Extended x-ray-absorption fine-structure (EXAFS) of copper has been measured from 4 to 500 K and analyzed by the cumulant method, to check the effectiveness of EXAFS as a probe of local dynamics and thermal expansion. The comparison between parallel mean square relative displacements (MSRD) of the first four coordination shells has allowed detecting a significant deviation from a pure Debye behavior. The firstshell EXAFS thermal expansion is larger than the crystallographic one: the difference has allowed evaluating the perpendicular MSRD, whose Debye temperature is slightly larger than the one of the parallel MSRD, due to anisotropy effects. High-order first-shell cumulants are in good agreement with quantum perturbative models. The anharmonic contribution to the first-shell parallel MSRD amounts to less than 1.5 percent. The third cumulant cannot be neglected in the analysis, if accurate values of the first cumulant are sought; it cannot however be used to directly estimate the thermal expansion. The shape of the effective pair potential is independent of temperature; a rigid shift, partially due to the relative motion perpendicular to the bond direction, is however observed.
We report on atomistic simulation of the folding of a natively-knotted protein, MJ0366, based on a realistic force field. To the best of our knowledge this is the first reported effort where a realistic force field is used to investigate the folding pathways of a protein with complex native topology. By using the dominant-reaction pathway scheme we collected about 30 successful folding trajectories for the 82-amino acid long trefoil-knotted protein. Despite the dissimilarity of their initial unfolded configuration, these trajectories reach the natively-knotted state through a remarkably similar succession of steps. In particular it is found that knotting occurs essentially through a threading mechanism, involving the passage of the C-terminal through an open region created by the formation of the native -sheet at an earlier stage. The dominance of the knotting by threading mechanism is not observed in MJ0366 folding simulations using simplified, native-centric models. This points to a previously underappreciated role of concerted amino acid interactions, including non-native ones, in aiding the appropriate order of contact formation to achieve knotting.
We investigate the folding mechanism of the WW domain Fip35 using a realistic atomistic force field by applying the Dominant Reaction Pathways approach. We find evidence for the existence of two folding pathways, which differ by the order of formation of the two hairpins. This result is consistent with the analysis of the experimental data on the folding kinetics of WW domains and with the results obtained from large-scale molecular dynamics simulations of this system. Free-energy calculations performed in two coarse-grained models support the robustness of our results and suggest that the qualitative structure of the dominant paths are mostly shaped by the native interactions. Computing a folding trajectory in atomistic detail only required about one hour on 48 Central Processing Units. The gain in computational efficiency opens the door to a systematic investigation of the folding pathways of a large number of globular proteins.atomistic simulations | protein folding U nveiling the mechanism by which proteins fold into their native structure remains one of the fundamental open problems at the interface of contemporary molecular biology, biochemistry, and biophysics. A critical point concerns the characterization of the ensemble of reactive trajectories connecting the denatured and native states, in configuration space.In this context, a fundamental question which has long been debated (1) is whether the folding of typical globular proteins involves a few dominant pathways; i.e., well defined and conserved sequences of secondary and tertiary contact formation, or if it can take place through a multitude of qualitatively different routes. A related important question concerns the role of nonnative interactions in determining the structure of the folding pathways (2, 3).In principle, atomistic molecular dynamics (MD) simulations provide a consistent framework to address these problems from a theoretical perspective. However, due to their high computational cost, MD simulations can presently only be used to investigate the conformational dynamics of relatively small polypeptide chains, and are only able to cover time intervals much smaller than the folding times of typical globular proteins.In view of these limitations, a considerable amount of theoretical and experimental activity has been devoted to investigate the folding of protein subdomains, which consist of only a few tens of amino acids, and fold on submillisecond time scales (4). In particular, a number of mutants of the 35 amino acid WW domain of human protein pin1 have been engineered which fold in few tens of microseconds (5). The mutant's small size and their ultrafast kinetics make them ideal benchmark systems, for which numerical simulations can be compared with a large body of experimental data (5-7).In particular, a MD simulation was performed to investigate the dynamics of a mutant named Fip35 (see Fig. 1), for a time interval longer than 10 μs. Unfortunately, in that simulation no folding transition was observed (8, 9).The folding of this WW dom...
A combined approach has been used to study thermal effects on the extended x-ray absorption fine-structure ͑EXAFS͒ of copper between 4 and 500 K. A phenomenological data analysis shows that the thermal expansions measured from the first and third cumulants significantly differ between each other and from the crystallographic thermal expansion. Path-integral Monte Carlo calculations of EXAFS cumulants have been performed, using a many-body potential. The good reproduction of experimental values validates the phenomenological analysis and opens more perspectives for applications to more complex systems. It is shown that the reproduction of EXAFS parameters allows for a test of the interaction potentials with regard to anharmonicity.
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