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Under certain conditions, the dynamics of coarse-grained models of solvatedproteins can be described using a Markov state model, which tracks theevolution of populations of configurations. The transition rates among statesthat appear in the Markov model can be determined by computing the relativeentropy of states and their mean first passage times. In this paper, we presentan adaptive method to evaluate the configurational entropy and the mean firstpassage times for linear chain models with discontinuous potentials. Theapproach is based on event-driven dynamical sampling in a massively parallelarchitecture. Using the fact that the transition rate matrix can be calculatedfor any choice of interaction energies at any temperature, it is demonstratedhow each state's energy can be chosen such that the average time to transitionbetween any two states is minimized. The methods are used to analyze theoptimization of the folding process of two protein systems: the crambinprotein, and a model with frustration and misfolding. It is shown that thefolding pathways for both systems are comprised of two regimes: first, therapid establishment of local bonds, followed by the subsequent formation ofmore distant contacts. The state energies that lead to the most rapid foldingencourage multiple pathways, and either penalize folding pathways throughkinetic traps by raising the energies of trapping states, or establish anescape route from the trapping states by lowering free energy barriers to otherstates that rapidly reach the native state.

Configurational entropy, transition rates, and optimal interactions for rapid folding in coarse-grained model proteins