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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This paper presents an efficient and novel computational protein prediction methodology called kineto-static compliance method. Successive kineto-static fold compliance is a methodology for predicting a protein molecule's motion under the effect of an interatomic force field without the need for molecular-dynamic simulation. Instead, the chain complies under the kineto-static effect of the force field in such a manner that each rotatable joint changes by an amount proportional to the effective torque on that joint. This process successively iterates until all of the joint torques have converged to a minimum. This configuration is equivalent to a stable, globally optimized potential energy state of the system or, in other words, the final conformation of the protein. This methodology is implemented in a computer software package named PROTOFOLD. In this paper, we have used PROTOFOLD to predict the final conformation of a small peptide chain segment, an alpha helix, and the Triponin protein chains from a denatured configuration. The results show that torques in each joint are minimized to values very close to zero, which demonstrates the method's effectiveness for protein conformation prediction. Part I. Biological Molecules 1. From Genes to RNA to Proteins 2. Nucleic Acid Structure 3. Glycans and Lipids 4. Protein Structure 5. Evolutionary Variation in Proteins Part II. Energy and Entropy 6. Energy and Intermolecular Forces 7. Entropy 8. Linking Energy and Entropy Part III. Free Energy 9. Free Energy 10. Chemical Potential and the Drive to Equilibrium 11. Voltages and Free Energy Part IV. Molecular Interactions 12. Molecular Recognition 13. Specificity of Macromolecular Recognition 14. Allostery Part V. Kinetics and Catalysis 15. Rates of Molecular Processes 16. Principles of Enzyme Catalysis 17. Diffusion and Transport Part VI. Assembly and Activity 18. Folding 19. Fidelity in DNA and Protein Synthesis