Kinetic and Equilibrium Properties of Regulatory Calcium Sensors of NCX1 Protein*

The crystal structures of the CBD1 and CBD2 domains of the Na+/Ca2+ exchanger protein (NCX1) provided a major breakthrough in Ca2+-dependent regulation of NCX1, although the dynamic aspects of the underlying molecular mechanisms are still not clear. Here we provide new experimental approaches for evaluating the kinetic and equilibrium properties of Ca2+ interaction with regulatory sites by using purified preparations of CBD1, CBD2, and CBD12 proteins. CBD12 binds ∼6 Ca2+ ions (mol/mol), whereas the binding of only ∼2 Ca2+ ions is observed (with a Hill coefficient of nH = ∼2) either for CBD1 or CBD2. In the absence of Mg2+, CBD1 has a much higher affinity for Ca2+ (Kd = 0.3 ± 1.2 μm) than CBD2 (Kd = 5.0 ± 1.2 μm). The Ca2+ dissociation from CBD2 (koff = 230 ± 70 s–1) is at least 25 times faster than from CBD1 (koff = 10 ± 3 s–1), whereas the kon values indicate fast kinetics for Ca2+ binding (kon = koff/Kd = 107–108 m–1 s–1) for both CBDs. At 2–5 mm Mg2+, both CBDs bind Ca2+, with a Kd of 1–2 μm (Mg2+ has very little effect on Ca2+ off rates). Mg2+ cannot occupy the primary site of CBD2, whereas the other Ca2+ sites of CBDs interact with Mg2+ as well. There is no competition between Na+ and Ca2+ for any CBD site. The kinetically diverse Ca2+ sensors may sense differentially the dynamic swings in [Ca2+] within specific subcellular compartments (dyadic cleft, submembrane space, bulk cytosol, etc.).

In cardiomyocytes the cytosolic Ca 2ϩ concentrations swing dramatically during the action potential, thereby requiring dynamic regulation of NCX1 during excitation-contraction coupling (2,3,8,9). Moreover, the Na ϩ /Ca 2ϩ exchange rates must meet ever-changing demands for cardiac output in health and disease. Any imbalance in Ca 2ϩ extrusion may lead to lifethreatening disorders caused by either Ca 2ϩ depletion or overload of Ca 2ϩ stories (7)(8)(9).
High resolution crystallography reveals four Ca 2ϩ sites in CBD1 (19) and two Ca 2ϩ sites in CBD2 (20). Unfolded structure of CBD1 becomes well folded upon Ca 2ϩ binding (19,22), whereas CBD2 is a fully folded protein, even in the absence of Ca 2ϩ (18,20). The mutations in the Ca 2ϩ sites of CBD1 decrease the Ca 2ϩ affinity but do not eliminate the Ca 2ϩ -dependent regulation, whereas the mutations in the primary Ca 2ϩ site of CBD2 abolish Ca 2ϩ regulation altogether (20).
The present work offers new experimental setups for measuring the equilibrium and rate constants of Ca 2ϩ binding/dissociation in purified preparations of CBD1, CBD2, and CBD12 proteins. These experimental approaches allow one to directly test specific ligands (e.g. Na ϩ , K ϩ , or Mg 2ϩ ) for their capacity to alter the Ca 2ϩ binding/dissociation in CBD preparations. We found that the CBD1 and CBD2 domains are kinetically distinct Ca 2ϩ sensors capable of sensing the Ca 2ϩ within the time scale of a single cardiac cycle. Kinetically distinct CBD sensors have a capacity to sense local Ca 2ϩ changes in distinct compartments of the cell and thus may serve as a feedback mechanism for distinct regulation of NCX in dyadic cleft, submembrane space, and bulk cytosol. 657, and 371-657 residues of canine NCX1 (Protein Data Bank accession code P23685; AD-splice variant) were cloned into a pET23b vector (generously provided by Dr. M. Hilge) and expressed in Escherichia coli Rosetta2 (DE3)-competent cells (Novagen) at 37°C for 5 h by using 1 mM isopropyl 1-thio-␤-Dgalactopyranoside for induction (18). Grown cells were diluted 1:100 in 2ϫ YT medium and grown again until A 595 nm reached 0.4 -0.6. Expression was induced with 1 mM isopropyl 1-thio-␤-D-galactopyranoside, and after a 5-h induction period, the cells were harvested by centrifugation (7000 ϫ g for 10 min) and then were flash-frozen and stored at Ϫ70°C. Thawed cells were suspended in 20 mM Tris-Cl, pH 8.0, 300 mM NaCl, 5% glycerol, 0.1% ␤-mercaptoethanol, 0.1% Triton X-100, 0.1 mM CaCl 2 with 1 g/ml DNase I (type DN-25; Sigma), and protease inhibitor mixture (Roche Applied Science). The cells were homogenized and disrupted twice in microfluidizer (Microfluidics, Newton, MA). CBD1, CBD2, or CBD12 was recovered by centrifugation at 12,000 rpm for 15 min at 4°C. The supernatant was mixed with 7 ml of nickel beads (HIS-Select TM , nickel affinity gel; Sigma) and washed (7 ϫ 25 ml) with 250 mM Mes, pH 6.3, 300 mM NaCl, 10% glycerol, and 0.1 mM CaCl 2 (MNG buffer). CBD1, CBD2, and CBD12 were eluted with 2 ϫ 15-ml portions of MNG buffer containing 300 mM imadozole, pH 7.4. Imidazole was removed by washing the protein preparations with 20 mM HEPES, pH 7.4, 20 mM ␤-mercaptoethanol, 0.05% sodium azide and then dialyzed against 10 mM Tris-Cl, pH 7.5 (at 4°C) buffer containing 10 g/liter Chelex-100 (Bio-Red). Dialyzed CBD preparations were washed twice with 0.1-0.2-mM EDTA using Ultracel-3k (Millipore), and EDTA was removed by ultrafiltration. The protein was determined at A 280 nm by using ⑀ ϭ 3105 M Ϫ1 cm Ϫ1 for CBD1, ⑀ ϭ 5960 M Ϫ1 cm Ϫ1 for CBD2, and ⑀ ϭ 9065 M Ϫ1 cm Ϫ1 for CBD12. Purified preparations of proteins (Ͼ95%, as judged by SDS-PAGE) were stored at Ϫ70°C. 45 Ca 2ϩ /Protein Equilibrium Binding-The 45 Ca 2ϩ binding assay was done by using the ultrafiltration procedure (36 -38). To remove Ca 2ϩ , all glassware and tubes were washed with 0.1 M HCl, and filters were pretreated with 5% NaHCO 3 (38). Decalcified buffers (containing 0.9 -2.3 M Ca 2ϩ ) were prepared by passing them through Chelex-100. All of the 45 Ca 2ϩ binding experiments were done with an Ultracel-3k (15-ml sample compartment, 3-kDa cut-off; Millipore Corp.). The assay medium (1 ml), containing 10 -40 M CBD1 or CBD2 in decalcified buffer, was placed into the upper compartment of the Ultracel-3k concentrator. For the binding assay, 1 l of 5.7 mM 45 Ca 2ϩ stock solution (ϳ3 Ci) was added to the assay medium with protein, carefully mixed, and allowed to equilibrate. After 10 min, the sample was centrifuged at 1000 ϫ g for 30 -50 s, forming 15-20 l of filtrate. The filtrate was returned to the upper chamber, mixed, and centrifuged again. 5-l samples of filtrate and protein were analyzed for radioactivity. Subsequently, nonradioactive CaCl 2 was added serially to the protein sample, and after centrifugation, 5-l samples of the filtrate and upper compartment were tested for radioactivity.  45 Ca 2ϩ in a 1-ml assay medium containing 10 mM Tris-HCl, pH 7.2, plus either 100 mM KCl (‚) or 100 mM choline chloride (Ⅺ). The concentrations of Ca 2ϩ were increased by adding stock solutions of nonradioactive Ca 2ϩ . At each concentration of Ca 2ϩ , the Ca 2ϩ -bound protein (in the upper chamber) was separated from the free ligand by ultrafiltration, yielding a 15-20-l filtrate. After centrifugation, 5-l samples were taken for radioactive counting from the filtrate and the upper chamber, and the data were plotted as bound 45 Ca 2ϩ per CBD1 or CBD2 (mol/mol) versus free concentrations of Ca 2ϩ (for details, see "Materials and Methods"). A Hill equation was used to fit the calculated lines to the experimental points yielding K d ϭ 0.43 Ϯ 0.02 M, n H ϭ 2.14 Ϯ 0.25, and Cap ϭ 1.79 Ϯ 0.11 45 Ca 2ϩ /CBD1 (mol/mol) for CBD1 and K d ϭ 6.2 Ϯ 0.12 M, n H ϭ 2.02 Ϯ 0.08, and Cap ϭ 1.70 Ϯ 0.12 45 Ca 2ϩ /CBD2 (mol/ mol) for CBD2. b, the Ca 2ϩ titration curves were obtained for 10 M CBD12, as described in a. The assay medium contained 10 mM Tris-HCl, pH 7. (mol/mol) was plotted versus [Ca 2ϩ ] free , and the data was fitted to a Hill equation,

Expression and Purification of CBD Proteins-The
or to the following Adair equation.
Ca 2ϩ /Protein Equilibrium Binding Assayed by Fluo-3-The experimental procedures of this assay were previously described (39,40). A F-96 MicroWell TM plate (Nunc) was prewashed to remove any contaminating Ca 2ϩ . The exact concentrations of Fluo-3 were determined photometrically using ⑀ 506 ϭ 86,000 M Ϫ1 cm Ϫ1 . Each well (140 l of assay medium) contained 11 M Fluo-3 with or without 10 M protein. Fluorescence was measured (at 25°C) on an Infinite-F200 microplate reader (TECAN) at ex ϭ 485 Ϯ 10 nm and a em value of 535 Ϯ 12.5 nm. The [Ca 2ϩ ] res and K d values were derived as fit parameters, whereas [F] t was held constant. For the Fluo-3 plus CBD1 titration curves, the obtained [Ca 2ϩ ] res and Fluo-3 K d values were used to subtract the Fluo-3-bound Ca 2ϩ species (F-Ca 2ϩ ) to yield the CBD1 curve. [F-Ca 2ϩ ] eq was calculated as [F-Ca 2ϩ ] eq ϭ x[F] t , and [Ca 2ϩ ] free was calculated as [Ca 2ϩ ] free ϭ xK d , whereas x represents the fractional saturation of Fluo-3 at each given point of the titration curve (x ϭ 1 and x ϭ ϳ0 were determined experimentally with saturating Ca 2ϩ and EDTA, respectively). The [Ca 2ϩ -CBD] levels were derived as follows.
The [Ca 2ϩ -CBD]/[CBD] values were plotted as bound Ca 2ϩ per CBD as a function of [Ca 2ϩ ] free , and the Ca 2ϩ titration curves were analyzed by using GraFit 3.01 software.
Stopped Flow Experiments-In the stopped flow experiments, 150 l of 20-40 M CBD1 or CBD2 with 20 -80 M Ca 2ϩ (syringe A) was mixed (t ϭ 10 -20 ms) with 150 l of buffer containing 150 M Quin-2 (syringe B) at 25°C. Under these conditions, [Ca 2ϩ ] i drops below 100 nM within Ͻ2 ms. The stopped flow machine SFM-3 (BioLogic) equipped with a TC-100/15 cuvette (a mixing dead time of ϳ2 ms). Quin-2 was excited at ex ϭ 333 nm from a monochromator with a hydrogen-xenon lamp (150 W), and the emission was monitored at em Ͼ 495 nm. The rapid mixing conditions were controlled with a MPF program, and the data were analyzed with Bio-Kine 32 V4.45 (BioLogic).
Statistics-The K d , k off , and n H values present the means Ϯ S.E. Statistical analysis was done by using the two sample independent t test (Origin 7.0, Northampton, MA). 45 Ca 2ϩ titration curves were analyzed for purified preparations of CBD1, CBD2, and CBD12 at pH 7.2 and 25°C. The proteinbound 45 Ca 2ϩ was quantified by ultrafiltration. In an assay medium of 100 mM choline chloride (or KCl), CBD1 binds ϳ1.  (Fig. 1a). Under comparable experimental conditions, CBD2 binds ϳ1.7 45 Ca (mol/mol) with a K d of 6.2 M and n H ϭ 2.0 ( Fig. 1a). Adair analysis reveals K d1 /K d2 ratios of 12.6 and 11.6 for CBD1 and CBD2, respectively (Table 1). This is consistent (within the experimental error) with measured values of Hill coefficient (n H ϭ 1.8 -2.0), although the maximal capacities for Ca 2ϩ binding are not exactly 2.0 (Table 1) for either protein (notably, Adair equation predefines a number of binding sites, whereas the Hill equation does not). Therefore, the derived values of K d1 and K d2 can be used (in combination with measured k off values) for calculating the k on values in a kinetic model describing a cooperative binding of two Ca 2ϩ ions to CBDs (see Fig. 7).

Equilibrium 45 Ca 2ϩ Binding Measurements-The
In the absence of Mg 2ϩ , the titration curve of CBD12 reaches saturation at [ 45 Ca 2ϩ ] free ϭ 60 -80 M with a maximal binding capacity of ϳ5.9 45 Ca/CBD12 (mol/mol), whereas Adair analysis reveals the intrinsic K d values for six Ca 2ϩ sites as 0.2, 1.5, 2.3, 25, 30, and 120 M (Fig. 1b). These data suggest that the CBD12 construct can bind two additional Ca 2ϩ ions with K d values of Ͼ 30 M as compared with CBD1 and CBD2 constructs (Fig. 1b). Considering the crystal structure data, according to which CBD1 contains four binding sites (19,22), whereas CBD2 contains only two sites (20), it is reasonable to assume that the "extra" two affinity sites observed in CBD12 belong to CBD1 and not to CBD2. In the presence of 5 mM Mg 2ϩ , CBD12 binds less Ca 2ϩ at any given concentration of [Ca 2ϩ ] free (Fig.  1b), meaning that Mg 2ϩ decreases the affinities of nearly all Ca 2ϩ -binding sites of CBD12.
Equilibrium Ca 2ϩ Binding Measurements by Fluo-3-The above-described radioactive assays of Ca 2ϩ binding exhibited a maximal capacity of ϳ2 bound Ca 2ϩ (mol/mol) for both CBD1 and CBD2 (Fig. 1a), whereas ϳ 6 Ca 2ϩ /CBD12 (mol/mol) bound species were detected in CBD12 (Fig. 1b). To resolve this discrepancy as well as to validate the accuracy of our radioactive measurements, the Ca 2ϩ binding properties of CBD1 were quantitatively evaluated by a complementary and independent approach. To this end, the fluorescence assay of Fluo-3 was performed because of its capacity to measure not only the K d values but also the Ca 2ϩ binding stoichiometry (39,40). This

TABLE 1 Equilibrium Ca 2؉ binding constants of CBD1 and CBD2
The Ca 2ϩ titration curves and data analysis were done as described in the legend of Fig. 1. The titration curves of binding data were fitted by using a Hill or Adair equation (see "Materials and Methods"). The n H represents a Hill coefficient. The mean Ϯ S.E. values represent the data collected from six independent experiments (n ϭ 6) for CBD1 or CBD2. The assays were done in the assay medium containing 100 mM KCl or choline chloride plus buffer, as described in the legend to Fig. 1.

Hill equation
Adair equation  (Fig. 2b). Very similar titration curves were obtained by using the radioactive and fluorescence assays (Fig. 2c). Therefore, in the isolated preparations of CBD1, both the radioactive and fluorescence assays reveal the maximal stoichiometry of ϳ2 Ca 2ϩ / CBD1 (mol/mol), meaning that the low affinity sites of the isolated CBD1 cannot be identified because of the conformational state of CBD1 and not because of methodological limitations.
Stopped Flow Measurements of Ca 2ϩ Off Rates-The stopped flow technique was used for measuring the rate constants of Ca 2ϩ dissociation from CBD1 and CBD2 by exploring Quin-2. The use of Quin-2 was preferred, because this probe has an extremely high affinity to Ca 2ϩ (K d ϳ50 nM), whereas k on ϭ ϳ10 9 M Ϫ1 s Ϫ1 is nearly a diffusion-controlled reaction (41,42).
In these experiments 10 -20 M CBD1 or CBD2 (pre-equilibrated with 40 -80 M Ca 2ϩ ) was mixed with 150 M Quin-2. The rationale behind this is that when Quin-2 is mixed with the Ca 2ϩ /protein, [Ca 2ϩ ] free drops rapidly (Ͻ2 ms) below K d , thereby inducing the Ca 2ϩ /protein dissociation. Subsequently, Ca 2ϩ dissociates from a protein complex (on a slower time scale) and binds to Quin-2, resulting in a rise in fluorescence. The observed increase in fluorescence matches the rate and amount of Ca 2ϩ dissociation from the complex. Under standard assay conditions (100 mM choline chloride or KCl), approximately two Ca 2ϩ ions dissociate from CBD1 with observed order rate constant of k off ϭ 13.3 Ϯ 0.1 s Ϫ1 (Fig. 3a). The Ca 2ϩ dissociation kinetics of CBD2 is much faster, exhibiting a k off of 155 Ϯ 3 s Ϫ1 (Fig. 3b). Comparable results were obtained for five different preparations of CBD1 (k off ϭ 6 -13 s Ϫ1 ) and CBD2 (k off ϭ 155-300 s Ϫ1 ) ( Table 2). In contrast to CBD1 and CBD2, the CBD12 construct shows the biphasic kinetics of Ca 2ϩ dissociation, exhibiting a k 1 value of 7 Ϯ 3 s Ϫ1 and a k 2 value of 125 Ϯ 50 s Ϫ1 (Fig. 3c). Because the k 1 and k 2 values are quite similar to the rate constants observed in the isolated CBD1 and CBD2, it is reasonable to assume that the CBDs retain their kinetic properties in the integrated CBD12 construct. The Ca 2ϩ dissociation from the low affinity sites of CBD1 is perhaps so fast that it cannot be detected by stopped flow techniques even in the CBD12 construct. Testing the Effects of Monovalent Cations on Ca 2ϩ Interactions with CBDs-To test the possible effect of monovalent cations on Ca 2ϩ binding/dissociation in CBD1 and CBD2, Na ϩ and K ϩ were examined for its effects on equilibrium 45 Ca 2ϩ titration curves and Ca 2ϩ dissociation kinetics by using the experimental protocols described above. Na ϩ or K ϩ (100 mM) has no appreciable effect on the K d values of CBD1 (Fig. 4a) or CBD2 (Fig. 4b), as compared with control (100 mM choline chloride). Na ϩ or K ϩ does not affect the 45 Ca 2ϩ titration curves of CBD12 as well (not shown), suggesting that these monovalent cations do not affect the Ca 2ϩ binding of two low affinity sites of CBD1 domain as well. In the other set of experiments, the effect of Na ϩ or K ϩ was tested on Ca 2ϩ dissociation kinetics. In these experiments the CBD preparations were pre-equilibrated with Ca 2ϩ and then mixed in the stopped flow machine with Quin-2 buffer containing 100 mM NaCl or KCl. Na ϩ or K ϩ has a rather small accelerating effect on the k off values of both CBDs, as compared with control experiments containing 100 mM choline chloride in the assay medium (Table 2). Because the observed effects of Na ϩ or K ϩ on the K d and k off values are relatively small (taking into account the experimental error), these effects are considered insignificant.
Mg 2ϩ Effects on Ca 2ϩ Interactions with CBDs-In contrast to monovalent cations, 5 mM Mg 2ϩ decreases the 45 Ca 2ϩ binding affinity of CBD1 from K d ϭ ϳ0.18 M (in the absence of Mg 2ϩ ) to K d ϭ ϳ1.26 M (in the presence of Mg 2ϩ ) (Fig. 5a). These data are statistically significant, suggesting that 2-5 mM Mg 2ϩ can decrease the Ca 2ϩ binding affinity for CBD1 by at least 5-8-fold (Table 2). In the presence of Mg 2ϩ (5 mM MgCl 2 ϩ 95 mM choline chloride), CBD2 binds only ϳ1 Ca 2ϩ (mol/mol), showing a K d of 1.1 M (Fig. 6a, closed circles). Control experiments without Mg 2ϩ reveal a typical binding of ϳ2 Ca 2ϩ /CBD2 (mol/mol), with a K d of 5.6 M and an n H of 2.5 (Fig. 6a, open  circles). These data suggest that Mg 2ϩ binding to the secondary of CBD2 increases the Ca 2ϩ affinity at the primary Ca 2ϩ site of CBD2. To elaborate a dose curve for Mg 2ϩ -dependent displacement of Ca 2ϩ at CBD2, increasing concentrations of Mg 2ϩ were added at nearly saturating concentrations of 45 (Fig. 6b). Therefore, Mg 2ϩ can displace Ca 2ϩ at the secondary site of CBD2, which in turn increases the Ca 2ϩ affinity at the primary site of CBD2. 2 mM Mg 2ϩ has a small decelerating effect on the k off values of CBD1 and CBD2 (Table 2), which probably represents very weak competition of Mg 2ϩ with Ca 2ϩ for Quin-2 binding rather than the effect of Mg 2ϩ on Ca 2ϩ dissociation kinetics of CBDs.

Ca 2ϩ Binding Properties of CBD Ca 2ϩ Sensors-Cooperative
interactions between two Ca 2ϩ -binding sites was primarily observed in the loop-f constructs (17,47), although later studies have shown that these constructs contain only the CBD1 fragment (18 -20). We found that under the equilibrium conditions, the CBD12 construct binds ϳ6 Ca 2ϩ ions (mol/mol) (Fig.  1b). Both the radioactive (Fig. 1a) and fluorescence assays (  coefficient of n H ϳ 2 (Fig. 1a). Notably, two extra low affinity sites (K d Ͼ 30 M) can be observed in CBD12 but not in CBD1. Because a crystal structure reveals four binding sites in CBD1 (19) and two binding sites in CBD2 (20), the "additional" two binding sites observed in CBD12 belong to CBD1 and not to CBD2. Most probably, CBD2 might have a stabilizing effect on CBD1 conformation in the CBD12 construct. Present findings support a notion that the CBD Ca 2ϩ sensors retain their equilibrium (Figs. 1 and 2) and kinetic properties (Fig. 3) in the CBD12 construct. This is consistent with a common notion that the CBD1 and CBD2 domains are autonomously folded C2 protein structures retaining their functional properties (18 -26). The fact that two low affinity Ca 2ϩ -binding sites of CBD1 can be detected only in CBD12 (but not in isolated CBD1) can be explained by the suggestion that a highly flexible loop near the Ca 2ϩ sites of CBD1 (18,19,22) become less flickering in the CBD12 (probably because of domain-domain interactions). The low affinity sites of CBDs may become occupied by Ca 2ϩ only in restricted compartments (e.g. in dyadic cleft) where the local Ca 2ϩ may reach 10 Ϫ4 M concentrations.
Considering the structural similarities of CBDs with other C2 proteins (44 -46), it was proposed that the negatively charged phospholipids may interact with the two weaker Ca 2ϩ sites of CBD1 (21). Notably, not all proteins containing C2 domains interact with lipids (52). Therefore, more dedicated investigation is required for examining a possibility for lipid interaction with CBD1 and/or CBD2.

CBD1 and CBD2 Are Kinetically Distinct Ca 2ϩ Sensors Even at Similar K d Values-
The experimental evidence suggests that the CBD domains undergo conformational changes in the cell within the excitation-contraction coupling (43,49). To this end, no kinetic measurements have been undertaken to analyze the Ca 2ϩ interactions with the CBD sites. Here we applied the stopped flow techniques for measuring the Ca 2ϩ dissociation kinetics and found that the primary sites of CBD1 and CBD2 have strikingly distinct off rates for Ca 2ϩ dissociation (even under conditions at which the K d values are similar). Namely, the Ca 2ϩ dissociation is much slower in CBD1 (k obs ϭ 6 -13 s Ϫ1 ) than in CBD2 (k obs ϭ 155-300 s Ϫ1 ) (Fig. 3 and Table 2). Notably, there is no experimental evidence that the individual Ca 2ϩ ions dissociate with distinct off rates. A kinetic model for cooperative binding of two Ca 2ϩ ions can be described (Fig. 7) on the basis of derived K d1 and K d2 values (Table 1) and observed off rates (Table 2). According to this model both CBDs are capable of sensing rapid changes in Ca 2ϩ concentrations within a single cycle of excitation-contraction coupling.
Although the Ca 2ϩ association/dissociation kinetics does not necessarily represent the exact dynamics of protein conformational changes, the observed kinetic properties may present the intrinsic features of autonomously folded CBD structures. The CBD12 domain resembles the biphasic kinetics for Ca 2ϩ dissociation (Fig. 3c), comprising the individual rate constants observed for CBD1 (Fig. 3a) and CBD2 (Fig. 3b). Therefore, it is reasonable to assume that the CBD1 and CBD2 domains retain their "autonomous" properties for Ca 2ϩ dissociation in the conjugated CBD12 construct.
Comparative Kinetics of Ca 2ϩ Sensors-In general, the Ca 2ϩ binding affinities and off rates could be very diverse even among proteins having very similar three-dimensional structures (23)(24)(25)(26)51). For example, EF-hand-containing proteins (usually having fast on rates) exhibit K d values that vary over a 1000-fold range, because of differences in the Ca 2ϩ off rates (23,51). Interestingly, the slow off rates (3-10 s Ϫ1 ) are found in proteins that act as Ca 2ϩ buffers (e.g. calciquestrin), whereas in Ca 2ϩsignaling proteins the off rates vary in the range of 10 -10 4 s Ϫ1 (for review see Ref. 51). Moreover, the Ca 2ϩ off rates of two distinct domains could be very different even in the same protein. For example, in calmodulin the off rate for the EF-hands in the N-terminal lobe is over 100 times faster than for the C-terminal domain, thereby allowing independent regulation by each lobe of calmodulin (23,51). Here, we demonstrate that the CBD1 and CBD2 domains have distinct Ca 2ϩ off rates even under conditions at which the K d values are similar at 2-5 mM Mg 2ϩ (Table 2).
Although we do not know how the conformational changes of CBD1 and CBD2 are integrated into the intact NCX protein, the kinetically distinct Ca 2ϩ sensors may represent a physical basis for differential sensing of Ca 2ϩ in dyadic, submembrane space, and bulk cytosol. This would be consistent with the notion that the NCX1 molecules are selectively co-localized and regulated within the cell (28 -31). Moreover, the Ca 2ϩ sensing kinetics (e.g. off rates) may vary among NCX isoforms and splice variants to fulfill tissue-specific demands of Ca 2ϩ homeostasis.
Ca 2ϩ Sensors of CBDs Are Insensitive to Na ϩ or K ϩ -Monovalent cations can modulate the partial reaction (Ca 2ϩ /Ca 2ϩ exchange) of the Na 2ϩ /Ca 2ϩ exchange cycle (11,34,35,50), which may or may not represent the interaction of modulatory

and equilibrium constants of Ca 2؉ interaction with CBD1 and CBD2 under various ionic conditions
The equilibrium constants for Ca 2ϩ binding to CBD1 or CBD2 were experimentally derived from titration curves as described in the legend of Fig. 1 by using a Hill equation (see also "Materials and Methods"). The assay medium contained 10 mM Tris-HCl, pH 7.2, with 100 mM choline chloride, KCl, or NaCl. The assay medium for Mg 2ϩ tests contained 95 mM choline chloride ϩ 5 mM Mg 2ϩ . The k off values were determined in stopped flow experiments (for details, see Fig. 3) by using the same set of buffers shown above. The means Ϯ S.E. represent the average values derived in multiple experiments, whereas n represents the number of independent experiments. The measured values of k off and K d were used to calculate the k on values as k on ϭ k off /K d .

CBD1
CBD2 cations with CBD domains. Here, we directly tested the effects of Na ϩ and K ϩ on the Ca 2ϩ binding/dissociation properties in the isolated preparations of CBD1, CBD2, and CBD12. We found that Na ϩ has no appreciable effect either on the K d or the k off values ( Fig. 4 and Table 2). These findings are consistent with a notion that the primary mechanisms underlying Na ϩdependent inactivation or Ca 2ϩ -induced relief of Na ϩ -dependent inactivation do not involve Na ϩ directly interacting with regulatory CBD sites. Because K ϩ also does not affect the Ca 2ϩ interaction with CBD1 or CBD2 (Table 2), the K ϩ -dependent activation of the Ca 2ϩ /Ca 2ϩ exchange (34, 35, 50) cannot be mediated by K ϩ interaction with CBD domains as well. Therefore, the Na ϩ -dependent inactivation may represent the Na ϩ interaction with the transport site(s) resulting in slow inactivation, as originally suggested by Hilgemann et al. (32,33). This is also consistent with a claim that the elevated Na ϩ induces a mode of activity that does not require allosteric Ca 2ϩ activation (27).
Only the Primary Site of CBD2 Is Highly Selective to Ca 2ϩ -Mg 2ϩ can decrease the Ca 2ϩ affinity to fusion proteins containing a high affinity site of loop-f (17). At this end it was not clear how Mg 2ϩ affects the specific Ca 2ϩ sensors of CBD1 and CBD2. We found that the Ca 2ϩ affinities of CBD1 (K d ϭ ϳ0.32 M) and CBD2 (K d ϭ ϳ5.0 M) are dissimilar only in the absence of Mg 2ϩ (Fig. 1a), whereas at 2-5 mM Mg 2ϩ , the K d of 1-2 M is observed for both CBDs (Table 2). Therefore, even under conditions at which the Ca 2ϩ affinities are similar, the kinetic properties of CBD1 and CBD2 are still diverse (Table 2).
Mg 2ϩ can compete with Ca 2ϩ for five sites of CBDs (Figs. 1b and 5) but not for the primary site of CBD2 (Figs. 5 and 6). In principle, Mg 2ϩ has opposite effects on the primary sites of CBD1 and CBD2 (Fig. 7). From one side Mg 2ϩ decreases the Ca 2ϩ affinity at the primary sites of CBD1 (Fig. 5), whereas on the other side Mg 2ϩ binding to the secondary site of CBD2 elevates the Ca 2ϩ affinity at the primary site of CBD2 ( Fig. 6 and Table 2). Most probably, Mg 2ϩ decelerates the Ca 2ϩ on rates at CBD1 sensors, whereas Mg 2ϩ accelerates the on rate at the primary site of CBD2 as a result of Mg 2ϩ interaction with the secondary site of CBD2 (Fig. 7b). In both cases no considerable FIGURE 4. Testing the effect of sodium on equilibrium 45 Ca 2؉ binding to CBD1 and CBD2. The 45 Ca 2ϩ titration curves of CBD1 or CBD2 were elaborated by using the ultrafiltration method, as described in Fig. 1 (see also "Materials and Methods"). The equilibrium binding assay was done with 10 mM Tris-HCl pH 7.2 buffer containing either 100 mM KCl (‚) or 100 mM NaCl (E) and varying concentrations of 45 CaCl 2 . a, the experimental data obtained for the CBD1 titration curves were independently fitted for K ϩ -and Na ϩ -containing buffers showing the following parameters for Na ϩ (Cap ϭ 2.00 Ϯ 0.05, K d ϭ 0.22 Ϯ 0.01 M, and n H ϭ 1.77 Ϯ 0.24) and K ϩ (Cap ϭ 2.00 Ϯ 0.08, K d ϭ 0.26 Ϯ 0.02 M, and n H ϭ 1.73 Ϯ 0.38. b, for CBD2 titration curves, the following fitting parameters were obtained for Na ϩ (Cap ϭ 1.88 Ϯ 0.03, K d ϭ 6.96 Ϯ 0.25 M, and n H ϭ 2.48 Ϯ 0.24) and K ϩ (Cap ϭ 1.74 Ϯ 0.04, K d ϭ 6.83 Ϯ 0.25 M, and n H ϭ 1.82 Ϯ 0.09). changes were detected on off rates by Mg 2ϩ (Table 2). Therefore, in the cell the primary sensor of CBD2 might have a much higher affinity than was previously thought (18,20). Although the effects of Mg 2ϩ on NCX ion currents were not systematically studied, it has been shown that the cytosolic Mg 2ϩ can attenuate inward and outward ion currents in cardiomyocytes by competing with Ca 2ϩ at the regulatory sites of NCX (48). The fluorescence resonance energy transfer analysis suggests that the cytosolic Mg 2ϩ can decrease nearly 3-fold the affinity of CBD Ca 2ϩ sensor (49).
Interacting Mechanisms of Mg 2ϩ with Ca 2ϩ Sensors-Presently found effects of Mg 2ϩ on CBD Ca 2ϩ sensors are especially interesting in light of structural differences between CBD1 and CBD2 (18 -22). Interestingly, the fluorescence resonance energy transfer analysis supports a notion that Mg 2ϩ can interact with regulatory Ca 2ϩ site(s) of NCX without inducing considerable conformational changes of the protein (49). Therefore, the Mg 2ϩ -dependent elevation of the Ca 2ϩ affinity at site 1 of CBD2 may represent some specific rearrangements of Ca 2ϩ coordinating groups at site 1 and 2 of CBD2. For example, the occupation of the CBD2 site 2 by Mg 2ϩ may alter the charge compensation mechanism with respect to Lys 585 . This may affect the arrangement of specific Ca 2ϩ -coordinating groups shared by site 1 and site 2. Because Mg 2ϩ has a stronger preference than Ca 2ϩ for retaining water molecules in its coordination sphere (23,52), the water-rich coordination sphere for the "secondary" Ca 2ϩ site (site 2) in the CBD2 structure implies that Mg 2ϩ could be substituted at this site with very little change in the overall geometry of the site in the Ca 2ϩ -bound form. It is likely that Mg 2ϩ binding pays the "entropic penalty" of increasing the structural rigidity in the binding site, thereby making it more thermodynamically favorable for Ca 2ϩ to bind, FIGURE 6. Effect of Mg 2؉ on equilibrium 45 Ca 2؉ binding to CBD2. The radioactive assay of 45 Ca 2؉ binding to CBD2 was performed as described in Figs. 1 and 5. a, the 45 Ca 2ϩ titration curve was obtained in the assay buffer containing 10 mM Tris-HCl buffer, pH 7.2, either with 100 mM choline chloride (E) or 95 mM choline chloride ϩ 5 mM MgCl 2 (F). In control experiments (without MgCl 2 ) the fitting parameters were Cap ϭ 1.64 Ϯ 0.03, K d ϭ 5.62 Ϯ 0.13 M, and n H ϭ 2.5 Ϯ 0.14. In the presence of 5 mM MgCl 2 the data were fitted to a single site model (n H ϭ 1) exhibiting Cap ϭ 0.76 Ϯ 0.01 and K d ϭ 1.05 Ϯ 0.10 M. b, Mg 2ϩ -dependent displacement of CBD2-bound 45 (Table 1) and the Ca 2ϩ off rates ( Table 2). The dotted lines depict the primary site of CBD2, which does not interact with Mg 2ϩ . as observed in some proteins (23). Mg 2ϩ may also help "form" the Ca 2ϩ site, as seen with the lectin family of Ca 2ϩ proteins (23). Because the splice variant segment is located within CBD2, Mg 2ϩ may contribute to tissue-specific regulation of NCX isoforms and splice variants. More dedicated studies are required for elucidating these issues.