Diffusive reaction dynamics on invariant free energy profiles

A fundamental problem in the anal. of protein folding and other complex reactions in which the entropy plays an important role is the detn. of the activation free energy from exptl. measurements or computer simulations. This article shows how to combine min.-​cut-​based free energy profiles (FC)​, obtained from equil. mol. dynamics simulations, with conventional histogram-​based free energy profiles (FH) to ext. the coordinate-​dependent diffusion coeff. on the FC (i.e., the method dets. free energies and a diffusive preexponential factor along an appropriate reaction coordinate)​. The FC, in contrast to the FH, is shown to be invariant with respect to arbitrary transformations of the reaction coordinate, which makes possible partition of configuration space into basins in an invariant way. A "natural coordinate,​" for which FH and FC differ by a multiplicative const. (const. diffusion coeff.)​, is introduced. The approach is illustrated by a model one-​dimensional system, the alanine dipeptide, and the folding reaction of a double β-​hairpin miniprotein. It is shown how the results can be used to test whether the putative reaction coordinate is a good reaction coordinate.