  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.
