Designing Calcium-sensitizing Mutations in the Regulatory Domain of Cardiac Troponin C*

Cardiac troponin C belongs to the EF-hand superfamily of calcium-binding proteins and plays an essential role in the regulation of muscle contraction and relaxation. To follow calcium binding and exchange with the regulatory N-terminal domain (N-domain) of human cardiac troponin C, we substituted Phe at position 27 with Trp, making a fluorescent cardiac troponin CF27W. Trp27 accurately reported the kinetics of calcium association and dissociation of the N-domain of cardiac troponin CF27W. To sensitize the N-domain of cardiac troponin CF27W to calcium, we individually substituted the hydrophobic residues Phe20, Val44, Met45, Leu48, and Met81 with polar Gln. These mutations were designed to increase the calcium affinity of the N-domain of cardiac troponin C by facilitating the movement of helices B and C (BC unit) away from helices N, A, and D (NAD unit). As anticipated, these selected hydrophobic residue substitutions increased the calcium affinity of the regulatory domain of cardiac troponin CF27W ∼2.1–15.2-fold. Surprisingly, the increased calcium affinity caused by the hydrophobic residue substitutions was largely due to faster calcium association rates (2.6–8.7-fold faster) rather than to slower calcium dissociation rates (1.2–2.9-fold slower). The regulatory N-domains of cardiac troponin CF27W and its mutants were also able to bind magnesium competitively and with physiologically relevant affinities (1.2–2.7 mm). The design of calcium-sensitizing cardiac troponin C mutants presented in this work enhances the understanding of how to control cation binding properties of EF-hand proteins and ultimately their structure and physiological function.

Ca 2ϩ buffering or transport (for review, see Ref. 16). Thus, cTnC is an unusual Ca 2ϩ sensor, because Ca 2ϩ binding alone to its regulatory N-domain does not cause large structural rearrangements. However, binding of the cardiac TnI peptide (encompassing residues 147-163) leads to the structural opening of the Ca 2ϩ -bound N-domain of cTnC (17).
Congestive heart failure can be associated with desensitization of the myocardium to Ca 2ϩ and depressed cardiac contractility (for review, see Ref. 18). Drugs known as "Ca 2ϩ sensitizers" increase the Ca 2ϩ sensitivity of the myocardial contractile apparatus without elevation of intracellular Ca 2ϩ (for review, see Refs. 19 -21). Because cTnC plays an essential role in the regulation of cardiac muscle mechanics, it represents an attractive target for therapeutic Ca 2ϩ -sensitizing compounds. However, there are no available drugs that selectively bind cTnC and increase its Ca 2ϩ binding affinity. Ideally, Ca 2ϩ -sensitizing agents should not decrease the rate of Ca 2ϩ dissociation from the regulatory domain of cTnC, because impaired relaxation would be an undesirable consequence of Ca 2ϩ sensitization. Understanding the factors controlling Ca 2ϩ binding and exchange with cTnC could lead to the rational design of drugs useful in the treatment of heart disease.
The main objective of this work was to design mutations that sensitize the regulatory N-domain of cTnC to Ca 2ϩ . Previous studies demonstrated that mutation of a single hydrophobic residue, which does not directly ligate Ca 2ϩ , can either dramatically increase or decrease Ca 2ϩ affinity, depending on the location of the residue within the tertiary structure of the EF-hand protein (22)(23)(24)(25). Ca 2ϩ binding to the second regulatory EF-hand of cTnC, its mutants, and its isoforms has been studied using the Phe 27 3 Trp substitution immediately preceding the first defunct Ca 2ϩ -binding loop (26 -29). We have utilized this substitution and introduced five additional individual mutations (based on their location within the tertiary structure of the protein) designed to increase the Ca 2ϩ sensitivity of the regulatory domain of cTnC.

EXPERIMENTAL PROCEDURES
Materials-Phenyl-Sepharose CL-4B and EGTA were purchased from Sigma. Quin-2 was purchased from Calbiochem (La Jolla, CA). All other chemicals were of analytical grade.
Protein Mutagenesis and Purification-The human cTnC pET3a plasmid was a generous gift from Dr. Lawrence B. Smillie (University of Alberta, Edmonton, Canada). cTnC F27W and its mutants were constructed from the cTnC plasmid by primer-based site-directed mutagenesis using Stratagene (La Jolla, CA) QuikChange site-directed mutagenesis kit. All of the mutations were confirmed by DNA sequence analysis. The plasmids for cTnC F27W and mutants were transformed into Escherichia coli BL21(DE3)pLysS cells (Novagen). Expression and purification of cTnC F27W and mutants were carried out as previously described for sTnC (25). The purified cTnC F27W and mutants were dialyzed against three exchanges of 4 liters of 10 mM MOPS, 90 mM KCl, 0.5 mM DTT, pH 7.0, at 4°C. Protein concentration was calculated by absorbance at 280 nm using an extinction coefficient of 9770 cm Ϫ1 M Ϫ1 . The purity of the proteins was checked by SDS-PAGE and was determined to be 98 Ϯ 1%, using Labworks 4.0 Software (UVP Bioimaging Systems, St. Louis Park, MN).
Determination of Ca 2ϩ Affinities-All of the steady state fluorescence measurements were performed using a PerkinElmer LS5 spectrofluorimeter at 15°C. Trp fluorescence was excited at 285 nm and monitored at 345 nm as microliter amounts of CaCl 2 were added to 1 ml of each cTnC F27W mutant (0.6 M) in 200 mM MOPS (to prevent pH changes upon the addition of Ca 2ϩ ), 90 mM KCl, 2 mM EGTA, 1 mM DTT, pH 7.0, in the absence or presence of 3 mM MgCl 2 , at 15°C. The [Ca 2ϩ ] free was calculated using the computer program EGCA02 developed by Robertson and Potter (30). The Ca 2ϩ affinities were reported as a dissociation constant, K d (Ca) , representing a mean of at least three separate titrations Ϯ S.D. The data were fit with a logistic sigmoid function (mathematically equivalent to the Hill equation), as previously described (25).
Determination of Mg 2ϩ Affinities-Two methods were utilized to determine the Mg 2ϩ binding affinities of the regulatory domain of cTnC F27W and its mutants. In the first method, Mg 2ϩ binding affinities (K d(Mg) ) were calculated from a decrease in the apparent Ca 2ϩ affinities caused by 3 mM Mg 2ϩ , using the equation K d (Mg) ϭ [Mg 2ϩ ]/(K d(Caapp) / K d (Ca) Ϫ 1), where K d (Ca) and K d (Caapp) are the Ca 2ϩ affinities in the absence and presence of 3 mM Mg 2ϩ , respectively (determined as described above). In the second method, Trp fluorescence was excited at 285 nm and monitored at 345 nm as microliter amounts of MgCl 2 were added to 1 ml of each cTnC F27W mutant (0.6 M) in 200 mM MOPS, 90 mM KCl, 2 mM EGTA, 1 mM DTT, pH 7.0, and 3.98 -10 M [Ca 2ϩ ] free (i.e. [Ca 2ϩ ] required to achieve at least 60% saturation of the N-domain of each individual protein) at 15°C. The Mg 2ϩ affinities were calculated using the equation is the negative logarithm of [Mg 2ϩ ] free producing half-maximal fluorescence.
Determination of Ca 2ϩ Dissociation Rates-Ca 2ϩ dissociation rates (k off(Ca) ) were measured using an Applied Photophysics Ltd. (Leatherhead, UK) model SX.18 MV stopped-flow instrument with a dead time of 1.6 ms at 15°C. The samples were excited using a 150-W xenon arc source. The Trp emission was monitored through a UV-transmitting black glass filter (UG1) from Oriel (Stratford, CT). The data were fit using a program (by P. J. King, Applied Photophysics Ltd.) that utilizes the nonlinear Levenberg-Marquardt algorithm. Each k off(Ca) value represents an average of at least three separate experiments, each averaging at least five traces fit with a single exponential equation (variance Ͻ 8 ϫ 10 Ϫ4 ). k off(Ca) was also directly measured using the fluorescent Ca 2ϩ chelator Quin-2. Quin-2 was excited at 330 nm with its emission monitored through a 510-nm broad band pass interference filter (Oriel (Stratford, CT)). Each k off(Ca) value represents an average of at least three separate experiments, each averaging at least five traces fit with a single or double exponential equation, depending on the time frame of data collection, because Quin-2 reports Ca 2ϩ dissociation rates from both the N-and C-domain of cTnC F27W proteins (variance Ͻ 9 ϫ 10 Ϫ5 ). Fitting the data with a single or double exponential equation gave similar results for the rate of Ca 2ϩ dissociation from the N-domain of cTnC F27W proteins within appropriately chosen time frames. The buffer used in the stopped-flow experiments was 10 mM MOPS, 90 mM KCl, 1 mM DTT, pH 7.0, in the absence or presence of 3 mM MgCl 2 .
Calculation of Ca 2ϩ Association Rates-The Ca 2ϩ association rates (k on(Ca) ) were calculated using the relationship k on(Ca) ϭ k off(Ca) /K d(Ca) , where k off(Ca) represents the release of a single Ca 2ϩ ion, and K d (Ca) represents the binding event of a single Ca 2ϩ ion to the N-domain of cTnC, as previously described (25).
Exposing cTnC F27W and Its Mutants to Artificial Ca 2ϩ Transients-ACTs of various amplitudes and durations can be generated in a stopped-flow apparatus by rapidly mixing one solution containing a known concentration of Ca 2ϩ against another solution containing a known concentration of Ca 2ϩ chelator (31). This technique can be used to estimate the Ca 2ϩ association rate to Ca 2ϩ -binding proteins/enzymes (31). The buffer used in the ACT experiments was 10 mM MOPS, 90 mM KCl, 1 mM DTT, 3 mM MgCl 2 , pH 7.0, at 15°C. ACTs were generated by rapidly mixing each cTnC F27W protein (2 M) ϩ 1 mM EGTA in buffer against buffer with increasing [Ca 2ϩ ]. As the [Ca 2ϩ ] was increased from 5 to 750 M (before mixing), the duration of the ACTs increased from 0.7 to 1.0 ms (as determined by computer simulations described below), whereas the amplitude (one-half of [Ca 2ϩ ] before mixing) of the ACTs increased 150-fold. Before mixing, the N-domain of each cTnC F27W protein was in the apo state. After mixing, the N-domain of each cTnC F27W  mutants from which k off(Mg) was too rapid to be measured, it was assumed to be 3000 s Ϫ1 . Simulations using the experimentally determined K d(Mg) for each cTnC F27W protein indicated that k off(Mg) could be increased 10-fold or decreased to a measurable rate (Յ1500 s Ϫ1 ) with negligible effects on the transient occupancy (after the mixing was complete). All of the other steady state and kinetic parameters were experimentally determined as described under "Results" and as summarized in Tables II and III. Each ACT was independently simulated by fluctuating only the k on(Ca) for each cTnC F27W protein, until the maximal and minimal values of k on(Ca) were found that matched the standard deviations from the mean transient occupancy, experimentally determined as described above. Each simulated k on(Ca) from the different ACTs was then used to calculate the average k on(Ca) for the N-domains of the cTnC F27W proteins.
Calculation of Solvent Accessibilities-The protein analysis software MOLMOL (34) was used to calculate the percentage of solvent-accessible surface area (SA) Ϯ S.D. for each of the five selected hydrophobic residues in the N-domain fragment of human cTnC (Table I). The average SA for each native residue was tabulated from the 40 apo or 40 Ca 2ϩ -bound NMR structures of the N-domain fragment (residues 1-89) of human cTnC available from the Protein Data Bank (1SPY and 1AP4 (15)). The percentage of SA for each native residue was calculated as the SA of the residue in the context of the protein structure divided by the SA of this residue extracted from the protein structure, with the resulting quotient multiplied by 100. F27W and Its Mutants in the Absence and Presence of 3 mM Mg 2ϩ -cTnC F27W undergoes an 1.44 Ϯ 0.04-fold increase in Trp fluorescence (at 345 nm) upon Ca 2ϩ binding to its N-terminal regulatory site (data not shown). To design cTnC F27W mutants with increased Ca 2ϩ sensitivity of the regulatory domain, we individually substituted Phe 20 , Val 44 , Met 45 , Leu 48 , and Met 81 (selected based on their location within the tertiary structure of the protein) with polar Gln (Fig. 1). The Ca 2ϩ -induced increases in Trp fluorescence, which occur when Ca 2ϩ binds to the regulatory domain of cTnC F27W , F20QcTnC F27W , V44QcTnC F27W , M45QcTnC F27W , L48QcTnC F27W , and M81QcTnC F27W , are shown in Fig. 2A (absence of Mg 2ϩ , summary in Table I) Table II). In the absence of Mg 2ϩ ( Fig. 2A) (Fig. 2B), cTnC F27W exhibited a halfmaximal Ca 2ϩ -dependent increase in its Trp fluorescence at 24 Ϯ 1 M. Thus, 3 mM Mg 2ϩ produced 3.4-fold decrease in the Ca 2ϩ sensitivity of the regulatory domain of cTnC F27W . Assuming competitive Mg 2ϩ binding, the K d(Mg) of the regulatory domain of cTnC F27W was calculated to be 1.2 Ϯ 0.2 mM. In the presence of 3 mM Mg 2ϩ , the Ca 2ϩ affinities for the mutants ranged from 9.5 Ϯ 0.9 M for F20QcTnC F27W to 1.62 Ϯ 0.06 M for V44QcTnC F27W . Thus, similar to the results in the absence of Mg 2ϩ , introduction of polar Gln at position 20, 44, 45, 48, or 81 produced ϳ2.5-14.8-fold increases in the Ca 2ϩ affinity of the regulatory domain of cTnC F27W , in the presence of 3 mM Mg 2ϩ . Again, assuming competitive Mg 2ϩ binding, the K d(Mg) for the mutants ranged from 1.2 Ϯ 0.1 mM for V44QcTnC F27W to 2.7 Ϯ 0.3 mM for M45QcTnC F27W (summary in Table III). Thus, selected hydrophobic residue substitutions in the regulatory domain of cTnC F27W dramatically increase Ca 2ϩ but not Mg 2ϩ affinity. The Hill coefficients for all the Ca 2ϩ titrations (in the absence or presence of 3 mM Mg 2ϩ ) were between 0.76 and 1.3, consistent with binding of a single Ca 2ϩ ion to the N-domain of cTnC F27W and its mutants (summary in Tables I and II).

Measurement of the Ca 2ϩ Binding Affinities for cTnC
Second Method for Measuring the Mg 2ϩ Binding Affinities for the cTnC F27W and Mutants- Fig. 2C shows that addition of Mg 2ϩ to cTnC F27W and its mutants (greater than 60% saturated with Ca 2ϩ ) reversed the Ca 2ϩ -induced increase in Trp fluorescence in a concentration-dependent matter. Knowing K d(Ca) and assuming competitive Mg 2ϩ binding, the K d(Mg) for cTnC F27W was calculated to be 1.9 Ϯ 0.4 mM. The calculated Mg 2ϩ affinities for the mutants ranged from 2.4 Ϯ 0.7 mM for V44QcTnC F27W to 3.5 Ϯ 0.5 mM for M45QcTnC F27W (summary in Table III). These values are in excellent agreement with the Mg 2ϩ affinities calculated from the shifts in Ca 2ϩ sensitivities, as described in the previous paragraph. Thus, using two differ- The black circles represent the hydrophobic residues that were individually mutated to Gln, excluding Trp 27 . All of the experimental data were obtained using full-length cTnC F27W , but the C-domain is not shown for the sake of simplicity. ent methods, the selected hydrophobic residue substitutions had only marginal effect on the Mg 2ϩ affinity of the regulatory site of cTnC F27W .

Measurements of Ca 2ϩ Dissociation Rates Using Trp and Quin-2 Fluorescence in the Absence and Presence of 3 mM
Mg 2ϩ -Fluorescence stopped-flow measurements were conducted to determine the rate of Ca 2ϩ dissociation from the regulatory domain of TnC F27W and its mutants. Fig. 3A shows the time course of the EGTA-induced decreases in Trp fluorescence as Ca 2ϩ was removed from cTnC F27W , F20QcTnC F27W , V44QcTnC F27W , M45QcTnC F27W , L48QcTnC F27W , and M81-QcTnC F27W in the presence of 3 mM Mg 2ϩ . At 15°C, excess EGTA removed Ca 2ϩ from cTnC F27W at 1263 Ϯ 188 s Ϫ1 . For the mutants, the Ca 2ϩ dissociation rates ranged from 1118 Ϯ 113 s Ϫ1 for F20QcTnC F27W to 473 Ϯ 14 s Ϫ1 for V44QcTnC F27W (summary in Table II). Thus, substitution of hydrophobic residues in position 20, 44, 45, 48, or 81 with polar Gln produced only ϳ1.1-2.7-fold decreases in the rate of Ca 2ϩ dissociation from the regulatory site of cTnC F27W . Similar Ca 2ϩ dissociation rates were measured in the absence of Mg 2ϩ (data not shown; summary in Table I). These results were consistent with the Ca 2ϩ dissociation rate from the regulatory domain of sTnC F29W not being affected by Mg 2ϩ (8), again indicative of competitive binding of Mg 2ϩ to the regulatory site of cTnC F27W .
To verify that the Trp signal changes were accurately reporting the true Ca 2ϩ dissociation rates and not a slower or faster structural change, Ca 2ϩ dissociation rates were also measured using the fluorescent Ca 2ϩ chelator Quin-2. Quin-2 fluorescence reported Ca 2ϩ dissociation from both the N-and Cdomains of cTnC F27W . However, the Ca 2ϩ dissociation rates from the N-domain site of cTnC F27W and its mutants were easily distinguished from the Ca 2ϩ dissociation rates from the C-domain sites (on average 0.772 Ϯ 0.007s Ϫ1 ) because the latter rates were Ͼ570-fold slower. Fig. 3B shows the time course of the increases in Quin-2 fluorescence as Ca 2ϩ dissociated from the N-domain site of cTnC F27W , F20QcTnC F27W , V44QcTnC F27W , M45QcTnC F27W , L48QcTnC F27W , and M81-QcTnC F27W at Ͼ1000 s Ϫ1 , Ͼ1000 s Ϫ1 , 444 Ϯ 28 s Ϫ1 , 691 Ϯ 64 s Ϫ1 , 476 Ϯ 22 s Ϫ1 , and 818 Ϯ 77 s Ϫ1 , respectively (in the presence of 3 mM Mg 2ϩ ; summary in Table II). Fitting the traces with a double exponential over longer times (to account for the Ca 2ϩ dissociation from the C-domain sites) gave similar N-domain rates (data not shown). Rates of Ca 2ϩ dissociation from cTnC F27W and F20QcTnC F27W were too fast to reliably measure using Quin-2 fluorescence at 15°C, so they were measured at 4°C (Fig. 3C). At 4°C, Quin-2 reported the rate of Ca 2ϩ dissociation from the N-domain of cTnC F27W at 1015 Ϯ 297 s Ϫ1 . This rate is in good agreement with the previously reported rate of Ca 2ϩ dissociation from the unlabeled chicken cTnC (772 Ϯ 10 s Ϫ1 ), which was also obtained following the fluorescence of Quin-2 at 4°C (35). In addition, the rates of Ca 2ϩ dissociation from cTnC F27W and F20QcTnC F27W measured using Quin-2 fluorescence were nearly identical to the rates measured following the EGTA-induced Trp changes at 4°C (Fig. 3C). The rates of Ca 2ϩ dissociation from V44QcTnC F27W , M45QcTnC F27W , L48QcTnC F27W , and M81QcTnC F27W measured using Quin-2 fluorescence were also nearly identical to the rates following EGTA-induced Trp changes at 4°C (data not shown; summary in Table II  fore, Trp 27 accurately reported the rate of Ca 2ϩ dissociation from the regulatory site of TnC F27W and its mutants. Measuring the rates of EGTA-induced Ca 2ϩ dissociation at 15 and 4°C enabled us to calculate the temperature coefficient Q 10 for cTnC F27W and its mutants (summary in Table I). cTnC F27W exhibited a Q 10 of 1.2 Ϯ 0.2, whereas for the rest of the mutants, Q 10 ranged from 1.
Calculations of Ca 2ϩ Association Rates to the N-domain Site of TnC F27W and Its Mutants-Knowing the affinity of Ca 2ϩ (K d(Ca) ) from the Ca 2ϩ dependence of the increase in Trp 27 fluorescence, and the rate of Ca 2ϩ dissociation (k off(Ca) ), we could calculate the rate of Ca 2ϩ association (k on(Ca) ) using the simple equation k on(Ca) ϭ k off(Ca) /K d (Ca) . The calculated value of k on(Ca) for cTnC F27W  is too fast to allow the experimental measurements of k on(Ca) using the standard pseudo-first order method in a stopped-flow apparatus (6), we estimated k on(Ca) by subjecting cTnC F27W and its mutants to ACTs of increasing duration and amplitude (8). The measurements were conducted in the presence of 3 or 12 mM Mg 2ϩ , to ensure complete Mg 2ϩ occupation of the C-domain sites. We were unable to adequately simulate the data obtained in the absence of Mg 2ϩ , possibly because of the interference of the C-domain sites through interdomain interactions (data not shown). However, because Mg 2ϩ binding to the regulatory domain of cTnC F27W or its mutants is competitive, the simulation of the experimental data obtained in the presence of Mg 2ϩ estimates the true Ca 2ϩ association rate, independent of [Mg 2ϩ ]. Fig. 4A shows the time course of Ca 2ϩ binding and subsequent dissociation from the N-domain site of cTnC F27W subjected to ACTs of increasing duration and amplitude at 15°C in the presence of 3 mM Mg 2ϩ . When 10 M Ca 2ϩ was mixed with an equal volume of 2 M TnC F27W in the presence of 1 mM EGTA, Ca 2ϩ bound and transiently occupied 5 Ϯ 1% (at 2 ms) of the regulatory site within cTnC F27W . Because Ca 2ϩ was subsequently chelated by EGTA and removed from cTnC F27W , the fluorescence decayed back to its Ca 2ϩ -free fluorescence level. As the [Ca 2ϩ ] was successively increased to 50, 100, 250, 500, 750, and 5000 M (Fig. 4A), Ca 2ϩ transiently occupied 17 Ϯ 1 (at 2 ms), 29 Ϯ 3 (at 2 ms), 44 Ϯ 4 (at 2.8 ms), 70 Ϯ 3 (at 2.5 ms), 81 Ϯ 2 (at 2.5 ms), and 100% of the N-terminal regulatory site of TnC F27W , respectively. Because the percentage of occupancy of Ca 2ϩ bound to the N-domain site of cTnC F27W during an ACT of given duration and amplitude is directly related to the Ca 2ϩ association a Mean values are utilized for the simulations. b The actual Mg 2ϩ dissociation rates were too fast to be accurately measured and were thus assumed to be 3000 s Ϫ1 for simulation purposes, which was then used to calculate the k on(Mg) . c cTnC F27W mutant Mg 2ϩ dissociation rates were measured by the rate of Ca 2ϩ displacement of a Mg 2ϩ -saturated N-domain site as described by Davis et al. (8). rate to this site, we were able to estimate the k on(Ca) to the regulatory site of cTnC F27W . Each individual trace was simulated using the computer program KSIM, which fixed the Ca 2ϩ dissociation rate from cTnC F27W at 1263 s Ϫ1 and let the Ca 2ϩ association rate vary until the modeled transient occupancy approximated the experimental data, taking into account the experimental error. The kinetic parameters used in the simulations are summarized under "Experimental Procedures " (Tables II and III). The final k on(Ca) was calculated as a mean of k on(Ca) for each individual trace Ϯ S.D. The modeling predicted that we should observe the percentage of occupancy obtained experimentally if the k on(Ca) to the N-domain site of cTnC F27W was 1.2 Ϯ 0.3 ϫ 10 8 M Ϫ1 s Ϫ1 . This value is in excellent agreement with the calculated value of 1.7 Ϯ 0.3 ϫ 10 8 M Ϫ1 s Ϫ1 . The simulation using k on(Ca) of 1. 2 ϫ 10 8 M Ϫ1 s Ϫ1 (Fig. 4A, Ⅺ) is shown overlaying the experimental data. To examine the effect of higher [Mg 2ϩ ] on the transient occupancy of cTnC F27W by Ca 2ϩ , cTnC F27W was subjected to ACTs of increasing duration and amplitude in the presence of 12 mM Mg 2ϩ . Fig. 4C shows the time course of Ca 2ϩ binding and subsequent dissociation from the N-domain site of cTnC F27W subjected to ACTs of increasing duration and amplitude at 15°C in the presence of 12 mM Mg 2ϩ . As the [Ca 2ϩ ] was successively increased from 10 to 50, 100, 250, 500, 750, and 5000 M (Fig. 4C), Ca 2ϩ transiently occupied 4 Ϯ 3 (at 2 ms), 9 Ϯ 4 (at 2 ms), 16 Ϯ 4 (at 2 ms), 25 Ϯ 3 (at 2.8 ms), 48 Ϯ 4 (at 2.5 ms), 62 Ϯ 2 (at 2.5 ms), and 100% of the N-terminal regulatory site of cTnC F27W , respectively. Thus, higher [Mg 2ϩ ] leads to a decreased percent occupancy of the regulatory site of cTnC F27W , because of a larger percentage of the N-domain of cTnC F27W being initially occupied by Mg 2ϩ . The simulation using k on(Ca) of 1.2 ϫ 10 8 M Ϫ1 s Ϫ1 in the presence of 12 mM Mg 2ϩ (Ⅺ) is shown overlaying the experimental data. Therefore, the k on(Ca) estimated from the experimental data in the presence of 3 mM Mg 2ϩ could be used to accurately predict the transient occupancy of cTnC F27W in the presence of 12 mM Mg 2ϩ . Furthermore, these data support the conclusion that Mg 2ϩ com- 45 M Ca 2ϩ in the same buffer as in A was rapidly mixed with an equal volume of Quin-2 (150 M) in the same buffer. Quin-2 fluorescence was monitored through a 510-nm broad band pass interference filter with excitation at 330 nm. The traces were fit with a single exponential after mixing was complete (variance Ͻ 9 ϫ 10 Ϫ5 ). The traces are not normalized but have been displaced vertically for clarity. C shows the time course of the decrease in Trp fluorescence as Ca 2ϩ was removed by EGTA from cTnC F27W and F20QcTnC F27W at 4°C (Trp traces). Each protein (2 M) with 500 M Ca 2ϩ in the same buffer as in A was rapidly mixed with an equal volume of EGTA (10 mM) in the same buffer. The traces have been normalized and displaced vertically for clarity. C also shows the time course of the increase in Quin-2 fluorescence as Ca 2ϩ was removed by Quin-2 from the N-terminal site of cTnC F27W and F20QcTnC F27W at 4°C (Quin-2 traces). Each protein (8 M) with 45 M Ca 2ϩ in the same buffer as in A was rapidly mixed with an equal volume of Quin-2 (150 M) in the same buffer. The traces have been normalized and displaced vertically for clarity.  Fig. 5A shows the time course of Ca 2ϩ binding and subsequent dissociation from the N-domain site of V44-QcTnC F27W subjected to ACTs of increasing duration and amplitude at 15°C in the presence of 3 mM Mg 2ϩ . As the [Ca 2ϩ ] was successively increased from 5 to 10, 25, 100, 250, 500, 750, and 2000 M (Fig. 4A), Ca 2ϩ transiently occupied 28 Ϯ 3 (at 2 ms), 38 Ϯ 3 (at 3 ms), 58 Ϯ 3 (at 3 ms), 78 Ϯ 4 (at 3.5 ms), 85 Ϯ 4 (at 4.3 ms), 86 Ϯ 3 (at 7.5 ms), 92 Ϯ 2 (at 10 ms), and 100% of the N-terminal regulatory site of V44QcTnC F27W , respectively. Each individual trace was simulated using the computer program KSIM, which fixed the Ca 2ϩ dissociation rate from V44QcTnC F27W at 473 s Ϫ1 and let the Ca 2ϩ association rate vary until the modeled transient occupancy approximated the experimental data. The simulation predicted that we should observe the percentage of occupancy obtained experimentally if the k on(Ca) to the N-domain site of V44QcTnC F27W was 9.6 Ϯ 1 ϫ 10 8 M Ϫ1 s Ϫ1. The simulation using k on(Ca) of 9.6 ϫ 10 8 M Ϫ1 s Ϫ1 (‚) is shown overlaying the experimental data. Clearly, the Ca 2ϩ association rate to the N-domain of cTnC F27W can be increased and thus is not diffusion-limited, as previously suggested for sTnC F29W (6).   Table I). These values are in excellent agreement with the values of k on(Ca) calculated using the equation k on(Ca) ϭ k off(Ca) /K d(Ca) (Table I). Thus, substitution of hydrophobic residues in positions 20, 44, 45, 48, or 81 with polar Gln produced ϳ2.6 -8.7-fold increases in k on(Ca) . DISCUSSION EF-hand Ca 2ϩ -binding proteins exhibit a wide range of Ca 2ϩ binding affinities (Ͼ10 6 -fold variation) and dissociation rates (Ͼ10 4 -fold variation) (for review, see Refs. 36 and 37). The mechanisms controlling the vast range of EF-hand Ca 2ϩ binding affinities and exchange rates remain elusive. Clearly, helical and Ca 2ϩ chelating and nonchelating loop residues can have a dramatic influence on cation affinity and exchange rates (8, 24, 25, 38 -41). The goal of this study was to design cTnC mutants with increased Ca 2ϩ affinity by substitution of selected hydrophobic residues in specific locations within the tertiary structure of the protein with polar Gln. To follow Ca 2 ϩ binding and exchange with the regulatory domain of cTnC, we utilized the intrinsic fluorescence of cTnC F27W , which has been previously used to study Ca 2ϩ binding to the N-domain site of cTnC and its mutants or isoforms (26 -29). This mutation is analogous to sTnC F29W , which enabled numerous studies of Ca 2ϩ and target protein binding to the N-domain of sTnC and its mutants (6,8,22,25,42).

Using ACTs to Estimate the Ca 2ϩ Association Rates to the N-domain Site of cTnC F27W Mutants in the Presence of 3 mM Mg 2ϩ -
Previously, we examined the role of hydrophobic residues in Ca 2ϩ binding and exchange with the regulatory domain of sTnC F29W by individually substituting 27 hydrophobic Phe, Ile, Leu, Val, and Met residues with polar Gln (25). The results demonstrated that individual substitution of hydrophobic residues with polar Gln could both dramatically increase or decrease the Ca 2ϩ affinity of the regulatory domain of sTnC F29W , depending on the location of the residue within the tertiary structure of the protein (25). No correlation was found between the Ca 2ϩ affinity of the 27 mutants and the solvent accessibility of the mutated residues in either the absence or presence of Ca 2ϩ (or the difference between the two states), indicating that the changes in solvent exposure were not the sole determinant in how the residue affects Ca 2ϩ binding. Substitution of Phe 22 , Val 45 Met 46 , Leu 49 , or Met 82 with polar Gln led to large (3.2-18.9-fold) increases in the Ca 2ϩ affinity. We concluded that these mutations increased Ca 2ϩ affinity because they shift the equilibrium from the apo state toward the Ca 2ϩ -bound state by reducing the hydrophobic contact between the BC and NAD units in the apo state. However, the N-domain of cTnC remains essentially closed in the Ca 2ϩ bound state, because the BC unit moves away only slightly from the NAD unit (15). Therefore, analogous residues in cTnC, Phe 20 , Val 44 , Met 45 , Leu 48 , and Met 81 exhibit no increase in their solvent accessibility upon Ca 2ϩ binding (Table I) (Table I and Ref. 15), with their side chains involved in extensive hydrophobic interactions between the BC and NAD units (Fig. 6). However, upon TnI 147-163 binding to the regulatory domain of cTnC in the presence of Ca 2ϩ , all of the interunit hydrophobic interactions are lost as the BC unit moves away from the NAD unit ( Fig. 6 and Ref. 17). Thus, substitution of either one of these residues with polar Gln could increase Ca 2ϩ affinity by facilitating the movement of the BC unit away from the NAD unit, mimicking the effects of cTnI binding. Indeed, the mutants exhibited ϳ2.1-15.2-fold increases in their Ca 2ϩ affinity, ranging from 3.4 M for F20QcTnC F27W to 0.46 M for V44QcTnC F27W . In this respect, the regulatory domain of cTnC behaved similarly to the regulatory domains of both sTnC and CaM, in which decreasing the hydrophobic interactions between the BC and (N)AD units in the apo state, through similar mutations, led to increased Ca 2ϩ affinity (22,23,25,43). Complementary to these findings, stabilizing the interactions between the BC and (N)AD units of sTnC or CaM, either through disulfide bond, salt bridge formation, or substitution of buried polar residues with hydrophobic Leu or Ile, led to decreased Ca 2ϩ affinity (44 -48). Our findings further support the idea that a change in solvent accessibility of a hydrophobic residue may not be the main determinant for how a mutation of this residue affects the Ca 2ϩ binding properties of an EF-hand protein (25).
The five cTnC F27W mutants studied in the present work possessed ϳ2.1-15.2-fold higher Ca 2ϩ affinities but only ϳ1.2-2.9-fold slower Ca 2ϩ dissociation rates. In this respect, the cTnC F27W mutants behaved differently from hydrophobic core mutants of calbindin D 9K , in which variations in the Ca 2ϩ affinity were a consequence of the perturbations of the Ca 2ϩ dissociation rate (24). Furthermore, Ca 2ϩ sensitizing mutants in cTnC F27W behaved differently from analogous mutants of sTnC F29W and the intact CaM mutant with a Phe 19 3 Trp mutation, in which the increase in Ca 2ϩ affinity was largely due to a decrease in Ca 2ϩ dissociation rate (25,43). This unusual behavior of cTnC could perhaps be related to the fact that despite being a regulatory Ca 2ϩ sensor, the N-domain of cTnC undergoes only a minor conformational transition upon Ca 2ϩ binding. Calculation of the Ca 2ϩ association rate using the equation k on(Ca) ϭ k off(Ca) /K d (Ca) suggested that the Ca 2ϩ -sensitizing mutations should cause ϳ1.7-5.3-fold increase in the Ca 2ϩ association rates to the N-domain of cTnC F27W . Limitations of the stopped-flow technique would not allow us to directly measure the rate of Ca 2ϩ association to the regulatory site of cTnC F27W using the standard pseudo-first order approach, because most of the reaction occurred during the dead time of the instrument. Previously, we demonstrated that by exposing Ca 2ϩ -binding proteins/enzymes to ACTs and examining the percent occupancy as a function of ACT duration and amplitude, we could experimentally determine the Ca 2ϩ association rate (31). Thus, to verify that the Ca 2ϩ -sensitizing mutations increase the rate of Ca 2ϩ association, cTnC F27W and its mutants were subjected to ACTs of increasing amplitude and duration. The experimental Ca 2ϩ association rate to the regulatory domain of cTnC F27W was estimated at 1.2 ϫ 10 8 M Ϫ1 s Ϫ1 , in excellent agreement with the calculated Ca 2ϩ association rate of 1.7 ϫ 10 8 M Ϫ1 s Ϫ1 . Our transient occupancy data were consistent with a one-step Ca 2ϩ association process and were not consistent with either a two-step (35) or a three-step mechanism of Ca 2ϩ association to the regulatory domain of cTnC (49). However, the intrinsic fluorescent Trp 27 used in the present study is located on helix A, immediately preceding the first defunct Ca 2ϩ binding loop, whereas Hazard et al. (35) and Dong et al. (49) utilized the extrinsic fluorescent probe IAANS linked to a single Cys 84 on helix D of cTnC C35S . Thus, the different location and properties of the two probes could be a reason why Trp 27 reports a true Ca 2ϩ association rate and does not sense any slow conformational transitions. In fact, Hazard et al. (35) reported that the fluorescence of IAANS covalently linked to Cys 84 of chicken cTnC C35S followed the rate of a slower conformational rearrangement rather than the faster true rate of Ca 2ϩ dissociation. On the other hand, the fluorescence of Trp 27 accurately reported the rate of Ca 2ϩ dissociation from the regulatory site of cTnC F27W . However, the different location and properties of two fluorescent reporters did not affect the Ca 2ϩsensitizing effect of the five individual mutations studied in the present work, because these mutations also produced ϳ2.4 -23fold increases in Ca 2ϩ binding to the N-domain of cTnC C35S labeled with IAANS on Cys 84 , which exhibited a K d(Ca) of 7.5 M (50). 2 The experimentally measured and calculated Ca 2ϩ associa-2 S. B. Tikunova and J. P. Davis, unpublished data.  (15)). The NMR structure of the Ca 2ϩ -bound N-domain fragment (residues 1-89) of human cTnC is shown in the middle (Protein Data Bank file 1AP4, model 14 (15)). The NMR structure of the Ca 2ϩ and TnI 147-163 bound N-domain fragment (residues 1-89) of human cTnC is shown on the right (Protein Data Bank file 1MXL, model 18 (17)). The cTnI 147-163 is not shown for the sake of clarity. The models shown in this figure are those stated to be the best representatives of the ensemble conformer (15,17). This figure was drawn using Rasmol (61). The helices are labeled (N, A, B, C, and D) and shown as ribbons; hydrophobic residues that were mutated to Gln (Phe 20 , Val 44 , Met 45 , Leu 48 , and Met 81 ) are shown in a ball-and-stick format and labeled. tion rates to the N-domain of cTnC F27W (ϳ1.2-1.7 ϫ 10 8 M Ϫ1 s Ϫ1 , reported in this work) and sTnC F29W (ϳ1.1-1.6 ϫ 10 8 M Ϫ1 s Ϫ1 ; 8, 25) were nearly identical at 15°C. The simulation of the transient occupancy data indicated that the Ca 2ϩ -sensitizing mutations increased the Ca 2ϩ association rates to the N-domain of cTnC F27W ϳ2.6 -8.7-fold. Clearly, the rate of Ca 2ϩ association to the regulatory domain of cTnC F27W can be increased and thus is not diffusion-controlled as previously suggested for sTnC F29W (6). Faster Ca 2ϩ association rates could indicate that the mutations decreased the energy of the transition state barrier (36), but this alone would not explain the altered equilibrium constants and lack of proportional changes in the Ca 2ϩ dissociation rates. For the Ca 2ϩ -sensitizing mutations in cTnC F27W , there was a strong correlation between the Ca 2ϩ association rate and Ca 2ϩ affinity (r 2 ϭ 0.76), contrasting with the weak correlation (r 2 ϭ 0.26) observed for analogous mutations in sTnC F29W (Fig. 7A and Ref. 25). Thus, the mechanisms behind the enhanced Ca 2ϩ sensitivity by analogous mutations in sTnC F29W and cTnC F27W were strikingly different. Clearly, Ca 2ϩ -sensitizing mutations in sTnC F29W primarily decreased Ca 2ϩ dissociation, whereas analogous mutations in cTnC F27W drastically increased Ca 2ϩ association. Because the changes in Ca 2ϩ association rate potentially reflect the perturbation of the apo state, the data obtained in the present work are consistent with the idea that reducing the hydrophobic interactions between the BC and NAD units destabilized the apo state of the N-domain leading to the increased Ca 2ϩ affinity. There is the possibility that these hydrophobic residue substitutions led to a slight opening of the N-domain in the apo state. On the other hand, the fact that Ca 2ϩ dissociates slower from the Ca 2ϩ -sensitizing cTnC F27W mutants also suggests possible perturbations of the Ca 2ϩ -bound state. Interestingly, FIG. 7. Comparison of k on(Ca) and Q 10 for k off(Ca) between Ca 2؉ sensitizing cTnC F27W and sTnC F29W mutants. A shows the correlation between the Ca 2ϩ association rate k on(Ca) and Ca 2ϩ affinity K d(Ca) for cTnC F27W (cTnC F27W , Ⅺ), F20QcTnC F27W (F20Q, Ⅺ), V44QcTnC F27W (V44Q, Ⅺ), M45QcTnC F27W (M45Q, Ⅺ), and M81QcTnC F27W (M81Q, Ⅺ). The solid line was obtained by fitting the data with a linear regression. Each data point represents the mean Ϯ S.D. of three to five separate experiments. The correlation coefficient (r 2 ) was 0.76. A also shows the correlation between the Ca 2ϩ association rate k on(Ca) and Ca 2ϩ affinity K d(Ca) for sTn- (L49Q, f), and M82QsTnC F29W (M82Q, f). The solid line was obtained by fitting the data with a linear regression. The correlation coefficient (r 2 ) was 0.26. The data for sTnC F29W have been adapted from Tikunova et al. (25). These data are shown for comparative purposes, because it was collected under identical experimental conditions, except the Ca 2ϩ association rate was calculated using the equation k on(Ca) ϭ k off(Ca) /K d (Ca) . B shows the relationship between the temperature coefficient Q 10 (for the Ca 2ϩ dissociation rate in the 4 -15°C range; Q 10 ϭ (k off(Ca) at 15°C/ k off(Ca) at 4°C) 10 the Ca 2ϩ -sensitizing mutations in cTnC F27W , but not in sTnC F29W , increased the temperature coefficient Q 10 for the rates of Ca 2ϩ dissociation in the 4 -15°C range (Fig. 7B). It is possible that the Ca 2ϩ -sensitizing mutations studied in the present work caused the N-domain of cTnC F27W to be more open in the Ca 2ϩ -bound state, perhaps to some extent mimicking cTnI binding, which also produces an ϳ10-fold increase in the Ca 2ϩ affinity of the regulatory site of cTnC (9). Clearly, structural studies are needed to examine whether the Ca 2ϩsensitizing mutations affect the tertiary structure of cTnC, as proposed in this study. Nuclear magnetic resonance studies are currently underway in collaboration with the laboratory of Dr. Paul Rosevear (University of Cincinnati).
The question of whether Mg 2ϩ affects the Ca 2ϩ sensitivity of actomyosin ATPase or force production in cardiac muscle is unresolved and controversial. Several studies have shown that increasing [Mg 2ϩ ] in the millimolar range led to the decrease in Ca 2ϩ sensitivity of myofibrillar actomyosin ATPase or force development in cardiac fibers (51)(52)(53)(54). However, a recent study reported that increasing Mg 2ϩ from 1 to 8 mM had no significant effect on the Ca 2ϩ sensitivity of actomyosin ATPase activity and force production in skinned rat cardiac cells (55). The N-domain site of cTnC is generally considered to be Ca 2ϩspecific under physiological Mg 2ϩ concentrations. The question of whether Mg 2ϩ binds to the N-domain site of cTnC and competes with Ca 2ϩ is also unresolved. An early study reported that Mg 2ϩ decreased the Ca 2ϩ sensitivity of the regulatory site of fluorescently labeled cTnC, with a K d(Mg) calculated to be ϳ3.8 mM at room temperature, assuming competitive Mg 2ϩ binding (56). Another study, using equilibrium dialysis, concluded that Mg 2ϩ did not compete with Ca 2ϩ for the N-domain site of cTnC but suggested the presence of several auxiliary Mg 2ϩ -binding sites (9).
Unlike Ca 2ϩ , Mg 2ϩ does not increase the fluorescence of cTnC F27W . However, under our experimental conditions, increasing Mg 2ϩ from 0 to 3 mM reduced the Ca 2ϩ sensitivity of the regulatory domain of cTnC F27W ϳ3.4-fold. In addition, Mg 2ϩ was able to reverse the Ca 2ϩ -induced increase in fluorescence of cTnC F27W in a concentration-dependent manner. Furthermore, higher [Mg 2ϩ ] led to a decrease in transient occupancy of cTnC F27W by Ca 2ϩ , suggesting increased occupation of the regulatory site by Mg 2ϩ . Thus, all of our results indicate that the regulatory site of cTnC F27W binds Mg 2ϩ competitively with 1.2-1.9 mM affinity at 15°C. Therefore, according to our data, the regulatory domain of cTnC would be 33-44% saturated at rest under physiological conditions of ϳ1 mM Mg 2ϩ (57) and 100 nm Ca 2ϩ , assuming that cTnC incorporated into cardiac muscle still possesses a similar ability to bind Mg 2ϩ . Interestingly, the Ca 2ϩ -sensitizing mutations had only marginal effects on the Mg 2ϩ binding properties of the regulatory domain of cTnC F27W . These findings are not surprising, because Mg 2ϩ binding to the EF-hands of Ca 2ϩ /Mg 2ϩ -binding proteins, such as calbindin D 9K and CaM, affected only the local structural environment of the cation-binding loop (58 -60). Thus, mutations of residues outside the loops are not expected to drastically modify Mg 2ϩ affinity, unless they grossly perturb the structure of the loop itself.
Because cTnC does not regulate muscle mechanics in isolation but as a part of the cTn complex, it is important to elucidate the Ca 2ϩ /Mg 2ϩ -dependent interactions between cTnC and cTnI/cardiac troponin T. Studies aimed toward understanding whether mutations sensitizing isolated cTnC to Ca 2ϩ also increase Ca 2ϩ sensitivity of the cTn complex and muscle force development are currently underway in our laboratory. The main goal of our laboratory is to delineate the influence of the rates of Ca 2ϩ exchange with the regulatory domain of TnC on the kinetics of striated muscle contraction and relaxation. Slowing of cardiac muscle relaxation would be an undesirable consequence of the increased sensitivity of contractile proteins to Ca 2ϩ . The cTnC F27W mutants designed for this study demonstrated that it is possible to drastically increase Ca 2ϩ affinity of the regulatory domain without dramatically slowing the Ca 2ϩ dissociation rate. These cTnC mutants could be used as molecular tools to examine whether it is possible to increase the Ca 2ϩ sensitivity of force development with minimal effect on the rate of cardiac muscle relaxation. Perhaps, in the future, the cTnC mutant proteins with desired properties can be used for the treatment of heart disease to enhance cardiac contractility without further impairing relaxation.
In summary, we utilized the Phe 27 3 Trp substitution to study Ca 2ϩ binding and exchange with the regulatory site of cTnC. We then designed five Ca 2ϩ -sensitizing cTnC F27W mutants, in which we individually substituted hydrophobic Phe 20 , Val 44 , Met 45 , Leu 48 , or Met 81 with polar Gln. None of the mutations affected the ability of cTnC F27W to competitively bind Mg 2ϩ with a physiologically relevant affinity. The cTnC F27W mutants exhibited a ϳ2.1-15.2-fold increase in Ca 2ϩ affinity, a ϳ1.2-2.9-fold decrease in Ca 2ϩ dissociation rate, and a ϳ2.6 -8.7-fold increase in Ca 2ϩ association rate. The rational design of Ca 2ϩ -sensitizing cTnC mutants presented in this work is a first step toward understanding how the sequence of an EF-hand protein determines its Ca 2ϩ binding properties, structure, and function.