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

TL;DR

This paper introduces an adaptive, parallel method to evaluate configurational entropy and transition times in coarse-grained protein models, optimizing folding pathways by adjusting state energies to minimize transition times.

Contribution

The paper presents a novel adaptive approach for calculating transition rates and optimizing folding pathways in coarse-grained protein models using event-driven sampling.

Findings

Folding pathways involve rapid local bond formation followed by distant contact establishment.

Optimized state energies can accelerate folding by reducing trapping and facilitating escape routes.

The method effectively analyzes and improves folding dynamics in protein models.

Abstract

Under certain conditions, the dynamics of coarse-grained models of solvated proteins can be described using a Markov state model, which tracks the evolution of populations of configurations. The transition rates among states that appear in the Markov model can be determined by computing the relative entropy of states and their mean first passage times. In this paper, we present an adaptive method to evaluate the configurational entropy and the mean first passage times for linear chain models with discontinuous potentials. The approach is based on event-driven dynamical sampling in a massively parallel architecture. Using the fact that the transition rate matrix can be calculated for any choice of interaction energies at any temperature, it is demonstrated how each state's energy can be chosen such that the average time to transition between any two states is minimized. The methods are used to analyze the optimization of the folding process of two protein systems: the crambin protein, and a model with frustration and misfolding. It is shown that the folding pathways for both systems are comprised of two regimes: first, the rapid establishment of local bonds, followed by the subsequent formation of more distant contacts. The state energies that lead to the most rapid folding encourage multiple pathways, and either penalize folding pathways through kinetic traps by raising the energies of trapping states, or establish an escape route from the trapping states by lowering free energy barriers to other states that rapidly reach the native state.