Unfolding trajectories

US studies can produce informative free energy landscapes but assume that degrees of freedom orthogonal to the surface equilibrate quickly. The MD time needed for significant chain or backbone movement could exceed the length of typical US simulations (which are each typically on the nanosecond timescale). However, in spite of this caveat, US approaches have been very successful. One explanation for this success lies in the choice of initial conditions US simulations employ initial coordinates provided by high-temperature unfolding trajectories, which themselves have been found to yield predictive information about the nature of the relevant conformational space. 

The advantage of the use of the segmental Q-coordinate system becomes apparent when we compare the unfolding trajectories represented in the conformational hypers pace of the segmental Q-coordinates and those in the hyperspace of the Cartesian coordinates (Fig. 2.11) [25]. Because unfolded conformations are very widely distributed in the hyperspace of the Cartesian... 

Fig. 2.11. Two-dimensional representations of the structural ensemble observed in the unfolding trajectories, which were mapped onto the two largest principal components in the 17-dimensional segmental Q-coordinates (a) and in the hyperspace of the Cartesian coordinates (b) [25]. Reproduced with permission from [25]...

By fc-mcans cluster analysis with Euclidean distance in the segmental Q-coordinates, we divided the structure ensemble of the MD unfolding trajectories into nine clusters [25]. The clustering was performed using all data obtained for the authentic and recombinant proteins, and the clusters were numbered in the order of the distance from the native structure. Figure 2.10(c)-(f) shows protein structures in four representative clusters (Clusters 1, 4, 5, and 9), in which Cluster 1 is almost identical to the native structure with all of the 17 Q-coordinates close to unity, whereas Cluster 9, which lost 84% of its native contacts, represents the unfolded state. 

Twenty MD unfolding trajectories were obtained at 498 K, i.e., 10 for the authentic protein and the remaining 10 for the recombinant protein [25]. Each trajectory was characterized by flows between different clusters of the MD structure ensemble. Such trajectory flows may thus represent the unfolding pathway. 

The simulated transition state structure is much closer to the native State than to an unfolded structure. The packing of the hydrophobic core of the simulated transition state is considerably weakened, with disruption of the associated secondary structure (Figure 3). The 0md values agreed well with the experimental values across the protein, giving a correlation coefficient of 0.9. Finally, all four unfolding trajectories provided comparable results confirming the robustness of the models employed. 

Two high temperature simulations (498 K) were done to unfold ubiquitin in water, with the protonation of residues consistent with low pH. Nine structures were then taken from various points along these unfolding trajectories to be used as starting points for the collapse simulations. The starting points fell into three groups, those most native-like with an rmsd(Ca) from the crystal structure of <5 A, those intermediate between native and unfolded, with 5 A < rmsd(Cd) < 10 A, and unfolded with rmsd(Cd) > 10 A. Each of the structures was resolvated in water at 335 K (at the correct density) and then simulated for at least I ns, and up to 2.4 ns. 

The one-dimensional reaction coordinate was constructed by compilation of 15 properties for each conformation within a trajectory chosen properties were native and nonnative contacts, radius of gyration, end-to-end distance, fraction of a-helix and -sheet content, and various SASA measures.The properties are normalized and then used to calculate a distance in property space between each individual conformation in an unfolding trajectory, /, and that of a structure from a reference ensemble, /, such as the native state ensemble. The distances in the 15-dimensional property space, dp p, were calculated using... 

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