UNRES representation of a protein. The interaction sites (shaded circles) are the side chains (SCs) and the peptide groups . The ’s are present to define the geometry. The variables in the force field are the main chain dihedral angles , the main chain bond angles , the side chain dihedral angles , and the side chain bond angles .
(Color online) Distribution of bond and dihedral angles for the nonglycine residues of 611 high-resolution protein structures with 90% or less sequence identity (Ref. 76). The contoured regions are the “allowed” regions (containing at least 10 residues). Adapted from Fig. 1(a) of Ref. 75, Copyright (1997), with permission from Elsevier. The rectangles show the region boundaries used in the biased-probability basin-hopping scheme.
(Color online) Global optimization results for 1UZC. Top left: Minimized PDB structure. The chain termini are labeled. Top right: Lowest-energy structure from the BHS run. Bottom left: Low-energy minimum from the BHS run with the smallest RMSD from the minimized PDB structure. Bottom right: Low-energy minimum from the BHBP run with the smallest RMSD from the minimized PDB structure. The three predicted structures are each shown in the orientation that minimizes the RMSD from the minimized PDB structure when the two centers of mass are superimposed. Throughout this paper, where relevant, all-atom structures were built as described in Sec. II F for ease of visualization, and the figures were prepared using MOLMOL (Ref. 130). The ribbons representing right-handed helices are dark gray (red) on the helix exterior, while those representing left-handed helices are light gray (yellow) on the exterior.
(Color online) The two endpoint minima for the initial connected path. Left: , the fully extended structure after local minimization. Right: , the locally minimized PDB structure. Certain residues are numbered from the terminus.
(Color online) Time evolution of the occupation probabilities of significant groups of minima, obtained from 100 KMC trajectories, as discussed in the text. is the occupation probability of group at time .
(Color online) The local minimum of lowest free energy at 298 K in groups , and . The corresponding group occupation probabilities as a function of time are shown in Fig. 5. Certain residues are numbered from the terminus.
(Color online) The local minimum of lowest free energy at 298 K in the on-path groups and . Certain residues are numbered from the terminus.
Order of events for folding at 298 K with the UNRES potential, in terms of groups. The nonobligatory groups that accumulate population significantly are given below the arrow linking the adjacent obligatory groups. Mean first-passage times from KMC simulations for transitions between the obligatory groups are also given.
A free-energy disconnectivity graph at 298 K. The minima from the final DPS database were grouped using the algorithm with a rate constant threshold of , as described in the text. The energy is in units of . The branches containing the minima shown in Figs. 6 and 7 are marked accordingly, and the branch containing is labeled .
Summary of the results from the global optimization simulations. BHS refers to basin-hopping with the standard step-taking procedure, and BHBP to basin-hopping with the biased-probability scheme. RMSDs were calculated between the stated structure and the native (minimized PDB) structure over atoms. is the percentage of native contacts. The structural comparisons were made for 1BDD over the 10–60 fragment and for 1UZC over the 14–71 fragment, as described in the text.
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