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Non-Markovian modeling of protein folding.

ABSTRACT: We extract the folding free energy landscape and the time-dependent friction function, the two ingredients of the generalized Langevin equation (GLE), from explicit-water molecular dynamics (MD) simulations of the α-helix forming polypeptide [Formula: see text] for a one-dimensional reaction coordinate based on the sum of the native H-bond distances. Folding and unfolding times from numerical integration of the GLE agree accurately with MD results, which demonstrate the robustness of our GLE-based non-Markovian model. In contrast, Markovian models do not accurately describe the peptide kinetics and in particular, cannot reproduce the folding and unfolding kinetics simultaneously, even if a spatially dependent friction profile is used. Analysis of the GLE demonstrates that memory effects in the friction significantly speed up peptide folding and unfolding kinetics, as predicted by the Grote-Hynes theory, and are the cause of anomalous diffusion in configuration space. Our methods are applicable to any reaction coordinate and in principle, also to experimental trajectories from single-molecule experiments. Our results demonstrate that a consistent description of protein-folding dynamics must account for memory friction effects.

SUBMITTER: Ayaz C

PROVIDER: S-EPMC8346879 | biostudies-literature | 2021 Aug

REPOSITORIES: biostudies-literature

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Non-Markovian modeling of protein folding.

Ayaz Cihan C Tepper Lucas L Brünig Florian N FN Kappler Julian J Daldrop Jan O JO Netz Roland R RR

Proceedings of the National Academy of Sciences of the United States of America 20210801 31

We extract the folding free energy landscape and the time-dependent friction function, the two ingredients of the generalized Langevin equation (GLE), from explicit-water molecular dynamics (MD) simulations of the α-helix forming polypeptide [Formula: see text] for a one-dimensional reaction coordinate based on the sum of the native H-bond distances. Folding and unfolding times from numerical integration of the GLE agree accurately with MD results, which demonstrate the robustness of our GLE-bas ...[more]

PMID: 34326249

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Project description:Background: Proteins fold robustly and reproducibly in vivo, but many cannot fold in vitro in isolation from cellular components. Despite the remarkable progress that has been achieved by the artificial intelligence approaches in predicting the protein native conformations, the pathways that lead to such conformations, either in vitro or in vivo, remain largely unknown. The slow progress in recapitulating protein folding pathways in silico may be an indication of the fundamental deficiencies in our understanding of folding as it occurs in nature. Here we consider the possibility that protein folding in living cells may not be driven solely by the decrease in Gibbs free energy and propose that protein folding in vivo should be modeled as an active energy-dependent process. The mechanism of action of such a protein folding machine might include direct manipulation of the peptide backbone. Methods: To show the feasibility of a protein folding machine, we conducted molecular dynamics simulations that were augmented by the application of mechanical force to rotate the C-terminal amino acid while simultaneously limiting the N-terminal amino acid movements. Results: Remarkably, the addition of this simple manipulation of peptide backbones to the standard molecular dynamics simulation indeed facilitated the formation of native structures in five diverse alpha-helical peptides. Steric clashes that arise in the peptides due to the forced directional rotation resulted in the behavior of the peptide backbone no longer resembling a freely jointed chain. Conclusions: These simulations show the feasibility of a protein folding machine operating under the conditions when the movements of the polypeptide backbone are restricted by applying external forces and constraints. Further investigation is needed to see whether such an effect may play a role during co-translational protein folding in vivo and how it can be utilized to facilitate folding of proteins in artificial environments.

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Non-Markovian modeling of protein folding.

Publications

Non-Markovian modeling of protein folding.

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