Analysis of Two-State Folding Using Parabolic Approximation IV: Non-Arrhenius Kinetics of FBP28 WW Part-II

A model which treats the denatured and the native conformers as being confined to harmonic Gibbs energy wells has been used to rationalize the physical basis for the non-Arrhenius behaviour of spontaneously-folding fixed two-state systems. It is shown that at constant pressure and solvent conditions: (i) the rate constant for folding will be a maximum when the heat released upon formation of net molecular interactions is exactly compensated by the heat absorbed to desolvate net polar and non-polar solvent accessible surface area (SASA), as the denatured conformers driven by thermal noise bury their SASA and diffuse on the Gibbs energy surface to reach the activated state; (ii) the rate constant for unfolding will be a minimum when the heat absorbed by the native conformers to break various net backbone and sidechain interactions is exactly compensated by the heat of hydration released due to the net increase in SASA, as the native conformers unravel to reach the activated state; (iii) the activation entropy for folding will be zero, and the Gibbs barrier to folding will be a minimum, when the decrease in the backbone and the sidechain mobility is exactly compensated by the increase in entropy due to solvent-release, as the denatured conformers bury their SASA to reach the activated state; (iv) the activation entropy for unfolding will be zero, and the Gibbs barrier to unfolding will be a maximum when the increase in the backbone and sidechain mobility is exactly compensated by the negentropy of solvent-capture on the protein surface, as the native conformers unravel to reach the activated state; (v) while cold denaturation is driven by solvent effects, heat denaturation is primarily due to chain effects; (vi) the speed-limit for the folding is ultimately due to conformational searching; and(vii) Levinthal's paradox may have little basis if the entropy of solvent-release that accompanies protein folding is taken into consideration.

BÉZIER SUBDIVISION FOR INVERSE MOLECULAR KINEMATICS

Conformational searching is a core task in inverse molecular kinematics. Algorithmic improvements affecting either the speed or quality of conformational searching will have a profound impact on applications including ligand-receptor docking, ab initio prediction of protein structure, and protein folding. In this paper, we investigate a specific geometry-constrained conformational searching problem, where some feature atoms have pre-specified target positions. Using Bézier subdivision, we present a method to locate and approximate the solutions of the equations derived from constraints on the feature atoms. The conformations corresponding to these solutions are all the conformations satisfying the target constraints. Three implementations of the subdivision method taking advantage of the sparsity of the coefficients of the polynomial equations are presented and the results are compared and contrasted.