Engineering Competitive Magnesium Binding into the First EF-hand of Skeletal Troponin C*

The goal of this study was to examine the mechanism of magnesium binding to the regulatory domain of skeletal troponin C (TnC). The fluorescence of Trp29, immediately preceding the first calcium-binding loop in TnCF29W, was unchanged by addition of magnesium, but increased upon calcium binding with an affinity of 3.3 μm. However, the calcium-dependent increase in TnCF29W fluorescence could be reversed by addition of magnesium, with a calculated competitive magnesium affinity of 2.2 mm. When a Z acid pair was introduced into the first EF-hand of TnCF29W, the fluorescence of G34DTnCF29W increased upon addition of magnesium or calcium with affinities of 295 and 1.9 μm, respectively. Addition of 3 mm magnesium decreased the calcium sensitivity of TnCF29W and G34DTnCF29W ∼2- and 6-fold, respectively. Exchange of G34DTnCF29W into skinned psoas muscle fibers decreased fiber calcium sensitivity ∼1.7-fold compared with TnCF29W at 1 mm [magnesium]free and ∼3.2-fold at 3 mm [magnesium]free. Thus, incorporation of a Z acid pair into the first EF-hand allows it to bind magnesium with high affinity. Furthermore, the data suggests that the second EF-hand, but not the first, of TnC is responsible for the competitive magnesium binding to the regulatory domain.

The EF-hand is the most common Ca 2ϩ binding motif found in nature (1). EF-hand proteins and their functions are numerous and diverse (for review see Ref. 2). In general, EF-hand domains can be classified functionally into two groups, those that regulate cellular activities through a reversible change in structure upon Ca 2ϩ binding and release (such as the N-terminal regulatory domain of troponin C (TnC) 1 and both domains of calmodulin (CaM)) and those that simply buffer/transport Ca 2ϩ (such as parvalbumin and calbindin D 9K ) or anchor protein complexes (such as the C-terminal domain of TnC). Often the nonregulatory EF-hand domains bind Mg 2ϩ competitively and display higher Ca 2ϩ affinity than do the regulatory domains. However, it is becoming clear that regulatory EF-hand proteins, such as the N-terminal of CaM can also bind Mg 2ϩ with a physiologically relevant affinity (3,4). Thus, it is important to elucidate the mechanisms behind EF-hand Mg 2ϩ binding.
The canonical EF-hand consists of 29 consecutive residues, with two helices flanking a 12-residue loop. The chelating loop residues in positions 1(ϩx), 3(ϩy), 5(ϩz), 7 (Ϫy), 9(Ϫx), and 12 (Ϫz) ligate Ca 2ϩ through seven oxygen atoms arranged three dimensionally on the axes of a pentagonal bipyramid (for review see Refs. 5 and 6). Factors that control Ca 2ϩ affinity are complex and involve residues within and outside of the Ca 2ϩbinding loop (7)(8)(9)(10)(11). The mechanisms utilized for EF-hand Mg 2ϩ binding are less understood. The smaller Mg 2ϩ cation is typically complexed by some of the same loop residues used for Ca 2ϩ binding, although through six oxygen atoms arranged in an octahedral geometry (for review see Refs. 11 and 12). Interestingly, synthetic EF-hand peptides were observed to bind Mg 2ϩ when their Ca 2ϩ -binding loops contained a Z acid pair, chelating residues at loop positions ϩz and Ϫz (13,14).
The metal binding properties of TnC have been studied extensively using various biophysical and biochemical techniques (15)(16)(17)(18)(19). These studies have demonstrated that the two C-domain EF-hands have ϳ10-fold higher Ca 2ϩ affinity and greater than 100-fold slower Ca 2ϩ exchange rates than the two N-domain EF-hands (18,20). In addition to Ca 2ϩ , the C-domain sites also competitively bind Mg 2ϩ with a physiologically relevant affinity. Because of their high Ca 2ϩ and Mg 2ϩ affinities and slow exchange rates, the C-domain sites are thought to play a structural role in muscle function by anchoring TnC into the Tn Complex.
The N-domain sites of TnC are considered to be Ca 2ϩ -specific under physiological Mg 2ϩ concentrations, and generally accepted to be directly involved in the Ca 2ϩ -dependent regulation of muscle contraction (for review see Refs. 21 and 22). However, addition of Mg 2ϩ has been shown to decrease the Ca 2ϩ sensitivity of the regulatory domain of fluorescent TnCs in isolation (19,(23)(24)(25)(26)(27), in the Tn complex (23,28), and in reconstituted muscle fibers (26,29). Furthermore, several groups have dem-onstrated that increased [Mg 2ϩ ] caused a decrease in Ca 2ϩ sensitivity of Tn-regulated actomyosin ATPase and force development (26,27,30,31). The question whether Mg 2ϩ competes with Ca 2ϩ for the N-domain sites remains unresolved and controversial. Some research groups have suggested the presence of auxiliary Mg 2ϩ binding sites in TnC (15,23), whereas others hypothesized Mg 2ϩ as a direct Ca 2ϩ competitor for the N-terminal regulatory sites (19,27,32).
Because TnC regulates muscle contraction as a part of the troponin complex and not in isolation, it is important to understand the interactions of TnC with TnI. The binding of TnI to TnC increases the Ca 2ϩ sensitivity of the N-and C-domains of TnC ϳ10-fold (15,33). TnC and TnI interact in an antiparallel orientation (34,35) such that the Ca 2ϩ -dependent binding of the N-terminal regulatory domain of TnC to the C-domain of TnI is an early step in the generation of force in skeletal muscle (21). Previous studies demonstrated that region 96 -116 of TnI interacts with actin and was largely responsible for the ability of TnI to inhibit the activity of the actomyosin ATPase that could be reversed upon TnC-Ca 2ϩ binding (36 -38). Recent studies implicated additional residues within 116 -148 of TnI as being important for the complete inhibitory activity and regulatory interactions with actin and TnC (39 -42). Thus, the Ca 2ϩ -dependent binding of the regulatory domain of TnC to TnI-(96 -148) may be a good model system to study the Ca 2ϩdependent interactions between TnI and TnC.
The F29W mutation in chicken skeletal TnC (TnC F29W ) has been frequently used to study metal and ligand interactions with the regulatory N-domain sites of TnC (9,20,(43)(44)(45)(46). TnC F29W is a physiologically active protein that produced maximal isometric tension with a Ca 2ϩ sensitivity indistinguishable from that of recombinant TnC, when reconstituted into skinned skeletal fibers (47). Interestingly, whereas Ca 2ϩ causes a large increase in TnC F29W fluorescence, Mg 2ϩ does not alter the fluorescence properties of Trp 29 (44,45,48). Previously, we have demonstrated that an endogenous Z acid pair was required for high affinity Mg 2ϩ binding to the first EFhand of fluorescent CaM F19W (3). We wanted to test if Mg 2ϩ binding could be engineered into the first EF-hand of TnC F29W by substituting Gly in position 34 with Asp, thus introducing a Z acid pair (Fig. 1). We also wanted to determine how compet-itive Mg 2ϩ binding to the first EF-hand of TnC would affect the physiological properties of G34DTnC F29W reconstituted into skinned skeletal muscle fibers.

EXPERIMENTAL PROCEDURES
Materials-Phenyl-Sepharose CL-4B, EDTA, and EGTA were purchased from Sigma. Quin-2 was purchased from Calbiochem (La Jolla, CA). All other chemicals were of analytical grade. The TnI-(96 -148) peptide was synthesized and purified by the Alberta Peptide Institute (Edmonton Alberta, Canada).
Protein Mutagenesis and Purification-The construction and expression of intact chicken skeletal TnC F29W and isolated N-domain residues 1-90, TnC 1-90 F29W , both in pET3a, have been described (44, 49 -50). Chicken skeletal fast TnI was prepared as described for the rabbit protein (51). The G34DTnC F29W mutant was constructed from the TnC F29W plasmid by primer-based site-directed mutagenesis using the QuikChange site-directed mutagenesis kit from Stratagene (La Jolla, CA). The mutation was confirmed by DNA sequence analysis. The plasmids for TnC F29W and G34DTnC F29W were transformed into Escherichia coli BL21(DE3)pLysS cells (Novagen) and purified as described previously (9).
Determination of Ca 2ϩ and Mg 2ϩ Affinities-All steady-state fluorescence measurements were performed using a PerkinElmer Life Sciences LS5 spectrofluorimeter at 15°C. Trp fluorescence was excited at 275 nm and monitored at 345 nm as microliter amounts of CaCl 2 or MgCl 2 were added to 1 (72). The F29W and G34D mutations were predicted by the computer software program WHAT IF (73) and constructed from the coordinates of the N-terminal domain crystal structure of chicken skeletal TnC (Protein Data Bank number 1AVS) (74). These cartoons are not meant to represent the actual structures but are used simply to demonstrate the potential effect of the G34D mutation and to demonstrate the location of the F29W mutation adjacent to the first Ca 2ϩbinding loop. The spherical Ca 2ϩ ion is shown to be coordinated by residues at positions 30 (ϩx), 32 (ϩy), 34 (ϩz), 36 (Ϫy), 38 (Ϫx), and 41 (Ϫz) that form the base and apexes of the pentagonal bipyramid geometry.
3-5 titrations fit with a logistic sigmoid function mathematically equivalent to the Hill equation, as previously described (8,9).
Determination of Ca 2ϩ and Mg 2ϩ Association and Dissociation Rates -Ca 2ϩ and Mg 2ϩ association (k on(Ca) and k on(Mg) ) and dissociation rates (k off(Ca) and k off(Mg) ) were measured using an Applied Photophysics Ltd. (Leatherhead, UK) model SX.18 MV stopped-flow instrument with a dead time of 1.4 ms at 15°C. The samples were excited using a 150-watt xenon arc source. Ca 2ϩ and Mg 2ϩ binding kinetics of the N-terminal domain within intact TnC F29W and G34DTnC F29W were obtained utilizing Trp fluorescence changes excited at 275 nm with emission monitored through a UV transmitting black glass filter (UG1 from Oriel, Stratford, CT). Ca 2ϩ dissociation rates in the absence of Mg 2؉ were also measured using the fluorescent Ca 2ϩ chelator Quin-2. Whereas the fluorescence of Trp 29 was selective for N-terminal Ca 2ϩ dissociation, Quin-2 fluorescence reported Ca 2ϩ dissociation from both the N-and C-domains within TnC F29W . However, the Ca 2ϩ dissociation rate from the N-terminal domain within TnC F29W was easily distinguished from the rate of Ca 2ϩ dissociation from the C-terminal domain because the latter rate was Ͼ95-fold slower in the absence and presence of TnI-(96 -148) or intact TnI. Quin-2 fluorescence was excited at 330 nm, with its emission monitored through a 510-nm broad band-pass interference filter (Oriel). Each data set represents an average of 10 -15 traces, fit with a single exponential (variance Ͻ2 ϫ 10 Ϫ4 ). The curve fitting program (by P. J. King, Applied Photophysics Ltd.) uses the nonlinear Levenberg-Marquardt algorithm. The buffer used in all the Ca 2ϩ stopped-flow experiments was 10 mM MOPS, 90 mM KCl, 1 mM DTT, pH 7.0.
Calculation of Ca 2ϩ and Mg 2ϩ Association Rates-The Ca 2ϩ and Mg 2ϩ association rates were calculated using the equation k on ϭ k off /K d , where k off represents the concerted release of two Ca 2ϩ or single Mg 2ϩ ions and K d represents the binding event of two Ca 2ϩ or one Mg 2ϩ to the N-domain of TnC, as previously described (3,8).
Muscle Fiber Experiments-Single fibers were isolated the day of use from bundles of rabbit psoas muscle that had been stored in a glycerinating solution at Ϫ20°C no longer than 1 month. Solutions and the mechanical setup utilized for force measurements were as previously described (53). Briefly, a single fiber was soaked in relaxing solution containing 1% (v/v) Triton X-100 for 5 min to remove any residual sarcolemma and sarcoplasmic reticulum. The fiber was then tied down with pens in troughs attached to a servo-controlled DC torque motor (Cambridge Technologies, Watertown, MA) and an isometric force transducer (model 403A, Cambridge Technologies) as previously described (54). Fiber sarcomere length, width, and depth were measured with a video camera (Sony model XC-ST70) and an image analysis system (Simple PCI, Compix Inc., Cranberry Township, PA). Resting sarcomere length was set between 2.50 and 2.60 m. The fiber was then activated in a pCa (-log[Ca 2ϩ ]) 4.0 solution and rapidly slackened after isometric force reached plateau. The analogue output of the force transducer was digitized using a DaqBoard/2000 and Daqview software (Iotech Inc., Cleveland, OH). The total force was measured between the plateau and baseline levels. The same procedure was utilized to obtain the resting force level of the fiber in a pCa 9.0 solution. The active force generated by the fiber in the various pCa solutions was calculated as the total force minus the resting force. Three active force measurements were performed in pCa 4.0 with the final activation taken as the maximal force generated by the native fiber (i.e. prior to extraction of FIG. 3 Fig. 2 plus 10 mM Mg 2ϩ was rapidly mixed with an equal volume of 20 mM EDTA in the same buffer at 15°C. Trp fluorescence was monitored through a UVtransmitting black glass filter (UG1 from Oriel) with excitation at 275 nm. The traces have been staggered for clarity. Each trace is an average of at least 15 traces, and the data were fit with a single exponential (excluding TnC F29W , which was flat, variance Ͻ2 ϫ 10 Ϫ4 ). The kinetic traces were triggered at time 0, the first ϳ2 ms of premixing time is shown (the apparent lag phase), and the average trace was fit after mixing was complete. Control experiments in which each protein (2 M) in the same buffer as Fig. 2 plus 10 mM Mg 2ϩ was rapidly mixed with an equal volume of the same buffer were flat lines.
TnC endogenous ), which led to an average force per cross-sectional area of 89 Ϯ 4 kilo newton/m 2 . Force versus pCa was then established or the fiber was then soaked for 2 min in a TnC extraction solution containing 5 mM EDTA, 10 mM HEPES, and 0.5 mM trifluoperazine dihydrochloride at pH 7.0 (55). The average force in pCa 4.0 generated after TnC endogenous extraction was 5 Ϯ 1% of the maximal force generated by the native fibers. The fiber was then washed three times in pCa 9.0 solution to remove any residual trifluoperazine dihydrochloride and then soaked for 2 min in a pCa 9.0 solution containing 16.7 M recombinant TnC F29W or G34DTnC F29W . The maximal force generated by the recombinant TnCs averaged 93 Ϯ 1 and 62 Ϯ 5% for TnC F29W and G34DTnC F29W , respectively. Because additional fibers reconstituted with 33.4 M G34DTnC F29W or TnC F29W did not improve the maximal amount of force recovery or affect the force versus pCa relationship, these data were then combined with the 16.7 M measurements. All of the reconstituted fibers were then exposed to a series of pCa solutions varying from pCa 9.0 to 3.0 and the active force versus pCa was measured. Every fourth activation was performed at pCa 4.0 to which each adjacent and randomized pCa was normalized. Because fibers reconstituted with recombinant TnC did not completely recover maximal force, force versus [Ca 2ϩ ] curves were also performed on fibers in which TnC was partially extracted. Four fibers were soaked in TnC extraction solution for variable times to partially extract TnC endogenous . F29W and G34DTnC F29W -TnC F29W undergoes an ϳ2.4-fold increase in Trp fluorescence upon Ca 2ϩ binding to its N-domain sites at 15°C ( Fig. 2A). No change in Trp fluorescence was observed upon addition of 50 mM Mg 2ϩ to TnC F29W ( Fig. 2A). We previously demonstrated that high Mg 2ϩ binding to the first EF-hand of CaM required the presence of an endogenous Z acid pair (3). When a Z acid pair was introduced into the first EF-hand of TnC F29W (i.e. G34DTnC F29W ), addition of Ca 2ϩ led to an ϳ2.2-fold increase in Trp fluorescence (Fig. 2B). Furthermore, G34DTnC F29W also underwent an ϳ1.4-fold increase in its Trp fluorescence upon addition of Mg 2ϩ (Fig. 2B). These results demonstrate that substitution of Gly-34 with Asp in the first EF-hand of TnC led to Mg 2ϩ binding to this EF-hand.

Effect of Ca 2ϩ and Mg 2ϩ on the Fluorescence Spectra of the N-terminal Domains within TnC
Measurement of the Mg 2ϩ Binding Affinity for TnC 1-90 F29W and the N-terminal Domains within TnC F29W and G34DTnC F29W - Fig. 3A shows the Mg 2ϩ -dependent increase in Trp fluorescence of G34DTnC F29W (OE). G34DTnC F29W exhibited a half-maximal increase in Trp fluorescence at 295 Ϯ 10 M. However, addition of Mg 2ϩ (up to 50 mM) caused no change in the Trp fluorescence signal of TnC F29W (Fig. 3A, f). Thus, as expected, the G34D mutation in TnC F29W incorporates physiological Mg 2ϩ binding to the first EF-hand of TnC F29W . Fig. 3B shows that in the presence of 10 M [Ca 2ϩ ] free the Trp fluorescence signal of TnC 1-90 F29W (q), TnC F29W (f), and G34DTnC F29W (OE) was greater than 90% saturated, which Mg 2ϩ subsequently decreased in a concentration-dependent manner. Mg 2ϩ half-maximally decreased the Trp fluorescence of TnC 1-90 F29W , TnC F29W and G34DTnC F29W at 7.3 Ϯ 0.8, 9 Ϯ 1, and 1.9 Ϯ 0.2 mM, respectively. Thus, the Ca 2ϩ -dependent fluorescence of TnC 1-90 F29W , TnC F29W , and G34DTnC F29W was reversed by Mg 2ϩ binding, presumably because of the closing of the N-terminal hydrophobic pocket of TnC and not because of any type of interference from Mg 2ϩ binding to the C-terminal domain. Knowing the K d (Ca) for each N-terminal domain protein (determined as described later) and assuming competitive Mg 2ϩ binding, the K d(Mg) of TnC 1-90 F29W , TnC F29W , and G34DTnC F29W was calculated to be ϳ1.8 mM, 2.2 mM, and 303 M, respectively. Thus, the calculated Mg 2ϩ affinity for G34DTnC F29W was identical to that measured directly as described above. Furthermore, even though TnC F29W does not undergo a change in fluorescence upon Mg 2ϩ binding (Fig. 3A, f) its N-terminal domain appears to bind Mg 2ϩ and displace Ca 2ϩ . Table I Fig. 4A shows that in the absence of Mg 2ϩ , TnC F29W (Ⅺ) and G34DTnC F29W (‚) exhibited half-maximal Ca 2ϩ -dependent increases in Trp fluorescence at 3.3 Ϯ 0.1 and 1.9 Ϯ 0.1 M Ca 2ϩ , respectively. Therefore, in the absence of Mg 2ϩ , G34DTnC F29W exhibited an ϳ1.7-fold increase in its Ca 2ϩ affinity, relative to that of TnC F29W . Fig. 4A also shows that in the presence of 3 mM Mg 2ϩ , TnC F29W (f) and G34DTnC F29W (OE) exhibited half-maximal increases in Trp fluorescence at 5.9 Ϯ 0.4 and 11.6 Ϯ 0.9 M Ca 2ϩ , respectively. Therefore, in the presence of 3 mM Mg 2ϩ , G34DTnC F29W exhibited an ϳ2-fold decrease in its Ca 2ϩ sensitivity, relative to that of TnC F29W . Furthermore, 3 mM Mg 2ϩ shifts the Ca 2ϩ sensitivity of TnC F29W and G34DTnC F29W ϳ1.8and 6-fold, respectively. Again, assuming competitive Mg 2ϩ binding, the K d (Mg) of TnC F29W and G34DTnC F29W was ϳ3.8 mM and 590 M, respectively. These values are in good agreement with the direct and competitive Mg 2ϩ binding studies described above (see Table I). Thus, in the presence of 3 mM Mg 2ϩ both proteins are capable of opening their N-terminal hydrophobic pockets in a Ca 2ϩ -dependent manner, albeit with decreased Ca 2ϩ sensitivity.  were nearly identical at 457 Ϯ 16 and 508 Ϯ 9 nM, respectively. Thus, any differences in Ca 2ϩ sensitivity observed between the two proteins in the presence of the peptide could not be because of differences in peptide affinities. The Ca 2ϩ binding affinities for the TnC F29W ⅐TnI-(96 -148) and G34DTnC F29W ⅐TnI-(96 -148) complexes were measured following the Ca 2ϩ -induced increases in Trp fluorescence in the absence and presence of 3 mM Mg 2ϩ at 15°C. Fig. 4C shows that in the absence of Mg 2ϩ , the TnC F29W ⅐TnI-(96 -148) (Ⅺ) and G34DTnC F29W ⅐TnI-(96 -148) (‚) complexes exhibited half-maximal Ca 2ϩ -dependent increases in Trp fluorescence at 267 Ϯ 3 and 147 Ϯ 2 nM Ca 2ϩ , respectively. Therefore, in the absence of Mg 2ϩ , the G34DTnC F29W ⅐TnI-(96 -148) complex exhibited an ϳ1.7-fold increase in its Ca 2ϩ affinity, relative to that of the TnC F29W ⅐TnI-(96 -148) complex. Consistent with intact TnI binding to TnC, TnI-(96 -148) enhanced the Ca 2ϩ sensitivity of the regulatory domain of TnC F29W ϳ12-fold (14,32) and to G34DTnC F29W ϳ13-fold (see Table II). Fig. 4C Table II). These results were consistent with the Ca 2ϩ dissociation rate from the regulatory sites of the fluorescent TnC Danz not being affected by Mg 2ϩ (56).
To verify that the Trp signal changes were accurately reporting the true Ca 2ϩ dissociation rates and not a slower or faster   (Quin-2 traces). Nearly identical Ca 2ϩ dissociation rates were measured using Quin-2 fluorescence for TnC F29W and G34DTnC F29W at 346 Ϯ 3 and 397 Ϯ 2 s Ϫ1 , respectively, as were measured by the EGTA-induced Trp changes. Therefore, G34DTnC F29W exhibited an ϳ1. To verify that TnI-(96 -148) is a satisfactory model system for the regulatory domain binding of TnC to TnI, stopped-flow studies were also conducted with intact chicken skeletal TnI. Fig. 5C also shows the time course of the Quin-2-induced increases in fluorescence as Ca 2ϩ was dissociated from the TnC F29W ⅐TnI complex at 9.1 Ϯ 0.8 s Ϫ1 and the G34DTnC F29W ⅐TnI complex at 5.4 Ϯ 0.5 s Ϫ1 (Quin-2 intact TnI traces). Thus, the Ca 2ϩ dissociation rates from the TnC F29W ⅐TnI and G34DTnC F29W ⅐TnI complexes were similar to the Ca 2ϩ dissociation rates when complexed with TnI-(96 -148). Furthermore, G34DTnC F29W complexed with either TnI or TnI-(96 -148) exhibited an ϳ1.7-fold slower Ca 2ϩ dissociation rate, relative to that of the TnC F29W complexes. Thus, the binding of TnI to the regulatory domain of G34DTnC F29W slows Ca 2ϩ dissociation ϳ73-fold, whereas this effect on TnC F29W was slowed only ϳ37-fold. However, both TnI-(96 -148) and intact TnI similarly slowed the Ca 2ϩ dissociation rate from the C-terminal domains within TnC F29W and G34DTnC F29W only ϳ4-fold (data not shown).
Following the Trp fluorescence signal, in the presence of TnI-(96 -148), 3 mM Mg 2ϩ did not affect the rate of Ca 2ϩ dissociation from TnC F29W but increased the Ca 2ϩ dissociation rate of the G34DTnC F29W ⅐TnI-(96 -148) complex to that of the TnC F29W ⅐TnI-(96 -148) complex (data not shown, Table II). The reason for this Mg 2ϩ effect on the G34DTnC F29W ⅐TnI-(96 -148) complex is currently unknown. One possibility is that the increased negative charge of Asp-34 decreased the rate of Ca 2ϩ dissociation from the regulatory domain of G34DTnC F29W in the presence of TnI-(96 -148), which becomes screened by the positive Mg 2ϩ ions.
Calculated Ca 2ϩ Association Rates to the N-terminal Domains within TnC F29W and G34DTnC F29W -Knowing the affinity of Ca 2ϩ (K d(Ca) ) from the Ca 2ϩ dependence of the increase in TnC F29W and G34DTnC F29W Trp fluorescence and the rate of Ca 2ϩ dissociation (k off(Ca) ) from these same sites, we could calculate the rate of Ca 2ϩ association (k on(Ca) ) from the equation: k on ϭ k off /K d . The calculated values of k on(Ca) for TnC F29W and G34DTnC F29W were 1.0 ϫ 10 8 and 2.1 ϫ 10 8 M Ϫ1 s Ϫ1 , respectively at 15°C. Thus, G34DTnC F29W possesses a ϳ2.1fold faster calculated Ca 2ϩ association rate than does TnC F29W . Furthermore, the k on(Mg) calculated for G34DTnC F29W was ϳ1.9 ϫ 10 6 M Ϫ1 s Ϫ1 , consistent with the slower dehydration rate of Mg 2ϩ compared with Ca 2ϩ that tends to limit the rate of Mg 2ϩ binding to proteins (12). F29W and G34DTnC F29W in the Absence and Presence of 3 mM Mg 2ϩ -To verify these rapid, nearly diffusion controlled Ca 2ϩ association rates, the Ca 2ϩ -induced increase in Trp fluorescence was measured in a stopped-flow apparatus. Fig. 6A shows the time course of the rapid Ca 2ϩinduced increase in Trp fluorescence of G34DTnC F29W as the [Ca 2ϩ ] was increased from 0 to 5 M. As the [Ca 2ϩ ] increases, the observed rate of Ca 2ϩ binding increases as expected for a second order reaction. At 1, 2.5, and 5 M Ca 2ϩ , the reaction occurred at 903 Ϯ 37, 1103 Ϯ 56, and 1660 Ϯ 126 s Ϫ1 , respectively. A plot of the observed rate versus [Ca 2ϩ ] was fit by a linear regression (r 2 ϭ 0.985, Fig. 6C, ‚) from which the Ca 2ϩ association rate to G34DTnC F29W was estimated at 1.9 Ϯ 0.2 ϫ 10 8 M Ϫ1 s Ϫ1 . Similar studies with TnC F29W yielded a Ca 2ϩ association rate of 1.57 Ϯ 0.06 ϫ 10 8 M Ϫ1 s Ϫ1 (r 2 ϭ 0.995, Fig.  6C, Ⅺ). Thus, the measured Ca 2ϩ association rates to the N-terminal domains of TnC F29W and G34DTnC F29W were extremely rapid and essentially the same as the calculated Ca 2ϩ association rates. At 3 mM Mg 2ϩ , G34DTnC F29W was greater than 90% saturated with Mg 2ϩ (Fig. 3A, OE). Fig. 6B shows the time course of the Ca 2ϩ -induced increase in Trp fluorescence of G34DTnC F29W in the presence of 3 mM Mg 2ϩ as the [Ca 2ϩ ] was increased from 0 to 25 M. As the [Ca 2ϩ ] increased, the rate of the reaction did not increase as expected for a second order reaction but remained fairly static at 440 Ϯ 24 s Ϫ1 (Fig. 6, B and C, OE). These static observed Ca 2ϩ association rates, close to the Mg 2ϩ dissociation rate from G34DTnC F29W (see Table I 0.999, Fig. 6C, f). Thus, at these [Mg 2ϩ ] and [Ca 2ϩ ] the Mg 2ϩ dissociation rate from the regulatory domain of TnC F29W was not rate-limiting for Ca 2ϩ binding, although it was slower than in the absence of Mg 2ϩ . Mathematical modeling of the Ca 2ϩ association rate experiments with TnC F29W in the presence of 3 mM Mg 2ϩ predicted the Mg 2ϩ dissociation rate to be ϳ6000 s Ϫ1 assuming a k on(Mg) of 2 ϫ 10 6 M Ϫ1 s Ϫ1 leading to a K d(Mg) of 3 mM (data not shown). Thus, 3 mM Mg 2ϩ slows the Ca 2ϩ association rate to TnC F29W only ϳ3.5-fold but drastically slows the Ca 2ϩ association rate to G34DTnC F29W by ϳ4.3 ϫ 10 5 -fold. Table II also compares the Ca 2ϩ binding properties of TnC F29W and G34DTnC F29W in the absence or presence of 3 mM Mg 2ϩ , with or without TnI-(96 -148).

Measurement of Ca 2ϩ Association Rates to the N-terminal Domains within TnC
Over longer times (0 -5 s), in the absence of Mg 2ϩ , as the [Ca 2ϩ ] was increased from 0 to 5 M slow decreases in the Trp fluorescence signal were observed (ϳ1-2 s Ϫ1 ) for both TnC F29W and G34DTnC F29W (less than 5% of the total Trp change, data not shown). The amplitudes of these slow decreases in Trp fluorescence decreased with increasing [Ca 2ϩ ] and were absent when the [Ca 2ϩ ] exceeded 5 M. Computer modeling of these reactions predicted that these decreases in Trp fluorescence were associated with Ca 2ϩ removal from the N-domain sites of the TnCs by the high affinity C-domain sites that possess an ϳ100-fold slower Ca 2ϩ association rate and ϳ10-fold higher Ca 2ϩ affinity (20). Furthermore, the rapid increase in Trp fluorescence for both TnC F29W and G34DTnC F29W became too fast to observe as the [Ca 2ϩ ] exceeded 5 M. Unexpectedly, as the [Ca 2ϩ ] was increased from 5 M up to 1 mM another slow second order rate constant was observed for TnC F29W and  G34DTnC F29W at ϳ1.0 ϫ 10 6 and 2.0 ϫ 10 6 M Ϫ1 s Ϫ1 , respectively (less than 10% of the total Trp signal change, data not shown). This second Ca 2ϩ association rate process was abolished in the presence of 3 mM Mg 2ϩ for both TnCs and was not observed with TnC 1-90 F29W , which was missing the C-terminal domain Ca 2ϩ binding sites (data not shown). Thus, these slow Ca 2ϩ association rates were associated with the C-terminal domain of the TnCs and were consistent with previously calculated Ca 2ϩ association rates to the C-terminal Ca 2ϩ /Mg 2ϩ sites of TnC (18,20). Thus, the Trp 29 fluorescence was marginally influenced by C-terminal Ca 2ϩ binding as has been reported for TnC Danz , TnC F52W , and TnC F78W (17,24,59).
Because the Mg 2ϩ affinity for the regulatory domain of G34DTnC F29W is higher than that of TnC F29W , as the [Mg 2ϩ ] in the fiber increases there should be a larger shift in the Ca 2ϩ sensitivity of force for muscle fibers containing G34DTnC F29W , compared with those containing TnC F29W . Fig. 7B shows the Ca 2ϩ -dependent increase in skinned psoas muscle force with TnC endogenous (ࡗ), TnC F29W (f), or G34DTnC F29W (OE) in the presence of 3 mM [Mg 2ϩ ] free . Half-maximal force occurred at 540 Ϯ 25, 770 Ϯ 18, and 5770 Ϯ 800 nM Ca 2ϩ for TnC endogenous , TnC F29W , and G34DTnC F29W , respectively. Thus, in the presence of 3 mM [Mg 2ϩ ] free the Ca 2ϩ sensitivity of force development was ϳ7.5-fold lower for G34DTnC F29W compared with TnC F29W . Furthermore, as the [Mg 2ϩ ] free was increased from 1 to 3 mM, the Ca 2ϩ sensitivity of force development with G34DTnC F29W was decreased ϳ3.2-fold. However, under the same conditions the Ca 2ϩ sensitivity of force development with TnC endogenous or TnC F29W was decreased only ϳ1.5-fold. These results are consistent with competitive Mg 2ϩ binding to the regulatory domains of all the TnC proteins, with the largest effect occurring with G34DTnC F29W because of its higher Mg 2ϩ affinity. Table III summarizes the skinned muscle results. After TnC was extracted, force was decreased to 5 Ϯ 1% of the maximal force generated with TnC endogenous (data not shown). TnC F29W was capable of recovering maximal force to 93 Ϯ 1%, whereas G34DTnC F29W recovered only 62 Ϯ 5% of the maximal force. It has been demonstrated that partial extraction of TnC can reduce maximal force recovery and decrease the Ca 2ϩ sensitivity of force development (61)(62)(63)(64). We were concerned that the decreased Ca 2ϩ sensitivity of force development generated by G34DTnC F29W could be explained by its incomplete force recovery and not by its increased Mg 2ϩ affinity. Fig.  7C shows that upon partial extraction of TnC endogenous (छ) to levels of 87, 69, 44, and 37%, maximal force recovery shifted the Ca 2ϩ sensitivity of force development 2.1-, 2.5-, 4.4-, and 5.4fold, respectively. This decrease in Ca 2ϩ sensitivity of force development caused by partial extraction of TnC endogenous was age Ϯ S.E. of at least three determinants. The data were fit with a linear regression where the slope represents the calculated Ca 2ϩ association rate, except for G34DTnC F29W in the presence of 3 mM Mg 2ϩ , which demonstrated no Ca 2ϩ dependence of its association rate as, described under "Results." ] represents the amount of Ca 2ϩ that was presented to the apo-TnC immediately after mixing was complete. Trp fluorescence was monitored as described in the legend to Fig. 3, panel C. Each trace is an average of at least 10 -15 traces fit with a single exponential as described in Fig. 3, panel C (except No Ca 2ϩ , which was flat, variance Ͻ2 ϫ 10 Ϫ4 ). Panel B shows the time course of the increases in Trp fluorescence of G34DTnC F29W as increasing concentrations of Ca 2ϩ were rapidly mixed with the protein in the presence of 3 mM Mg 2ϩ . The experimental conditions and analysis were identical to the reactions as demonstrated in panel A, except 3 mM Mg 2ϩ was added to the buffer and greater concentrations of Ca 2ϩ were required to achieve similar fluorescence values. Panel C shows plots of the observed Ca 2ϩ association rate versus the [Ca 2ϩ ] in the mixing chamber immediately after mixing was complete for TnC F29W (Ⅺ), G34DTnC F29W (‚), TnC F29W plus 3 mM Mg 2ϩ (f), or G34DTnC F29W plus 3 mM Mg 2ϩ (OE). Each point represents the aver-nearly identical to that determined by Brandt et al. (62). A linear regression fit to our data (r 2 ϭ 0.934) predicted that at the average force recovery observed with G34DTnC F29W of 62%, the Ca 2ϩ sensitivity of force development would be decreased ϳ3.3-fold due only to incomplete force recovery. Fig. 7C also shows that the average decrease in Ca 2ϩ sensitivity of force development for G34DTnC F29W compared with TnC endogenous at 1 (‚) and 3 mM (OE) [Mg 2ϩ ] free was 5.5-and 10.7-fold, respectively. However, after taking into account incomplete force recovery, Mg 2ϩ actually decreased the Ca 2ϩ sensitivity of force generated by G34DTnC F29W at 1 and 3 mM ϳ1.7and 3.2-fold, respectively, compared with TnC endogenous . Treating the data similarly for TnC F29W predicted that the shifts in Ca 2ϩ sensitivity of force development with TnC F29W compared with TnC endogenous could be entirely explained by incomplete force recovery. Therefore, in the presence of 3 mM [Mg 2ϩ ] free , the ϳ3.2-fold shift in Ca 2ϩ sensitivity of force development with G34DTnC F29W was similar to the ϳ2.0-fold shift in Ca 2ϩ affinity of G34DTnC F29W compared with TnC F29W either in isolation or in the presence of TnI-(96 -148).

DISCUSSION
Whether Mg 2ϩ competes with Ca 2ϩ for the N-terminal regulatory domain of TnC is unresolved (15,19,23,27,32). Several groups demonstrated that as the [Mg 2ϩ ] was increased, the Ca 2ϩ sensitivity of TnC, Tn-activated actomyosin ATPase, and force development decreased (19,(23)(24)(25)(26)(27)(28)(29)(30)(31). These results suggested that Mg 2ϩ binding to the regulatory domain of TnC, competitive or otherwise, affected its biochemical and physiological properties. We studied Mg 2ϩ binding and exchange with the regulatory domain of TnC and its mutant, utilizing the Trp fluorescence of TnC F29W , which possesses a Phe 3 Trp mutation immediately preceding the first Ca 2ϩ -binding loop.
We have previously demonstrated that an endogenous Z acid pair in the first EF-hand of CaM F19W was required for physiologically relevant Mg 2ϩ binding to this EF-hand (3). Because the first EF-hand of TnC has a Gly at the ϩz position, we hypothesized that substitution of Gly with Asp should enable the first EF-hand of TnC to bind Mg 2ϩ . Indeed, when Gly-34 at the ϩz position was substituted with Asp, the Trp fluorescence of G34DTnC F29W increased ϳ1.4-fold upon addition of Mg 2ϩ , with a K d(Mg) ϳ 295 M. This same mutation in the absence of Mg 2ϩ led to an ϳ1.8-fold increase in Ca 2ϩ affinity of the regulatory domain. However, in the presence of 3 mM Mg 2ϩ , the Ca 2ϩ sensitivity of G34DTnC F29W decreased ϳ6-fold. From the K d(Ca) obtained in the absence and presence of Mg 2ϩ , we calculated the K d(Mg) to be ϳ588 M for G34DTnC F29W . Thus, the measured K d(Mg) was in good agreement with the calculated K d (Mg) . These experiments demonstrate that introduction of an Asp residue at the ϩz position in the first EF-hand of TnC F29W enabled this EF-hand to competitively bind Mg 2ϩ with a physiologically relevant affinity. Consistent with our results, introduction of a Z acid pair into the CD site of oncomodulin led to an ϳ12and 52-fold increased Ca 2ϩ and Mg 2ϩ affinity to this site, respectively (65). Similarly, in CaM F19W , replacement of Asp with Asn at the ϩz position of the first EF-hand led to an ϳ5and 58-fold decreased Ca 2ϩ and Mg 2ϩ affinity to the Nterminal sites, respectively (3,8 50 for fibers in which TnC endogenous was partially extracted versus percent of maximal force recovery compared with [Ca 2ϩ ] 50 endogenous (TnC endogenous Extraction, छ). The data from four fibers were fit with a linear regression to determine the relationship between incomplete force recovery and decreased Ca 2ϩ sensitivity as described under "Results." modification of the ϩz position in some EF-hand proteins modulates the Mg 2ϩ affinity more so than the Ca 2ϩ affinity.
Interestingly, the fluorescence of TnC F29W did not change upon binding Mg 2ϩ but increased upon binding Ca 2ϩ to the regulatory sites (43,44,48 Because TnC regulates muscle contraction as a part of the Tn complex, we have also studied Ca 2ϩ and Mg 2ϩ binding to TnC F29W and G34DTnC F29W in the presence of the TnI-(96 -148) peptide. The addition of the TnI-(96 -148) peptide to TnC F29W and G34DTnC F29W produced ϳ12and 14-fold increases in their N-domain Ca 2ϩ binding affinities, respectively, as has been previously reported for intact TnI (15,33 Functionally, Mg 2ϩ did not cause force development in reconstituted skeletal muscle fibers at 1 or 3 mM [Mg 2ϩ ] free with G34DTnC F29W or TnC F29W , consistent with Mg 2ϩ binding not inducing the same structural changes as does Ca 2ϩ . In the absence of Mg 2ϩ , the Ca 2ϩ affinity of G34DTnC F29W was ϳ2fold higher than that of TnC F29W , yet the Ca 2ϩ sensitivity of force development in the presence of 1 and 3 mM [Mg 2ϩ ] free with G34DTnC F29W was decreased compared with TnC F29W , consistent with competitive Mg 2ϩ binding to G34DTnC F29W . Furthermore, the Ca 2ϩ sensitivity of force was decreased only ϳ1.5-fold with TnC endogenous and TnC F29W , but was decreased ϳ3.2-fold with G34DTnC F29W as the [Mg 2ϩ ] free was increased from 1 to 3 mM. These results were also consistent with competitive Mg 2ϩ binding to the regulatory domains of TnC endogenous and TnC F29W . After taking incomplete force recovery into consideration, in the presence of 3 mM Mg 2ϩ , G34DTnC F29W was ϳ3.2fold less sensitive to Ca 2ϩ compared with TnC endogenous or TnC F29W . However, the magnitude of the shift in Ca 2ϩ sensitivity could vary depending upon the cause of the reduced force recovery (partial TnC extraction versus substitution by a mutant). In any case, the force produced by G34DTnC F29W was less sensitive to Ca 2ϩ than that of TnC F29W , consistent with G34DTnC F29W possessing a higher Mg 2ϩ affinity.
Unexpectedly, G34DTnC F29W recovered only ϳ62% of maximal force. Our results demonstrated that reduced affinity of the regulatory domain within G34DTnC F29W for the inhibitory region of TnI was not the cause for the decreased force recovery. However, we cannot rule out the possibility that the conformation of the G34DTnC F29W ⅐TnI complex was somehow different from that of the TnC F29W ⅐TnI complex, leading to reduced force. The extent of force recovery by G34DTnC F29W  50 caused by incomplete force recovery was calculated for each mutant using the linear fit to the partial TnC extraction data in Fig. 7C (-fold decrease in [Ca 2ϩ ] 50 ϭ Ϫ0.07 *(percent maximal force) ϩ 7.5, with 93 and 62% maximal force for TnC F29W and G43D TnC F29W , respectively). Second, the experimentally measured -fold decrease in [Ca 2ϩ ] 50 was divided by the -fold decrease in [Ca 2ϩ ] 50 caused by incomplete force recovery to obtain the corrected [Ca 2ϩ ] 50 , which was then converted to pCa 50 . was similar to that of psoas muscle fibers reconstituted with cTnC (69,70). The G34D mutation is in the first EF-hand of TnC, which is the same EF-hand in cTnC that does not bind Ca 2ϩ . It may be that the mechanism(s) that underlie the decreased force recovery of fast twitch skeletal muscle reconstituted with cTnC are the same for G34DTnC F29W . It has been speculated that the decreased force recovery with cTnC may be due in part to its decreased actomyosin-ATPase rate in reconstituted skeletal muscle systems and lack of Ca 2ϩ binding cooperativity because of its single regulatory Ca 2ϩ binding site (71). There does appear to be decreased cooperativity of force development with the G34DTnC F29W reconstituted muscle fibers (Table I). However, a N-helix deleted TnC mutant also displayed decreased actomyosin-ATPase activity but recovered near maximal force in reconstituted psoas muscle (47). Thus, the reason for the lack of maximal force recovery for G34DTnC F29W remains unresolved.
A major consequence of the high Mg 2ϩ affinity and relatively slow Mg 2ϩ dissociation rate of G34DTnC F29W (at a rate comparable with its Ca 2ϩ dissociation rate) would be to drastically slow the Ca 2ϩ association rate in the presence of physiological Mg 2ϩ by a factor of ϳ4 ϫ 10 5 . Our laboratory is interested in delineating the influence that the Ca 2ϩ kinetics of the regulatory domain of TnC has on striated muscle contraction and relaxation. G34DTnC F29W could be used as a molecular tool to test whether slower Ca 2ϩ association rates to the regulatory domain of TnC could slow Ca 2ϩ -induced rates of muscle contraction.
In conclusion, the data suggests that the second EF-hand, but not the first, of TnC F29W was able to competitively bind Mg 2ϩ . Physiologically relevant Mg 2ϩ binding could be engineered into the first EF-hand of TnC F29W by substituting Gly 34 with Asp creating a Z acid pair. In the absence of Mg 2ϩ , the Gly 34 3 Asp mutation also increased the Ca 2ϩ affinity of TnC F29W and the TnC F29W ⅐TnI-(96 -148) complex. However, in the presence of Mg 2ϩ , the Gly 34 3 Asp mutation decreased the Ca 2ϩ affinity of TnC F29W and the TnC F29W ⅐TnI-(96 -148) complex. Consistent with competitive Mg 2ϩ binding to the first EF-hand of G34DTnC F29W , exchange of this protein into skinned skeletal psoas muscle fibers led to lower Ca 2ϩ sensitivity of force development.