When Size Is Important

The accommodation of Mg2+ in the N-terminal domain of calmodulin was followed through amide1H and 15N chemical shifts and line widths in heteronuclear single-quantum coherence spectroscopy NMR spectra. Mg2+ binds sequentially to the two Ca2+-binding loops in this domain, with affinities such that nearly half of the loops would be occupied by Mg2+ in resting eukaryotic cells. Mg2+ binding seems to occur without ligation to the residue in the 12th loop position, previously proven largely responsible for the major rearrangements induced by binding of the larger Ca2+. Consequently, smaller Mg2+-induced structural changes are indicated throughout the protein. The two Ca2+-binding loops have different Mg2+ binding characteristics. Ligands in the N-terminal loop I are better positioned for cation binding, resulting in higher affinity and slower binding kinetics compared with the C-terminal loop II (k off = 380 ± 40 s–1compared with ∼10,000 s−1 at 25 °C). The Mg2+-saturated loop II undergoes conformational exchange on the 100-μs time scale. Available data suggest that this exchange occurs between a conformation providing a ligand geometry optimized for Mg2+ binding and a conformation more similar to that of the empty loop.

The accommodation of Mg 2؉ in the N-terminal domain of calmodulin was followed through amide 1 H and 15 N chemical shifts and line widths in heteronuclear singlequantum coherence spectroscopy NMR spectra. Mg 2؉ binds sequentially to the two Ca 2؉ -binding loops in this domain, with affinities such that nearly half of the loops would be occupied by Mg 2؉ in resting eukaryotic cells. Mg 2؉ binding seems to occur without ligation to the residue in the 12th loop position, previously proven largely responsible for the major rearrangements induced by binding of the larger Ca 2؉ . Consequently, smaller Mg 2؉ -induced structural changes are indicated throughout the protein. The two Ca 2؉ -binding loops have different Mg 2؉ binding characteristics. Ligands in the N-terminal loop I are better positioned for cation binding, resulting in higher affinity and slower binding kinetics compared with the C-terminal loop II (k off ‫؍‬ 380 ؎ 40 s -1 compared with ϳ10,000 s ؊1 at 25°C). The Mg 2؉ -saturated loop II undergoes conformational exchange on the 100-s time scale. Available data suggest that this exchange occurs between a conformation providing a ligand geometry optimized for Mg 2؉ binding and a conformation more similar to that of the empty loop.
Mg 2ϩ is an essential ion in biological systems, with structural and catalytic functions (1,2). It is the most abundant divalent metal ion in mammalian cells, with the cytosolic free concentration kept nearly constant at 0.5-2.0 mM (3). In this milieu, Ca 2ϩ is able to regulate a vast number of cellular activities through transient increases in cytosolic concentration from less than 0.1 M in a resting cell to 1-10 M in an activated cell (4). Thus, the primary protein targets of Ca 2ϩ , in many cases calmodulin (CaM) 1 or other EF-hand proteins, must be able to respond in a 100 -10,000-fold excess of Mg 2ϩ .
Due to the high abundance of Mg 2ϩ , intracellular Mg 2ϩ -specific proteins need no structural discrimination against Ca 2ϩ (5). In contrast, Ca 2ϩ -binding proteins may accomplish discrimination against Mg 2ϩ by taking advantage of the larger ionic radius of Ca 2ϩ and its less stringent demands on the number (often 6 -8) and spatial arrangement of coordinating oxygen ligands, as compared with Mg 2ϩ , which has a strong preference for 6-fold coordination in an octahedral symmetry (6,7). For example, the Mg 2ϩ affinities of the two sites in toad parvalbumin are about a factor of 6000 lower than the Ca 2ϩ affinities (8). However, the high cytosolic Mg 2ϩ concentration implies that many Ca 2ϩ sites are occupied by Mg 2ϩ in resting cells.
The EF-hand family of Ca 2ϩ -binding proteins may be divided into distinct subfamilies, e.g. CaM, troponin C, parvalbumins, and S100 proteins (9). In these proteins, Ca 2ϩ binds in the loop region of a 29-residue-long EF-hand helix-loop-helix motif (10). This motif, which is among the five most common protein motifs in animal cells (11), usually appears in pairs, where cooperative Ca 2ϩ binding frequently is observed (7). The consensus EF-hand loop comprises 12 residues arranged to coordinate the Ca 2ϩ with pentagonal bipyramid symmetry, with the seven ligands provided by five side chain carboxylate oxygens, one backbone carbonyl oxygen, and one water oxygen (12). Two of the side chain ligands are provided by a conserved, bidentate Glu in the 12th and last loop position (Fig. 1a).
Calmodulin, the ubiquitous regulatory Ca 2ϩ -binding protein in eukaryotic cells, consists of two distinct domains connected by a flexible tether. The two domains are structurally similar, and each has two EF-hands packed in a roughly parallel fashion with a short ␤-sheet connecting the Ca 2ϩ -binding loops (Fig. 1). The eight helices and four binding loops are denoted A-H and I-IV, respectively. Within each domain, the two EFhands are connected by a short linker, i.e. between helices B and C and between F and G. Each domain binds two Ca 2ϩ with positive cooperativity (13,14). Upon Ca 2ϩ binding, the secondary structure in both domains remains essentially unchanged, while the relative orientations of the helices change in such a way that the domains go from a relatively compact, "closed" structure ( Fig. 1b) to an "open" structure with well defined hydrophobic patches where target proteins may bind (Fig. 1c) (15)(16)(17)(18)(19). The two domains of CaM can be expressed and produced independently (20), fold independently (18,21), and have Ca 2ϩ binding characteristics similar to intact CaM (13). These protein "fragments" were originally produced by trypsin cleavage of CaM in presence of Ca 2ϩ and are named TR 1 C and TR 2 C, respectively (22,23).
The Mg 2ϩ dissociation constants of CaM are in the millimolar range (24,25), and Mg 2ϩ has generally been assumed to bind to the same sites as Ca 2ϩ (25,26) but to induce only small structural rearrangements (24,26). This was recently verified by Ohki et al. using 1 H-15 N NMR (27). The Mg 2ϩ -loaded form of CaM is reported to cause only negligible activation of CaM target proteins (28,29). At the time of writing, x-ray structures of Mg 2ϩ -loaded EF-hand sites are only available for pike parvalbumin (30), myosin regulatory light chain (31), and calbindin D 9k (32). In parvalbumin and myosin regulatory light chain, the only difference between Mg 2ϩ and Ca 2ϩ ligation is that the residues in the 12th loop positions serve as monodentate ligands in the Mg 2ϩ structures but bidentate in the Ca 2ϩ structures. In calbindin D 9k , the Glu in the 12th position is not used for direct Mg 2ϩ ligation. Instead, a water molecule is inserted between the side chain and Mg 2ϩ . The Glu in the 12th loop position has been shown to be very important for the structural rearrangements from a "closed" to an "open" conformation occurring upon Ca 2ϩ binding (33)(34)(35).
In the present study, the TR 1 C fragment of vertebrate CaM was titrated by Mg 2ϩ and followed by 1 H-15 N NMR, in order to address the questions regarding the detailed Mg 2ϩ binding characteristics of this CaM domain and the structural and dynamic nature of protein states at different levels of Mg 2ϩ saturation.

EXPERIMENTAL PROCEDURES
Protein Synthesis-The synthetic gene for TR 1 C was constructed from overlapping oligonucleotides, 2 essentially as described for calbindin D 9k (36). The TR 1 C gene was cloned into the pRCB1 plasmid. Unlabeled and uniformly 15 N-labeled TR 1 C was expressed in Escherichia coli and purified as reported previously for the TR 2 C fragment (18).
NMR Experimental Parameters-1 H and 15 N chemical shifts of (Mg 2ϩ ) 2 -TR 1 C were assigned at 25°C, pH 7.2, on 4 mM protein samples of unlabeled and 15 N-labeled TR 1  Amide 1 H and 15 N chemical shifts were followed using sensitivityenhanced and gradient-selected two-dimensional HSQC spectra, recorded with spectral widths of 1600 and 7692 Hz, sampled over 256 and 2048 complex data points in the 15 N and 1 H dimension, respectively. Using 18 scans per t 1 -increment and a relaxation delay of 1.5 s, the total experimental time was 3.5 h/spectrum. 15 N nuclei were decoupled during acquisition using the GARP-1 sequence (46). All NMR spectra were recorded on a Varian Unity Plus spectrometer at a 1 H frequency of 599.89 MHz. 1 H chemical shifts were referenced to dimethylsilapentanesulfonic acid at 0 ppm and 15 N chemical shifts indirectly via the 1 H frequency using the frequency ratio ( 15 N/ 1 H) of 0.101329118 (47).
Data Processing-Amide chemical shifts were measured in the HSQC spectra at different Mg 2ϩ concentrations. The spectra were processed for either resolution or sensitivity, using Lorentzian-Gaussian or Lorentzian line-broadening window functions in 2 , and Kaiser or sine squared window functions in 1 . After zero filling in 1 , the matrix size was 1024 ϫ 512 real points.
Amide line widths were measured from HSQC spectra processed using a Lorentzian line-broadening window function in both dimensions and zero-filling to 1024 points in 1 . The final matrix size was 1024 ϫ 1024. NMR line widths were determined from the HSQC spectra using the in house curve fitting software CFIT. 3,4 Fitting was performed by minimizing the error squared sum between a one-dimensional slice taken through the peak center and a pure Lorentzian line shape, as exemplified for Gly 33 HN in Fig. 2. The Levenberg-Marquardt algorithm (48) was used, and starting parameters were obtained through an automatic search procedure.
Assignments-Sequential assignments of 1 H and 15 N resonances for (Mg 2ϩ ) 2 -TR 1 C were obtained following standard procedures (49,50), using the FELIX 95 software (MSI Inc.), GENXPK (51), 4 and the in house assignment tool ASSAR. The assignment procedure was facilitated by the close similarity of the chemical shifts to those of the ion-free state of intact CaM, kindly provided by Ad Bax. The complete 1 H and 15 N resonance assignments for (Mg 2ϩ ) 2 -TR 1 C at 25°C, pH 7.2, are deposited in BioMagResBank. 1 H and 15 N chemical shifts of ion-free TR 1 C were assigned using the HSQC-TOCSY spectra and comparisons with the chemical shifts of ion-free intact CaM. Similarly, the Ca 2ϩloaded form of the protein was assigned using the chemical shifts of Ca 2ϩ -loaded intact CaM (52). The chemical shifts of the amide resonances in the HSQC spectra at different Mg 2ϩ concentrations were assigned at increasing Mg 2ϩ concentrations using the ion-free assignment and at decreasing Mg 2ϩ concentrations using the (Mg 2ϩ ) 2 -TR 1 C assignment.
Chemical Shifts-The binding kinetics of Mg 2ϩ occur on the fast to intermediate NMR chemical shift time scale. Nuclei for which the FIG. 1. Amino acid sequence and secondary structure (a), and threedimensional structures of the "closed" ion-free (16) (b) and "open" Ca 2؉ -loaded (15) (c) states of the Nterminal domain of calmodulin. a, the one-letter codes for amino acid residues are used. The ion-free TR 1 C secondary structure (16) is indicated with helical residues in italic type and ␤-sheet residues underlined. Ca 2ϩ coordination is indicated as follows: main chain carbonyl oxygens (asterisks), monodentate carboxylates (single daggers), and bidentate carboxylates (double daggers). The helices are denoted A-D. b and c, residues Thr 5 -Ile 27 and Ile 63 -Lys 75 are shown in light gray, and Thr 28 -Thr 62 are dark gray. The ␤-strands (Thr 26 -Thr 28 , Thr 62 -Asp 64 ) are oriented similarly in the two structures. This figure was generated using UCSF software Midas Plus (60). chemical shift changes induced by Mg 2ϩ -binding, ⌬␦ (ppm), result in small resonance frequency changes compared with the exchange rate between two states, k ex , are in the fast exchange regime; 2 0 ⌬␦ Ͻ Ͻ k ex , where 0 (MHz) is the spectrometer frequency of the nucleus observed. For these nuclei, the observed chemical shift is a populationweighted average of the shifts of the ion-free and Mg 2ϩ -bound forms, where p I , p II , and p I,II are the relative populations of the protein with an Mg 2ϩ in site I, site II, and both site I and II, respectively, at a given Mg 2ϩ concentration; ␦ ion-free is the chemical shift of the ion-free state; and ⌬␦ I , ⌬␦ II , and ⌬␦ I,II are the chemical shift changes induced by Mg 2ϩ binding to sites I, II, and both I and II, respectively. Nuclei experiencing resonance frequency changes of the same order of magnitude as the exchange rate (2 0 ⌬␦ Ϸ k ex ) are in the intermediate exchange regime, where resonances are severely broadened by Mg 2ϩ exchange. Their chemical shifts depend not only on the populations but also on the binding kinetics (53). Therefore, only resonances experiencing no or only moderate line broadening were used in the binding constant calculations.
Line Shapes-For a nucleus experiencing intermediate to fast exchange the contributions to the line width from the exchange process, ⌬ 1/2,ex , can be calculated as follows, and where p A and p B are the relative populations of the two states, k off is the off-rate, k on is the on-rate, and [Mg 2ϩ ] is the free Mg 2ϩ concentration. In the case where Mg 2ϩ binding to a protein site is studied by adding Mg 2ϩ to a given protein solution, the equation is readily rearranged to the following, where K is the binding constant to the site (54). If line broadening is an effect of fast to intermediate conformational exchange within a certain state, the contribution to the total line width is approximately as follows, where p is the relative population of the state and is the line width at 100% of that state, which may be calculated from Equation 2.
Due to the generally larger changes in resonance frequency, 0 ⌬␦, for 1 H compared with 15 N, a larger number of 1 H resonances than 15 N resonances are broadened during the titration. Broadening in the 1 H dimension renders the evaluation of 15 N line widths uncertain. Therefore, 15 N line widths will generally not be discussed in this paper.
Mg 2ϩ Binding Constants and Exchange Rates-Mg 2ϩ binding constants were derived from chemical shifts and line widths using a simulated annealing algorithm similar to that used previously (33). In the present study, however, the binding constants were determined for individual residues, and the average was calculated. The microscopic binding constants of loop I and II (K I and K II ) were determined from chemical shifts of 12 residues. The ion-free shifts, ␦ ion-free , were taken directly from the 15 N HSQC spectrum of the ion-free state. The two microscopic binding constants, K I and K II , and the chemical shift changes induced by binding an Mg 2ϩ to loop I, II, and both loops, ⌬␦ I , ⌬␦ II and ⌬␦ I,II , were determined minimizing the following expression, where p I (i), p II (i) and p I, II (i) are the relative populations of the Mg 2ϩ bound to loop I, II, and both I and II, respectively, calculated from the binding constants and the protein concentration, and ␦ obs (i) is the observed chemical shift for the nucleus at Mg 2ϩ concentration i. All of the nuclei chosen had a Mg 2ϩ -induced chemical shift change of between 0.04 and 0.15 ppm for 1 H and 0.1 and 0.4 ppm for 15 N and showed no or only moderate broadening. The uncertainties were estimated as the maximal deviation causing a doubling of 2 .
The microscopic binding constant of loop I (K I ) was also determined from line widths of six residues at or near this loop that experience moderate line broadening (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20). K I , the line width without exchange broadening before and after this binding event ( 1/2,nat ), and the ratio of the squared Mg 2ϩ -induced chemical shift change and the off-rate ((⌬␦) 2 /k off ) were determined by minimizing the following expression, where [Mg 2ϩ ] is the free Mg 2ϩ concentration calculated from the fitted K I and a fixed K II , and 1/2,obs is the measured line width.
The rates of the dynamic processes in loop II were estimated from a comparison of experimental and calculated line shapes. A four-site exchange program, based on the Bloch-McConnell equations (55), was used in this analysis.

RESULTS AND DISCUSSION
Chemical shifts of backbone and side chain 1 H-15 N pairs were determined from HSQC spectra at 12 Mg 2ϩ concentrations ranging from 0 to 190 mM, in 150 mM KCl at 25°C, pH 7.5. The titration provides evidence for two binding events, both characterized by dissociation constants in the millimolar range. As shown in Fig. 3, the major chemical shift changes occur in or around the N-terminal parts of the Ca 2ϩ binding loops. The chemical shift changes in these regions are very similar to the Ca 2ϩ -induced changes, clearly identifying the location of the Mg 2ϩ binding sites to the Ca 2ϩ binding loops. The first binding event is characterized by effects that are intermediate on the chemical shift time scale; the amide signals of residues Asp 20 -Ile 27 in the N-terminal part of loop I become broadened beyond detection at intermediate Mg 2ϩ concentrations, and a large number of other signals are significantly broadened (Figs. 4 and 5b). This exchange broadening can be attributed purely to binding to loop I, because all chemical shift changes of the same size do not result in the same degree of line broadening. When Mg 2ϩ binds to loop II, no line width maxima appear at intermediate Mg 2ϩ occupancies, but some signals are continuously broadened as the loop is filled (Fig. 5c). This indicates faster binding kinetics of this loop and a conformational exchange within the Mg 2ϩ -bound form. Sequential binding of two Mg 2ϩ is possible to demonstrate using the present method, because the two events are characterized by different degrees of exchange broadening and, for some signals, chemical shift changes of different signs, cf. Leu 69 HN in Fig. 5a ) at 0, 0.2, 0.4, 0.8, 1.2, 2.0, 3.6 state, nonspecific effects of the very high ionic strength, and/or transient aggregation.
Mg 2ϩ Binding Constants-The microscopic Mg 2ϩ binding constants (K I and K II ) at high salt (150 mM KCl) for loops I and II in TR 1 C were calculated using data exemplified in Fig. 5, a and b. K I was calculated from the Mg 2ϩ -induced line broadening (Fig. 5b), and K I and K II were calculated from the Mg 2ϩinduced chemical shift changes (Fig. 5a). The line shape calculations were based on the assumption that contributions to the signals included in the optimization from Mg 2ϩ binding to loop II could be neglected. The chemical shift-based calculations were made using a number of different models, some including cooperative interactions. However, from the present data no additional information was obtained using more complicated models than a model with two independent binding loops. Binding constants obtained from chemical shifts and line shapes agree well. Since the precision of K I was better using line shape analysis, this value was used to calculate K II from the shift changes. The calculated microscopic Mg 2ϩ binding constants are log 10 K I ϭ 3.07 Ϯ 0.04 and log 10 K II ϭ 2.7 Ϯ 0.2 (Table I). These values agree well with values obtained from Mg 2ϩ /Ca 2ϩ competition studies, 5 and earlier but less accurate determinations (24,25). It is important to note that with such a small difference between the two binding constants, microscopic (K I and K II ) and macroscopic (K 1 and K 2 ) binding constants are not equal (K 1 ϭ K I ϩ K II and K 2 ϭ K I K II /(K I ϩ K II ) under nonco- 5 A. Malmendal, unpublished results. operative conditions). The Mg 2ϩ affinity is low compared with the Ca 2ϩ affinity, but since the intracellular Mg 2ϩ concentration is about 1 mM, the binding constants imply that almost 50% of the EF-hand loops in this domain will be occupied by Mg 2ϩ at resting Ca 2ϩ levels (Fig. 6).

FIG. 3. Backbone amide 1 H (a) and 15 N (b) chemical shift changes induced by binding two Mg 2؉ (bars) and two Ca 2؉ (line) to ion-free TR 1 C as a function
(Mg 2ϩ ) 2 TR 1 C-Upon Ca 2ϩ binding to CaM domains, the helix packing changes drastically (Fig. 1, b and c) (Refs. 16 -18; see above). This major structural rearrangement is manifested in large backbone chemical shift changes, not only in the binding loops but also in the rearranging helices. The Mg 2ϩ -induced backbone chemical shifts are more localized, with the larger changes appearing primarily in the N-terminal parts of the binding loops (Fig. 3). Relatively minor shift changes in the C-terminal parts of the loops in Mg 2ϩ loaded TR 1 C suggest that the Glu residues in the 12th position of the loops do not directly coordinate the smaller Mg 2ϩ . The chemical shift changes in the N-terminal part of loop I are generally similar to those obtained upon Ca 2ϩ binding. The differences indicate a slightly different accommodation by the ligands around the smaller Mg 2ϩ . A plausible mode of Mg 2ϩ coordination would be that observed in loop II of calbindin D 9k , where all Ca 2ϩ ligands, except the bidentate Glu, also coordinate Mg 2ϩ (32). In the case of loop I of TR 1 C, a strikingly similar relation between the amide proton chemical shifts of the Mg 2ϩ -and Ca 2ϩ -loaded states of this loop and the same two states of loop II in calbindin D 9k corroborates this hypothesis. Such a mode of binding would explain why Mg 2ϩ binding does not induce the same global structural rearrangements in the domain as Ca 2ϩ binding does, and it further emphasizes the importance of the Glu in the 12th loop position. In the Mg 2ϩ -loaded loop II, many resonances appear halfway between the chemical shifts of the ion-free and Ca 2ϩ -loaded states (Fig. 3). This can be explained by a local rapid conformational exchange within the Mg 2ϩ -loaded state of this site (see below).
Mg 2ϩ Binding to Loop I, the Higher Affinity Site-During the first Mg 2ϩ -binding event, the majority of signals from amide protons in the core of the N-terminal EF-hand are significantly broadened. The maximal line widths during this Mg 2ϩ binding event are found at 0.8 mM added Mg 2ϩ (Fig. 5b), and most signals have normal line widths above 18 mM (when loop I is 95% saturated). The observed line broadening is attributed to chemical exchange of Mg 2ϩ in loop I. Assuming that the total amide proton chemical shift changes for residues Phe 12 , Lys 13 , Ala 15 , and Ser 17 in helix A originate entirely from this binding event, the off-rate is 380 Ϯ 40 s -1 at 25°C (Table I). On the same assumption, the absolute chemical shift changes associated with Mg 2ϩ binding to loop I were estimated (Fig. 7). A number of signals from residues in helix C and helix D also experience significant line broadening (Figs. 4 and 7). In the structure of ion-free CaM (16,17), many of them are in close proximity to the broadened residues in the N-terminal EFhand (19). A significant number of these residues are located around the bidentate Ca 2ϩ ligand Glu 67 in the 12th position of loop II (Fig. 1a). At lower Mg 2ϩ concentrations, this residue displays one of the most markedly broadened 1 H resonances outside of loop I, and it experiences large chemical shift changes of different signs due to the two binding events. The rearrangements necessary to accommodate Mg 2ϩ in loop I may thus be transmitted through the hydrophobic core of the Nterminal EF-hand so as to reposition essential residues at the C-terminal end of loop II.
In the E140Q mutant of TR 2 C, the bidentate Glu in the 12th position of the C-terminal loop IV is replaced by a Gln. Essentially, this mutant protein binds Ca 2ϩ sequentially and does not seem to adopt the "open" conformation when only loop III is occupied by Ca 2ϩ (33). The chemical shift changes induced by Ca 2ϩ binding to loop III of this mutant protein are exceedingly similar in magnitude and location to those induced by Mg 2ϩ binding to loop I of TR 1 C, indicating that these two different ions have similar effects on the overall structure of the two different proteins. An interesting feature is that the C-terminal end of the occupied loop and the spatially close N-terminal end of the empty loop are much more affected by Ca 2ϩ than Mg 2ϩ . These different responses of the local environments may be explained by the different accommodation of the two ions: Mg 2ϩ is ligated using only residues in the N-terminal part of loop I in (Mg 2ϩ ) 1 -TR 1 C, while Ca 2ϩ is ligated using also residues in the C-terminal part of loop III of (Ca 2ϩ ) 1 -E140Q-TR 2 C. The antiparallel arrangement of the two loops, with coupling between the N-terminal half of one loop and the C-terminal half of the other and vice versa, provides a mechanism for cooperative Ca 2ϩ binding. Since Mg 2ϩ only binds to the N-terminal parts of the loops, it cannot employ this mechanism of cooperativity.
Mg 2ϩ Binding to Loop II, the Lower Affinity Site-At the  second Mg 2ϩ binding event, the major shift changes are located in loop II, where some signals (e.g. Ala 57 , Asp 58 , Asn 60 , Gly 61 , Ile 63 , and Asp 64 HN) are continuously broadened as MgCl 2 is added. At a first glance this broadening seems to be caused by Mg 2ϩ exchange. However, in perspective of the calculated binding constants, implying loop II to be nearly saturated at the highest Mg 2ϩ concentrations, these effects are more likely to be caused by exchange processes within the Mg 2ϩ -loaded state.
When plotting the line broadening of residues in loop II versus the calculated degree of Mg 2ϩ saturation of this loop, a linear dependence according to Equation 5 was obtained, as shown in Fig. 5c. According to Equation 2, the estimated line widths for a saturated loop II correlate well with the total Mg 2ϩ -induced chemical shift changes for these residues, indicating exchange between a conformation similar to that in the ion-free state and a conformation optimizing the coordination of Mg 2ϩ . Interestingly, the chemical shift changes of some amide signals in loop II are about 50% of those caused by Ca 2ϩ binding (Fig. 3). The line broadening is interpreted assuming a four-state model with an empty and a Mg 2ϩ -loaded state of the loop, each exchanging between a "low affinity conformation" and a "high affinity conformation" as shown in Fig. 8. If the chemical shift differences between the two conformations of the Mg 2ϩ -loaded state is twice as large as the observed Mg 2ϩinduced shift changes, i.e. equal to the Ca 2ϩ -induced shift changes for some residues, and if their populations are of equal magnitude, the exchange rate within this state would be ϳ10,000 s -1 at 25°C. Similar exchange rates have been observed within Ca 2ϩ -loaded states of TR 2 C mutants (33,34). If the population of the "high affinity conformation" is negligible in the absence of Mg 2ϩ and the maximal chemical shift differences between the bound and unbound states of the "low affinity conformation" are of the same order as the maximal Mg 2ϩinduced chemical shift change for residues that do not show any line broadening during the titration (0.07 ppm), this model implies a lower limit for the Mg 2ϩ off-rate from the "low affinity conformation" of the same order as the exchange within the Mg 2ϩ -loaded state, i.e. ϳ10,000 s -1 at 25°C. A slower off-rate would imply line width maxima at semisaturated states, as observed for binding to loop I. This value may be compared with the Mg 2ϩ off-rate of ϳ3,000 s Ϫ1 at 25°C and low ionic strength that was previously determined using 25 Mg NMR (25) under the assumption that the two Mg 2ϩ exchange equally fast. With our present understanding of the slower Mg 2ϩ exchange in loop I, the off-rate of the faster site can be recalculated as ϳ6,000 s Ϫ1 . Considering the difference in ionic strength, this is in good agreement with our present results.
Comparing the total Mg 2ϩ -induced chemical shift changes with those calculated for the first binding event, the changes caused by the second event appear to be smaller. However, the signals in helices B, C, and D that experience chemical shift changes of different signs due to the two binding events show that also this binding event has effects all over the protein.
Amide proton line widths of Leu 32 , Gly 33 (Fig. 2), Asn 60 , Asp 64 , and Glu 67 are affected both by binding to loop I and the exchange process in loop II (Fig. 4) and experience line width minima at intermediate Mg 2ϩ concentrations. The amides of Leu 32 and Gly 33 in helix B have an ␣-helical hydrogen bonding pattern in the Ca 2ϩ -loaded state (15) but change this pattern due to a kink in the helix around Glu 31 in the ion-free state (16,17). This part of helix B may thus be structurally poorly defined in the Mg 2ϩ -loaded states.
Mg 2ϩ Accommodation in "Closed" EF-hands-The binding of ions of different sizes to EF-hands have been studied thoroughly (6,7). Additional negative charges in the sites have been shown to increase the affinity for small ions less than for large ions (7). In the present case, the net charges of loop I and II are Ϫ3.8 and Ϫ4.4, respectively. If equal Ca 2ϩ affinities of the two sites are assumed, stronger Mg 2ϩ binding to loop I compared with loop II is successfully predicted. Drake et al. (56) have shown that in the EF-hand of E. coli galactose-binding protein the size and charge of the residue in the so called "gateway" position 9 of the loop is important for the binding kinetics. If this is the dominating determinant here, loop II should be the slower site. However, if the major structural rearrangements associated with Ca 2ϩ coordination do not occur in the Mg 2ϩ case, then the appearance of the CaM EF-hand sites may be so different that the "gateway" argument may not be applicable.
An important part of the Ca 2ϩ -induced structural rearrangements in CaM take place around a hinge in the middle of the loops. This hinge is located asymmetrically in the two loops: between loop positions 8 and 9 at the end of the short ␤-sheet region in loop I and between loop positions 6 and 8 just before this ␤-sheet region in loop II (16) (Figs. 1 and 9). This has implications for the locations of the Ca 2ϩ ligating backbone carbonyl oxygens in loop position 7, i.e. Thr 26 and Thr 62 , in the "closed" structure, which has not been subjected to the major Ca 2ϩ -induced rearrangements. In Ca 2ϩ -loaded CaM, the distances from Ca 2ϩ to both of these oxygens are 2.3 Å (15). When the backbone atoms of the six N-terminal residues in loops I and II of the energy-minimized average structure of the ionfree state (16) are superimposed onto their respective counterparts in the Ca 2ϩ -loaded state (root mean square deviation of 0.57 and 0.62 Å, respectively) the corresponding distance is still 2.3 Å for Thr 26 but is 3.3 Å for Thr 62 . This implies that the backbone conformation around Thr 26 in loop I is suitable for Mg 2ϩ ligation, while in loop II, the backbone carbonyl oxygen of Thr 62 has to approach helix C in order to ligate Mg 2ϩ (Fig. 9). The different levels of "preformation" of the two sites are probably reflected in the different Mg 2ϩ affinities and Mg 2ϩ binding FIG. 8. A four-site model of Mg 2؉ binding to loop II. The state with an empty site is shown to the left, and the state with a filled site to the right. In each state, the "lower affinity conformation" is shown at the top, and the "higher affinity conformation" at the bottom. The empty "higher affinity conformation" is negligibly populated if k Ϫ1 Ͼ Ͼ k 1 and kЈ on ϫ [Mg 2ϩ ] Ͼ Ͼ kЈ off . kinetics, with lower affinity, and faster kinetics in loop II. These features of loop II also support the hypothesis of exchange in the Mg 2ϩ -loaded loop between a "high affinity conformation," providing a ligand geometry optimized for Mg 2ϩ , and a relaxed "low affinity conformation" similar to the ion-free loop (Fig. 8).
An important residue in EF-hand loops is the conserved Gly in loop position 6, which allows the loop to make a sharp bend (12). A hydrogen bond between the amide proton of this Gly and a carboxylate oxygen of the Asp in the first loop position cause a downfield chemical shift of the amide proton (57,58). In loops I and II, as in most EF-hand loops, these hydrogen bonds are strengthened upon Ca 2ϩ binding (15)(16)(17). The chemical shift changes upon binding of two Mg 2ϩ or two Ca 2ϩ are virtually identical for the amide proton of Gly 25 in loop I, showing the similarity of the N-terminal part of loop I when coordinating the two different ions. With this in mind, a Mg 2ϩ -induced amide proton chemical shift change of Gly 61 that is roughly 50% of that induced by Ca 2ϩ binding and a continuous broadening of this signal upon Mg 2ϩ saturation of loop II (Fig. 5c) favor the model with exchange between "high and low affinity conformations." In a recent study (59), the 15 N chemical shift of Ile 27 in position 8 of loop I was shown to depend on contributions of equal size from 1) polarization due to Ca 2ϩ ligation by the preceding Thr 26 backbone carbonyl oxygen and 2) changes in its side chain rotamer that are attributed to Ca 2ϩ binding to loop II. At Mg 2ϩ saturating conditions, the amide nitrogen of Ile 27 has experienced a chemical shift change of 10.8 ppm compared with the Ca 2ϩ -induced 16.1 ppm, and the signal is negligibly broadened. The line width at Mg 2ϩ saturating conditions excludes chemical exchange at the rates observed for loop II between states with chemical shift differences comparable with the remaining 5.3 ppm and attributes the observed chemical shift to ligation by Thr 26 only, with the difference compared with the Ca 2ϩ -induced chemical shift explained by a lack of side chain rotation due to Mg 2ϩ binding to loop II. The 15 N chemical shift of Ile 63 in the same position of loop II does only depend on Ca 2ϩ ligation by the preceding Thr 62 , since the side chain rotamer is unaffected by Ca 2ϩ binding. The Mg 2ϩinduced change is 3.0 ppm compared with 4.9 ppm induced by Ca 2ϩ , and the signal is very broad at Mg 2ϩ saturating conditions, which further supports the hypothesis of exchange between conformations with and without ligation by Thr 62 in loop II.
To summarize, the (Mg 2ϩ ) 2 state of TR 1 C has the ions bound to the N-terminal part of the Ca 2ϩ -binding loops in a manner similar to the (Ca 2ϩ ) 2 state, but the overall conformation is "closed" as for the ion-free protein, since the smaller Mg 2ϩ does not allow the side chain carboxylates of the Glu in the 12th loop position into the coordination sphere. The rearrangements in loop I are probably limited to the displacement of side chains to allow Mg 2ϩ coordination. More significant side chain and backbone rearrangements in loop II are required to optimize coordination of Mg 2ϩ , which result in the observed conformational exchange and a faster Mg 2ϩ off-rate compared with loop I. The similar time scales observed for the conformational change and Mg 2ϩ exchange suggest a coupling between the two events.
Conclusion-In a resting eukaryotic cell, the N-terminal domain of CaM is predicted to be almost half-saturated by Mg 2ϩ . The protein does not exhibit the conformational rearrangements that occur upon Ca 2ϩ binding, because coordination of the smaller Mg 2ϩ involves only residues in the N-terminal part of the EF-hand loops, thus enabling the role of CaM as a specific mediator of Ca 2ϩ signals. The different Mg 2ϩ binding characteristics of the two loops reveal the asymmetry in the closed state of CaM. Ligands in loop I are better positioned for Mg 2ϩ ligation, resulting in higher affinity and slower binding kinetics compared with loop II, in which exchange between a loop conformation optimizing the Mg 2ϩ accommodation and a loop conformation more similar to that of the ion-free state is likely to occur. A relevant view of the N-terminal domain of CaM at resting Ca 2ϩ levels may thus be that of a protein ensemble structurally similar to the ion-free protein but with significant populations of all of the half and fully Mg 2ϩ -saturated states and with the dynamic behavior colored by a variety of Mg 2ϩ -dependent effects.