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)