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NMR detection of multiple transitions to low-populated states in azurin

¹ Swedish NMR Centre, Göteborg University, 40530 Göteborg, Sweden
² Department of Molecular Biotechnology, Chalmers University of Technology, 40530 Göteborg, Sweden
³ Biochemistry and Biophysics, Göteborg University, 40530 Göteborg, Sweden

Reprint requests to: Martin Billeter, Biochemistry and Biophysics, Göteborg University, Box 462, 40530 Göteborg, Sweden; e-mail: martin.billeter{at}bcbp.gu.se; fax: +46 31 773 3910.

(RECEIVED July 26, 2002; ACCEPTED October 1, 2002)

⁴ Present address: Department of Medical Genetics, University of Toronto, Toronto, Ontario M5S 1A8, Canada

Article and publication are at http://www.proteinscience.org/cgi/doi/10.1110/ps.0225403.

	Abstract

TOP Abstract Introduction Results Discussion Materials and methods References

 
Transitions to conformational states with very low populations were detected for the reduced blue copper protein azurin from Pseudomonas aeruginosa by applying constant relaxation time CPMG measurements to the backbone ¹⁵N nuclei at three magnetic fields (11.7, 14.1, and 18.8 T) and three temperatures (25.7, 35.4, and 44.8°C). Two exchange processes with different rate constants could be discriminated despite populations of the excited states below 1% and spatial neighborhood of the two processes. The group of ¹⁵N nuclei involved in the faster process exhibits at 44.8°C a forward rate constant of 11.7±2.4 s^-1 and a population of the exited state of 0.39±0.07%. They surround the aromatic ring of histidine 35 whose protonation state is coupled to the flipping of a neighboring peptide plane. For the slower process, the forward rate constant and population of the exited state at 44.8°C are 4.1±0.1 s^-1 and 0.45±0.02%, respectively. The residues involved cluster nearby the copper ion, which is separated from the protonation site of histidine 35 by about 8 Å, indicating conformational rearrangements involving the copper coordinating loops. The dependence of the equilibrium constant on the temperature is consistent with an enthalpy-dominated transition around the copper, but an entropy-controlled transition near histidine 35. The detection by nuclear magnetic resonance of millisecond to second conformational transitions near the copper ion suggests a low energy-cost rearrangement of the copper-binding site that may be necessary for efficient electron transfer.

Keywords: Blue copper proteins; dynamics; NMR relaxation; CPMG; conformational exchange

	Introduction

TOP Abstract Introduction Results Discussion Materials and methods References

 
The stability of a protein is determined by the free energy differences between the native state and accessible alternatives, and by the balance between enthalpy and entropy that determines these. For many proteins, it is essential that they not only undergo breathing motions but that they can also reach states that are both structurally and energetically more distant (Branden and Tooze 1999). To name a few examples, these states may allow substrate binding to an enzyme by exposing an active site such as in the cyclin-dependent kinase CDK2 (Jeffrey et al. 1995), they may correspond to different states of the subunits of an allosteric protein such as phosphofructokinase (Schirmer and Evans 1990), or they may represent the excited states in the proton translocation cycle of bacteriorhodopsin (Henderson et al. 1990). In crystallographic studies, breathing motions result in lowered electron densities, whereas more sizeable conformational changes can sometimes be observed as alternative structures in the same electron density map provided that they are significantly populated. Nuclear magnetic resonance (NMR) can provide a detailed description of breathing motions, for example, by applying "model-free" analyses to relaxation data (Lipari and Szabo 1982). However, NMR is also a very sensitive tool for detecting interconversions between multiple conformations and for characterizing their thermodynamic interplay.

Heteronuclear NMR relaxation provides us with unique probes of protein conformational dynamics at atomic resolution. Approaches for studying pico to nanosecond time-scale motions (Palmer et al. 1996; Korzhnev et al. 2001a), slow conformational transitions on the second time scale (Montelione and Wagner 1989; Wider et al. 1991; Farrow et al. 1994) as well as intermediate microsecond-to-millisecond processes (Palmer et al. 2001) are now well established. Quantification of the latter type of processes relies on modulations of exchange line broadening as a result of radiofrequency irradiation applied at various field strengths and/or carrier frequencies (Szyperski et al. 1993; Akke and Palmer 1996), or on CPMG sequence with variable pulse repetition rate (Orekhov et al. 1994; Ishima et al. 1999; Loria et al. 1999; Mulder et al. 2001b; Skrynnikov et al. 2001; Wang et al. 2001). The initially proposed methods provide access to protein motions in the time range from tenths or hundredths of microseconds to milliseconds (Szyperski et al. 1993; Orekhov et al. 1994; Akke and Palmer 1996). Recently, constant relaxation time CPMG experiments have been introduced, which effectively sort out exchange contributions to transverse relaxation from those of other relaxation mechanisms, allowing quantitative descriptions of conformational exchange in milliseconds to seconds (Loria et al. 1999; Mulder et al. 2001b; Skrynnikov et al. 2001). For CPMG data obtained at several magnetic fields, these experiments can provide thermodynamic information including rate constants of an exchange process as well as populations of the structures involved (Millet et al. 2000). In a recent example, a T4 lysozyme mutant creating a cavity was studied, and millisecond time-scale excursions to a partially disordered high-energy state with a population of a few percents were revealed; the latter are likely to facilitate ligand entry into the deeply buried cavity (Mulder et al. 2001a,b; Skrynnikov et al. 2001).

The blue copper protein azurin from Pseudomonas aeruginosa is among the most thoroughly investigated electron-transfer metalloproteins (Adman 1991; Malmström 1994). Spatial structures have been determined for reduced wild-type azurin and for its oxidized form at different pH values (Shepard et al. 1990; Nar et al. 1991) as well as for the apo-protein (Nar et al. 1992). These structural studies have shown that the copper-binding site is essentially the same in the apo-form and in metal-loaded azurin, and it undergoes minimal changes upon oxidation. The copper coordination in both reduced and oxidized forms is close to trigonal, which is typical for Cu^I but quite unusual for Cu^II complexes (Gray et al. 2000). These observations support an early suggestion that the rigid protein matrix serves as a rack to constrain the copper in its coordination geometry (Malmström 1964, 1994) ensuring minimal reorganization energy associated with the electron transfer. However, the finding that oxidized azurin is more stable than reduced (Leckner et al. 1997) and model calculations of optimal copper coordination geometry (Ryde et al. 1996) raise strong doubts against the hypothesis of an essentially rigid environment imposed by the protein on the metal. Recently, slow conformational exchange was reported for the residues surrounding the side chain of histidine 35, which is located about 8 Å away from the copper site. This exchange was attributed to the protonation/deprotonation equilibrium of this side chain, which in turn appears coupled to the flipping of a neighboring peptide plane (Kalverda et al. 1999).

This work reports the detection of slow millisecond-to-second conformational transitions in reduced azurin to exited, low-populated conformations based on relaxation dispersion profiles obtained from constant relaxation time CPMG experiments. The data allowed us to separate at least two processes likely related to the protonation of the side chain of histidine 35 and a conformational rearrangement involving the copper-coordinating loops. The rate constants and population of the exchanged states were obtained using data measured at three magnetic fields (11.7, 14.1, and 18.8 T) and at three temperatures (25.7, 35.4, and 44.8°C). Thermodynamic characteristics of the exited states were estimated from the temperature dependence of the equilibrium and rate constants. The results presented provide experimental evidence for low energy-cost conformational rearrangements of the copper-binding site in azurin.

	Results

TOP Abstract Introduction Results Discussion Materials and methods References

 
Processing of CPMG data for individual residues
After the initial removal of the residues with resonance overlap in the ¹H-¹⁵N correlation spectra at any of three temperatures, the statistical analysis of the CPMG data on the remaining residues with both a simple model and the exchange model based on the equation by Carver and Richards (1972) yielded 30 residues for which the exchange model was statistically confirmed (see Materials and Methods). These residues, when mapped to the three-dimensional (3D) structure of azurin, cover about half of the protein in an asymmetric distribution that is centered near the copper-binding site (Fig. 1A; the 30 residues are listed in the figure caption).

View larger version (47K): [in this window] [in a new window]   Figure 1. Azurin structure with copper location (brown) and numbering of selected residue positions. (A) The 30 residues, which were found to exhibit conformational exchange, are indicated by green spheres at their backbone amide positions (residues 9–11, 37, 42–48, 50, 58, 61, 71, 82, 87–90, 111–113, 116–117, 120, and 123–124). (B) Nitrogen atoms are displayed as spheres for the residues listed in Table 1, with colors identifying the three groups: red, green, and black for the first, second, and third group, respectively. The side chain of histidine 35 is shown in yellow, and the hydrogen bond between this side chain and the carbonyl group of proline 36 is indicated as a dashed magenta connection. Residue numbers are provided for the first and second group.

The fitting of the experimental relaxation dispersion data using the Carver and Richards model is illustrated in Figure 2 for glycine 45. For most of the residues considered the fitting results in rate constants k_A<<k_B indicating transitions to exited low-populated states. For many residues, the k_A values are determined with a better precision compared to the k_B values (or the k_ex values obtained using the Bloom formula). The uncertainties of k_B and k_ex are coupled with the precision at which one finds a plateau value of R₂*(_CPMG) at _CPMG. Because most of the residues have k_B (k_ex) of the order of thousands of inverse seconds, plateau values are still not reached at the highest CPMG frequency used. This results for many residues in a better precision of the k_A values compared to the k_B values (or the k_ex values when using the Bloom formula). Therefore, in the following analysis of individual residues, we mostly rely on the information provided by the values of the forward rate constants k_A. The analysis was restricted to residues for which the error of k_A is smaller than its value at all temperatures. For the resulting 18 residues, the model by Carver and Richards provides a significantly better description than the one by Bloom with the exception of serine 89.

View larger version (27K): [in this window] [in a new window]   Figure 2. Plot of relaxation rates R2* vs. the CPMG frequency CPMG for glycine 45. Squares and corresponding error bars describe the experimental data, while the curves represent fits to the model by (Carver and Richards 1972) for three temperatures. Each fit is given in a different panel (top: 25.7°C, middle: 35.4°C, bottom: 44.8°C) and calculated using data from three different fields (lowest curve for 11.7 T, middle curve for 14.1 T, highest curve for 18.8 T).

Multiple exchange processes in azurin
The main question arising from the data analysis for individual residues is how to group the residues into sets that are subjected to the same dynamic process. Because for a given residue the scattering of the parameter k_A at different temperatures is much smaller than the variation of k_A between different residues, the observed rate constants are likely to reflect multiple dynamic processes in azurin. Thus, in the next step of the data analysis, the 18 residues obtained from the previous steps are classified using their reaction rate constants k_A together with the slope of ln(k_A) vs. 1/T calculated using k_A values at 25.7 and 35.4°C (Table 1). The residues in Table 1 are ordered according to decreasing values of ln(k_A) at T = 35.4°C. In addition, values of k_B are given if they are sufficiently well defined, that is, when the value exceeds its error. Based on these entities, the residues are classified into three groups. The first group consists of six residues (Gly 90, Gly 45, Gly 37, Ser 89, Ile 87, and His 46), which are characterized by high k_A values, strictly negative slopes of ln(k_A) vs. 1/T, and large and well-defined k_B values. The six residues in the second group (Trp 48, Thr 113, Asn 47, Cys 112, His 117, and Phe 111) have smaller k_A values, again sizeable negative slopes, and smaller k_B values. The final six residues have low k_A values that do not exhibit a pronounced dependence on the temperature, and poorly defined k_B values. Figure 3 is a plot of ln(k_A) vs. 1/T for the 12 residues of the first two groups. The main difference between these two groups is the size of k_A and the size and uncertainty of the k_B values, while the slopes of ln(k_A) vs. 1/T do not provide a clear-cut criterion (the deviation from linear behavior of three of the curves is addressed later).

View larger version (25K): [in this window] [in a new window]   Figure 3. Plot of ln(kA) vs. 1/T for the residues of the first (solid lines) and second group (broken lines) of Table 1. (Units of rate constants kA are s-1.) From top to bottom at T = 44.8°C, the solid lines correspond to residues 90, 45, 89, 37, 46, and 87 and the broken lines to residues 113, 48, 47, 117, 112, and 111. On the horizontal axis, centigrade temperatures are given in parentheses.

A different source for conformational exchange has been described (Kalverda et al. 1999) that may explain the observed effects for the residues of the first group. This exchange process was related to the pH dependent protonation state of the side chain of histidine 35. This side chain forms at low pH a hydrogen bond with the carbonyl oxygen group of proline 36 (situation shown in Fig. 1B) and at high pH a hydrogen bond with the HN of glycine 37. In addition, a hydrogen bond connects the ring of histidine 35 to the CO group of methionine 44, a neighbor to glycine 45. Histidine 35 is located approximately in the middle of the first group of residues of Table 1, and it appears well suited to explain the differing reaction rates of this group.

Refinement of the exchange rate constants
The exchange parameters obtained for many individual residues are not precise enough to thermodynamically characterize the processes. Based on the evidence provided by Figure 1B and Table 1 about the presence of (at least) two distinct dynamic processes in azurin on the microsecond-second time scale, the relaxation dispersion data were processed jointly for residues within regions that surround the proposed sources for exchange. Because for all residues within a region the same values of k_A and k_B can be assumed, the data fit is expected to yield more precise values for these parameters. Therefore, all 30 residues for which exchange has been statistically confirmed (see above) were reconsidered. There is no reason to restrict the set of residues here, as at this stage two distinct exchange regions on azurin structure have already been located. Regions were defined using the following criteria (Table 2). Region one residues are near the protonation site of histidine 35; their backbone nitrogens are closer than 10 Å to this site, more than 8 Å away from the copper ion, and the distance ratio to these two sites exceeds 1.5. Region two residues are near the copper ion; their backbone nitrogens are closer than 10 Å to this ion, more than 8 Å away from the protonation site of histidine 35, and the distance ratio to these two sites exceeds 1.5. Region three residues are located between histidine 35 and the copper, with distances not exceeding 8 Å to both sites. The latter residues are likely to feel both exchange processes. Table 2 lists for all regions the residues that satisfy the corresponding criteria together with the relevant distances in the crystal structure. The residues of the first group of Table 1 are distributed over regions one and three, and supplemented by a few additional residues. Region two contains all six residues of the second group from Table 1, augmented by three more residues.

View larger version (25K): [in this window] [in a new window]   Figure 4. Dependencies of reaction constants on temperature. The logarithms and error estimates of kA (top), kB (middle), and keq = kB/kA (bottom) are plotted versus 1/T for residues of region one (heavy solid lines), region two (heavy dashed lines), and region three (solid thin lines). Regions include residues listed in Table 2. On the horizontal axis, temperatures in centigrade are given in parentheses.

	Discussion

TOP Abstract Introduction Results Discussion Materials and methods References

The classification of residues exhibiting exchange based on the values and temperature dependencies of the forward rate constants k_A (Table 1, Fig. 3), and the subsequent mapping of these groups onto the structure (Fig. 1B) provides sufficient evidence to suggest two exchange processes, one involving the copper ion and one occurring near histidine 35. In addition, the behavior of intermediate residues might indicate that the two processes are largely uncoupled (see Results). The separation of residues into two regions, each corresponding to a single exchange process (Table 2), should however be considered an approximation, as the cutoffs of Table 2 do not ensure that a nucleus close to one anticipated exchange source is not affected by the other. Also, the presence of exactly two exchange processes is only an assumption, but the limited set of residues considered and the precision of extracted rate constants do not allow a separation into more regions. Thus, the nonlinear dependencies of ln(k_A) vs. 1/T observed for residues 37, 46, and 87 (Fig. 3) might indicate a more complex dynamic process near histidine 35. Note also that two of these residues adopt an intermediate position between the copper ion and histidine 35 (Table 2), while residue 37 is located quite far from the copper, directly besides the peptide plane with pH-dependent orientation. The two regions selected, "near histidine 35" and "near copper" (Table 2), appear nevertheless reasonable, and the joint processing of the relaxation dispersion data for the residues of each region result in substantial improvement of the precision of equilibrium and rate constants. For the intermediate third region, "between copper and histidine 35", the two-state assumption is too simple, and therefore the further discussion is restricted to the other two regions.

The equilibrium constants for all regions show a close to linear dependency on the inverse temperature (Fig. 4). Although our measurements were carried out for only three different temperatures, we present in this section an attempt to decompose the Gibbs free energies into enthalpic and entropic contributions using linear fits of the logarithm of equilibrium constants versus the inverse temperature for the transitions near histidine 35 and near the copper. The resulting thermodynamic parameters, which are summarized in Table 4, suggest an entropy-driven process around histidine 35 with relatively small enthalpy change. This may be explained by the earlier mentioned protonation of the histidine side chain that is coupled to the flip of an adjacent peptide plane (Nar et al. 1991; Kalverda et al. 1999). The major change of an enthalpic interaction, the removal of the hydrogen bond between the histidine ring and proline 36, is replaced by another hydrogen bond to glycine 37. The minor state might represent a trapped state with higher order (strain) but similar interaction energy. In contrast, the process near the copper ion, for which a detailed description of the mechanism is missing, results in a pronounced unfavorable enthalpy change that is partially compensated by an entropy gain, which might indicate a transition to a less-stable and more disordered state.

To our knowledge, no mechanism has been described that can explain the modulation of the ¹⁵N chemical shifts observed in this study around the copper ion. The dynamic process observed is unlikely to reflect an exchange with low amounts of an oxidized species with chemical shift differences induced by paramagnetic Cu^II. Already with the minor state population reported in Table 3, 0.45%, an oxidized species would exceed the detection limit for absorption at 628 nm of 0.2%. Furthermore, paramagnetic Cu^II would significantly enhance the ¹⁵N relaxation resulting in higher values for R_2B, which in turn would increase the population of the minor state with respect to those calculated using R_2A = R_2B. For example, fitting of the relaxation dispersion data with a 10 (20) times increase of R_2B would result in a p_B of 0.55% (0.69%). Such a population of the oxidized species would not escape detection by optical methods. Therefore, we believe that the exchange involving the copper ion is connected with conformational transitions in reduced azurin with chemical shift modulation arising from rearrangements of the local structure.

Efficient functioning of blue copper proteins relies on low reorganization energies associated with the electron transfer. For azurin, this energy was estimated to 0.6–0.8 eV (1 eV corresponds to 96.5 kJ/mole), with the inner-sphere reorganization energy for the copper site being <0.2 eV (DiBilio et al. 1997). The coordination of copper in both reduced and oxidized azurin is close to trigonal, which is typical for Cu^I but unusual for Cu^II complexes (Gray et al. 2000). An early suggestion was that the protein matrix must be essentially rigid to constrain the copper coordination geometry, thus minimizing the reorganization energy (Malmström 1964, 1994). Our experimental results suggest, in contrast, that the copper site of azurin is flexible enough to adopt detectable multiple conformational states. This finding is further confirmed by the recent observation of increased B-factors around the copper ion in crystal structures at various temperatures (L. Sjölin, pers. comm.). The observed excited states are relatively similar in free energy to the ground state with G 14 kJ/mole at 44.8°C (Table 3), and barrier heights with respect to the minor state of about 60 kJ/mole. Other recent studies also suggest that there is little if any strain imposed by the protein on the metal. Quantum chemical calculations showed that the optimal vacuum structures of Cu^II and Cu^I binding to corresponding ligands are similar to those observed in the crystal structures of blue copper proteins (Ryde et al. 1996). Moreover, it was found that these conformations do not represent a unique energy minimum and that there are other energetically close conformations for Cu^II as well as Cu^I. The observation that the oxidized azurin is the most stable form (Leckner et al. 1997) is also in contrast to the idea that a basically rigid protein matrix enforces an unusual coordination geometry of blue copper.

The introduction of constant relaxation time CPMG relaxation dispersion measurements (Loria et al. 1999) made it possible to detect by NMR the conformational transitions of proteins to low-populated excited conformational states. (Mulder et al. 2001a) showed recently that this type of NMR experiment is capable of providing a comprehensive thermodynamic description of the exchange processes. In the presented study, we apply ¹⁵N relaxation dispersion measurements for quantification of multiple exchange processes in azurin, thus demonstrating the potential of this analysis in studies of proteins undergoing several internal exchange processes and with low-populated states. The data collected allowed us to separate and describe a so far unknown dynamic process involving the copper-binding site of azurin.

	Materials and methods

TOP Abstract Introduction Results Discussion Materials and methods References

 
Azurin expression and purification: Sample preparation
Azurin was expressed and purified as described previously (Karlsson et al. 1989), with the exception that 100 mM CuSO₄ was added to the cultivation medium (600 mL M9 minimal medium supplemented with 4 g algae extract). The A628/A280 absorbance ratio was 0.58 for the fully oxidized Cu^II-coordinating wild-type azurin. All stock chemicals were from Merck & Co. and of reagent grade. ¹⁵N labeled algae extract was obtained from Martek.

The sample of uniformly ¹⁵N labeled reduced azurin was prepared as follows. The protein was brought to 50 mM phosphate buffer through ultra filtration. It was then deoxygenated with concomitant reduction of Cu^II to Cu^I using a few grains of platinum black (from Fluka) and bubbling of H₂ gas in septum-sealed containers for 30 minutes. At the end of this procedure, the 628-nm absorption band had disappeared providing an upper limit of the amount of protein with oxidized copper of 0.2%. The sample was then transferred to a restricted NMR tube under N₂ atmosphere and sealed. The final conditions of the sealed NMR sample were 1 mM of uniformly ¹⁵N-labeled reduced protein with 0.2% oxidized protein (measurement in sealed sample), 8% D₂O, and a pH of about 5.

Relaxation dispersion measurements
Constant relaxation time CPMG experiments were performed for the backbone ¹⁵N nuclei of azurin using a pulse sequence described by (Tollinger et al. 2001), which implements an idea originally proposed by (Loria et al. 1999). Namely, an element is introduced to the pulse sequence, which exchanges in-phase and antiphase ¹⁵N magnetization in the middle of the constant time relaxation period, flanked by two identical elements composed of CPMG pulse trains, each of the length T_CP/2. In the absence of microsecond conformational exchange affecting the chemical shift of a nucleus, the resulting effective ¹⁵N transverse relaxation rate R₂* is independent of the CPMG pulse repetition rate. Otherwise, peak intensities in the spectra are modulated by exchange contribution to transverse relaxation. The peak intensities in a set of spectra recorded with different CPMG frequencies _CPMG = 1/(4), where is the delay of the -180_(x)- CPMG block, are converted into R₂* via:

1

I(_CPMG) is the peak intensity in the spectrum recorded at _CPMG and I₀ is the peak intensity in the reference spectrum obtained by omitting the CPMG intervals (i.e., for T_CP = 0 ms). The relaxation dispersion profiles R₂*(_CPMG) are then used to extract conformational exchange parameters.

NMR experiments were carried out on 11.7, 14.1, and 18.8 T Varian Inova spectrometers at 25.7, 35.4, and 44.8°C. For each temperature and magnetic field, a series of two-dimensional (2D) spectra were recorded with T_CP = 60 ms and different _CPMG frequencies, followed by a reference spectrum with T_CP = 0. The spectra were collected in interleaved manner (Orekhov et al. 1999) with a delay of 2.5 s between the scans. To minimize off-resonance effects (Korzhnev et al. 2000), the ¹⁵N 180° pulses in the CPMG pulse train were applied at a high field of 6.5 kHz. The spectra were zero-filled to 8k x 2k and Fourier transformed with Gaussian and sine-bell weighting functions applied along the ¹H and ¹⁵N dimensions, respectively. The cross-peak intensities were obtained using the MUNIN approach (Orekhov et al. 2001), that is, by three-way decomposition of a 3D data set composed of the series of 2D spectra (Korzhnev et al. 2001b). The resulting relaxation dispersion profiles R₂*(_CPMG) comprise 12 (11.7, 14.1 T) or 14 (18.8 T) points with _CPMG varied from 33.3 to 800 Hz. For each combination of magnetic field and temperature, uncertainties in R₂* were estimated using spectra recorded twice for at least three values of _CPMG. To account for possible systematic biases affecting peak intensities, uncertainties in R₂* were set to at least 1.5%.

Analysis of relaxation dispersion data for individual nuclei
Relaxation dispersion profiles resulting from ¹⁵N CPMG experiment were analyzed for each nucleus to obtain chemical shift differences for the spin in each of the exchanged conformations as well as the rates of interconversion between the states. In practice, interpretation of relaxation dispersion data requires a priori assumptions about the exchange process. Usually, one accepts the simplest model of reversible transitions between two states A and B with a frequency difference = _exN, where _ex is the chemical shift difference and _N is the Larmor frequency of the ¹⁵N nucleus. Several closed-form analytic expressions were proposed to approximate the rate of decay for CPMG echoes for a nucleus undergoing two-state chemical exchange (Luz and Meiboom 1963; Bloom et al. 1965; Carver and Richards 1972). For fast exchange (k_ex/>>1, where k_ex = k_A + k_B, and k_A and k_B are forward and reverse rate constants, respectively), one can, for example, apply the equation of (Bloom et al. 1965) using a modification described in reference (Orekhov et al. 1994):

2

The populations of the states in exchange are p_A and p_B, is the delay of the -180_(x)- CPMG block, R₂ = p_AR_2A+p_BR_2B, with R_2A and R_2B being the transverse relaxation rates in the two states. A general expression proposed by (Carver and Richards 1972) and modified by (Davis et al. 1994) extends the applicability to CPMG data describing fast and intermediate (k_ex/1) exchange regimes with unequally populated conformations:

3

where

Exchange effects in the CPMG experiments were investigated for individual residues of azurin, provided that detectable cross-peaks of backbone ¹H-¹⁵N groups are observed. Residues with spectral overlap at any of the three temperatures were not considered; this eliminates 18 residues. At each temperature and for each resonance, the relaxation dispersion profiles obtained at three magnetic fields were analyzed using two models. A simple model with no dependence of apparent transverse relaxation rates on _CPMG was opposed to a model assuming conformational exchange between two states, for which equal relaxation rates are assumed, that is, R_2A = R_2B. The former model includes three adjustable parameters, the effective transverse relaxation rates R₂ at 11.7, 14.1, and 18.8 T. The latter, based on the expression by Carver and Richards (equation 3), depends on six parameters: R₂ (= R_2A = R_2B) at 11.7, 14.1, and 18.8 T, the rate constants k_A and k_B and the chemical shift difference _ex. The model parameters were extracted from least square fitting of the experimental relaxation dispersion data by the theoretical expressions. Minimization was carried out using the Levenberg-Marquart algorithm (Press 1997). Uncertainties of the optimized model parameters were estimated using the covariance matrix method. Those residues that satisfy the following three statistical criteria for at least two temperatures were considered to be involved into conformational exchange and were kept for further analysis. (1) The simple model is rejected on a 95% confidence level based on ² statistics, that is, on the quality with which the model fits the data. (2) The exchange model cannot be rejected on a 95% confidence level. (3) The F-test confirms the significance for the ² reduction upon transition form simple to exchange model with at least 90% confidence.

The selected residues of azurin were classified into groups based on the forward k_A and reverse k_B rate constants determined for individual ¹⁵N nuclei, provided that the parameters are estimated with sufficient precision (i.e., the value exceeds the anticipated uncertainty). To check the group compactness the resulting groups of residues were mapped to the 3D structure of azurin (Nar et al. 1991; PDB-code 4AZU).

Data analysis for residue groups involved in a single exchange process
Assuming that a single exchange process in the millisecond-second time scale modulates the chemical shifts of multiple nuclei, the joint processing of all relaxation dispersion data for these residues should result in a considerable improvement of the precision of the estimated k_A and k_B values (Mulder et al. 2001a). In this case, the optimized model based on the equation by Carver and Richards (equation 3) includes two parameters common for all residues, the forward and reverse rate constants k_A and k_B. The additional parameters, the chemical shift differences _ex, and the effective transverse relaxation rates R₂ (= R_2A = R_2B) at all magnetic fields are characteristic for each nucleus. The relaxation dispersion data for sets of residues were processed jointly following the procedure described for individual residues.

	Acknowledgments

 
This work was supported by NFR grant K-AA/KU 12071–302 and a post-doctoral fellowship from the Wenner-Gren Foundation to D.M.K. All NMR experiments were performed at the Swedish NMR Centre.

The publication costs of this article were defrayed in part by payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 USC section 1734 solely to indicate this fact.

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