Kinetic studies of calcium binding to the regulatory site of troponin C from cardiac muscle.

We have studied the kinetics of the structural transitions induced by calcium binding to the single, regulatory site of cardiac troponin C by measuring the rates of calcium-mediated fluorescence changes with a monocysteine mutant of the protein (C35S) specifically labeled at Cys-84 with the fluorescent probe 2-[4′-(iodoacetamido)anilino]naphthalene-6-sulfonic acid. At 4°C, the binding kinetics determined in the presence of Mg2+ was resolved into two phases with positive amplitude, which were completed in less than 100 ms. The rate of the fast phase increased linearly with [Ca2+] reaching a maximum of ∼590 s−1, and that of the slow phase was approximately 100 s−1 and did not depend on Ca2+ concentration. Dissociation of bound Ca2+ from the regulatory site occurred with a rate of 102 s−1, whereas the dissociation from the two high affinity sites was about two orders of magnitude slower. These results are consistent with the following scheme for the binding of Ca2+ to the regulatory site: where the asterisks denote states with enhanced fluorescence. The apparent second-order rate constant for calcium binding is Kok1 = 1.4 × 108M−1 s−1. The two first-order transitions occur with observed rates of k1 + k−1 ≈ 590 s−1 and k2 + k−2 ≈ 100 s−1, and the binding of Ca2+ to the regulatory site is not a simple diffusion-controlled reaction. These transitions provide the first information on the rates of Ca2+-induced conformational changes involving helix movements in the regulatory domain.

where the asterisks denote states with enhanced fluorescence. The apparent second-order rate constant for calcium binding is K o k 1 ‫؍‬ 1.4 ؋ 10 8 M ؊1 s ؊1 . The two first-order transitions occur with observed rates of k 1 ؉ k ؊1 Ϸ 590 s ؊1 and k 2 ؉ k ؊2 Ϸ 100 s ؊1 , and the binding of Ca 2؉ to the regulatory site is not a simple diffusioncontrolled reaction. These transitions provide the first information on the rates of Ca 2؉ -induced conformational changes involving helix movements in the regulatory domain.
Troponin C (TnC) 1 is the calcium-binding subunit of the three-subunit troponin complex, which, together with tropomyosin, constitutes the regulatory system in vertebrate skeletal and cardiac muscle. TnC from skeletal muscle has two classes of calcium-binding sites. The two carboxyl-terminal sites (sites 3 and 4) bind calcium with a high affinity (K Ca Ϸ 2 ϫ 10 7 M Ϫ1 ) and also bind magnesium competitively with a lower affinity (K Mg Ϸ 5 ϫ 10 3 M Ϫ1 ) . These two sites appear to have a structural role and do not contribute to calcium-dependent regulation (Zot and Potter, 1987). The two amino-terminal sites (sites 1 and 2) are calcium-specific, bind calcium with a low affinity (K Ca Ϸ 3.2 ϫ 10 5 M Ϫ1 ) (Potter and Gergely, 1975;, and are the sites that regulate contraction. TnC from cardiac muscle differs from skeletal muscle TnC most significantly in the amino-terminal half, where several critical amino acid substitutions have rendered site 1 incapable of binding calcium (Van Eerd and Takahashi, 1976; Leavis and Kraft, 1978). The calcium affinities of the two classes of binding sites in cTnC (Holroyde et al., 1980) are essentially the same as the corresponding ones for skeletal muscle TnC.
The x-ray crystallographic structures of TnC from chicken (Sundaralingam et al., 1985) and turkey skeletal muscle (Herzberg and James, 1985) show that the protein has an elongated, dumbbell-like shape in which the polypeptide is folded into two globular domains at the amino-and carboxyl-terminal ends. These domains are connected by a long ␣-helix, the middle of which is exposed to the solvent. The crystal structure provides a structural basis for understanding the potential conformational changes that may occur in the regulatory, amino-terminal domain of TnC when calcium binds to sites 1 and 2 (Herzberg et al., 1986;Strynadk and James, 1989). These putative conformational changes may involve movements of helices B and C relative to helices A and D. It has been suggested that these movements expose a segment of hydrophobic residues in the amino-terminal domain, which then become available for calcium-mediated interaction with TnI. Fluorescence (Wang and Cheung, 1986;Tao et al., 1990) and thermodynamic (Wang and Cheung, 1985;Cheung et al., 1987) studies have suggested that the interaction between TnC and TnI may serve as the Ca 2ϩ switch for calcium-dependent regulation of contraction.
Maximum tension in fast skeletal muscle is observed in 10 -13 ms after excitation and decays after an additional 40 -50 ms (Close, 1965). During a cycle of contraction and relaxation, calcium must bind to the regulatory sites and induce structural changes in both TnC and the other thin filament regulatory proteins within 10 -13 ms after excitation. Likewise, calcium dissociation from the regulatory sites and reversal of the calcium-induced conformational changes must occur within 40 -50 ms after excitation. These physiologic constraints place limits within which reversible Ca 2ϩ binding to TnC and subsequent conformational changes must occur. Several groups (Iio and Kondo, 1982;Rosenfeld and Taylor, 1985a;Johnson et al., 1994) reported the kinetics of calcium binding to both classes of sites in isolated skeletal TnC and in regulatory complexes containing TnC. Calcium binding to the low affinity sites of skeletal TnC has been reported to be diffusion controlled (Johnson et al., 1994). However, given the fact that most protein conformational changes occur more slowly than this, it would be expected that the kinetics of calcium binding to the regulatory sites should be saturable. Little information is available on the kinetic mechanism of calcium binding to the regulatory site of cardiac TnC, as most of the reported information is confined to the dissociation kinetics (Robertson et al., 1981(Robertson et al., , 1982. Cardiac TnC has two cysteine residues that can be readily alkylated by a variety of sulfhydryl-specific reagents. Mutants containing a single cysteine at either position 35 (C84S) or 84 (C35S) have been generated . The calciuminduced fluorescence change of IAANS-labeled mutant cTnC(C35S) has been shown to be coincident with calciumactivated force development Kerrick et al., 1992) and ATPase activity  in skinned cardiac muscle fibers. An advantage of using IAANS-labeled mutant cTnC(C35S) to study calcium-induced structural changes is that the fluorophore is located at a single site, which simplifies interpretation of the observed fluorescence change in terms of structural transitions.
In the present work, we have studied the kinetics of calcium binding to the single regulatory site of cTnC using a monocysteine mutant labeled with IAANS at Cys-84. The observed kinetics suggest a three-step binding model. Because the IAANS probe is strategically located, the observed kinetics of the fluorescence change also provide insight into the time course of structural changes induced by calcium binding. Saiki et al. (1985) was used to synthesize first strand cDNA from total RNA obtained from the left ventricle of rat heart (Chomczynski et al., 1987). The product of the first strand cDNA reaction was used in a PCR with a pair of appropriate primers. PCR products were purified using agarose gels and subsequently treated with restriction enzymes. The digested cDNAs were further purified by agarose gels and subcloned into a vector. The cDNA clone for cTnC was verified by sequence analysis and compared with the sequence of cDNA for cTnC (Parmacek and Leiden, 1989). The clone was ligated into the polylinker sites of the expression vector pET-24a(ϩ) (Novagen). The recombinant DNA was transformed into Escherichia coli strain BL21(DE3) lysogen (Novagen) containing a gene induced by IPTG to synthesize T7 RNA polymerase, which transcribed the inert DNA in the vector. Transformed cells were grown on LB agar plates in the presence of kanamycin. Colonies were screened for inserts by either PCR or digestion of restriction enzymes. After positive clones were identified, a culture of transformed BL21(DE3) containing insert was inoculated into LB medium containing kanamycin at 37°C. The expression of target protein was induced by adding IPTG to a final concentration of 1 mM. The induced culture was incubated for 3 more hours and harvested by centrifugation. The synthesized cTnC was purified from the induced cells according to methods provided by the supplier of the pET vector. cDNA for mutated cTnC was obtained by PCR site-directed mutagenesis (Higuchi et al., 1988). The same procedures used to clone and purify wild-type cDNA were followed for mutant cDNA, and mutant proteins were expressed and purified as described for wild-type protein. The expressed protein was purified on a DE52 column equilibrated in 6 M urea, 25 mM Tris at pH 8.0, 1 mM EGTA, and 1 mM DTT. cTnC or mutant was eluted with a salt gradient in the same buffer from 0.05 to 0.4 M KCl. The fractions containing the desired protein were pooled and dialyzed against the same buffer without urea. The dialyzed protein was adjusted to 5 mM in Ca 2ϩ and rechromatographed in a phenyl-Sepharose CL B4 column equilibrated in 50 mM Tris at pH 7.5, 0.3 M KCl, 1 mM DTT, and 20 mM EGTA. The purity of the eluted protein was monitored by SDS-polyacrylamide gel electrophoresis.

Preparation of Cardiac TnC Mutants-The method of
cTnC mutants were tested for their ability to support Ca 2ϩ regulation of force development using chemically skinned rabbit skeletal muscle fibers. Briefly, endogenous TnC was extracted from the fibers, and the TnC-depleted fibers were reconstituted with an exogenous TnC to be tested. Force was measured on the reconstituted fibers as a function of free Ca 2ϩ concentration as described previously (Martyn and Gordon, 1988).
Preparation of Labeled cTnC Mutants-Mutant cTnC(C35S) was first dialyzed against 0.1 mM DTT in a solution containing 0.2 M KCl, 30 mM Mops at pH 7.0, followed by a second dialysis in which DTT was omitted. The sulfhydryl-reduced protein was reacted with a 2-fold excess of IAANS in the presence of 6 M urea at 4°C for 10 h. The reaction was terminated with a 3-5-fold molar excess of DTT, and the solution was exhaustively dialyzed against 6 M urea, 30 mM Mops at pH 7.0, 0.2 M KCl, and 2 mM EGTA at 4°C to remove unreacted fluorophore and DTT. A further dialysis against the same buffer without urea was repeated three times. The concentration of the labeled protein was determined with either a turbidimetric tannin micromethod (Mejbaum-Katzenelenbogen and Dobryszycka, 1959) or the Bradford method (Bradford, 1976), and the amount of label covalently attached to the protein was determined by absorbance, using a molar extinction of 24,900 M Ϫ1 cm Ϫ1 at 325 nm . The degree of labeling was Ͼ0.9 mol of fluorophore/mol of protein. The same procedure was used to modify the sulfhydryl group of mutant cTnC(C84S).
Fluorescence Measurements-Steady-state fluorescence measurements were carried out at 20.0 Ϯ 0.1°C in an SLM 8000C spectrofluorometer, with both monochromators set at a 3-nm bandwidth. All measurements were made with the ratio mode. The emission spectra were corrected for variations of the response of the detector system with wavelengths. The Ca 2ϩ concentration was controlled by using EGTA. Free calcium concentrations were calculated by an algorithm from Dr. A. Fabiato (1988), using known stability constants of the chelator for proton and cations.
Kinetic Measurements-Transient kinetic measurements were performed on a Hi-Tech Scientific PQ/SF-53 stopped-flow spectrometer. The dead time of the instrument was determined to be 1.8 ms. The optical system consisted of a 150-watt high pressure xenon lamp with the excitation monochromator set at 325 nm. The excitation light was directed to the observation chamber by a quartz light guide, and the emitted light was isolated at a right angle by a cut-off filter (OG 380) and detected by an EMI9798QB photomultiplier.
In a typical binding experiment, one syringe contained labeled protein in 30 mM Mops at pH 7.0, 200 mM KCl, 3.0 mM MgCl 2 , and 5.0 M EGTA. The other syringe contained the same solution but without protein, plus different levels of total Ca 2ϩ . After mixing, the concentration of labeled protein was usually 1 M, and the total concentration of Ca 2ϩ was in the range of 0 -500 M. These conditions ensured that the two carboxyl-terminal high affinity sites were presaturated by Mg 2ϩ , and the single low affinity calcium-specific site remained calcium free prior to mixing. The free Ca 2ϩ level was controlled by the chelator. The control was quite adequate when the total Ca 2ϩ concentration was low. This is important because the rate data obtained at low levels of free Ca 2ϩ were used to calculate the bimolecular binding rate constant. At higher total Ca 2ϩ concentrations, there was some uncertainty in the calculated free Ca 2ϩ levels. As shown in Fig. 4A, the observed fast rate constant approached a limiting value at large free Ca 2ϩ concentration. Since it was this limiting rate constant that was important in our kinetic model, the uncertainty in free Ca 2ϩ concentration did not affect the analysis. For each experimental condition, 8 -10 tracings were obtained. The tracings were averaged, and the resultant tracing was fitted to a sum of exponentials by a nonlinear least squares method (Bevington, 1969). To measure dissociation of bound cations, a buffer containing either EGTA or EDTA was mixed with an equal volume of protein saturated with bound cations either at sites 3 and 4 or at all three sites.
Chemicals and Reagents-Restriction enzymes, T4 DNA ligase, and IPTG were obtained from Boehringer Mannheim, pfu DNA polymerase was from Stratagene Cloning Systems, and reverse transcriptase was from Invitrogen. Oligonucleotides used as primers were obtained from Integrated DNA Technologies, and radiolabeled dATP was from Amersham. Taq DNA polymerase, nucleotides, and dNTP were from Perkin Elmer and Boehringer Mannheim. Enzyme-grade urea and ammonium sulfate were purchased from Schwartz/Mann, and a standard CaCl 2 solution was obtained from Orion. IAANS was purchased from Molecular Probes. All other chemicals were of reagent grade or better.

RESULTS
Characterization of cTnC Mutants-Skinned skeletal muscle fibers depleted of endogenous TnC lose Ca 2ϩ regulation of force development. Calcium-activated force, however, can be restored upon reincorporation of TnC. This was the assay used to characterize cTnC mutants C35S and C84S. At pCa 4.0, the force was 92 restored, relative to intact fibers, upon reincorporation of native skeletal TnC and 86% restored upon reincorporation of wild-type cTnC. The force was 73% restored with mutant C35S and 62% restored with mutant C84S. These results indicate that the functional properties of mutant C35S are not significantly altered.
Fluorescence Properties of cTnC Mutants- Fig. 1 shows fluorescence emission spectra of mutant C35S labeled with IAANS at Cys-84 in the presence of Mg 2ϩ and different levels of free Ca 2ϩ . The presence of 2 mM Mg 2ϩ reduced the intensity by about 10%. With increasing [Ca 2ϩ ] over the range of pCa 6.1-4.2, the intensity progressively increased by a factor of 1.6, with a small blue spectral shift of 6 nm. A calcium titration curve of the labeled mutant cTnC is shown in the inset of Fig. 1. The half-maximum increase in fluorescence occurred at pCa 5.78 with a Hill coefficient of 1.2, corresponding to an apparent association constant of 6.1 ϫ 10 5 M Ϫ1 . Control experiments with native cTnC IAANS yielded a Ca 2ϩ titration curve very similar to that shown in Fig. 1, with the half-maximum change in fluorescence at pCa 5.68, corresponding to an apparent association constant of 4.8 ϫ 10 5 M Ϫ1 and a 1.8-fold increase in maximum fluorescence (results not shown). These results indicate that the monocysteine mutant labeled at Cys-84 has similar fluorescence properties to native cTnC labeled at both Cys-35 and Cys-84. The values of the apparent affinities, as determined by fluorescence, are also similar to those determined by equilibrium dialysis. Mutant C84S labeled with IAANS at Cys-35 showed a small increase (Ͻ30%) in fluorescence over the pCa range of 8 -6.7, followed by a decrease to the 10% level with further decrease in pCa. The insensitivity of labeled mutant C84S to Ca 2ϩ is in agreement with a previous report .
Kinetics of Ca 2ϩ Binding to the Regulatory Site of Mutant C35S-The results from the Ca 2ϩ titration indicate that the fluorescence increase in mutant C35S labeled at Cys-84 is suitable for monitoring the kinetics of Ca 2ϩ binding to the regulatory site. Since our concern here was to monitor the binding kinetics of the regulatory site, it was necessary to block sites 3 and 4 by preincubation of the protein with an excess of Mg 2ϩ prior to mixing with Ca 2ϩ . Two components with opposite amplitudes were observed after mixing magnesium-saturated IAANS-labeled cTnC(C35S) with saturating calcium. The first, consisting of a 1.6-fold fluorescence enhancement, was completed in Ͻ100 ms and corresponded to calcium binding to the regulatory site, while the second, consisting of a 10% fluorescence decrease, was observed over several seconds after the first component was completed and presumably was due to calcium displacement of magnesium from the high affinity sites. Thus, these two components were temporally well separated from each other. The following discussion will focus only on the first, positive amplitude phase. Fig. 2 shows kinetic tracings of this phase at increasing free Ca 2ϩ concentrations. At very low [Ca 2ϩ ] (Ͻ2 M), these tracings could be fitted with a single exponential, but above 2 M, fitting required two exponentials. Fig. 3 shows a typical tracing at [Ca 2ϩ ] Ͼ2 M. The monoexponential fit was only marginally adequate with a square ratio of 1.51, but the biexponential fit was considerably improved with a square ratio of 1.07. A comparison of the Inset, Ca 2ϩ titration of the labeled mutant carried out in the same buffer; ex ϭ 325 nm, and em ϭ 450 nm. The experimental points (filled circles) were analyzed by a nonlinear least squares procedure using the following equation: residual plots for the two fits also indicate an improvement of the biexponential fit over the monoexponential fit, particularly at early times. Two observed rate constants were obtained above 2 M calcium concentration. The fast rate constant, f , increased with increasing Ca 2ϩ concentration, while the slow rate constant ( s ) appeared to be insensitive to Ca 2ϩ concentration. This is illustrated in Fig. 4A. The amplitude of the fast phase varied from about 60 to 30% of the total signal above 2 M Ca 2ϩ . The ratio of the amplitude of the slow phase to that of the fast phase increased from less than 0.5 to a limiting value of about 2.5 with increasing [Ca 2ϩ ], and the shape of this plot of amplitude ratio (not shown) resembled that shown in Fig. 4A for f . The recovered limiting value of f was close to the dead time of the instrument, and some signal of the fast phase (about 15%) was lost at higher [Ca 2ϩ ]. This loss was reflected in the larger uncertainty for f as indicated in Fig. 4A but in no way limited the analysis. The data of f versus [Ca 2ϩ ] were fitted to Equation 2 with a maximum rate of 590 s Ϫ1 . The initial slope of this plot (Fig. 4B) defines an apparent second-order rate constant of 1.4 ϫ 10 8 M Ϫ1 s Ϫ1 for calcium binding to the low affinity site.
Kinetics of Calcium Dissociation from the Amino-terminal and Carboxyl-terminal Domains-The kinetics of calcium dissociation from the low affinity site of cTnC was measured by mixing EGTA with cTnC saturated with Ca 2ϩ in the presence of Mg 2ϩ . Upon mixing, there was a fast phase with a large negative amplitude (decreasing fluorescence), which was completed in about 20 ms at 20°C and 60 ms at 4°C (Fig. 5), followed by a slow phase with a small positive amplitude (increasing fluorescence), which was observed over several seconds (data not shown). Similar results were obtained in the absence of Mg 2ϩ . Both fast and slow phases each could be fitted adequately with a single exponential function. The rate constant for the fast phase was 102 s Ϫ1 at 4°C and 296 s Ϫ1 at 20°C, and the rate constant of the slow phase was 0.65 Ϯ 0.06 s Ϫ1 (data not shown). To establish whether this slow phase arose from dissociation of bound Ca 2ϩ at the two high affinity sites in the carboxyl-terminal domain, a dissociation experiment was performed by mixing EDTA with IAANS-labeled mutant C35S, which was saturated with Mg 2ϩ or Ca 2ϩ at sites 3 and 4. The resulting kinetic tracings are shown in Fig. 6. The tracing for Mg 2ϩ dissociation was adequately fitted to a single exponential function, with a rate constant of 0.83 s Ϫ1 . This experiment was also carried out under identical conditions over a short time interval. There was no evidence of a fast phase with a negative amplitude, indicating that the slow fluorescence transient in Fig. 6 was due to dissociation of bound Mg 2ϩ from the two carboxyl-terminal domain, high affinity sites. Also shown in Fig. 6 is a tracing obtained by mixing EDTA with labeled mutant C35S at pCa 7.0. At this pCa, sites 3 and 4 would be expected to be close to fully saturated with Ca 2ϩ , while site 2 would be Ca 2ϩ free. The increase in fluorescence also followed a single exponential function with a rate constant of 0.73 s Ϫ1 . A lag phase was apparent in both dissociation tracings. This could be due to different rates of Ca 2ϩ /Mg 2ϩ dissociation from the two high affinity sites (Rosenfeld and FIG. 3. A typical kinetic tracing fitted to a one-exponential and a two-exponential function. The tracing was obtained as described in Fig. 2. After mixing, [protein] ϭ 1 M and free [Ca 2ϩ ] ϭ 6.3 M. Panel A shows the best two-exponential fit (solid curve) with two rate constants, f ϭ 517 s Ϫ1 , and s ϭ 127 s Ϫ1 ; R 2 ϭ 1.07. Panel B is the residual plot of the two-exponential fit. Panel C shows the residual plot for the best one-exponential fit with a rate constant of 156 s Ϫ1 (the best fitted curve not shown); R 2 ϭ 1.51. Note the differences between the two residual plots, particularly at early times. Taylor, 1985a). The slower dissociation process might dominate the observed overall fluorescence change. Taken together, these results indicate that the dissociation of Mg 2ϩ or Ca 2ϩ from the carboxyl-terminal domain sites occurs with slow but very comparable rates. These rates were comparable to the rate (0.65 s Ϫ1 ) of the slow phase with positive amplitude observed upon mixing EGTA with labeled mutant fully saturated with Ca 2ϩ in the presence of Mg 2ϩ . Thus, Ca 2ϩ and Mg 2ϩ dissociated from the carboxyl-terminal domain sites with rates that were at least two orders of magnitude slower than dissociation of Ca 2ϩ from the regulatory site.
Effect of Temperature on the Kinetics of Calcium Binding to the Regulatory Site-The experiment described for the binding of Ca 2ϩ to the regulatory site was repeated at several temperatures and at a saturating level of Ca 2ϩ . The observed rate constants of the fast and slow phases are plotted versus reciprocal temperature, as shown in Fig. 7. The activation energy for the fast phase was 7.2 Ϯ 0.4 kJ/mol and that for the slow phase was 26 Ϯ 3 kJ/mol.

DISCUSSION
In this paper, we have studied the kinetics of the binding of Ca 2ϩ to the single regulatory site of cardiac TnC. Native cTnC labeled with IAANS at both Cys-35 and Cys-84 has been extensively used to investigate the equilibrium properties of Ca 2ϩ binding to the single regulatory site of the isolated protein and of the protein reconstituted into myofibrils and skinned muscle fibers. Because the label is located at two different sites that are far separated in the x-ray structure of TnC, the question arises as to whether the labels at both sites sense the same events. Using bacterially produced mutants containing a single cysteine residue, recent studies have shown that the fluorescence of IAANS attached to Cys-84 in mutant C35S tracks Ca 2ϩ binding to the single regulatory site and produces Ca 2ϩ titration curves that superimpose on those for the Ca 2ϩ activation of ATPase and force development in skinned muscle fibers . As will be further elaborated below, Cys-84 is strategically located in the amino-terminal domain, and a probe linked to this position might sense Ca 2ϩ -activated conformational changes involving specific helices.
To focus on the kinetics of Ca 2ϩ binding to the regulatory site, the binding kinetics were studied in the presence of a large excess of Mg 2ϩ so that the two carboxyl-terminal sites were occupied throughout the binding reaction. Since the dissociation of bound Mg 2ϩ is at least two orders of magnitude slower than the binding of Ca 2ϩ to the amino-terminal domain, this protocol enables us to follow the time course of the binding reaction directly. The kinetic transients for calcium binding to the low affinity site were biexponential at high Ca 2ϩ concentration. The rate constant of the fast phase ( f ) varies with increasing [Ca 2ϩ ] in a hyperbolic manner, whereas s is insensitive to [Ca 2ϩ ]. We propose a three-step mechanism to account for these kinetic data: The initial binding in the bimolecular step is assumed to be a rapid equilibrium, which is characterized by K o , followed by two sequential first-order transitions in which fluorescence enhancement occurs. In this scheme, if k 1 ϩ k Ϫ1 Ͼ Ͼ k 2 ϩ k Ϫ2 , the normalized fluorescence transient can be described by two exponential terms (Bernasconi, 1976). The rate constants from the fluorescence transient are identified with f and s . The relationships of the observed rate constants to the kinetic parameters in Scheme I are as follows: The initial slope of a plot of f versus [Ca 2ϩ ] (Fig. 4)  and k Ϫ2 is approximately 100 s Ϫ1 . While their individual values cannot be directly extracted from the present kinetic data, they can be estimated from the experimental value of the equilibrium constant K eq ϭ 3.2 ϫ 10 5 M Ϫ1 obtained from the Ca 2ϩ titration at the same temperature: K eq ϭ K o (k 1 /k Ϫ1 )(k 2 / k Ϫ2 ). This yields k 2 ϭ 20 s Ϫ1 and k Ϫ2 ϭ 80 s Ϫ1 . These parameters are listed in Table I. Alternately, Scheme I can be treated as described previously (Benson, 1960), and similar conclusions are obtained. The present model is the first kinetic mechanism for cardiac TnC using any preparation of the protein.
The kinetic data indicate that step 1 is thermodynamically favorable with an equilibrium constant of about 4, but step 2 is unfavorable. This is consistent with a 3.5-fold higher activation for the slow phase. Equilibrium studies have shown that the K eq for calcium binding to the regulatory site of a TnC⅐TnI complex is considerably larger than that for isolated TnC. If the same kinetic scheme holds for the complex, this enhanced affinity must arise from increases in the equilibrium constants of one or all steps of the model. Since step 2 is unfavorable with isolated TnC, this step may become more favorable in the binary protein complex. This possibility can be tested with either the cTnC⅐cTnI complex or reconstituted troponin.
The dissociation kinetics of Ca 2ϩ from the regulatory site are monoexponential at both 4 and 20°C.
Step 1 is thermodynamically favorable, but step 2 is unfavorable with an equilibrium constant of 0.25. The observed initial fluorescence change in dissociation kinetics is expected to arise from the dominant species, (CaTnC)*, with only a small contribution from (CaTnC)**. Thus, the observed dissociation rate constant of 102 s Ϫ1 largely reflects k Ϫ1 . Furthermore, the dissociation rate constant for the (CaTnC)** state is predicted to be k Ϫ1 k Ϫ2 /(k Ϫ1 ϩ k 2 ϩ k Ϫ2 ), which is approximately 50 -60 s Ϫ1 (Trybus and Taylor, 1982). It would be unlikely that a small amplitude phase in the dissociation transient occurring at 50 -60 s Ϫ1 could be resolved from the main phase, occurring at 117 s Ϫ1 determined from the intercept in Fig. 4B.
The x-ray structure of skeletal TnC shows that in the aminoterminal domain Cys-84 is located on helix D and is surrounded by helices B and C. The calcium-saturated structural model of the amino-terminal domain suggests that Ca 2ϩ binding to the two amino-terminal domain sites induces movements of helices B and C relative to helices A and D, such that two EF hands are formed. These movements result in a more "open" conformation of the amino-terminal domain (Strynadk and James, 1989) and expose a hydrophobic patch on helix B. This exposed patch may be a site for calcium-mediated interactions with troponin I. In this model, helix D in the 4Ca state is stationary relative to the 2Ca state. A recent study of cTnC suggests similar helix movements in the amino-terminal domain when the single regulatory site is occupied (Ovsak and Taskinen, 1991). These models suggest that the observed Ca 2ϩ -mediated fluorescence enhancement of IAANS attached to Cys-84 on helix D may result from movements of helices B and C away from helix D. A recent study (Dong and Cheung, 1995) with native cTnC, which was selectively modified at Cys-84 with fluorescent probes, showed that the Ca 2ϩ -mediated enhancement of probe fluorescence was related to strong internal quenching by interactions of a dipolar nature in the apo and 2Mg states. This quenching is reduced or eliminated upon reorientation of helices B and C from helix D. This lends further support to the interpretation that the two first-order transitions that lead to fluorescence enhancement of the IAANS probe may reflect these helix movements. It is not known whether the movements actually occur in two steps, but it is unlikely that they move independently of each other because only the first fluorescence transition is Ca 2ϩ dependent. At a saturating level of Ca 2ϩ , these transitions would take about 5 ms to reach a 95% completion. This rate and the observed dissociation rate are likely overestimates of the rates that would occur in muscle. It is well known that both the time-to-peak-tension after excitation and the relaxation time can vary widely with temperature, and they are species-dependent. These time windows are generally longer in cardiac muscle than skeletal muscle, but structural transitions occurring in 5 ms in isolated cTnC may be too fast to be compatible with physiologic events. However, the Ca 2ϩ on-and off-rates in reconstituted troponin are expected to be slower, as the Ca 2ϩ dissociation rate from the regulatory site in the cTnC IAANS ⅐cTnI complex is only 21 s Ϫ1 at 20°C (Robertson et al., 1982), a factor of 10 slower than with cTnC determined in the present work. The on-rate in reconstituted troponin or in the regulated thin filament can also be expected to be significantly slower (Robertson et al., 1981). If tension transients follow Ca 2ϩ transients, this anticipated reduction in the rates of reversible Ca 2ϩ binding should still be fast enough to support contraction.
In contrast to cardiac TnC, several studies on the kinetics of Ca 2ϩ binding to skeletal TnC have been reported. The early studies of Iio and Kondo (1980a, 1980b, based on tyro- 1.4 ϫ 10 8 2.95 ϫ 10 5 470 117 20 80 3.2 ϫ 10 5 sine fluorescence, proposed a rapid diffusion-controlled binding step followed by conformational changes. Taylor (1985a, 1985b) investigated the binding of Ca 2ϩ to both classes of sites with isolated skeletal TnC and reconstituted troponin, using a fluorescently labeled preparation. A two-step binding mechanism with a second-order rate constant of 1.3 ϫ 10 6 M Ϫ1 s Ϫ1 was proposed for Ca 2ϩ binding to the high affinity sites. This value is about 100 times slower than that for Ca 2ϩ binding to the low affinity site in cTnC determined in the present work. Taylor (1985a, 1985b) also reported very fast Ca 2ϩ binding rates to the regulatory sites at low calcium concentration, and the rates at high [Ca 2ϩ ] became too large to be measured. It could not be determined whether the rate reached a maximum, and the binding data did not establish whether the binding kinetics could be described by a two-step or a three-step model. However, the rates increased linearly with increasing [Ca 2ϩ ] at low concentration, and an apparent second-order binding rate constant of 5 ϫ 10 7 M Ϫ1 s Ϫ1 was obtained. This is at least one order of magnitude larger than the corresponding rate at the high affinity sites determined using the same protein preparation. More recently, Johnson et al. (1994) reported the kinetics of Ca 2ϩ binding to the two regulatory sites with a tryptophan mutant of skeletal TnC(F29W). They observed monoexponential kinetic traces over a narrow range of [Ca 2ϩ ] (0 -6 M) and assumed a simple one-step, diffusion-controlled mechanism for the binding of Ca 2ϩ to the two regulatory sites. Since no data were reported at higher Ca 2ϩ concentrations, it is not known whether the observed rate would have saturated at high [Ca 2ϩ ]. Their apparent second-order binding rate constant is in the range of 1 ϫ 10 8 M Ϫ1 s Ϫ1 to 2 ϫ 10 8 M Ϫ1 s Ϫ1 , essentially the same as that reported here for cardiac TnC (1.4 ϫ 10 8 M Ϫ1 s Ϫ1 ). It appears that the Ca 2ϩ binding rate at the regulatory sites is one to two orders of magnitude faster than that at the high affinity sites, regardless of isoform. The previous interpretation of calcium binding to the regulatory sites as a simple diffusion-controlled process (Johnson et al., 1989;1994), however, is not consistent with the present evidence. The reporter group of the skeletal TnC mutant is Trp-29 located on helix A immediately adjacent to the amino-terminal end of the Ca 2ϩ -binding loop 1, whereas in the present work the reporter group is located on helix D. The different locations of the two probes may be a reason why first-order transitions arising from activator Ca 2ϩ -mediated movements of helices B and C were not sensed with mutant F29W.
In summary, we have used the fluorescence of an extrinsic probe linked to the single cysteine residue on helix D of a monocysteine mutant to investigate the kinetics of Ca 2ϩ binding to cardiac TnC. The dissociation of Ca 2ϩ from the regulatory site is two orders of magnitude faster than the dissociation of Ca 2ϩ or Mg 2ϩ from the two carboxyl-terminal domain sites. The kinetics of Ca 2ϩ binding to the regulatory sites is consistent with a three-step mechanism in which the bimolecular binding step is in rapid equilibrium and is followed by two sequential first-order transitions.