Folding of a β‑Sheet Miniprotein: Probability Fluxes, Streamlines, and the Potential for the Driving Force

In this work we continue the study of the first-passage folding of an antiparallel β-sheet miniprotein (beta3s) that was initiated in the previous work [Kalgin et al. J. Phys. Chem. B, 2014, 118, 4287 ]. We consider a larger ensemble of folding trajectories, which allows us to gain a closer insight into the folding dynamics. In particular, we calculate the potential for the driving force of folding in a reduced space of collective variables. The potential has two components. One component (Φ) is responsible for the source and sink of the folding flow, which are formed, respectively, in the regions of the unfolded and native states of the protein, and the other (Ψ) accounts for the flow vorticity inherently generated at the sides of the reaction channel and provides the canalization of the folding flow between the source and sink. We show that both components obey Poisson’s equations with the corresponding source/sink terms. The resulting components have a very simple form: the Φ-surface consists of two well-defined peaks of different signs, which correspond, respectively, to the source and sink of the folding flow, and the Ψ-surface consists of two ridges of different signs that connect the source and sink of the flow.