Dynamics of the Transition between Open and Closed Conformations in a Calmodulin C-Terminal Domain Mutant

Structure, Vol. 9, 185–195, March, 2001, 2001 Elsevier Science Ltd. All rights reserved.

PII S0969-2126(01)00575-5

Dynamics of the Transition between Open and Closed Conformations in a Calmodulin C-Terminal Domain Mutant Johan Evena¨s,† Anders Malmendal,‡ and Mikael Akke* Physical Chemistry 2 Lund University P.O. Box 124 SE-221 00 Lund Sweden

Summary Background: Calmodulin is a ubiquitous Ca2⫹-activated regulator of cellular processes in eukaryotes. The structures of the Ca2⫹-free (apo) and Ca2⫹-loaded states of calmodulin have revealed that Ca2⫹ binding is associated with a transition in each of the two domains from a closed to an open conformation that is central to target recognition. However, little is known about the dynamics of this conformational switch. Results: The dynamics of the transition between closed and open conformations in the Ca2⫹-loaded state of the E140Q mutant of the calmodulin C-terminal domain were characterized under equilibrium conditions. The exchange time constants (␶ex) measured for 42 residues range from 13 to 46 ␮s, with a mean of 21 ⫾ 3 ␮s. The results suggest that ␶ex varies significantly between different groups of residues and that residues with similar values exhibit spatial proximity in the structures of apo and/or Ca2⫹-saturated wild-type calmodulin. Using data for one of these groups, we obtained an open population of po ⫽ 0.50 ⫾ 0.17 and a closed → open rate constant of ko ⫽ (2.7 ⫾ 1.0) ⫻ 104 s⫺1. Conclusions: The conformational exchange dynamics appear to involve locally collective processes that depend on the structural topology. Comparisons with previous results indicate that similar processes occur in the wild-type protein. The measured rates match the estimated Ca2⫹ off rate, suggesting that Ca2⫹ release may be gated by the conformational dynamics. Structural interpretation of estimated chemical shifts suggests a mechanism for ion release. Introduction The conformational fluctuations and dynamical properties of a protein are intimately coupled to its function [1–6]. Conformational transitions on microsecond to millisecond timescales are believed to be particularly im* To whom correspondence should be addressed (e-mail: mikael. [email protected]). † Present address: Department of Medicinal Chemistry, AstraZeneca R&D Lund, SE-221 87 Lund, Sweden. ‡ Present address: Vanderbilt Structural Biology Center, Vanderbilt University, 2220 Pierce Avenue, 896 MRB II, Nashville, Tennessee 37232.

portant for processes such as molecular recognition by “induced fit” and enzyme activity [7–10]. Nuclear magnetic resonance (NMR) spectroscopy provides a powerful means to study the dynamics of proteins and other biomolecules at atomic resolution over a wide range of timescales [11–14]. Heteronuclear spin relaxation measurements commonly identify regions of proteins that experience conformational fluctuations on a timescale of microseconds to milliseconds, but detailed analyses of the microscopic time constants and the structural nature of the exchange process have so far been rare [15–18]. Recent developments in NMR enable characterization of conformational exchange with correlation times as short as ⵑ10 ␮s in solution, using off-resonance rotating-frame 15N spin relaxation [19–22]. In the present study, we have utilized this method to characterize the dynamics of a large-scale transition between folded conformations in the C-terminal domain of calmodulin (CaM). CaM is a ubiquitous eukaryotic protein that couples transient increases in intracellular Ca2⫹ concentration with numerous regulatory processes by undergoing a conformational transition that triggers target recognition [23]. CaM consists of two structurally homologous domains joined by a flexible linker. Each domain contains two Ca2⫹ binding helix-loop-helix motifs called EFhands [24, 25] that are packed in a head-to-head orientation with a short ␤-type interaction connecting the two loops. The ␣ helices and Ca2⫹ binding loops of CaM are denoted A–H and I–IV, respectively. Each CaM domain binds two calcium ions with positive cooperativity and dissociation constants in the micromolar range [26]. Upon Ca2⫹ binding to CaM, the helices in each EF-hand change their relative orientations from approximately antiparallel to orthogonal, corresponding to a “closedto-open” structural transition of the domain [27–31], which also involves significant repacking of the hydrophobic core. In the open conformation, the domain exposes a large hydrophobic patch that forms the binding sites for various targets [23, 32–35]. This conformational switch is thus central to CaM-mediated signal transduction in the cell. The time-averaged structures of the open and closed states have been characterized by X-ray crystallography [27, 28] and NMR spectroscopy [29–31]. Recent X-ray crystallographic studies of calcium-loaded CaM at 1.0 A˚ resolution reveal correlated disorder of the backbone and side chains, suggesting a hierarchy of conformational substates [36]. 15N spin relaxation experiments have been used to characterize the intramolecular dynamics of apo [37] and Ca2⫹loaded CaM [38], as well as of a complex between Ca2⫹– CaM and a target peptide [39]. In contrast, the dynamics of the structural transition have not been addressed in detail, although semiquantitative results have been obtained for the C-terminal domain, indicating that the apo state transiently samples open conformations on Key words: NMR; dynamics; off-resonance rotating-frame 15N spin relaxation; conformational exchange

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a timescale of microseconds to milliseconds [40]. In addition, molecular dynamics simulations have been used to study motions on timescales of nanoseconds that appear to sample the initial stages of the transition process [41]. Recent studies have indicated that conformational transitions in CaM occur with rates similar to the Ca2⫹ and Mg2⫹ off-rates from CaM, suggesting that the release of cations may be gated by the intramolecular dynamics [40, 42, 43]. The isolated N- and C-terminal domain fragments of CaM denoted Tr1C and Tr2C retain the Ca2⫹ binding properties [26] and structural response to Ca2⫹ binding [31, 44] observed for the corresponding domains in intact CaM. We have focused on wild-type Tr2C (wt-Tr2C) and two mutants in a series of studies that aims at characterizing the molecular processes of the Ca2⫹induced conformational switch. The mutants E104Q and E140Q modify the critical bidentate Ca2⫹-ligating carboxylate residue in the twelfth position of loops III and IV, respectively. The structure, dynamics, and Ca2⫹ binding properties of both mutants have been investigated previously using 1H and 15N NMR spectroscopy [45, 46]. The E→Q mutations decrease the Ca2⫹ affinity of the mutated site such that sequential binding is observed; E140Q binds the first Ca2⫹ in loop III and the second Ca2⫹ in loop IV, while the reverse is observed for E104Q. NMR studies have shown that the (Ca2⫹)2-bound states of both mutants exchange between at least two conformations on a submillisecond timescale [43, 45, 46]. The two major conformations appear similar to the apo (closed) and Ca2⫹-loaded (open) structures of wt-Tr2C, as gauged by the simultaneous observation of two sets of interproton distances, derived from NOESY spectra, that are mutually exclusive in the sense that one set is satisfied in the apo structure but violated in the Ca2⫹loaded structure and vice versa [45]. In addition, the majority of the residues have chemical shifts that are in between those of apo and (Ca2⫹)2 wt-Tr2C [45]. Apparently, the mutation E→Q destabilizes the open conformation that predominates in the (Ca2⫹)2 state of the wildtype protein. Similar observations have been made for site I of the homologous protein troponin C, where the corresponding residue was mutated E→A, with the result that the protein remained closed in the Ca2⫹-bound state [47]. Recently, we used the temperature dependence of the 15N spin relaxation rates in the laboratory frame to obtain unequivocal evidence for conformational exchange affecting essentially all residues of the protein and to evaluate semiquantitatively the timescales and energetics of the exchange process [43]. The present study provides a detailed analysis of the microscopic exchange dynamics of the transition between open and closed conformations in (Ca2⫹)2-E140Q. Off-resonance rotating-frame 15N spin relaxation experiments [19–22] yield residue-specific microscopic exchange time constants, as well as estimates of the populations and chemical shift differences between the conformations, thereby providing unique insights into the nature of the conformational dynamics. Results and Discussion R1␳ Relaxation Dispersion Measurements We have measured off-resonance rotating-frame 15N spin relaxation rate constants (R1␳) at eight different ef-

fective fields and a temperature of 301 K. E140Q Tr2C (corresponding to residues M76–K148 of CaM and including the mutation E140Q) contains 73 backbone amide groups. The resonances of the two N-terminal residues were not observed in the NMR spectra, presumably due to rapid amide proton exchange with the solvent. Measurements could not be obtained for N97 and Q140 due to severe spectral overlap. For the remaining 69 residues, R1␳ values were obtained at nominal tilt angles ranging from 19⬚ to 64⬚ (measured at the midpoint of the 15N spectrum). The rapidly decaying intensities of I100, Y138, and E139 precluded reliable R1␳ measurements for these residues at the largest nominal tilt angle, ␪ ⫽ 64⬚, where the R2 contribution is largest. Except for the cases mentioned above, fits of single-exponential decays to the experimental data were accepted on the 95% confidence level for all residues at all tilt angles. Representative relaxation curves at a nominal tilt angle of ␪ ⫽ 54⬚ are shown in Figure 1a. The eight data pairs (␪, R1␳) form a relaxation dispersion curve [c.f. equation (1)], as exemplified in Figure 1b. An alternative representation of these data are given by (R1␳ ⫺ R1)/sin2␪ plotted as a function of ␻2e, as shown in Figure 1c. Exchange Model and Optimization of Dynamic Parameters Based on our previous observations indicating two major conformations [43, 45], a minimal two-state exchange model was applied here. Two parameters, ␶ex and φ, were included to describe the exchange for each residue. The exchange time constant (␶ex) is the effective mean lifetime of the two conformations and is related to the microscopic opening and closing rates ko and kc [see equation (3)]. The parameter φ contains information on the populations and 15N chemical shifts of the exchanging conformations [see equation (4)]. The optimized model included also as free parameters the longitudinal and transverse relaxation rate constants R1opt and R02opt. For each 15N spin, these four parameters (␶ex, φ, R1opt, and R02opt) were fit to the experimental relaxation data (R1, R02, R2, and the eight values of R1␳), as outlined in equations (9)–(12). The significance of any resulting relaxation dispersion was assessed by F-statistical testing [48], comparing the four-parameter fit with a twoparameter fit that included only the optimized parameters R1opt and R02opt, (i.e., conformational exchange was excluded in the latter fit). For 57 residues out of the 69, the quality of the fit was significantly improved when exchange was included. Figures 1b and 1c show representative R1␳ relaxation dispersion curves. Precise measurements of φ and ␶ex were obtained for 42 residues. The remaining 15 residues exhibit small degrees of relaxation dispersion, yielding either fits of poor quality or substantial uncertainties in the optimized parameters (with few exceptions, ␶ex falls in the range of 10–100 ␮s). Limited relaxation dispersion is expected for these residues because the 15N chemical shift changes observed upon Ca2⫹ binding to wt-Tr2C are small, with a mean value of ⬍⌬␦(wt)⬎ ⫽ 0.91 ⫾ 0.65 ppm and a maximal shift difference of 2.8 ppm (observed for G98). The following discussion involves only the set of 42 residues for which well-determined exchange parameters were obtained.

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mental data acquired several months apart and on different samples, are mutually consistent. Equation (12) is derived for the fast exchange limit ␶ex␦␻ ⬍⬍ 1. The optimized parameters obtained here (see below) yield ␶ex␦␻ ⬍ 0.1 in all cases, suggesting that the fast exchange limit is fulfilled. We investigated further the extent of agreement between actual and optimized parameters by simulating off-resonance R1␳ relaxation data using the homogeneous Bloch–McConnell equations [49–52] using MATLAB (The MathWorks, Inc.), and subsequently fitting equation (12) against the simulated data (J. E. and M. A., unpublished data). The simulations indicate that for the ranges of ␶ex and φ values reported here [13–46 ␮s and (0.02 ⫺ 2) ⫻ 106 s⫺2, respectively] the results should be accurate to within 15% (␶ex) and 12% (φ). These maximal errors are obtained for heavily skewed populations, po ⫽ 0.9, and large chemical shift differences, |⌬␦| ⫽ 10 ppm, while for more equal populations and smaller chemical shift differences the errors are substantially smaller. Thus, for the large majority of residues (see below) the systematic error is within 5% for both ␶ex and φ, which is less than the estimated random errors of ⵑ6%–60%. Faster exchange processes (␶ex ⬍ 5 ␮s) are not subject to misinterpretation, because they do not yield appreciable dispersion, given the effective fields used in the present study. In summary, the simulations validate the exchange parameters extracted using equation (12).

Figure 1. Off-Resonance Rotating-Frame 15N Relaxation Data Representative data are shown for R86 (filled circles), S101 (filled triangles), and D131 (open squares). (a) R1␳ decay curves obtained at a nominal tilt angle of ␪ ⫽ 54⬚. The lines show the single-exponential fits of the equation I(t) ⫽ I(0)exp(⫺R1␳t) to the experimental data for each residue. The bars represent the estimated uncertainties (one standard deviation) in the measured intensities. The tilt angles and optimized values of R1␳ are 57.5⬚, 8.0 ⫾ 0.2 s⫺1 (R86); 57.5⬚, 15.8 ⫾ 0.5 s⫺1 (S101); and 52.1⬚, 10.4 ⫾ 0.2 s⫺1 (D131). The rotatingframe 15N relaxation rate constants (R1␳) are shown as a function of (b) tilt angle, ␪, and (c) the effective field squared, ␻e2 [c.f. equations (1) and (2)]. R1 is included at ␪ ⫽ 0⬚, and R2 (inverted symbols) and R20 at ␪ ⫽ 90⬚ [43]. The solid lines represent the nonlinear fits, as described in detail in the text [c.f. equations (9)–(12)]. Error bars represent one standard deviation. The dashed lines show the curves expected in absence of conformational exchange, Rex ⫽ 0 [c.f. equation (1)]. The optimized values of ␶ex and φ are 20.3 ⫾ 2.1 ␮s, (269 ⫾ 27) ⫻ 103 s⫺1 (R86); 16.9 ⫾ 1.7 ␮s, (980 ⫾ 104) ⫻ 103 s⫺1 (S101); and 23.3 ⫾ 1.5 ␮s, (484 ⫾ 36) ⫻ 103 s⫺1 (D131).

The optimized values of R1opt and R02opt agree with the experimentally determined values R1 and R02 [43] to within the experimental errors, yielding mean deviations of ⬍R1opt ⫺ R1⬎ ⫽ ⫺0.01 ⫾ 0.02 s⫺1 and ⬍R02opt ⫺ R20⬎ ⫽ ⫺0.02 ⫾ 0.08 s⫺1. This observation indicates that the different sets of relaxation rates, obtained from experi-

Residue-Specific Exchange Time Constants The resulting values of ␶ex are shown as a function of amino acid sequence in Figure 2a. The ␶ex values range between 13 and 46 ␮s, with a weighted mean of ⬍␶ex⬎ ⫽ 21 and weighted uncertainty of ⬍␴␶⬎ ⫽ 3 ␮s. The well-defined mean exchange time constant for the opening–closing process corroborates earlier estimates of ␶ex ⵑ17–20 ␮s [43]. Although the majority of residues exhibit values of ␶ex ⵑ20 ␮s, the results suggest that there is a significant variation in ␶ex between different residues. The heterogeneity among the ␶ex values is further revealed by the shape of the sum of normal distributions derived from the ␶ex values and their standard deviations (Figure 2b). The current experiment does not detect conformational exchange processes with time constants much less than 10 ␮s, implying that the skewed distribution could potentially be due to experimental limitations. Geary’s test of normality [48] indicates that the distribution of ␶ex values deviates only weakly from a gaussian. The site-to-site variability in ␶ex was estimated as follows. The standardized variable Z ⫽ (␶ex – ⬍␶ex⬎)/␴␶, in which ␴␶ is the estimated standard deviation of ␶ex for the individual residue, was evaluated for the entire set of 42 residues. The standard deviation of Z, denoted ␴Z, is related to the standard deviation in site-to-site variability in ␶ex, denoted ⌳, through the relationship ␴Z2 ⫽ 1 ⫹ (⌳/⬍␴␶ ⬎)2 [53]. Here, ␴Z ⫽ 1.50, corresponding to ⌳ ⫽ 3.2 ␮s. We analyzed the variation in ␶ex in more detail by partitioning objectively the 42 residues into three different groups using cluster analysis based on hill-climbing algorithms [54], modified to weight each datum by its estimated uncertainty. The resulting three groups indicated in Figure 2 have the following weighted mean values of ␶ex: 18.5 ⫾ 2.6 ␮s

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faster than that studied here. It is thus likely that the conformational transition can be initiated from a large number of substates, such that there exists a multitude of possible paths across the energy landscape connecting the two basins. (Note, however, that the transition process does not involve a significant population of unfolded molecules, as gauged from the fast timescale [ps–ns] order parameters [43].) Because the 15N chemical shift is sensitive primarily to local interactions [57], the chemical shift modulation that is studied in the present experiment reflects mainly local conformational changes. Based on these considerations, we propose that the distribution of residue-specific ␶ex values may reflect ensemble-averaged hierarchical formation of local structure characteristic of the open and closed basins. Further experiments conducted over a range of temperatures and static magnetic fields will be needed to address this issue.

Figure 2. Exchange Correlation Times: ␶ex Three different groups identified using cluster analysis are represented by colored symbols: red triangles, ␶ex ⫽ 18.5 ⫾ 2.6 ␮s; green circles, ␶ex ⫽ 25.2 ⫾ 2.7 ␮s; and blue diamonds, ␶ex ⫽ 41.2 ⫾ 10.3 ␮s (see the text for details). (a) ␶ex values shown as a function of amino acid sequence. Error bars represent one standard deviation. Locations of the helices are indicated at the top. (b) The distributions of ␶ex values derived from the sums of residuespecific normal distributions given by the optimized values and standard deviations. The total sum is represented by the black line.

(red group, 24 residues), 25.2 ⫾ 2.7 ␮s (green group, 12 residues), and 41.4 ⫾ 10.3 ␮s (blue group, 6 residues). Evaluating the distribution of Z for each of the three groups indicates that there is no significant site-to-site variability within these. It should be noted that the statistical significance of results obtained from cluster analyses is not readily assessed in a formal manner [54]. Here, the cluster analysis is not applied to evaluate different distributions of ␶ex in a quantitative sense but serves mainly to facilitate further investigations of the microdynamic parameters (see the following sections), as well as the spatial distribution in the molecular structures of residues with different exchange time constants. As stated above, the results of the cluster analysis do not necessarily imply that there are only three distinct exchange processes active. An alternative view is that there exists a continuous distribution of effective exchange time constants that can be rationalized as follows. The open and closed conformations are probably best viewed as two different basins of attraction in the energy landscape [5, 55, 56]. Within each of the open and closed basins, the molecule is interconverting between lower level conformational substates on a timescale

Relative Populations and Chemical Shift Differences The quadratic dependence of φ on the chemical shift difference between the exchanging conformations results in a wide range of values, φ ⫽ (0.02–2) ⫻ 106 s–2, c.f. Equation (4). The φ parameter encapsulates both the populations and the chemical shift difference, and these two terms are not directly separable in the present analysis. However, we compared φ1/2 and the absolute 15 N chemical shift differences, |⌬␦(wt)|, between the apo and (Ca2⫹)2 states of wt-Tr2C in order to investigate the extent of agreement between the current data and the assumed exchange process between open and closed conformations (Figure 3a). The largest φ values are obtained for residues I100 and E139, which also exhibit the largest chemical shift changes upon Ca2⫹ binding to wt-Tr2C (13.6 and 7.3 ppm, respectively). Weighted least-squares minimization of |φ1/2/␥NB0| versus |⌬␦(wt)| using all 42 residues yields a slope corresponding to an open population of po ⫽ 0.88 ⫾ 0.03, as indicated by the black line in Figure 3a; the sample correlation coefficient of the data is rc ⫽ 0.66. However, a variation in ␶ex between different groups of residues likely implies a variation also in the effective populations. A substantially better correlation is obtained if we consider only the red group (22 residues, excluding I100 and I130, as explained below), which contains residues with welldetermined exchange parameters and the largest variation in φ. These data yield po ⫽ 0.50 ⫾ 0.17 and rc ⫽ 0.86, as indicated by the red line in Figure 3a. The value of po obtained for the red group agrees reasonably well with an earlier estimate of the populations, po ⫽ 0.65 ⫾ 0.15, which was based on the intensities of the two mutually exclusive sets of NOEs [45]. Thus, the results obtained for the red group strongly support the notion that the observed exchange involves open and closed conformations similar to apo and Ca2⫹-saturated wildtype CaM. In contrast, the green and blue groups exhibit more limited ranges of φ and poorer correlations with |⌬␦(wt)| that correspond to more skewed populations. The slopes of the linear fits are dominated by only a few points for these two groups, and the results can hardly be taken as significant. It is possible that the exchange

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of one side chain oxygen not only impairs the bidentate coordination of Ca2⫹ but also affects the hydrogen bond network in the Ca2⫹ binding loop [45, 58], which can result in significant chemical shift differences for certain residues between the open conformations of the mutant and wild-type proteins. For example, the shift deviation observed for I130 may be caused by such mutationspecific effects, because the mutated side chain cannot simultaneously form the hydrogen bonds that are observed in the wild-type protein to this amide group and to those of D131 and N137 [27, 28, 45]. Clearly, discrepancies between the |⌬␦(E140Q)| and |⌬␦(wt)| values could also result from other structural differences between the two conformations of (Ca2⫹)2-E140Q and the apo and Ca2⫹-saturated states of wt-Tr2C. Another possible source of chemical shift discrepancies might be that the dynamic chemical shift averaging between substates within each of the open and closed conformations of (Ca2⫹)2-E140Q may be different from that occurring in the wild-type protein. We emphasize that the detailed structures of the open and closed conformations of (Ca2⫹)2-E140Q are unknown, although the present data together with the observed NOEs as well as the 1H and 15 N chemical shifts indicate that the conformations resemble the apo and Ca2⫹-saturated states of wild-type CaM [43, 45].

Figure 3. Populations and Chemical Shift Differences Comparison of the φ values of (Ca2⫹)2-E140Q and the Ca2⫹-induced 15 N chemical shift changes in wt-Tr2C at 301 K. The data are color coded (red triangles, green circles, and blue diamonds) according to clusters, based on the values of ␶ex, see Figures (2)–(4) and the text for details. (a) |φ1/2/(␥NB0)| plotted versus |⌬␦(wt)|. Black line: linear regression using all data, yielding po ⫽ 0.88 ⫾ 0.03 (rc ⫽ 0.66). Red line: linear regression using the red group only, yielding po ⫽ 0.50 ⫾ 0.17 (rc ⫽ 0.86). Open red triangles indicate residues that have not been included in the linear regression of the red group (see the text for details). (b) The 15N chemical shift differences |⌬␦(wt)| (open circles) and |⌬␦(E140Q)| (colored symbols) are shown as a function of the amino acid sequence. |⌬␦(E140Q)| was calculated from the φ values, assuming an open population of po ⫽ 0.50.

observed for the green and blue groups does not correspond to one predominant transition between open and closed conformations but that additional processes may be active for these residues (see also discussion above). 15 N chemical shift differences between the exchanging conformations, |⌬␦(E140Q)|, were calculated for each residue from the respective φ values and po ⫽ 0.50 (as obtained for the red group), yielding values ranging between 0.8 and 7.5 ppm. Figure 3b shows a comparison between |⌬␦(E140Q)| and |⌬␦(wt)|, plotted against the amino acid sequence. As expected, the two sets of values are highly similar for the residues in the red group, whereas larger deviations are observed for the green and blue groups. The presence of two calcium ions in the closed conformation of E140Q most likely distorts the local geometry and hence the chemical shifts of residues located in and around the Ca2⫹ binding sites, as compared to the apo state of wt-Tr2C. The removal

Rate Constants of the Opening and Closing Processes In the case of the red group, the determination of exchange time constant as well as populations enables extraction of the forward and backward rate constants. Using equation (3) with a mean exchange time constant of ⬍␶ex⬎ ⫽ 18.5 ⫾ 2.6 ␮s and an open population of po ⫽ 0.50 ⫾ 0.17, we estimate the rate constants for the opening (closed→open) and closing (open→closed) processes to be ko ⫽ kc ⫽ (2.7 ⫾ 1.0) ⫻ 104 s⫺1. In a previous study we noted that the estimated conformational exchange rate was of the same magnitude as the estimated Ca2⫹ off-rate from loop IV and speculated that Ca2⫹ dissociation from loop IV may occur predominantly from the closed conformation so that it is effectively gated by the conformational dynamics [43]. Given a Ca2⫹ binding constant of K ⫽ 1.4 ⫻ 103 M⫺1 [45] and assuming an on-rate of kon ⵑ108 M⫺1s⫺1 [59, 60], the off-rate is estimated to koff ⵑ7 ⫻ 104 s⫺1. The present measurement of the actual rate constant for the closing process is in general agreement with the estimated Ca2⫹ off-rate. Relevance for the Ca2ⴙ-Induced Structural Activation of Calmodulin The present results on (Ca2⫹)2-E140Q are likely to be relevant for understanding the conformational transition also in the wild-type protein. NMR studies of apo CaM [29, 30, 37] and apo wt-Tr2C [40] have revealed pronounced conformational exchange for many residues in the C-terminal domain. Importantly, the patterns of exchange contributions to the laboratory frame transverse relaxation rates Rex,CPMG are similar in all three systems, indicating that they exhibit similar fluctuations. Again, the largest differences in Rex,CPMG between (Ca2⫹)2E140Q and the two apo states are observed for residues

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Figure 4. Location in the Structures of Residues Exhibiting Different Exchange Correlation Times The residues are color coded according to cluster (see the text for details): red, ␶ex ⫽ 18.5 ⫾ 2.6 ␮s; green, ␶ex ⫽ 25.2 ⫾ 2.7 ␮s; blue, ␶ex ⫽ 41.2 ⫾ 10.3 ␮s; and gray, ␶ex not determined. The backbone C␣ trace is shown for all residues. The side chain heavy atoms are shown only for those residues for which reliable estimates of the dynamic parameters could be obtained (i.e., red, green, and blue groups). The closed (a) and open (b) states of (Ca2⫹)2-E140Q are represented by the C-terminal domain (residues M76–K148) of apo CaM (PDB entry: 1CFC [29]) and (Ca2⫹)2bound wt-Tr2C (PDB entry: 1CMG [31]), respectively. The figure was generated using MOLMOL [84] and POVRAY. For clarity, the calcium ions have been omitted.

located in the Ca2⫹ binding loops (c.f. discussion above). Disregarding six significant outliers, least-squares minimization of φ (determined here for E140Q) against Rex,CPMG (determined previously for apo wt-Tr2C at a temperature of 291 K [40]) yields a slope of φ/Rex,CPMG ⫽ 51,044 ⫾ 2697 s⫺1, with a medium degree of correlation of rc ⫽ 0.62. The slope yields an approximate value of the rate constants in apo wt-Tr2C as follows. Assuming that the second term of equation (8) can be neglected and that the exchange samples identical conformations in E140Q and apo wt-Tr2C [i.e., ⌬␦(E140Q) ⫽ ⌬␦(apo)], the slope φ/Rex,CPMG corresponds to kex(apo)po(E140Q) pc(E140Q)/[po(apo)pc(apo)]. Taking po(apo) ⵑ5%–10% as a reasonable estimate of the populations in apo wt-Tr2C [40], we obtain kc(apo) ⵑ(1.0–1.8) ⫻ 104 s⫺1. Although the temperature dependence of the rate is not known, the inference is that the rate constants of E140Q and apo wt-Tr2C agree well, in accord with previous conclusions [40]. This may suggest that the E140Q mutation affects the rates mainly by altering the free energy of the open conformation and to a lesser extent the energies of the closed conformation and the effective barrier between the conformations; in this case, the exchange rate of E140Q cannot exceed that of wt-Tr2C by more than a factor of two. The conformational exchange observed here most likely involves repacking of interior side chains and significant displacement of backbone atoms, implying excursions across the energy landscape over a large number of local barriers connecting distinct substates. The E140Q mutation is likely to cause small effects on the barriers related to the repacking of interior side chains, even though it significantly affects the difference in free energy between the two major conformations. Because the populations are nearly equal in E140Q, the effects of conformational exchange on the transverse spin relaxation are significantly enhanced (approximately by a factor of three to ten) relative to the apo states of intact CaM and wt-Tr2C. To this extent,

E140Q may serve as a model system for probing in detail the dynamics and energy landscape of the structural transition in wt-Tr2C and CaM. Detailed Structural Information from Chemical Shift Differences Valuable information on the structural details of the exchanging species is further provided by the chemical shift differences of I100 [⌬␦(wt) ⫽ 13.6 ppm] and V136 [⌬␦(wt) ⫽ 5.5 ppm], located in the middle of the ␤ strand (corresponding to loop position 8) of loops III and IV, respectively. The 15N chemical shifts of these two residues have been shown to be reliable indicators of Ca2⫹ coordination [61]. Ca2⫹ coordination in loop III involves the carbonyl group of Y99 in loop III, causing appreciable deshielding of the adjacent 15N nucleus of I100 due to polarization of the amide group, with a resulting increase of the chemical shift by 4–8 ppm [61]. The remaining chemical shift change of ⵑ7 ppm of I100 is attributed to a change in the side chain ␹1 torsion angle from gauche to trans, which is likely to be associated with the open–closed transition [61]. In the present study, the estimated value for I100 is ⌬␦(E140Q) ⫽ 7.0 ppm. This finding is consistent with persistent coordination of Ca2⫹ in loop III by the backbone oxygen of Y99 and further suggests that the exchange between closed and open conformations is associated with conformational changes of the I100 side chain. In the case of V136, the Ca2⫹-induced chemical shift change in the wild-type protein is caused only by polarization effects due to the Ca2⫹ coordination by the backbone oxygen of Q135 in loop IV [61]. Previous characterization of Ca2⫹ binding to E140Q has established that the (Ca2⫹)2 state of E140Q is populated to 98% under the present experimental conditions. Given the chemical shifts and Ca2⫹ exchange rates estimated, any relaxation contributions due to Ca2⫹ exchange between fully saturated and halfsaturated states are at least one order of magnitude

Conformational Exchange in Calmodulin 191

Figure 5. Pulse Sequence for the Off-Resonance Rotating-Frame 15N Relaxation Experiment Narrow and wide bars indicate 90⬚ and 180⬚ pulses, respectively. Gradient pulses are indicated by hatched bars, except for the gradient pulses used for coherence selection, which are stippled. At point a, a water-selective 1H 90⬚ pulse is applied as a rectangular pulse (␻1 ⵑ125 Hz). At point b, a 5 ms hyperbolic secant-shaped amplitude-modulated adiabatic pulse is applied off-resonance along the x axis to rotate the z magnetization into alignment with the effective field. During the relaxation delay T, a 15N off-resonance spin-lock field is applied by continuous-wave irradiation. An even number of relaxation cycles are employed with a 1H 180⬚ pulse applied in the middle of each cycle as an ⵑ540 ␮s cosine-modulated rectangular pulse [85] with excitation maxima positioned 2 kHz from the carrier (on water). Following the relaxation delay, a second reversed adiabatic pulse is applied to bring the magnetization back to the z axis. To ensure the same amount of heating of the sample in all experiments, a compensating spin-lock field of length T⬘ ⫽ Tmax ⫺ T is applied far off-resonance (300 kHz) in the beginning of each recycle delay. In all experiments, Tmax was set to 500 ms and the recycle delay (D) to 2 s. The delays ␶a, ␶b, and ␶c were set to 2.25, 2.75, and 0.5 ms, respectively. The delay ␶⬘b is given by ␶b ⫹ 2pw, where pw is the length of the 1H 90⬚ pulse. The experiment employs gradient and phase cycling schemes as described by Farrow et al. [78]. Gradient levels used were g1 ⫽ 1 ms, 5 Gcm⫺1; g2 ⫽ 0.5 ms, 4 Gcm⫺1; g3 ⫽ 1 ms, 10 Gcm⫺1; g4 ⫽ 0.5 ms, 8 Gcm⫺1; g5 ⫽ 1.25 ms, 30 Gcm⫺1; and g6 ⫽ 0.125 ms, 29.5 Gcm⫺1. The phase cycling used was φ1 ⫽ x, ⫺x; φ2 ⫽ y; φ3 ⫽ 2(x), 2(y), 2(⫺x), 2(⫺y); φ4 ⫽ x; and receiver was x, ⫺x, ⫺x, x. For each increment of t1, two free induction decays (FIDs) were collected with the phase of φ4 and the amplitude of g6 inverted for the second FID. For each increment of t1, the phases of φ4 and the receiver were incremented by 180⬚.

smaller than those observed here and can thus be safely neglected [43, 45]. The present estimate of ⌬␦(E140Q) ⫽ 4.5 ppm for V136 therefore suggests that the backbone oxygen of Q135 coordinates Ca2⫹ only in the open conformation. This is in agreement with the structural difference of the Ca2⫹ binding site between the closed and open states of the wild-type protein [28–30], which reveals a hinge-like motion around residue 6 of the loop [29, 42]. The hinge positions the carbonyl oxygen of residue 7 (Q135) close to the Ca2⫹ site in the open conformation but significantly further away from the site in the closed conformation; the distance is 2.2 A˚ in the crystal structure of the Ca2⫹-loaded state (Protein Data Bank [PDB] entry 1CLL [28]) and 8.5 ⫾ 0.2 A˚ in the NMR structure ensemble of the apo state (PDB entry 1CFC [29]), as measured by superimposing the first five loop residues of the apo and Ca2⫹-loaded structures. The proposed hypothesis that Ca2⫹ dissociation from loop IV may be gated by the conformational dynamics is supported by the present interpretation of the V136 shift differences in terms of a reduced number of Ca2⫹ ligands contributed by the protein in the closed conformation. For comparison, in loop III the distances are 2.2 A˚ and 2.4 ⫾ 1.9 A˚, respectively, suggesting that Ca2⫹ coordination by the carbonyl oxygen in position 7 is maintained in the closed conformation. This difference between the two loops is mirrored by the N-terminal domain, where the corresponding distances are 2.3 A˚ and 1.9 ⫾ 0.2 A˚ for loop I and 2.3 A˚ and 3.2 ⫾ 0.4 A˚ for loop II. Interestingly, loop II of Mg2⫹-saturated wt-Tr1C also exchanges between two conformations, only one of which appears to coordinate the ion with the backbone oxygen in position 7 [42]. Also in this case, the exchange rate is similar to the rate of ion release [42]. The similarities between

the exchange processes in (Ca2⫹)2-E140Q and (Mg2⫹)2wt-Tr1C suggest that the phenomenon is not specific to the mutant but rather is general for the second loop of each domain. However, the exchange in (Mg2⫹)2-wt-Tr1C appears to be restricted to the loop region and does not involve the hydrophobic core. In this context, it is instructive to consider the differences in ion coordination by the residue in position 12: in (Mg2⫹)2-wt-Tr1C, the E in position 12 does not appear to coordinate Mg2⫹ (which is a smaller ion than Ca2⫹) [42], and the chemical shifts indicate that the conformation is predominantly closed; in (Ca2⫹)2-E140Q, the Q in position 12 coordinates the Ca2⫹ with a single oxygen and approximately equal populations of open and closed conformations are observed; in (Ca2⫹)2-wt-Tr2C, the E in position 12 coordinates Ca2⫹ with two oxygens, and the conformation is predominantly open. The emerging picture shows that interactions between the ion and the oxygen(s) in position 12 are required for stabilizing the open conformation [42, 45, 46, 62] and that loss of these interactions promotes fluctuations in the second loop of the EF-hand pair, such that the carbonyl oxygen in position 7 moves away from the ion, possibly triggering ion release. The comparative analysis of exchange in (Mg2⫹)2-wt-Tr1C and (Ca2⫹)2-E140Q suggests that these fluctuations occur also in the wild-type protein. However, in the Ca2⫹saturated state the population of the open conformation totally dominates, which makes the exchange contributions to the spin relaxation rates undetectably small. Residues with Similar Exchange Time Constants Cluster in the Structure In Figure 4, the residues are color coded by ␶ex groups in the apo and Ca2⫹-loaded structures of wt-Tr2C. Certain

Structure 192

patterns can be identified from the spatial distribution of residues belonging to the different groups. Residues belonging to the red group are primarily located on the surface of the protein (Figure 4). In addition, the red group includes the central residues of the ␤ sheet, I100 and V136, as well as a cluster of residues, I85, M109, L116, and M145, located at the “bottom” (in the view of Figure 4) of the hydrophobic core in the apo structure (Figure 4a). The latter cluster is not present in the Ca2⫹loaded structure, although the interactions are maintained between residues I85 and M145 and between M109 and L116 (Figure 4b). Similar observations are made for the green group: F89 packs against V108, forming a hydrophobic cluster together with L112 in the apo state (Figure 4a) but not in the Ca2⫹-loaded state (Figure 4b). The green group includes several residues located in helix F. The different sides of helix F and to some extent also helix E are characterized by different ␶ex values (red and green groups; Figure 4). Finally, the blue group comprises six residues that all have large uncertainties in ␶ex. Three residues of the blue group are located in the very center of the core; the side chains of L105, I125, and F141 form a hydrophobic cluster in the apo structure (Figure 4a). In the Ca2⫹-loaded state, the side chain of F141 has a totally different orientation, while L105 and I125 are still packed together (Figure 4b). G134, situated in loop IV, interacts only with I125 in the Ca2⫹-saturated state, and it does not pack against any other residue of the blue group in the apo state. The blue group also includes two residues (G113 and E119) in the linker region that do not exhibit contacts with any other residue in the same group. Overall, the proximal location of residues belonging to the same group substantiates in an independent manner the qualitative results of the cluster analysis and provides inferential support for the notion that different groups of residues exhibit different values of ␶ex. Similarly, temperature-dependent macroscopic exchange terms obtained previously from CPMG experiments [Rex,CPMG; equation (8)] revealed different apparent activation barriers for different residues in (Ca2⫹)2-E140Q [43]. There is no obvious correlation between the microscopic exchange time constants reported here and the apparent activation barriers reported previously. However, such a correlation is not necessarily expected, because the macroscopic exchange terms correspond approximately to the product ␶ex ⫻ φ rather than ␶ex. The spatial clustering of residues with similar time constants suggests that the exchange involves locally collective processes that depend on the structural topologies of the open and closed conformations.

Biological Implications The conformational fluctuations and dynamics of a protein are intimately coupled to its function, as evidenced by a large number of atomic resolution structures of proteins revealing significant structural rearrangements upon binding of low molecular weight ligands or macromolecular receptors. While there is a rich database available on the amplitudes of structural change obtained from the static pictures of the end states, very little is

known about the dynamics of these transitions. The ultimate goal of understanding protein function from a molecular perspective requires that the dynamic processes and energy landscape of structural changes be investigated. CaM is a ubiquitous Ca2⫹-activated regulator of numerous cellular processes in eukaryotic organisms. Ca2⫹ binding to CaM triggers a structural transition in each of its two domains from a closed (inactive) to an open (active) conformation that is central to target recognition. Here, we have used NMR relaxation experiments to characterize the dynamics of this transition in a model system—the E140Q mutant of the C-terminal domain of CaM. The conformational transition occurs with a mean time constant of ⬍␶ex⬎ ⫽ 21 ⫾ 3 ␮s. The results suggest that ␶ex varies significantly between different groups of residues and that residues with similar values exhibit spatial proximity in the structures of apo and/or Ca2⫹saturated wild-type CaM. These observations suggest that the conformational exchange involves locally collective processes, which depend on the structural topology. Transition rates were estimated for a subset of residues, yielding ko ⫽ (2.7 ⫾ 1.0) ⫻ 104 s⫺1. Comparisons with previous results indicate that similar processes occur also in the wild-type protein. The measured rates match the estimated Ca2⫹ off-rate, suggesting that Ca2⫹ release may be gated by the conformational dynamics. Structural interpretation of estimated chemical shifts suggests a mechanism for ion release. Experimental Procedures Theory The off-resonance rotating-frame relaxation rate constant R1␳ is given by [19, 63, 64] R1␳ ⫽ R1cos2 ␪ ⫹ R20 sin2 ␪ ⫹ Rex sin2 ␪

(1)

where R1 and R20 are the longitudinal and exchange-free transverse autorelaxation rate constants, respectively; Rex is the conformational exchange contribution to transverse relaxation; ␪ ⫽ arctan(␻1/⌬␻) is the tilt angle between the reduced static magnetic field ⌬␻ ⫽ ␻ ⫺ ␻0 and the effective field ␻e ⫽ (⌬␻2 ⫹ ␻12)1/2 in the rotating frame; ␻ is the spin-lock frequency; ␻0 is the population-averaged Larmor frequency; and ␻1 is the precession frequency around the spin-lock field. The conformational exchange contribution is dependent on ␻e and ␪, such that an excess dispersion in the relaxation rate reveals the existence of conformational exchange (c.f. Figures 1b and 1c). For a two-state exchange process between closed (c) and open (o) conformations [63, 64], the exchange contribution in the fastexchange limit (␶ex ␦␻ ⬍⬍ 1) is given by 2 Rex ⫽ φ␶ex/(1 ⫹ ␶ex ␻e2)

(2)

␶ex ⫽ 1/kex ⫽ p0/k0 ⫽ pc/kc ⫽ 1/(k0 ⫹ kc)

(3)

φ ⫽ p0pc␦␻2

(4)

in which

and

where ␶ex is the time constant for the exchange process; kex is the exchange rate constant; ko and kc are rate constants for the opening and closing reactions, respectively; pi is the population of spins in state i; ␦␻ ⫽ ␥NB0⌬␦; ␥N is the gyromagnetic ratio of 15N; B0 is the strength of the static magnetic field; and ⌬␦ is the chemical shift difference (in ppm) between the two states. The exchange-free transverse autorelaxation rate constant can be obtained as [65]

Conformational Exchange in Calmodulin 193

R20 ⫽ (␩xy/␩z) (R1 ⫺ 1.249␴NH) ⫹ 1.079␴NH

(5)

where ␩z and ␩xy are the rate constants of longitudinal and transverse cross-relaxation caused by interference between 1H-15N dipolar and 15 N chemical shift anisotropy (CSA) relaxation mechanisms [66], and ␴NH is the heteronuclear cross-relaxation rate constant, which is related to the steady-state {1H}-15N NOE by ␴NH ⫽ R1(␥N/␥H) (NOE ⫺ 1)

(6)

in which ␥H and ␥N are the gyromagnetic ratios of H and N, respectively. Equation (5) is based on the fact that ␩z and ␩xy depend on the same interaction strengths and that ␩xy does not contain contributions from exchange [65, 67]. Furthermore, it is assumed that ␩z is negligibly affected by 1H-1H cross-relaxation. Equation (5) is derived using reduced spectral density mapping [68–70], based on the assumption that spectral densities at frequencies in the interval (␻H ⫹ ␻N; ␻H ⫺ ␻N) may be written as J(⑀␻H) ⫽ (0.87/⑀)2J(0.87␻H) [65, 68]. The transverse autorelaxation measured in a CPMG experiment [71, 72] can be represented by 1

R2 ⫽ R20 ⫹ Rex,CPMG

15

(7)

The exchange contributions Rex,CPMG can be interpreted in terms of the microscopic exchange time constants using the following approximate expression for two-site exchange [73] Rex,CPMG ⫽ φ␶ex[1 ⫺ (2␶ex/␶cp)tanh(␶cp/2␶ex)]

(8)

in which ␶cp is the delay between the 15N 180⬚ pulses in the CPMG sequence. Numerical calculations indicate that equation (8) is accurate to within 6% for parameter values expected here: ␶ex ⬍ 100 ␮s, ␶cp ⫽ 1.2 ms, 0.5 ⬍ po ⬍ 0.9, and ⌬␦ ⱕ 10 ppm. NMR Spectroscopy Expression and purification of 15N-labeled E140Q were carried out as reported previously [45]. The NMR sample contained 600 ␮l of 2.3 mM protein, 0.2 mM NaN3, 0.1 mM DSS, and 41 mM CaCl2, dissolved in 90% H2O/10% D2O at pH 6.0. At this Ca2⫹ level, the (Ca2⫹)2 state of E140Q is populated to 98% and the (Ca2⫹)1 state to 2%, as calculated from the binding constants determined previously [45]. 1H and 15N assignments of (Ca2⫹)2 E140Q at 301 K have been reported previously [45]. All NMR experiments were run at 301 K on a 600 MHz Varian Inova spectrometer operating at a 1H Larmor frequency of 599.89 MHz and using a Varian single-axis pulsed field gradient inverse broadband probe. The pulse sequence used to record the 15N R1␳ spectra is shown in Figure 5. At point b, where longitudinal 15N magnetization is established, the pulsed field gradient (g1) is applied to dephase any remaining transverse magnetization, and the 15N carrier frequency is switched to a value determined by the desired effective field. The magnetization is aligned along the effective field using a 5 ms hyperbolic secant-shaped amplitude-modulated adiabatic pulse [74] applied along the x axis. Calculations indicate that the adiabatic pulse achieves an alignment better than 99.9% for the largest tilt angle, where the performance of the pulse is poorest. During the following relaxation delay (T) the magnetization is spin locked in the tilted frame using continuous-wave irradiation. In order to eliminate effects of cross-correlation between 1H-15N dipolar and 15N CSA relaxation mechanisms in the R1␳ experiments, 1H 180⬚ pulses are applied during the relaxation delay [75–77]. After the relaxation delay, the remaining magnetization is returned to the z axis using a reverse adiabatic pulse, and the 15N carrier frequency is switched back to the value corresponding to the midpoint of the 15N spectrum. In other respects, this 15N off-resonance R1␳ experiment is virtually identical to the 15N R1 experiment described previously [78]. The recycle delay between transients was 2.3 s, including the acquisition period. 15N decoupling during acquisition was achieved using the GARP-1 decoupling sequence [79]. The spin lock may cause substantial heating of the sample. Differential sample heating during the R1␳ series was avoided by applying continuous-wave irradiation far off-resonance (⌬␻ ⫽ 300 kHz) during the recycle delay for a period T⬘ ⫽ Tmax – T, with Tmax held constant at 500 ms for all tilt angles. The sample temperature was calibrated

by measuring the frequency difference between the temperatureindependent resonance signal of DSS [80] and the carrier frequency, which follows the temperature-dependent HDO resonance used for the field/frequency lock [81]. The set point temperature of the VT unit was adjusted so that the sample temperature was stable at the target value of 301 K after a preparation period of “dummy scans.” R1␳ values were measured at eight different effective fields, achieved by varying the radio frequency of the spin lock (␻) while keeping the B1 field strength constant at a value corresponding to ␻1 ⫽ 2164 ⫾ 43 Hz. The B1 field strength was measured by monitoring residual scalar couplings as a function of off-set during continuouswave irradiation. Measurements were performed with the following nominal tilt angles (corresponding to the midpoint of the spectrum), with the range between the smallest and largest actual tilt angles (corresponding to residues G132 and A147, respectively) given within parentheses: 19⬚ (17⬚–20⬚), 22⬚ (20⬚–25⬚), 27⬚ (24⬚–30⬚), 34⬚ (30⬚–39⬚), 39⬚ (34⬚–46⬚), 46⬚ (39⬚–54⬚), 54⬚ (45⬚–64⬚), and 64⬚ (53⬚–76⬚). At each tilt angle, NMR spectra were obtained for eight different relaxation delays, and duplicate spectra were recorded for two of these. The longest relaxation delay used for each tilt angle was chosen such that the magnetization of each spin had decayed to less than 30% of its initial value. All spectra were recorded with spectral widths of 8000 Hz over 2048 complex points in ␻2 (1H) and 1300 Hz over 128 complex points in ␻1 (15N). The 1H carrier frequency was set on the H2O signal. NMR Data Processing and Analysis Processing and analysis of the NMR spectra were performed using Felix97 (MSI). All spectra were processed using two protocols to optimize either signal-to-noise or resolution of the crosspeaks. The former protocol involved exponential and cosine bell apodization functions in ␻2 and ␻1, respectively, while the latter involved Lorentzian-to-Gaussian transformation in ␻2 and extension of the interferogram by linear prediction followed by a cosine bell in ␻1. The final size of the matrices was 1024 ⫻ 1024 real points after zero filling in ␻1 and Fourier transformation. Peak intensities were measured as peak heights. Uncertainties of the intensities were estimated from duplicate spectra and from standard deviations of the base-plane noise [82]. R1␳ values were obtained at each tilt angle by nonlinear optimization of single-exponential decays to the experimental data [83]. The rate constants at 301 K for the 15N longitudinal and transverse autorelaxation (R1 and R2, respectively), the longitudinal and transverse cross-relaxation (␩z and ␩xy, respectively) due to interference between 1H-15N dipolar and 15N CSA relaxation mechanisms, and the steady-state {1H}-15N NOE values have been reported previously [43]. Determination of Dynamic Parameters 0 , ␶ex, and φ were optimized simultaneThe four parameters R1opt, R2opt ously for each 15N spin against the experimental values of R1, R2, R20, and the eight values of R1␳ as a function of ␪, using the following relations [c.f. equations (1), (2), (7), and (8)]: R1 ⫽ R1opt 0 R20 ⫽ R2opt 0 ⫹ φ␶ex [1 ⫺ (2␶ex/␶cp) tanh(␶cp/2␶ex)] R2 ⫽ R2opt 0 2 sin2 ␪ ⫹ [φ␶ex/(1 ⫹ ␶ex ␻e2)]sin2 ␪ R1␳ ⫽ R1optcos2 ␪ ⫹ R2opt

(9) (10) (11) (12)

Nonlinear least-squares optimization using the Levenberg–Marquardt algorithm and Monte Carlo error analyses were performed following standard procedures [83]. In order to assess the statistical significance of any obtained relaxation dispersion, an additional fit was performed that excluded the conformational exchange parame0 , ters φ and ␶ex (i.e., only two optimized parameters, R1opt and R2opt were used in this fit). F-statistical testing was used to select between the two- and four-parameter models [48]. Acknowledgments This research was supported by a grant from the Swedish Natural Science Research Council (NFR) awarded to M. A. The 600 MHz NMR spectrometer was funded by the Knut and Alice Wallenberg Foundation. We thank Eva Thulin for protein expression and purification.

Structure 194

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