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...

Stochastic simulations of coarse-grained protein models are used to investigate the propensity to form knots in early stages of protein folding. The study is carried out comparatively for two homologous carbamoyltransferases, a natively-knotted N-acetylornithine carbamoyltransferase (AOTCase) and an unknotted ornithine carbamoyltransferase (OTCase). In addition, two different sets of pairwise amino acid interactions are considered: one promoting exclusively native interactions, and the other additionally including non-native quasi-chemical and electrostatic interactions. With the former model neither protein shows a propensity to form knots. With the additional non-native interactions, knotting propensity remains negligible for the natively-unknotted OTCase while for AOTCase it is much enhanced. Analysis of the trajectories suggests that the different entanglement of the two transcarbamylases follows from the tendency of the C-terminal to point away from (for OTCase) or approach and eventually thread (for AOTCase) other regions of partly-folded protein. The analysis of the OTCase/AOTCase pair clarifies that natively-knotted proteins can spontaneously knot during early folding stages and that non-native sequence-dependent interactions are important for promoting and disfavouring early knotting events.

Taking protein G with 56 residues for a case study, we investigate the mechanism of protein folding. In addition to its native structure possessing α-helix and β-sheet contents of 27% and 39%, respectively, we construct a number of misfolded decoys with a wide variety of α-helix and β-sheet contents. We then consider a hierarchy of 8 different models with increasing level of detail in terms of the number of entropic and energetic physical factors incorporated. The polyatomic structure is always taken into account, but the side chains are removed in half of the models. The solvent is formed by either neutral hard spheres or water molecules. Protein intramolecular hydrogen bonds (H-bonds) and protein-solvent H-bonds (the latter is present only in water) are accounted for or not, depending on the model considered. We then apply a physics-based free-energy function (FEF) corresponding to each model and investigate which structures are most stabilized. This special approach taken on a step-by-step basis enables us to clarify the role of each physical factor in contributing to the structural stability and separately elucidate its effect. Depending on the model employed, significantly different structures such as very compact configurations with no secondary structures and configurations of associated α-helices are optimally stabilized. The native structure can be identified as that with lowest FEF only when the most detailed model is employed. This result is significant for at least the two reasons: The most detailed model considered here is able to capture the fundamental aspects of protein folding notwithstanding its simplicity; and it is shown that the native structure is stabilized by a complex interplay of minimal multiple factors that must be all included in the description. In the absence of even a single of these factors, the protein is likely to be driven towards a different, more stable state.