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Ab initio protein folding simulations, with the aim to reach the native state under the native condition, are far more challenging due to the constraints of reproducing folding time scales (thus folding reaction cannot be artificially accelerated) and reproducing time-dependent folding events (thus dynamics trajectories cannot be interrupted as in the multicanonical methods, Ref. 24). There are only a handful of ab initio folding simulations reported in the literature, including the works on an all a protein, villin headpiece (Refs. 50 and 91), and several α-β proteins such as Trp-cage and BBA5 (Refs. 44, 49, and 92-94), These simulations use various approximations and are still very limited.
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The simulated time scales are at least 200 shorter the physical time scales due to the enhanced sampling method (about a factor of 20, Ref. 55) and the use of no friction (at least a factor of 10, Ref. 95) in implicit solvation.
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One cause for such a low percentage of β hairpin is due to the rather stringent standard used for β-hairpin definition: when applied to the 35 frames in the NMR structure of BBA1, the β hairpin can only be observed once. The NMR structures at residues 2-7 are mostly classified as strand (S) or nonstructured.
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73
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Statistical dependence of the native hairpin upon the native helix is difficult to obtain because the native hairpin population is too low to make a quantitative conclusion.
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It should be pointed out that local protein environments strongly influence the strength of a salt bridge. It is possible that a salt bridge is highly unfavorable, for example, in a buried environment due to desolvation. With the much confined set of solvent-exposed salt bridges, a counterexample still exists: addition of oppositely charged groups in T4 lysozyme in solvent-exposed positions that might permit them to form, salt bridges led to little if any net stabilization of the native state (Ref. 96). The seemingly contradictory claims are in part due to the fact that they do not express the energy of a salt bridge relative to the same reference state. In computational studies, salt bridges are broken not by deleting the charged groups from the protein, but by moving the charged groups away from each other. However in the experimental study, salt bridges are broken by deleting one or both charged groups. This results in a very different reference state, because adding charged groups to certain sites on a protein can be intrinsically destabilizing, as observed in the same T4 lysozyme study (Ref. 9.6). This issue has been discussed previously (Refs. 78 and 80).
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Both hydrophobic and salt-bridge populations are generally higher in the native state when preorganized backbone restricts side-chain motions involved in such interactions.
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84
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4043129213
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note
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This is the average simulation time interval separating the occurrences of the full native helix.
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