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Published online before print November 10, 2004, 10.1110/ps.04926604
Protein Science (2004), 13:3322-3330. Published by Cold Spring Harbor Laboratory Press. Copyright © 2004 The Protein Society
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FOR THE RECORD

Analysis of side chain mobility among protein G B1 domain mutants with widely varying stabilities

Virginia A. Goehlert1, Ewa Krupinska1, Lynne Regan2 and Martin J. Stone1

1 Department of Chemistry, Indiana University, Bloomington, Indiana 47405-0001, USA
2 Department of Chemistry and Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut 06520-8114, USA

Reprint requests to: Martin J. Stone, Department of Chemistry, Indiana University, Bloomington, IN 47405-0001, USA; e-mail: mastone{at}indiana.edu; fax: (812) 855-8300.

(RECEIVED June 10, 2004; FINAL REVISION August 16, 2004; ACCEPTED August 17, 2004)


   Abstract
TOP
 Abstract
Introduction
 Results and Discussion
 Materials and methods
 Electronic supplemental material
 References
 
"Host–guest" studies of the B1 domain from Streptococcal protein G have been used previously to establish a thermodynamic scale for the {beta}-sheet-forming propensities of the 20 common amino acids. To investigate the contribution of side chain conformational entropy to the relative stabilities of B1 domain mutants, we have determined the dynamics of side chain methyl groups in 10 of the 20 mutants used in a previous study. Deuterium relaxation rates were measured using two-dimensional NMR techniques for 13CH2D groups. Analysis of the relaxation data using the Lipari–Szabo model-free formalism showed that mutations introduced at the guest position caused small but statistically significant changes in the methyl group dynamics. In addition, there was a low level of covariation of the Lipari–Szabo order parameters among the 10 mutants. The variations in conformational free energy estimated from the order parameters were comparable in magnitude to the variations in global stability of the 10 mutants but did not correlate with the global stability of the domain or with the structural properties of the guest amino acids. The data support the view that conformational entropy in the folded state is one of many factors that can influence the folding thermodynamics of proteins.

Keywords: {beta}-sheet propensity; B1 domain; conformational entropy; dynamics; GB1; NMR; protein G; protein stability

Abbreviations: ASA, accessible surface area • {Delta}Gconf, conformational free energy • HSQC, heteronuclear single quantum coherence • NMR, nuclear magnetic resonance • R1, longitudinal relaxation rate constant • R1{rho}, transverse relaxation rate constant • S2, order parameter • S2axis, methyl axis order parameter • Sconf, conformational entropy • {tau}e, internal correlation time

Article published online ahead of print. Article and publication date are at http://www.proteinscience.org/cgi/doi/10.1110/ps.04926604.


   Introduction
TOP
 Abstract
 Introduction
Results and Discussion
 Materials and methods
 Electronic supplemental material
 References
 
The relative stabilities of folded and unfolded proteins are determined by the interplay of many enthalpic and entropic factors. In this communication we describe an experimental study of the role of conformational entropy within the folded state. It is widely appreciated that folded proteins have substantially reduced conformational entropy relative to the unfolded state, yet retain some residual flexibility. Although the reduction in entropy upon folding is thermodynamically unfavorable, it is compensated by the formation of enthalpically favorable interactions and by a favorable increase in solvent entropy. The native ensemble represents the optimal trade-off between these various factors. Mutation of a protein (or ligand-binding, changes in pH, ionic strength, temperature, pressure, etc.) could potentially affect any of these thermodynamic factors. Therefore, to understand the influence of mutations on protein stability, it would be advantageous to understand, among other things, the effect of the mutations on conformational entropy.

Recent advances in the collection and analysis of NMR relaxation data have made it possible to obtain information about the conformational flexibility of proteins at an unprecedented level of detail (Fischer et al. 1998; Kay 1998; Palmer 2001; Stone 2001; Wand 2001; Akke 2002; Brüschweiler 2003). Typically, data are interpreted using the formalism of Lipari and Szabo (Lipari and Szabo 1982a, b), which yields a timescale of internal motions ({tau}e) and an order parameter (S2) representing the spatial restriction of internal motions for each bond vector investigated. Because entropy is a measure of accessible conformational states, it is possible to relate the order parameter to the apparent conformational entropy of the bond vector (Akke et al. 1993; Li et al. 1996; Yang and Kay 1996). However, making this connection requires an assumption regarding the physical nature of the bond vector motion. Moreover, calculating the total conformational entropy of the protein from the measured order parameter is not rigorously valid because (1) the measurements are limited to a subset of bond vectors; (2) the measurements are not sensitive to rotational motions slower than molecular tumbling (a few nanoseconds) or to translational motions; (3) the measurements are insensitive to rotations about the interactions vector; and (4) the motions of individual bond vectors may not be independent of each other (Forman-Kay 1999; Cavanagh and Akke 2000; Stone 2001; Wang et al. 2003). The first three factors would tend to reduce the estimated entropy whereas the fourth factor would increase it relative to the correct value. Notwithstanding these shortcomings, comparison of different mutants of the same protein using these methods has the potential to provide some insights regarding how the mutations affect the conformational entropy of the protein.

Herein we compare the flexibility of methyl groups in the side chains of 10 mutants of a small protein, the B1 domain from the Streptococcal IgG-binding protein (protein G) (Björck and Åkerström 1990). The 56-residue B1 domain (Fig. 1Go) contains a four-stranded mixed parallel/antiparallel {beta}-sheet packed against an {alpha}-helix (Gronenborn et al. 1991). The 10 mutants differ only at position 53 (the "guest position") on the exposed surface of the {beta}-sheet; guest amino acids include unbranched (Ala, Ser, Met), {beta}-branched (Thr, Val, Ile), {gamma}-branched (Leu), aromatic (Trp), and charged (Asp, His) amino acids. The folding free energies of the mutants vary over a range of 2.2 kcal/mol, but all 10 are >99% folded under the conditions of this study. These mutants (and 10 others) were previously used by Smith et al. (1994) to estimate the intrinsic {beta}-sheet-forming propensities of the natural amino acids. Although the derived scale differs in its detail from {beta}-sheet propensity scales determined in other studies (Kim and Berg 1993; Minor and Kim 1994), all of these studies agree that {beta}-branched residues as well as the aromatic residues (Phe, Trp, Tyr) have the highest preference for a {beta}-sheet. Previously, we found that the conformational entropy estimated for backbone NH groups varies substantially among the 10 mutants but does not correlate with stability. Here we report comparative data for the side chain methyl groups.



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  		Figure 1. Ribbon diagram of the protein G B1 domain, showing the positions of residue 53 and the "guest position," as well as neighboring residues Ala 6 and Ala 44. This figure was generated from the NMR structure of the protein G B1 domain, PDB code 2GB1 [PDB] (Gronenborn et al. 1991).

 

   Results and Discussion
TOP
 Abstract
 Introduction
 Results and Discussion
Materials and methods
 Electronic supplemental material
 References
 
Choice of mutants
This study included a series of 10 mutants of the B1 domain (containing T2Q, I6A, and T44A background mutations) substituted with each of 10 amino acids (Ala, Asp, His, Ile, Leu, Met, Ser, Thr, Trp, and Val) at position 53. Position 53 ("the guest position") is located in the center of the {beta}-sheet and has a solvent-exposed side chain that extends from the face of the {beta}-sheet opposite the {alpha}-helix (Gronenborn et al. 1991). These mutants are well suited for an investigation of the relationship between dynamics and stability because they are known to have substantially different folding free energies (Smith et al. 1994), but almost identical structures, as judged from fingerprint NMR spectra. For each of the 10 mutants, stereospecific 1H and 13C resonance assignments were made for the side chain methyl groups (31 methyl groups not including those at position 53; for Val and Leu mutants, residue 53 assignments were nonstereospecific). An example of an assigned 13C-1H correlation spectrum of the B1 domain (Ser mutant) is shown in Figure 2Go and assignments for all mutants are listed in Table S1 of the Supplemental Material.



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  		Figure 2. Example assigned 13C-1H constant time correlation spectrum of the serine mutant of the protein G B1 domain.

 
Relaxation and dynamics parameters
2H longitudinal (R1) and transverse (R1{rho}) relaxation rates were measured at 30°C for 23–27 methyl groups in each mutant (Tables S2 and S3 of the Supplemental Material); relaxation rates R1 and R1{rho} were not determined for certain methyl groups because of partial or complete spectral overlap or line broadening. Order parameters (S2 axis) and internal correlation times ({tau}e) (Tables S4 and S5 of the Supplemental Material) were obtained by fitting to the Lipari–Szabo model-free formalism (Lipari and Szabo 1982a, b). In general, there are only small differences between the relaxation and dynamics parameters for a particular residue in the different mutants (vide infra), whereas there are substantial differences between parameters for different residues within the same protein. The following discussion focuses on the order parameters, S2axis, which represent the degree of restriction of motion of the methyl group symmetry axis (completely restricted motions have S2axis = 1; completely unrestricted motions have S2axis = 0).

Variations in dynamics throughout the domain
The relaxation and dynamics parameters for each residue are presented in Figure 3Go as averages and standard deviations among the 10 mutants. The distributions of S2 axis values differ substantially for different amino acid types, with decreasing average values and increasing variability as the separation between the methyl group and the backbone increases (average ± standard deviation = 0.66 ± 0.05 for Ala, 0.48 ± 0.05 for Val, 0.57 ± 0.08 for Thr, and 0.23 ± 0.04 for Leu). This trend has been observed previously in a survey of side chain dynamics for eight proteins (Mittermaier et al. 1999). The uniformity of order parameters for Ala residues is notable in light of the fact that these residues are spread throughout the structure with differing degrees of burial (Fig. 3EGo) and secondary structure locations. For other residue types, the S2axis variations can often be rationalized according to structural features. For example, among the three consecutive threonine residues in the second {beta}-strand, the methyl groups of hydrophobic core residues Thr 16 and Thr 18 are >95% buried and have S2 axis values of 0.53 and 0.62, respectively, whereas the methyl group of surface residue Thr 17 is only 75% buried and has a lower S2 axis value (0.36). However, the order parameters of threonine methyl groups in the B1 domain mutants do not correlate with the participation of the threonine side chain hydroxyl groups in hydrogen bonds. The order parameters for valine side chains indicate that the diastereotopic methyl groups within the same valine residue always have very similar degrees of motional restriction, suggesting that the observed relaxation is dominated by rotation of or around the C{alpha}-C{beta} bond, rather than rotation around one of the C{beta}-C{gamma} bonds (Daragan and Mayo 1998; Ramirez-Alvarado et al. 1998). The variability between different valine residues is also reflective of structural location. For example, Val 21 and Val 39 are both located in turn/loop regions but Val 21 methyl groups are more highly exposed (20.8%–37.2% accessible surface area [ASA]) and have lower order parameters (0.31–0.33), whereas Val 39 methyl group are more buried (0%–3.5% ASA) and have higher order parameters (0.48–0.49). Similarly, the methyl groups of Val 29 are slightly more accessible (12.0%–17.4% ASA) and slightly more flexible (S2axis = 0.51–0.56) than those of Val 54 (ASA = 0%, S2axis = 0.57–0.62), although both of these residues are in regular secondary structures ({alpha}-helix and {beta}-sheet, respectively). Finally, among leucine residues, the Leu 5 {delta}1 methyl group has much more restricted motion (S2axis = 0.55) than the two Leu 12 methyl groups (S2axis<0.15), probably reflecting the locations of Leu 5 in the hydrophobic core and Leu 12 on the exposed surface of the {beta}1-{beta}2 turn. In contrast, the Leu 7 {delta}2 is also buried in the hydrophobic core yet displays a very low S2axis value (0.15). As noted by Lee et al. (2002), such low order parameters can result from "barrier crossing" between multiple rotomeric states of the buried leucine side chain, even in cases for which the population of the minor rotamer is quite low. The dynamics of the other methyl resonances of these two buried leucine residues (Leu 5 {delta}2 and Leu 7 {delta}1) could not be determined because of apparent exchange broadening, suggesting that the transverse relaxation of Leu 5 {delta}1 and/or Leu 7{delta}2 may also be influenced by conformational exchange. The dynamics formalism used herein does not account for such effects; a larger number of relaxation parameters would be required to determine whether chemical exchange is present (Millet et al. 2002). The presence of such exchange would cause an artifactual decrease in fitted order parameters, suggesting that the S2axis values determined for Leu 5 {delta}1 and Leu 7 {delta}2 should be considered upper limits.



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  		Figure 3. Plots of the average values of (A) R1, (B) R1{rho}, (C) S2 axis, and (D) {tau}e for each side chain methyl group in the B1 domain. Error bars represent the standard deviations of the relaxation or dynamics parameter at each position among the 10 mutants. (E) The percentage accessible surface area (ASA; relative to the central amino acid of an Ala-Xaa-Ala tripeptide) estimated for the Ala mutant, using the PDB file 2GB1 [PDB] (Gronenborn et al. 1991).

 
Variations in dynamics between mutants
As noted above, there are only small differences between the S2axis and {tau}e values for a particular residue in the different mutants. For each residue, the standard deviation (SD) of dynamics parameters among the 10 mutants is on the same order as the standard error (SE) in the dynamics parameters, suggesting that much of the variation between mutants results from the errors in the measurements. Nevertheless, a careful statistical analysis of the variations indicates that they are slightly greater than would be expected solely based upon random error. For example, randomly one would expect the ratio SD/SE to be >1.0 for ~44% of residues, >1.5 for ~2% of residues, and >2.0 for ~0% of residues, whereas we observe that this ratio is >1.0 for ~58% of residues, >1.5 for ~19% of residues, and >2.0 for ~4% of residues; similar results were obtained for variation of the {tau}e values among mutants. Thus, we conclude that the mutations introduced at the guest position have caused changes in the methyl group dynamics but that these changes are not much larger than the uncertainties in the measurements. This result contrasts with the observation by Johnson et al. (1999) that single mutations of ubiquitin resulted in a substantial redistribution of dynamics, although the overall flexibility remained similar. This difference may be attributed to the fact that the ubiquitin mutations are in the hydrophobic core whereas the B1 domain mutations are on the surface of the protein.

To determine the relationship of methyl group conformational entropy to the stability of the B1 domain mutants, it is necessary to estimate the conformational entropy from the order parameters (S2axis). Available methods to do this require the assumption of a particular physical model for the motions of the bond vectors and also the assumption that the motions of different bond vectors are independent; these assumptions have been discussed in detail previously (Yang and Kay 1996; Forman-Kay 1999; Cavanagh and Akke 2000; Stone 2001; Wand 2001). Molecular dynamics simulations suggest that the "diffusion-in-a-cone" model may be a reasonable approximation of the bond vector fluctuations (Yang and Kay 1996). However, the assumption of independent motions is much more difficult to verify. If the motions of two bond vectors are highly correlated (synchronized), then the total entropy of the system will be lower than the entropy one would estimate by considering their motions to be independent. For example, simulations by Lee et al. (2002) suggest that introducing interactions within a cluster of four fluctuating vectors causes a reduction in the entropy of the cluster by approximately 40%. In an effort to probe the existence of correlated motions, we recently proposed an analysis of the covariation of motions among a set of protein mutants (or other states of a protein that are perturbed relative to each other) (Mayer et al. 2003). We have applied this method to the B1 domain side chain dynamics data. The logic behind this approach is as follows: If the motion of two groups is strongly coupled, then introducing a perturbation that affects the dynamics of one group should affect the motion of the second group in a correlated manner. Typically, such coupling is thought of in terms of positive correlations, in which a change in the order parameter of one side chain results in a change of similar sign and magnitude for the order parameter of a neighboring side chain. However, negative correlations in which a decrease in the order parameter of one side chain results in a decreased dynamic volume available to a neighboring side chain and thus an increased order parameter have been demonstrated (Lee et al. 2002). In either case, the observation that the dynamics parameters for the two groups are statistically correlated among a set of mutants (or perturbed states) suggests that their motions are coupled. It is important to emphasize that "coupled" motions do not necessarily indicate "correlated" (i.e., synchronized) motions. For example, if the volume of one amino acid affects the space available for movement of two other amino acids then mutation of this first amino acid may cause correlated changes in the dynamics of the latter two groups (i.e., these two groups are "coupled"), even if they do not move synchronously. On the other hand, if the motion of two groups is strongly correlated (synchronous), then one would expect to see strong covariation of their dynamics parameters. Therefore, the absence of substantial covariation indicates the absence of extensive correlated motions. There are two main caveats to this approach. First, the perturbations must be sufficiently severe to cause measurable changes in the dynamics parameters; this condition is met, albeit weakly, by the B1 domain methyl group data. Second, the degree to which motions of two groups are coupled may vary among the different perturbed states; in this situation the method will not reveal coupled motions even though they exist in some of the states.

The covariation of motions between each pair of methyl groups (325 pairs) was probed by correlating the S2axis or {tau}e values for the two methyl groups for all 10 mutants. The resulting distribution of the 325 correlation coefficients was then compared with the distribution expected using simulated random S2axis or {tau}e values. The normalized frequency of good correlations (high r2 values) observed is slightly higher than randomly expected for both S2axis and {tau}e values (Fig. 4A,BGo). Furthermore, the observed distributions of Pearson correlation coefficients (r) and slopes for both S2axis and {tau}e values are shifted slightly to positive values compared with the random distribution, indicating positive covariation of methyl group dynamics (Fig. 4C–FGo). In general, the pairs of methyl groups that exhibit high covariation are scattered throughout the domain in a manner that does not offer an obvious structural explanation. Interestingly, the structural distribution of dynamical covariations was more readily interpretable in our previous study of backbone NH groups (Mayer et al. 2003). One exception is that a positive correlation (r = 0.77) was observed between the methyl groups of Ala 6 and Ala 44, whose side chains sandwich the side chain of the amino acid at the guest position (Fig. 1Go). It is possible that the dynamics of both these methyl groups are influenced in a similar manner by the side chain of residue 53. However, we were unable to identify any strong correlations between the dynamics parameters for the methyl groups and the volumes or branching properties of the guest amino acids.



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  		Figure 4. Covariation of dynamics parameters for the protein G B1 domain. Normalized distributions of (A,B) squared Pearson correlation coefficients (r2), (C,D) raw Pearson correlation coefficients (r), and (E,F) slopes for covariation analyses of (A,C,E) S2axis values and (B,D,F) {tau}e values. Observed distributions are indicated by solid lines, whereas randomly expected distributions are indicated by dashed lines.

 
We propose three possible explanations for the observation of weak but nonrandom covariation of methyl group dynamics among B1 domain mutants (Fig. 4Go):

  1. The motions of the different methyl groups in the B1 domain are very weakly coupled; the lack of extensive correlated motions would allow increased confidence in the entropy estimates.
  2. Extensive correlated motions are present but the motional coupling between different residues is disrupted by the mutations. Although we cannot rule out this possibility, it appears unlikely because the observed dynamics are so similar for the different mutants.
  3. Extensive correlated motions are present but the perturbations are not severe enough to alter the motions and to see the covariation. Considering the small differences between the measured dynamics of the mutants, this may well be the case. Nevertheless, if this is true, then entropy estimates should be influenced to a similar extent in all mutants, so calculated entropy differences should at least be proportional to true differences.

We estimated the conformational entropy for the 26 methyl groups that were used in covariation analysis using the "diffusion-in-a-cone" relationship determined by Yang and Kay (1996):


Although the estimates for individual methyl groups will be substantially affected by the standard errors in the S2axis values, random cancellation of these errors for the 26 residues leads to more precise determination of the total conformational entropy for each mutant (Table 1Go). The estimated total conformational free energy ({Delta}Gconf = –T{Delta}Sconf) varies by ~4.5 kcal/mol among the 10 mutants, which is comparable in magnitude to the 2.2 kcal/mol variation in folding free energy (Smith et al. 1994). It is important to note that the current estimate only takes into account a small fraction of the side chain groups in the protein, so it is probably an underestimate of the true total side chain conformational entropy. Using the same approach, we previously found that the backbone entropy estimated from NH order parameters for 43 residues in the 10 B1 domain mutants varies by more than 4.1 kcal/mol (Table 1Go). However, the backbone entropy values do not correlate with the methyl side chain entropy values for the 10 mutants and neither correlates with global stability. Notwithstanding the underlying assumptions of this entropy analysis, and the fact that only a subset of bond vectors was observed, it appears that differences in the conformational entropy of the folded state may have a significant effect on the overall stability of the domain, but that conformational entropy alone is, not surprisingly, insufficient to account for the mutant stabilities.


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  		Table 1. NMR order parameter-derived {Delta}Gconf values for backbone amide and side chain methyl groups
 
Although the current data were all recorded at 30°C, it is worthwhile to consider the influence of temperature on the relationship between conformational entropy and overall stability. The order parameters of side chain methyl groups in proteins generally decrease with increasing temperature, but the magnitudes of the changes vary significantly and a temperature-dependent increase has been observed in at least one case (Lee et al. 2002). These changes are indicative of a redistribution of residual entropy with temperature, so it is possible that order parameters determined at a different temperature would yield an improved correlation of conformational entropy with overall stability. Without an extensive temperature variation study, it is difficult to predict the appropriate temperature for such measurements. However, a practical limitation is that the least stable mutants would have substantial populations of the unfolded state at higher temperatures leading to difficulties in both the calculation and interpretation of the order parameters. Finally, we note that the folding free energy values listed in Table 1Go were determined at 60°C (Smith et al. 1994). Folding free energy values calculated at 30°C, assuming that all mutants have the same heat capacity change ({Delta}Cp) for unfolding as the wild-type protein, also exhibit a poor correlation with conformational free energy values. However, variations in the {Delta}Cp values for different mutants (currently not known) would change the relative free energy values at other temperatures and possibly reveal an improved correlation.

Other influences on {beta}-sheet propensity
The above analysis of order parameters indicates that conformational entropy in the folded state does not play a dominant role in controlling the relative stabilities of the B1 domain mutants and, by inference, the {beta}-sheet propensities of the guest amino acids. At least two alternative theories have been proposed to explain the intrinsic {beta}-sheet propensities of the amino acids. Street and Mayo (1999) have shown that different amino acid side chains influence the local backbone entropy of the unfolded state to different extents and that these differences correlate with observed {beta}-sheet propensities. Our current data do not speak to this theory because they are limited to the folded state of the protein. The second alternative, proposed by Bai and Englander (1994), is that intrinsic {beta}-sheet propensities reflect different strengths (enthalpies) of interstrand (backbone–backbone) hydrogen bonds in the folded {beta}-sheet. These hydrogen bonds are sensitive to side chain structure because bulkier side chains sterically hinder the formation of solvent–backbone hydrogen bonds that compete with the intramolecular interactions. Side chain-dependent steric blocking factors can be determined from hydrogen exchange measurements and have been found to correlate with observed {beta}-sheet propensities (Bai and Englander 1994). Because these latter effects are dependent on hydrogen bond strength in the folded state of the protein, one would hypothesize that they would be associated with small structural alterations in the vicinity of the substituted amino acid. To investigate this possibility we examined the small but significant variations in both backbone and methyl side chain chemical shifts among the 10 B1 domain mutants. As indicated in Figure 5Go, the greatest variations in chemical shifts for both backbone NH and side chain CH2D groups occur close to the guest position, with decreasing effects radiating away from this region. Although some of these chemical shift changes may result directly from magnetic (de)shielding by the substituted side chain, others are almost certainly reflective of real structural differences. For example, the {delta}2 methyl group of Val 54 undergoes substantial changes in chemical shifts between mutants but is located in the hydrophobic core, on the opposite side of the sheet from the guest side chain. The Val 54 {delta}2 methyl group is positioned over the indole group of Trp 43. Thus it appears that small structural changes originating from the guest amino acid are propagated to the hydrophobic core residues and lead to a difference in the Trp ring current experienced by the valine methyl group. Such variations in chemical shifts indicate that there are subtle differences in the average three-dimensional structures of the 10 mutants and hence lend support to Bai and Englander’s theory. A detailed analysis of hydrogen exchange rates in the different mutants would be required to further verify this proposal.



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  		Figure 5. The protein G B1 domain color coded to show changes in amide and methyl group chemical shifts between mutants. Coloring of the ribbon indicates the variation ({sigma}bb) in backbone NH group chemical shift, defined as {sigma}bb = {sigma}HN + 0.2 {sigma}N, in which {sigma}HN and {sigma}N are the standard deviations of 1HN and 15NH chemical shifts among the 10 mutants. The coloring scheme is on a continuous scale from blue to red, corresponding to {sigma}bb = 0–0.30. Spheres, which represent side chain methyl groups, are color coded to indicate the variation ({sigma}sc) in side chain methyl group chemical shift, defined as {sigma}sc = {sigma}HC + 0.4 {sigma}C, in which {sigma}HC and {sigma}C are the standard deviations of 1HC and 13CH chemical shifts among the 10 mutants. The coloring scheme is on a six-part scale from blue to red, corresponding to {sigma}sc = 0–0.10. Position 53, the "guest position," is represented as a yellow sphere. This figure was generated from the NMR structure of the protein G B1 domain, PDB code 2GB1 [PDB] (Gronenborn et al. 1991), using Insight II (Accelrys).

 
Concluding remarks
This study was initiated to explore the relationships of protein side chain dynamics to global stability among a set of well-characterized mutants. The data indicate that, despite the substantial differences in mutant stabilities, the methyl group dynamics of the 10 B1 domain mutants are very similar to each other. Nevertheless, the small differences observed are large enough to have a significant influence on the overall stability of the domain. On the other hand there is no simple relationship of the observed side chain motions to the global stability or the properties of the guest amino acid, supporting the prevailing view that protein stability results from a complex combination of many enthalpic and entropic factors.


   Materials and methods
TOP
 Abstract
 Introduction
 Results and Discussion
 Materials and methods
Electronic supplemental material
 References
 
Sample preparation
Experimental methods were primarily as described for the wild-type B1 domain (Seewald et al. 2000). In a modification to these methods, samples prepared for side chain dynamics experiments were grown in M9 minimal media containing 2.0 g/L 13C-glucose, 3.0 g/L KH2PO4, 0.5 g/L NaCl, 6.0 g/L Na2HPO4, 2.0 g/L 15NH4Cl and D2O:H2O ratio of 3:2. In addition, phenylmethylsulfonyl fluoride was not added to the cells following centrifugation.

NMR spectroscopy
The protein samples were prepared by dialyzing labeled B1 domain in 50 mM phosphate, 0.02% NaN3, H2O:D2O (90%:10%) at pH 5.2. The protein concentrations of the B1 domain samples were 0.9 ± 0.1 mM. NMR spectra were acquired at 30°C on a Varian UnityINOVA 500 MHz spectrometer equipped with three radio-frequency channels, pulsed field gradients, and a 1H-detect triple resonance (HCN) probe. Methyl resonance assignments were obtained from two- and three-dimensional H(CC-TOCSY-CO)NH and (H)C(C-TOCSY-CO)NH spectra (Montelione et al. 1992; Grzesiek et al. 1993; Logan et al. 1993) on the basis of previously assigned 15N-1H backbone amide resonances (Mayer et al. 2003). Stereospecific methyl resonance assignments for leucine and valine residues were obtained from 13C-1H HSQC spectra of leucine and valine protein G B1 domain mutants grown in M9 minimal media containing 10% 13C6-glucose and 90% natural abundance glucose (Neri et al. 1989). Deuterium R1 and R1{rho} relaxation rates were measured using published pulse sequences (Muhandiram et al. 1995). The relaxation delay {tau} was varied between nine different times. Experiments at four of these times were duplicated to estimate peak height uncertainty. For the R1 experiments, delays used were {tau} = 0.05*, 5, 10, 15, 21*, 28, 36*, 45, and 58* msec. For the R1{rho} experiments, delays used were {tau} = 0.2*, 1.5, 4, 6.5, 9*, 12, 16*, 21, and 29* msec. Asterisks indicate delays at which data were collected in duplicate.

Determination of relaxation and dynamics parameters
NMR data were processed using FELIX98 (Molecular Simulation, Inc.). All spectra were processed using 3-Hz line broadening in the direct dimension, 90° shifted sine bell functions in the indirect dimensions, a lowpass filter to suppress solvent signal, and polynomial baseline correction. R1 and R1{rho} relaxation rates were determined by fitting the peak heights to an exponential decay curve. R1 and R1{rho} relaxation rates were then fit to the Lipari–Szabo model-free dynamics formalism using the program Matlab (Lipari and Szabo 1982a,b; Millet et al. 2002). Model-free calculations assumed isotropic rotational diffusion with the correlation time ({tau}m = 3.43 nsec) determined previously (Mayer et al. 2003), although simulations indicated that the deuterium relaxation parameters are insensitive to rotational anisotropy and to small variations in {tau}m. The quadrupolar coupling constant (e2qQ/h) was set to 167 kHz (Mittermaier and Kay 1999).


   Electronic supplemental material
TOP
 Abstract
 Introduction
 Results and Discussion
 Materials and methods
 Electronic supplemental material
References
 
Supplemental research material is available, consisting of five tables. Tables contain chemical shift assignments, relaxation parameters and associated errors, and dynamics parameters and associated errors for all 10 mutants.


   Footnotes
 
Supplemental material: see www.proteinscience.org


   Acknowledgments
 
We thank Drs. I.D. Kahari, M. Rance (University of Cincinnati), J. Vaughn, and J. Tomaszewski (Indiana University NMR Facility) for helpful discussions and Drs. O. Millet and L.E. Kay (University of Toronto) for providing pulse programs and data processing scripts. This work was supported by grants awarded to M.J.S. from the NSF (MCB-0212746) and to L.R. from NIH (GM57265).


   References
TOP
 Abstract
 Introduction
 Results and Discussion
 Materials and methods
 Electronic supplemental material
 References
 
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