The goal of Protein Structure Prediction (PSP) problem is to predict a protein's 3D structure (confirmation) from its amino acid sequence. The approach addresses the calculation by difference, a shortcut that avoids having to simulate the protein folding time, which is very often unfeasible computationally. The method proves to be also suitable to obtain changes in stability due to changes in solution pH, or stability differences between a wild-type protein and a variant. The devised approach enables accurate calculation of two essential magnitudes governing the stability of proteins −the changes in enthalpy and in heat capacity associated to protein unfolding−, which are used to obtain accurate values of the change in Gibbs free-energy, also known as the protein conformational stability. The proteins successfully computed are representative of the main protein structural classes, their sequences range from 84 to 169 residues, and their isoelectric points from 4.0 to 8.9. Following an initial explorative study, we extend here the application of a Molecular Dynamics-based approach −with the most accurate force field/water model combination previously found (Charmm22-CMAP/Tip3p)− to computing the folding energetics of a set of two-state and three-state proteins that do or do not carry a bound cofactor. Progress in this direction can help boost related fields such as protein engineering, drug design, or genetic interpretation, but the task seems not to have been addressed by the scientific community. The continuous development of algorithms and methods to explore longer simulation timescales of biological systems, as well as the enhanced accuracy of potential functions (force fields and solvent models) have not yet led to significant progress in the calculation of the thermodynamics quantities associated to protein folding from first principles. Here we demonstrate yet another one, emphasizing the role of the phase of a wave-function as an optimal RC.ĭespite impressive advances by AlphaFold2 in the field of computational biology, the protein folding problem remains an enigma to be solved. Deep fundamental connections between quantum mechanics and stochastic processes, in particular, between the Schr\"odinger and diffusion equations, are well established. The developments are illustrated on simple examples. We show how the potential can be introduced in to the formalism self-consistently. Nevertheless, we show that one family of addev solutions for diffusion is described by equations of classical mechanics, while another family can be approximated by quantum mechanical equations. While the addev conditioning is a reasonable requirement for a RC, it is rather peculiar for physics in general. In particular, we show that the forward and time-reversed committors are functions of the addev, meaning a diffusive model along an addev RC can be used to compute important properties of non-equilibrium dynamics exactly. Here we continue the fundamental development of the framework and illustrate it by analysing diffusion. The sub-ensemble is conditioned to have a single RC optimal for both the forward and time-reversed non-equilibrium dynamics of the sub-ensemble. An addev describes a sub-ensemble of trajectories together with an optimal RC. Recently, additive eigenvector (addevs) have been introduced in order to extend the formalism to non-equilibrium dynamics. The committor is a primary example of an optimal RC. If the RCs are optimally selected important properties of dynamics can be computed exactly. Complex multidimensional stochastic dynamics can be approximately described as a diffusion along reaction coordinates (RCs).
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