Quantitative molecular ensemble interpretation of NMR dipolar couplings without restraints.

At room temperature, proteins undergo dynamic excursions away from their average three-dimensional structure, which plays an essential role for function.1 Molecular dynamics (MD) computer simulations can provide detailed insights into the nature of these motions by representing the state of a protein as a conformational ensemble that follows the laws of statistical thermodynamics.2 While the complexity of the protein energy landscape makes the accurate representation of protein motions challenging, recent improvements made to commonly used molecular mechanics force fields show significant promise.3,4 To properly assess force-field modifications, comparison with high-quality experimental data is essential. For sub-ns time-scale dynamics, NMR spin relaxation parameters are well suited for this task.5 By contrast, NMR residual dipolar couplings (RDCs),6 which occur when proteins are weakly aligned, probe a much larger time-scale range from ps to ms.7 Because RDCs can be measured for many different spin pairs and alignment media with high accuracy and because they simultaneously reflect structure and dynamics, these parameters represent benchmarks that are both rigorous and comprehensive. Here we report remarkable agreement achieved between a 50 ns MD ensemble of ubiquitin, using the recently refined AMBER99SB force field,4 and RDCs for ubiquitin measured in multiple alignment media.8 Starting from the X-ray structure (PDB entry 1ubq9), a 50 ns MD trajectory of ubiquitin in a cubic box with 6080 explicit SPC water molecules has been generated at constant temperature of 300 K and 1 atm pressure. N-H RDCs were computed from the trajectory as described previously.10 Normalized backbone N-H bond vectors v ) (x,y,z) were extracted every ps, after each snapshot was aligned with respect to the snapshot at 25 ns, and averages of the 6 bilinear terms 〈x2〉, 〈y2〉, 〈z2〉, 〈xy〉, 〈xz〉, and 〈yz〉 were calculated over all 50 000 snapshots. These averages are then used to determine the alignment tensors for all 10 alignment media by singular value decomposition (SVD),11 from which the best fitting RDCs are backcalculated (see Supporting Information for details). The difference between calculated and experimental RDCs is then expressed in terms of the Q value for each medium.12 In addition, a cumulative Q value, Qcum, is calculated as the sum of the Q values over all 10 media.13 Q values are also calculated for a 20 ns MD simulation (20 000 snapshots) that uses the older AMBER99 force field, the crystal structure (1ubq9), and the NMR structure (1d3z14). All residues were included in the analysis, except for the highly flexible C-terminal residues 72-76, whose RDCs are not well reproduced by individual structures, and Ile 36 that terminates the central R-helix, which behaves as an outlier for most media (results including the C-terminus are given in Supporting Information). The distribution of individual Qcum values of all 50 000 snapshots is depicted in Figure 1A (blue histogram) and for the final 20 000 snapshots (red histogram). The corresponding distribution for the 20 000 snapshots of the AMBER99 simulation (green) is shifted toward larger Q values by a substantial amount (∆Qcum ) 0.92 between the histogram means), reflecting poorer agreement between individual snapshots and experiment for the AMBER99 ensemble. Ensemble averaging of the RDCs leads to a substantial improvement of the Qcum values with the 50 ns trajectory producing a value of 2.2 that is lower than the corresponding values of the two 20 ns MD simulations (Qcum ) 2.4 for AMBER99SB, and Qcum ) 3.5 for AMBER99). The 50 ns ensemble-averaged RDCs perform better than the RDCs predicted by any individual snapshot of the ensemble, as well as those of the X-ray structure (1ubq), which was the starting structure for the simulation (Figure 1B). Only the NMR structure (1d3z), which was refined using 2 of the 10 RDC sets, has a Qcum that is lower by 10% than the 50 ns ensemble. Exclusion of the RDCs used in the refinement of 1d3z reduces the difference in Qcum Figure 1. Residual dipolar coupling Qcum factors of ubiquitin for the 50 ns AMBER99SB MD simulation (blue), the final 20 ns of the AMBER99SB simulation (red), the 20 ns AMBER99 simulation (green), and the NMR ensemble 1D3Z (yellow). The blue, red, and green arrows indicate the Qcum values for the ensemble averaged RDCs and the black arrows for individual PDB structures. Only residues 2-71 were used for comparison, while the flexible tail (residues 72-76) was excluded. Published on Web 03/17/2007