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.
In the earlier stages of the development, the energetics were limited to intramolecular interactions in the gas-phase of the protein---e.g., Coulombic and van der Waals forces exchanged between atoms of the protein itself, ignoring the interactions with solvent molecules. However, an important class of biologically significant proteins are water-soluble, whose folding process is predominantly driven by the interactions with the solvent, particularly the so-called hydrophobic effect' The hydrophobic effect is explained as the strong tendency of nonpolar sidechains to pack together to form a hydrophobic core protected from the solvent by a hydrophilic surface @cite_64 . This effect is formulated in terms of entropic changes in the solvent molecules surrounding the protein surface. which was missing from Protofold I @cite_36 .
@cite_36 @cite_64
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Protein structure prediction remains one of the significant challenges in computational biology. We have previously shown that our kinetostatic compliance method can overcome some of the key difficulties faced by other de novo structural prediction methods, such as the very small time steps required by the molecular dynamics approaches, or the very large number of samples required by the sampling based techniques. In this paper we extend the previous free energy formulation by adding the solvent effects, which contribute predominantly to the folding phenomena. We show that the addition of the solvation effects, which complement the existing Coulombic and van der Waals interactions, lead to a physically effective energy function. Furthermore, we achieve significant computational speed-up by employing efficient algorithms and data structures that effectively reduce the time complexity from O(n2) to O(n), n being the number of atoms. Our simulations are consistent with the general behavior observed in protein folding, and show that the hydrophobic atoms tend to pack inside the core of the molecule in an aqueous solvent, while a vacuum environment produces no such effect.Copyright © 2013 by ASME Successful modeling of the processes of protein folding and aggregation may ultimately require accurate descriptions of proteins’ diffusive characteristics, which are expected to be influenced by hydrodynamic effects; a comprehensive study of the diffusion and folding of 11 model proteins with an established simulation model extended to include hydrodynamic interactions between residues has therefore been carried out. Molecular simulations that neglect hydrodynamic interactions are incapable of simultaneously reproducing the expected experimental translational and rotational diffusion coefficients of folded proteins, drastically underestimating both when reasonable hydrodynamic radii are employed. In contrast, simulations that include hydrodynamic interactions produce diffusion coefficients that match very well with the expected experimental values for translation and rotation and also correctly capture the significant decrease in translational diffusion coefficient that accompanies protein unfolding. The... A realistic computer simulation of protein folding requires a comprehensive account of interaction energetics, placing a substantial demand on processing power. This paper presents an improved computational framework for protein folding software package PROTOFOLD, that enables efficient computation of solvation free energy effects in addition to Coulombic and van der Waals interactions. Efficient data structures have been utilized to speed-up the sequential running times from O(n2) to O(n), n being the number of atoms. It turns out, however, that an accurate evaluation of molecular surface areas characterizing the solvation effects imposes a computational bottleneck to the entire simulation. Massive computational power offered by Graphics Processing Units (GPU) was exploited to develop a simple and efficient Single-Instruction Multiple-Thread (SIMT) algorithm for the latter step. The running times were monitored for different steps of the folding simulation for different molecular sizes. Significant performance improvements were observed, yielding promising results where numerous iterative runs are needed.© 2013 ASME Abstract The rate of protein-protein association limits the response time due to protein-protein interactions. The bimolecular association rate may be diffusion-controlled or influenced, and in such cases, Brownian dynamics simulations of protein-protein diffusional association may be used to compute association rates. Here, we report Brownian dynamics simulations of the diffusional association of five different protein-protein pairs: barnase and barstar, acetylcholinesterase and fasciculin-2, cytochrome c peroxidase and cytochrome c, the HyHEL-5 antibody and hen egg lysozyme (HEL), and the HyHEL-10 antibody and HEL. The same protocol was used to compute the diffusional association rates for all the protein pairs in order to assess, by comparison to experimentally measured rates, whether the association of these proteins can be explained solely on the basis of diffusional encounter. The simulation protocol is similar to those previously derived for simulation of the association of barnase and barstar, and of acetylcholinesterase and fasciculin-2; these produced results in excellent agreement with experimental data for these protein pairs, with changes in association rate due to mutations reproduced within the limits of expected computational and modeling errors. Here, we find that for all protein pairs, the effects of mutations can be well reproduced by the simulations, even though the degree of the electrostatic translational and orientational steering varies widely between the cases. However, the absolute values of association rates for the acetylcholinesterase: fasciculin-2 and HyHEL-10 antibody: HEL pairs are overestimated. Comparison of bound and unbound protein structures shows that this may be due to gating resulting from protein flexibility in some of the proteins. This may lower the association rates compared to their bimolecular diffusional encounter rates.