A reliable prediction of 3D protein structures from sequence data remains a big challenge due to both theoretical and computational difficulties. We have previously shown that our kinetostatic compliance method (KCM) implemented into the Protofold package can overcome some of the key difficulties faced by other de novo structure prediction methods, such as the very small time steps required by the molecular dynamics (MD) approaches or the very large number of samples needed by the Monte Carlo (MC) sampling techniques. In this article, we improve the free energy formulation used in Protofold by including the typically underrated entropic effects, imparted due to differences in hydrophobicity of the chemical groups, which dominate the folding of most water-soluble proteins. In addition to the model enhancement, we revisit the numerical implementation by redesigning the algorithms and introducing efficient data structures that reduce the expected complexity from quadratic to linear. Moreover, we develop and optimize parallel implementations of the algorithms on both central and graphics processing units (CPU GPU) achieving speed-ups up to two orders of magnitude on the GPU. Our simulations are consistent with the general behavior observed in the folding process in aqueous solvent, confirming the effectiveness of model improvements. We report on the folding process at multiple levels; namely, the formation of secondary structural elements and tertiary interactions between secondary elements or across larger domains. We also observe significant enhancements in running times that make the folding simulation tractable for large molecules.
The explicit methods use all-atom force field models such as SPC, SPC E, TIP3P, TIP5P @cite_20 @cite_72 , or coarse-grained (CG) models @cite_54 @cite_49 which are less structured representations of the solvent obtained by mapping two or more particles onto a single interaction site @cite_20 . A prohibitive computational cost is associated with the large number of solvent molecules required to model a bulk solution.
@cite_54 @cite_72 @cite_49 @cite_20
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We employ the inverse Boltzmann method to coarse-grain three commonly used three-site water models (TIP3P, SPC and SPC E) where one molecule is replaced with one coarse-grained particle with isotropic two-body interactions only. The shape of the coarse-grained potentials is dominated by the ratio of two lengths, which can be rationalized by the geometric constraints of the water clusters. It is shown that for simple two-body potentials either the radial distribution function or the geometrical packing can be optimized. In a similar way, as needed for multiscale methods, either the pressure or the compressibility can be fitted to the all atom liquid. In total, a speed-up by a factor of about 50 in computational time can be reached by this coarse-graining procedure. An overview is provided on the development and status of potential energy functions that are used in atomic-level statistical mechanics and molecular dynamics simulations of water and of organic and biomolecular systems. Some topics that are considered are the form of force fields, their parameterization and performance, simulations of organic liquids, computation of free energies of hydration, universal extension for organic molecules, and choice of atomic charges. The discussion of water models covers some history, performance issues, and special topics such as nuclear quantum effects. A methodology is described to systematically derive coarse-grained (CG) force fields for molecular liquids from the underlying atomistic-scale forces. The coarse graining of an interparticle force field is accomplished by the application of a force-matching method to the trajectories and forces obtained from the atomistic trajectory and force data for the CG sites of the targeted system. The CG sites can be associated with the centers of mass of atomic groups because of the simplicity in the evaluation of forces acting on these sites from the atomistic data. The resulting system is called a multiscale coarse-grained (MS-CG) representation. The MS-CG method for liquids is applied here to water and methanol. For both liquids one-site and two-site CG representations without an explicit treatment of the long-ranged electrostatics have been derived. In addition, for water a two-site model having the explicit long-ranged electrostatics has been developed. To improve the thermodynamic properties (e.g., pressure and density) for the MS-CG models, the constraint for the instantaneous virial was included into the force-match procedure. The performance of the resulting models was evaluated against the underlying atomistic simulations and experiment. In contrast with existing approaches for coarse graining of liquid systems, the MS-CG approach is general, relies only on the interatomic interactions in the reference atomistic system.