium binding at a low-affinity site which induces a change in environment of the fluorophore but this high- fluorescence intermediate is converted to a lower fluorescence state by a transition at a high-affinity site. For simplicity we consider the kinetic scheme for a single site in each class.

of TN-C.

hl,/T-cafh Ca + T x h ~ $T+.CwCah

T.Cah

where 1 and h refer to low- and high-affinity sites and A1 and

Ah are the apparent first-order rate constants for the two-step binding process as defined in Equation 3. It is assumed that the fluorescence enhancement of T Cal is approximately twice as large as T Cah or T . Gal. Cah.

Various lines of evidence support this model. The fast transition to a high-fluorescence state is not observed for TR2 which lacks the low-affinity sites. The fast transition increases in amplitude over the calcium concentration range from 0.1 to 20 KM which corresponds to the binding of calcium to the low-affinity site. The second-order rate constant for these sites is 50-100 times larger than for the high-affinity sites and the maximum value of X1 is too large to measure and is thus 5-10 times larger than the maximum value of Ah.

Therefore at very-low calcium concentrations only T.Cah is formed and k" for this process agrees with the value obtained for TR2. At very-high calcium concentrations the

reaction pathway is essentially T T - C 4 - T. Gal. Cah. The first step is completed during the mixing time of the apparatus and a fluorescence decrease is observed with rate constant Ah which agrees with the value obtained for TR2 (Figs. 6 and 7). The concentration dependence of both processes and the absence of the fast process at very-low calcium concentrations is not consistent with a scheme in which the high-fluorescence state is an intermediate on the pathway of calcium binding to the high-affinity sites.

The scheme accounts for the kinetic evidence at very-low and very-high calcium concentrations. It is not practical to considdr a complete model since there are 16 possible states whose fluorescence enhancements must be specified. How- ever, the derivation of the equilibrium titration curve is straightforward and by making plausable assumptions concerning the fluorescence enhancements the general features of the titration curves are explained. The three simplest cases are that a transition at either high-affinity site or only at both high-affinity sites or at a particular high-affinity site eliminates the fluorescence enhancement induced by calcium binding at either or both low-affinity sites. The normalized fluorescence curve is the ratio of two fourth-degree polyno- mials in b = KCa where K is the association constant of the high-affinity site and the coefficients are functions of two parameters, r the ratio of the binding constants of the Iow- and high-affinity sites and g the ratio of the fluorescence enhancements of the states with two calciums bound to the low-affinity sites and two calciums bound to the high-affinity sites. From the kinetic experiments at high calcium concentrations, g is approximately two. Calculations for a range of r values show that the first case does not yield a maximum

+ Ca + Ca


value for the titration curve. For the second and third case, the titration curve shows a maximum value for r = 0.1 to 0.2 while for r = 0.05 the maximum is too small to be detected but the titration curve is slightly steeper than a simple binding isotherm. Thus the general features of the titration curves of Fig. 1C can be accounted for qualitatively by the mechanism deduced from the kinetic evidence. The change in shape with decreasing ionic strength may be explained by an increase in the binding constant of the low-affinity sites. It should be noted that the kinetic constants for the high-affinity sites are essentially independent of ionic strength.

The details of the calculations are not presented because the model is too simple to be in quantitative agreement with the titration data. The assumptions concerning fluorescence enhancements can be only approximately correct since there is a small enhancement (5-8%) for binding of calcium in the range from 2 X to 2 X M, a range in which calcium binds to low-affinity sites with the high-affinity sites already occupied. The interaction between low- and high-affinity binding sites was introduced in terms of the change in fluorescence enhancement but the equilibrium constant for one class of sites was assumed to be unchanged by binding to the other class of sites. Wang et al. (29) have shown that there could be up to a 4-fold increase in binding constants from an interaction of the transitions at the low- and high-affinity sites Adding this interaction to the model increases the steepness of the binding curves and improves the agreement with experiments. However, we prefer to stress the general features of the mechanism rather than detailed model calculations which depend on several parameters. Calcium binding to the high-affinity sites yields essentially independent changes in structure as measured by the fluorophore near binding site 111, while calcium binding to the low-affinity sites also alters the environment of the fluorophore and there is an interaction between the transitions at the low- and high-affinity sites.

The mechanism of magnesium binding at the high-affinity sites is essentially the same as for calcium binding but a steep titration curve and a decrease in the fluorescence signal at very-high magnesium concentrations was obtained for TN-C. These results cannot be explained by binding of magnesium to the low-affinity sites. However, the structure of TN-C as measured by helical content and fluorescence enhancement is altered by increasing the ionic strength (25). Part of the enhancement observed at 2-5 mM MgC12 may arise from nonspecific ion binding to carboxyl groups and the enhancement may be reduced by magnesium binding to the high- affinity sites.

The interpretation of calcium binding as a simple diffusion limited process (6, 7) is not consistent with the evidence presented here. At low temperature the apparent second-order rate constant is lo6 M" s-l which is more than two orders of magnitude smaller than a diffusion limited process and the very strong binding of calcium is determined by a first-order transition with a rate constant of 700 s-'. At 20 "C; k" is IO7

s" and the first-order transition is too fast to measure which may account for the different interpretation based on

studies at a higher temperature. Our results are in partial agreement with the extensive work of Iio et aL(8-14) although their studies were done at 20 "C and a first-order transition was not observed. The results are in disagreement in that we did not observe an effect of magnesium concentration on the rate of calcium dissociation and the evidence does not support their proposal of a rapid exchange of magnesium and calcium at the high-affinity sites.

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lo7 m-’. lo3 (3-5). et › content › 260 › 1 › 242.full.pdf · affinity constant of 3 x lo3...

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