3.3 Molecular dynamics simulation
We sought to characterize the locally disordered intermediate conformation of OspA from PRE data. However, a conversion ofR 2PRE into distance is not straightforward in this case since the protein exists as a mixture of different conformational states, including ~80% locally disordered, ~20% native, and minimal amounts of completely unfolded protein. Even for the completely unfolded state, it is not easy to reconstruct the probability distribution of the distance between the paramagnetic probe and each amide proton, as multiple sources of stochastic dynamics in the system must be considered.30 Here, to produce potential structural models of the intermediate conformations of WT* OspA, we performed a 1 µs MD simulation with the NVT ensemble (350 K). The MD simulation demonstrated that temperature-induced disordering of the β-sheet began at the C-terminal region, followed by the central region.
Distance distributions were calculated between the paramagnetic probe and each amide proton for four different time-regions in the MD trajectory, corresponding to the different levels of disorder in β9–β11. Figure S14 presents the distance distribution between the Cβ of residue 118/128/140 (a substitute for the paramagnetic center) and the amide proton of residue 37 for the folded, partially disordered, and completely disordered ensembles. A specific simulation snapshot was obtained in the folded and partially disordered ensembles, in which β11, β10, and β9 are disordered (Figure 8A). The distance for the closest approach d 0 and that of the maximum separation L for the ensembles were obtained from the distance distribution. In the partially disordered and completely disordered ensembles, the distance distribution became wider than that of the folded ensemble.I para/I dia profiles of the folded and the partially disordered ensembles, as predicted by the MD simulation, are shown in Figure 8B (see Methods). Increasing the ratios for residues 33, 93, and 94 of the D118C variant can be explained by the partially disordered ensemble 3 (PDE3, Figure S8). Meanwhile, the increased ratios of residues 80–83, 103, and 106 of the E128C may have resulted from partially disordered ensembles 1 and 2 (PDE1 and PDE2). Further, PDE1 and PDE2 can explain the incremental ratios for residues 36, 37, 94, and 95 of the A140C variant. However, no ensemble can explain the decreases observed in the ratios of residues 33-37, 59, and 62. In short, any single specific ensemble cannot explain the entire profile of I para/I dia. Moreover, there is no evidence to suggest that the new peaks corresponding to the residues in the central β-sheet appeared in the central portion of the spectrum. Hence, we do not deny broadening and missing of HSQC cross-peaks owing to conformational dynamics; however, we speculate that the central β-sheet does not become unfolded, but rather partially disordered, and contains heterogeneous conformations in the intermediates.
Thus, the intermediate state of the protein is likely a mixture of conformations, with different levels of partial disorder in the central β-sheet. This idea is consistent with the conformational heterogeneity of the equilibrium intermediate mapped by native state hydrogen exchange NMR and scanning mutagenesis.10,11 To satisfy the entire profile more quantitatively, PRE should be measured under conditions in which the intermediate state is more dominantly stabilized, and larger numbers of snapshots should be generated via MD simulation of the partially disordered protein.