Correlation between MFA and dynamic ensembles
In recent years, a number of independent computational ensembles have been calculated to fulfill both structural restraints and dynamical information (Clore and Schwieters 2004, 2006; Markwick et al. 2007; Lindorff-Larsen et al. 2005; Richter et al. 2007; Lange et al. 2008; Friedland et al. 2009). From a number of available ubiquitin ensembles, we have back-calculated the average spherical harmonics and related MF parameters and compared them to the new data presented in this study. Thus, further insight into the conformations adopted by the side chains, especially in the ns-ms time scale can be obtained. Data for the ensembles of structures used here are presented in the Table 3.
Table 3 Conformational heterogeneity for methyl groups from the average structure and dynamic ensembles of ubiquitin and correlation with RDC-derived average spherical harmonics
PDB Number of conformers Positional rmsd of all methyl group carbons Av ± st dev order parameter Pearson correlation (<Y2,M>) rmsd (<Y2,M>) References
1d3z 10 0.54 ± 0.23 Å 0.87 ± 0.19 0.8379 0.0758 Cornilescu et al. (1998)
1xqq 128 1.76 ± 0.32 Å 0.59 ± 0.27 0.8497 0.0597 Lindorff-Larsen et al. (2005)
2nr2 144 1.43 ± 0.24 Å 0.66 ± 0.21 0.8748 0.0588 Richter et al. (2007)
2k39 116 2.28 ± 0.43 Å 0.45 ± 0.29 0.8568 0.0496 Lange et al. (2008)
«brub» 50 1.77 ± 0.28 Å 0.59 ± 0.26 0.8092 0.0648 Friedland et al. (2009)
Figure 6 displays a per-residue comparison of the order parameters from the highly restrained lowest-energy average NMR structures (pdb:1d3z), from the three dynamically-refined ensembles (pdb:1xqq, 2nr2 and 2k39) and from the “Backrub”-generated ensembles (“brub”) with those obtained from the MFA. While the pdb:1d3z structure can be considered as a good approximation for the average structure in solution for the backbone (Cornilescu et al. 1998), our results indicate that a single structure representation is not appropriate to describe the large amplitude side chain motions observed for ubiquitin. Not surprisingly, all the order parameters for this ensemble are larger than those from the MFA. Accordingly, the fit of the back-calculated order parameters with the experimental ones is the worst, both in terms of correlation factor (r) as well as rmsd as shown in Table 3.
Fig. 6 Order parameters plotted against residue position as back-calculated from different structural ensembles (blue:1d3z, green: 2nr2, yellow: 1xqq, red: 2k39, cyan: “backrub”-ensemble (brub), black: MFA)
In comparison, the dynamic ensembles pdb:1xqq and pdb:2nr2 show a much higher level of conformational heterogeneity, by virtue of their refinement against not only backbone but also side chain (methyl group) relaxation-based order parameters. However, as discussed previously, these order parameters are insensitive to supra-τc motion. Predictably, the back-calculated order parameters from these ensembles do not reproduce very well those acquired from RDCs, which are smaller for the large majority of residues. The average order parameters  (σ = 0.27) and  (σ = 0.27) are both significantly larger than the average from the MFA  Agreement within error ranges only occur in 33% of the cases.
The EROS ensemble (pdb:2k39) is also a dynamically refined structure, with the important difference that the ensemble refinement is not performed against order parameters but rather against orientational restraints provided from RDCs (including backbone DNH and methyl group DCC). As a consequence, it is anticipated that the conformational heterogeneity present in the ensemble reflect fluctuations over a wider time scale (fs-ms).
Of the five ensembles, the pdb:2k39 boasts together with pdb:1xqq the best correlation (Pearson correlation r = 0.857) and by quite a big margin the best overall agreement (rmsd = 0.0496) with the MFA results. The average order parameter  is almost identical to the average from the MFA. Agreement is present in 66% of the residues measured. Despite the high fluidity reproduced in the Lipari-Szabo-based dynamic ensembles, this supports that there is a large amount of motion that is not sampled by relaxation techniques because it occurs in the ns-ms time scale.
The “Backrub”-generated ensemble (brub) is an ensemble of ubiquitin structures in solution that is created by sampling conformational space without experimental information using the “Backrub” motions, inspired by alternative conformations observed in sub-Angstrom resolution crystal structures (Davis et al. 2006). An ensemble of 50 Backrub-generated structures was selected to optimize agreement with 23 datasets of NH backbone RDCs for ubiquitin (PDB entry pending; Friedland et al. 2009). As opposed to the other ensembles, the methyl group RDCs were not used as restraints to generate the brub ensemble. The ensemble represents therefore an intermediate between 1d3z which has not been optimized to match conformational averaging seen by RDCs and 2k39 where backbone and side chain RDCs were utilized. Accordingly, the brub ensemble demonstrates an average methyl group order parameter of 0.59 that resides between the ones reported for 1d3z and 2k39 (Table 4). Interestingly, the rmsd to the RDC-derived average spherical harmonics is also reduced with respect to 1d3z but elevated when compared to 2k39.
Table 4 Ideal rotamer populations derived from the grid search against RDC-based average spherical harmonics and comparison to rotamer statistics from three dynamic ensembles, the backrub ensemble and the rotameric fitting to J-couplings
1xqqa 2nr2b 2k39c brubd Je MFAf
V5
    0 0 0.04 0 0.02 0.09 (0.04)
    1 1 0.88 1 0.92 0.70 (0.03)
    0 0 0.08 0 0.06 0.21 (0.04)
    0.88 (0)g
   ssd 0.037
I3
    1 1 1 0.78 0.47 0.84 (0.05)
    0 0 0 0.22 0.21 0 (0)
    0 0 0 0 0.32 0.16 (0.05)
    0.06 0.01 0.06 0.05 – 0.38 (0.06)
    0.94 0.99 0.94 0.95 – 0.48 (0.06)
    0 0 0 0 – 0.14 (0.05)
    – – – 0 – –
    – – – 1 – –
    – – – 0 – –
    – – – – – 0.08 (0.09)
    – – – – – 0.06 (0.09)
    – – – – – 0.86 (0.10)
    0.96 (0.03)g
    0.75 (0.03)g
   ssd 0.072
I44
    0.05 0 0.05 0 0.03 0
    0.02 0 0.07 0 0.06 0.10 (0.0)
    0.94 1 0.88 1 0.91 0.90 (0.0)
    0 – 0 – – –
    1 – 1 – – –
    0 – 0 – – –
    0.5 – 0 – – 0.18 (0.17)
    0.5 – 0.63 – – 0.16 (0.17)
    0 – 0.38 – – 0.66 (0.20)
    0 0.02 0.08 0.04 – 0.03 (0.04)
    0.45 0.43 0.59 0.60 – 0.46 (0.05)
    0.55 0.55 0.33 0.36 – 0.51 (0.05)
    0.76 (0.01)g
    0.70 (0)
   ssd 0.047
L8
    0 0 0.18 0 – 0.15 (0.06)
    0.66 0.4 0.28 0 – 0.40 (0.08)
    0.34 0.6 0.54 1 – 0.44 (0.06)
    – – 0.33 – – 0.37 (0.19)
    – – 0.52 – – 0.12 (0.12)
    – – 0.14 – – 0.52 (0.15)
    0.92 0.98 0.5 – – 0.42 (0.06)
    0.08 0.02 0.16 – – 0.03 (0.05)
    0 0 0.34 – – 0.54 (0.06)
    0.07 0 0.17 0.24 – 0.03 (0.04)
    0.93 0.99 0.68 0.76 – 0.68 (0.06)
    0 0.01 0.14 0 – 0.30 (0.04)
    1h
    0.78 (0.14)
   ssd 0.021
V70
    0 0 0.04 0 0.02 0.09 (0.04)
    1 1 0.88 1 0.92 0.70 (0.03)
    0 0 0.08 0 0.06 0.21 (0.04)
    0.88 (0)g
   ssd 0.037
I36
    0 0 0.04 0 0 0
    0.05 0 0.03 0 0.1 0.2 (0.0)
    0.95 1 0.93 1 0.9 0.8 (0.0)
    – – 0 – – –
    – – 0.8 – – –
    – – 0.2 – – –
    0 – 0.67 – – 0.53 (0.21)
    1 – 0.33 – – 0.18 (0.17)
    0 – 0 – – 0.28 (0.13)
    0 0.03 0.02 0 – 0 (0)
    0.87 0.92 0.81 0.58 – 0.80 (0.05)
    0.13 0.05 0.18 0.42 – 0.20 (0.05)
    0.83 (0.05)g
    0.78 (0.07)g
   ssd 0.013
I61
    0 0 0.01 0 0.01 0.15 (0.05)
    0 0 0 0 0.01 0.01 (0.03)
    1 1 0.99 1 0.98 0.84 (0.05)
    – – – – – 0.57 (0.18)
    – – – – – 0.11 (0.11)
    – – – – – 0.32 (0.17)
    – – – – – –
    – – – – – –
    – – – – – –
    0 0.01 0 0 – 0.01 (0.02)
    0.85 0.9 0.88 0.70 – 0.87 (0.05)
    0.15 0.09 0.12 0.30 – 0.12 (0.04)
    0.95 (0.04)g
    0.81 (0.09)
   ssd 0.025
L67
    0 0 0.08 0 – 0.17 (0.02)
    0.01 0 0.07 0.1 – 0.08 (0.04)
    0.99 1 0.85 0.9 – 0.72 (0.04)
    – – 0.89 – – 0.69 (0.11)
    – – 0 – – 0.23 (0.13)
    – – 0.11 – – 0.07 (0.07)
    1 – 0.5 1 – 0.15 (0.10)
    0 – 0.38 0 – 0.33 (0.21)
    0 – 0.13 0 – 0.57 (0.25)
    0.52 0.58 0.64 0.26 – 0.54 (0.04)
    0.48 0.42 0.3 0.74 – 0.45 (0.04)
    0.01 0.01 0.06 0 – 0.00 (0.01)
    1h
    0.87 (0.09)
   ssd 0.015
aLindorff-Larsen et al. (2005)
bRichter et al. (2007)
cLange et al. (2008)
dFriedland et al. (2009)
eValues from Chou et al. (2003)
fAverage values (with standard deviation) among grid search solutions within 10% of overall minimum
gWithin allowed range of corresponding  value Lee et al. (1999)
hFixed at 1 (no variation in grid search)
Side chain coordinates within the brub ensemble are constructed using a rotamer library (Dunbrack and Karplus 1993). The improved agreement of RDC-derived average spherical harmonics when compared to 1d3z is therefore triggered by accurate representation of backbone conformational averaging that is propagated to the side chains. Thus, an accurate representation of backbone dynamics induces an improved but imperfect representation of side chain conformational averaging in the brub ensemble. This result supports the notion that backbone and side chain motions are coupled and therefore correlated. The accuracy of conformational averaging in side chains of the brub ensemble would benefit from a rotamer selection protocol that optimizes agreement with methyl group RDCs.