Experimental restraints and structure calculations
1H and 15N chemical shift assignments for native hen lysozyme have been reported previously (Redfield and Dobson 1988; Buck et al. 1995). 13C resonance assignments were made using HNCA, HNCO, HCCH-TOCSY, and (H)CCH-TOCSY spectra (Fesik et al. 1990; Kay et al. 1993; Sattler et al. 1995) recorded using a double-labeled (13C,15N) lysozyme sample (Fig. 2). These assignments have been deposited in BioMagRes Bank (BMRB accession number 4831). NOEs were identified in 15N NOESY-HMQC and 13C NOESY-HMQC spectra (Driscoll et al. 1990; Ikura et al. 1990). The lysozyme NMR structures of Smith et al. (1993) were used to solve any ambiguities in the NOE assignments resulting from chemical shift degeneracy. NOE intensities were estimated by measuring peak heights and were used to assign interproton distance ranges to the NOE restraints as described in the Materials and Methods section. The final NOE data set consists of 1632 restraints (Table 1), 1096 of these coming from the previous homonuclear NMR studies (Smith et al. 1993).
3J(HN,Hα) and 3J(Hα,Hβ) coupling constant data measured using homonuclear NMR methods for hen lysozyme have been reported (Smith et al. 1991; Bartik and Redfield 1993). Additional coupling constant values that could not be obtained previously because of low signal intensity or resonance overlap were determined using an HMQCJ experiment (Kay and Bax 1990) on a 15N-labeled lysozyme sample for 3J(HN,Hα) coupling constants and a soft HCCH-E.COSY experiment (Eggenberger et al. 1992) for 3J(Hα,Hβ) side-chain coupling constants. 3J(Hβ,C′) coupling constants were also measured for 45 residues in hen lysozyme using a soft HCCH-COSY experiment (Eggenberger et al. 1992). The coupling constants were converted into dihedral angle restraints as described in the Materials and Methods section, 51 ϕ and 59 κ1 torsion angle restraints being obtained.
1H-15N residual dipolar couplings were measured for lysozyme in two different bicelle solutions, one containing 5% DMPC:DHPC (2.9:1.0) and the other 7.5% DMPC: DHPC:CTAB (2.9: 1.0: 0.1). Details of sample preparation are given in the Materials and Methods section. Residual dipolar couplings were measured for 107 residues in the 5% DMPC:DHPC bicelles and for 102 residues in the 7.5% DMPC:DHPC:CTAB bicelles. Measurements were not possible for 19 and 24 residues in the 5% and 7.5% bicelle solutions, respectively, either as a result of peak overlap or the absence of peaks at pH 6.5 resulting from exchange with the solvent.
A region of the NMR spectra acquired at 34.5°C for an isotropic solution, and for bicelle solutions with 5% DMPC:DHPC and 7.5% DMPC:DHPC:CTAB, is shown in Figure 3. It is interesting to note from these spectra, and from the histograms shown in Figure 4, that the spread of the residual dipolar couplings measured in 5% DMPC: DHPC is larger than that measured in 7.5% DMPC: DHPC:CTAB. An increase in bicelle concentration from 5% to 7.5% should lead to a 50% increase in the magnitude of dipolar couplings if the alignment arises from only steric factors (Bax and Tjandra 1997; Zweckstetter and Bax 2000). The observed decrease in dipolar couplings shows the influence of electrostatic effects on the partial alignment of proteins in bicelle solutions. The results for the 5% DMPC:DHPC solution are consistent with the observation of Losonczi and Prestegard (1998); these authors suggest that the DMPC:DHPC bicelles are not neutral but have a slight negative charge arising from some hydrolysis of the DMPC. Lysozyme is a positively charged protein at pH 6.5 and, therefore, an electrostatic attraction between lysozyme and the bicelle surface will contribute to the orientation of the protein and lead to larger than expected dipolar couplings. The addition of positively charged cetyltrimethylammonium bromide (CTAB) to the bicelles will remove the electrostatic attraction and lead to alignment based on steric factors alone (Zweckstetter and Bax 2000). It is clear from an inspection of Figure 3 that the orientation of the alignment tensor in the two bicelle solutions differs. The measured residual dipolar coupling for Arg 125 has a different sign in the two solutions. For Ala 82 a coupling of −0.5 Hz is observed in the 5% bicelles and a value of 10.3 Hz in the less strongly aligned 7.5% CTAB containing bicelles. The use of two sets of dipolar couplings, with different alignment tensors, in structure refinement is useful for resolving ambiguities that can arise if only a single set of data is used (Ramirez and Bax 1998). In the structure calculations described below, the orientation of the principle component of the alignment tensors for the two bicelle solutions are found to differ by 9.2±0.3°.
The refinement of a protein structure using additional residual dipolar coupling restraints and the program XPLOR requires that information about the alignment tensor be specified. Clore et al. (1998a) have shown that the axial and rhombic components of the alignment tensor (Da and Dr) can be estimated from the high and low extreme values and from the most populated value in a histogram showing the distribution of residual dipolar couplings. The distributions of residual dipolar couplings measured for the 5% DMPC:DHPC and 7.5% DMPC:DHPC:CTAB bicelles are plotted in Figure 4. In both cases it is difficult to determine the most populated value of the dipolar coupling from the histograms and, therefore, the estimates of Da and R (R = Dr/Da) have been determined from the high and low extreme values only; for the 5% DMPC:DHPC solution Da = 15.1 and R = 0.34, whereas for the 7.5% DMPC: DHPC:CTAB solution Da = 12.2 and R = 0.16. The larger rhombicity (R) for 5% DMPC:DHPC bicelles is consistent with a larger electrostatic contribution to the orientation of the protein (Sass et al. 1999). The values of Da and R were further refined using the procedure of Clore et al. (1998b) as described in Materials and Methods.
Using the NOE, hydrogen bond, and torsion angle restraints for hen lysozyme summarized in Table 1, a set of structures for hen lysozyme was calculated with an extended simulated annealing protocol (Nilges et al. 1988; Wiles et al. 1997), and the 15 lowest energy structures were selected. From each of these structures, 20 conformers were calculated using the 209 restraints from the residual dipolar coupling data using the protocol described in the Materials and Methods section. The 50 lowest energy structures from these calculations were then analyzed (structure set 1). The structural statistics for the final ensemble of structures are given in Table 2. The ensemble of structures and the input NMR restraints have been deposited in the Brookhaven Protein Databank (code 1E8L).
Characteristics of the NMR structure of hen lysozyme in solution
The mean structure calculated from the ensemble of NMR structures for hen lysozyme is shown in Figure 5A. The quality of the structure is very significantly improved compared with the structure reported previously (mean backbone RMSD to the average structure is 0.50±0.13Å compared with 1.71±0.25Å for the 1993 structures). The RMSD of the NMR structures to the crystal structure of hen lysozyme of Vaney et al. (1996; structure of the tetragonal form at 1.33Å with pdb code 193L; referred to here as the X-ray structure) is also reduced (mean backbone RMSD is 1.49±0.10Å compared with 2.33±0.33Å for the 1993 structures). There is also a substantial improvement in the stereochemical quality; an analysis using PROCHECK (Laskowski et al. 1993) showed that 74.2% of the ϕ,ψ; torsion angles of residues in the protein lie in the most favored regions of the Ramachandran plot (compared with 54.5% for the 1993 structures).
Regions of secondary structure in the NMR structures have been identified according to the criteria of Kabsch and Sander (1983). In agreement with the X-ray structure, three long α-helices are present in all members of the family of NMR structures (A helix: Cys 6-His 15; B helix: Leu 25-Ser 36; C helix: Thr 89-Ser 100). The fourth α-helix (D) in the X-ray structure is present in 41 of the 50 NMR structures, although it is slightly reduced in length (Trp 111-Arg 114 compared with Val 109-Arg 114 in the X-ray structure); a series of turns is formed for this sequence in the other nine NMR structures. A β-bridge involving Val 2 and Asn 39 is present in all of the NMR structures (also in the X-ray structure), but only the first two strands of the triple stranded antiparallel β-sheet present in the X-ray structure are defined in the NMR structures (Thr 43-Arg 45 and Thr 51-Tyr 53; in 14 of the structures the length of these strands is reduced). This irregularity in the β-sheet may result from slight variations in the relative positions of NH and CO groups because of the inclusion of the dipolar coupling restraints in the structure calculations, which we discuss in the next section. Helices are also identified in the NMR structures for Ser 81-Leu 83/84 (310-helix in 30 structures, an α-helix in 16 structures and turns in four structures in the NMR ensemble) and Val 120-Trp 123 (α-helix in 33 structures and turns in 17 structures); no hydrogen bond restraints were included for these residues in the structure calculations, but both these regions form short 310-helices in the X-ray structure. Interestingly, recent MD simulations of native hen lysozyme in solution and crystal environments show in both of these regions higher populations of CO(i)-NH(i+4) α-helical hydrogen bonds than the CO(i)NH(i+3) hydrogen bonds expected for a 310-helix (Stocker et al. 2000). This behavior, and the results from the NMR structure calculations, may reflect the similarity in the energy of α- and 310-helices for these residues in hen lysozyme.
Figure 1a shows the backbone RMSD relative to the mean structure for each residue in the protein. Some disorder in the family of structures remains in four regions of the sequence, involving particularly Gly 22, Thr 47 and Asp 48, Arg 68 to Gly 71, and Gly 102 (backbone RMSD to the mean structure greater than 0.9Å for these residues). All these regions include residues that have a significant solvent accessibility for the polypeptide backbone (main-chain accessibility >70% for Gly 22, Thr 47, Gly 71, Gly 102). Although experimental 15N relaxation measurements for the main-chain amide groups of hen lysozyme (Buck et al. 1995) show that most residues have order parameter values greater than 0.8, order parameters in the range 0.7 to 0.8 are seen for Arg 45, Thr 47, Asp 48, Arg 68, Thr 69, Gly 71, Ser 72, Cys 115, Thr 118, Cys 127, Arg 128, and Leu 129. In addition, Ser 85, Gly 102, Asn 103, and Gly 104 have order parameters less than 0.7. Thus six of the eight residues with significant disorder in the NMR ensemble have backbone order parameters less than 0.8. Furthermore, an elevated T1/T2 ratio of 4.18 for Gly 22 (the mean ratio for hen lysozyme is 3.32±0.13) indicates that there are motions on the microsecond to millisecond timescale for this residue (Buck et al. 1995). Therefore, these data suggest that at least some of the disorder in the NMR ensemble reflects the presence of internal motions in the protein in solution rather than merely a lack of NMR restraints.
A comparison of the backbone RMSD for the average coordinates of the set of NMR structures from the X-ray structure of lysozyme is shown in Figure 1b. Deviations are seen for the four regions that have some disorder in the family of NMR structures. Interestingly, residues in three of these regions also have the highest main-chain crystallographic temperature factors (excluding the C terminus) in the X-ray structure (Fig. 1c). Temperature factors greater than 20 Å2 are seen for the amide N atoms of Thr 47, Asp 48, Pro 70-Arg 73, and Asp 101-Asn 103 (also Arg 125-Leu 129). Furthermore, comparisons of 33 crystal structures of hen lysozyme show variations between the structures in the main-chain conformation for Pro 70-Ser 72 and reveal that the orientation of the turn between the first two strands of the β-sheet (particularly Thr 47-Gly 49) may be affected by crystal contacts (C. Redfield, unpubl.). The fact that there are some differences between the solution and crystal structures of the protein in these regions is consistent with this observation. Gly 22 is incorporated in a β-bridge motif in the X-ray structure, involving Tyr 20 and Tyr 23, and does not have elevated main-chain B factors. This β-bridge is also present in 13 of the 50 NMR structures; these structures show much lower backbone RMSD values to the X-ray structure for Gly 22 (∼1.2Å) than does the mean NMR structure (2.7Å). The ensemble of NMR conformers therefore includes the turn orientation found in the X-ray structure, along with a variety of other orientations. This is consistent with the evidence from 15N relaxation studies for motions involving Gly 22 on a microsecond to millisecond timescale in solution.
A significant deviation between the average NMR structure and the X-ray structure is also seen for Lys 116-Thr 118, a region that is not found to be disordered in the ensemble of NMR structures. Gly 117 has, however, the highest main-chain solvent accessibility (97%) of any residue in the protein, and there are no long range NOEs (i,i +5 or greater) identified for these residues. Consequently, the NMR data set may not be sufficient to define the correct conformation of the protein in this region; despite this lack of NOEs, the absence of significant disorder within the NMR ensemble probably reflects the close proximity of these residues to the restraints provided by the Cys 30-Cys115 disulphide bridge. It is interesting in this respect, however, that MD simulations of native hen lysozyme showed a significant rearrangement of residues Cys 115-Asp 119 during 2ns simulations in solution and crystal environments (Stocker et al. 2000). In addition, analysis of 15N T1/T2 ratios using an anisotropic rotational diffusion model shows poor agreement with T1/T2 values predicted from the X-ray structure for Thr 118 (C. Redfield, unpubl.).
Assessing the importance of the dipolar coupling restraints in the NMR structure determination
As described in the previous section, the quality of the NMR structure of hen lysozyme reported here is significantly improved compared with the structure reported in 1993. This difference reflects the enlarged data set of NOE and dihedral angle restraints, improvements to the force field used in the structure calculations, and the inclusion of the dipolar coupling data. To identify separately the effects that result from adding the dipolar couplings, the final ensemble of structures of hen lysozyme (structure set 1) has been compared with an ensemble of 50 low-energy structures calculated using the same refinement protocol but excluding the residual dipolar coupling data (structure set 2).
The inclusion of the dipolar coupling data gives an overall increased precision in the definition of the structure (average backbone RMSD to mean 0.50±0.13 Å for set 1 compared with 0.60±0.14 Å for set 2) and a closer similarity to the X-ray structure (average backbone RMSD to X-ray structure 1.49±0.10 Å for set 1 compared with 1.69±0.12 Å for set 2). The addition of the dipolar coupling data also results in structures with improved stereochemical quality (for structures in set 1, 74.2±2.0% of the ϕ,ψ; torsion angles lie in the most favored region of the Ramachandran plot compared with 65.9±2.6% for structures in set 2).
The definition of the relative orientations of the two structural domains in the protein is very substantially improved for the structures in sets 1 and 2 compared with the definition in the structures reported previously. To characterize this, we have determined the angle between helix C in the α-domain and the first strand of the β-sheet in the β-domain. This helix-strand angle has a value of 48.7° in the X-ray structure. In the structures reported previously, this angle is 34.3±13.4°, whereas it has values of 52.6±4.0° and 53.6±5.6° in structure sets 1 and 2, respectively. The better definition of the helix-strand angle and the closer agreement with the value observed in the X-ray structure for the structures in set 1 reflects both the additional NOEs from the heteronuclear spectra (82 inter-domain NOEs compared with 45 in the 1993 data set) and the dipolar coupling data. The improved definition of the domain orientations is further shown by the relative values of the backbone RMSD from the mean structure for residues in the β-domain of the protein when the structures are superimposed using the full sequence (0.58±0.19Å for set 1, 0.74±0.25Å for set 2, and 2.23±0.40Å for the 1993 structures) or only the α-domain residues (0.73±0.2Å for set 1, 0.91±0.30Å for set 2, and 2.63±0.49Å for the 1993 structures).
Cornilescu et al. (1998) have shown that the quality of NMR structures can be assessed by comparison of predicted NMR parameters with experimental NMR data that were not used in the refinement process. They have introduced a quality, Q, factor defined as
in which param is a measurable NMR parameter such as a residual dipolar coupling or orientation-induced chemical shift change. Here we have used this approach to compare the lysozyme solution structures calculated with and without the two sets of residual dipolar couplings. The additional data used to determine the Q factor are, firstly, orientation-induced 15N chemical shift changes measured for the 5% and 7.5% bicelle solutions (Boyd and Redfield, 1999); secondly, a set of residual dipolar couplings measured for lysozyme in a bicelle mixture composed of 3.8% DTDPC: DHPC:CTAB:DMPE-DTPA:La+3 (3.0: 1.0: 0.4: 0.07: 0.06; J. Boyd and C. Redfield, unpubl.); and thirdly, T1/T2 values obtained from 15N relaxation measurements (Buck et al. 1995). The Q factors obtained with the 15N chemical shift changes are 0.36 +/−0.01 and 0.75 +/−0.03 for the structures in sets 1 and 2 obtained with and without the residual dipolar couplings, respectively. The Q factors obtained with the additional set of dipolar couplings are 0.30 +/−0.01 and 0.65 +/−0.03 for the structures in sets 1 and 2, respectively. The Q factors obtained with the T1/T2 ratios are 0.030 +/−0.001 and 0.0455 +/−0.001 for the structures in sets 1 and 2, respectively. Thus in all three cases the Q values are substantially lower for the structures refined using the dipolar couplings than for those refined without these data. The agreement between the experimental T1/T2 values and those calculated using the structures refined with dipolar couplings is comparable to that obtained with the X-ray structure. The average anisotropy (D∥/D⊥) of 1.26±0.01 obtained from the family of 50 structures in set 1 is the same as that found for the X-ray structure. The structures refined without the dipolar couplings give significantly worse agreement with the T1/T2 data with an average anisotropy of only 1.18±0.02.
Figure 6 compares the variation along the protein sequence in backbone RMSD values with the mean structure, and between the mean and X-ray structures for the two sets of structures. The improvements for set 1 on the inclusion of the dipolar couplings are concentrated around residues Asn 46-Gly 49, Arg 68-Pro 70, and Ala 82-Leu 84. These are the three areas in which particularly large deviations are seen in the ensemble of NMR structures reported previously (Smith et al. 1993). The changes for residues Ala 82-Leu 84 on the addition of the dipolar coupling data are particularly interesting. Residues Cys 80-Leu 84 form a 310-helix in the X-ray structure, but the conformation of these residues is disordered in the ensemble of structures reported previously (Smith et al. 1993). Despite the addition of NOEs from the heteronuclear spectra, such as Ser 81 Hα-Leu 84 Hβ1, which help in the definition of this region, significant deviations from the X-ray structure are still seen for the NMR structures in set 2 (Fig. 6b). The dipolar coupling data set includes two restraints for the NH bond vectors of each of the residues in the range Cys 80-Leu 84. The inclusion of these data leads to the substantial increase in the similarity of the NMR and X-ray structures in this region (e.g., RMSD between the mean and X-ray structure for Leu 83 is reduced from 4.24 Å for set 2 to 2.03 Å for set 1).
There is also a significant difference between the two sets of NMR structures for the region surrounding Gly 22, a larger RMSD to the mean structure being seen for set 1 (0.95 Å for Gly 22) than set 2 (0.23 Å for Gly 22). As discussed above, a β-bridge involving Tyr 20 and Tyr 23, which is also defined in the X-ray structure, is present in 13 of the 50 structures of set 1. This β-bridge is not present in any of the structures in set 2; in this case, therefore, the addition of the dipolar coupling data enables the β-bridge to be defined. However, there is an incompatibility between the dipolar coupling of Gly 22 measured in the 5% bicelle solution and an NOE observed between Tyr 23 HN and Trp 28 HZ2. In the structures in which the β-bridge is defined, there is close agreement between the calculated and experimental dipolar couplings of Gly 22 (difference <0.5 Hz), but the NOE is violated by 0.3–0.4 Å. In contrast, in the structures in which there is no β-bridge, there is a violation of 2.3–4.1 Hz for the experimental dipolar coupling of Gly 22, but there are no violations of the Tyr 23 HN-Trp 28 HZ2 NOE greater than 0.3Å. This incompatibility between the data presumably reflects the mobility of this region in solution and means that the β-bridge is not the only conformation that is observed in the ensemble of set 1 structures. This observation suggests that a simple comparison of RMSD values may not be a definitive measure of the quality of the structure in solution where motional effects are significant, and the average structure does not represent the ensemble of contributing conformers in a meaningful way.
Interestingly, the β-strand secondary structure in the triple stranded antiparallel β-sheet is better defined in the structures in set 2 than those in set 1. The first two strands are defined in all 50 of the structures in set 2, whereas in set 1 these full strands are only defined in 32 structures and there is a β-bridge in 14 structures. In addition, a β-bridge involving Asn 59 in the third strand is defined in 25 of the structures of set 2 but this is missing in all the structures in set 1. A closer analysis of the structures shows that this difference does not reflect large structural changes in this region but, instead, slight alterations in the relative orientations of the amide and carbonyl pairs for 54NH-42CO and 58NH-53CO because of the dipolar coupling restraints. These alterations result in the hydrogen bonds no longer being identified by the Kabsch and Sander method, but do not result in significant violations of the hydrogen bond restraints as only weak restraints of this type (NH(i) to O(i-4) 1.3–2.3Å and N(i) to O(i-4) 2.3–3.3Å) are included in the structure calculations.