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We develop a theoretical approach to the protein folding problem based on out-of-equilibrium stochastic dynamics. Within this framework, the computational difficulties related to the existence of large time scale gaps in the protein folding problem are removed and simulating the entire reaction in atomistic details using existing computers becomes feasible. In addition, this formalism provides a natural framework to investigate the relationships between thermodynamical and kinetic aspects of the folding. For example, it is possible to show that, in order to have a large probability to remain unchanged under Langevin diffusion, the native state has to be characterized by a small conformational entropy. We discuss how to determine the most probable folding pathway, to identify configurations representative of the transition state and to compute the most probable transition time. We perform an illustrative application of these ideas, studying the conformational evolution of alanine di-peptide, within an all-atom model based on the empiric GROMOS96 force field.
Drug resistance to HIV-1 Protease involves accumulation of multiple mutations in the protein. Here we investigate the role of these mutations by using molecular dynamics simulations which exploit the influence of the native-state topology in the fold
The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, an
Machine-learning models that learn from data to predict how protein sequence encodes function are emerging as a useful protein engineering tool. However, when using these models to suggest new protein designs, one must deal with the vast combinatoria
We introduce a powerful iterative algorithm to compute protein folding pathways, with realistic all-atom force fields. Using the path integral formalism, we explicitly derive a modified Langevin equation which samples directly the ensemble of reactiv
An exactly solvable model based on the topology of a protein native state is applied to identify bottlenecks and key-sites for the folding of HIV-1 Protease. The predicted sites are found to correlate well with clinical data on resistance to FDA-appr