A study of coarse-grained protein folding using Markov state models

Abstract

Under certain conditions, the dynamics of a coarse-grained representation of a solvated protein 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 when the monomer dynamics is diffusive can be determined by computing the relative entropy of states and their mean first passage times. For linear chain models with discontinuous potentials, these quantities can be evaluated using an adaptive method based on event-driven dynamical sampling in a massively parallel architecture. Since the transitionrate matrix can be calculated for any choice of interaction energies at any temperature, the method of choosing each state’s energy to minimize the average transition time between any two states is demonstrated. The adaptive method is used to analyze the optimization of the folding process of two proteins: crambin, and a model with frustration and misfolding. The folding dynamics of crambin is then verified under three distinct solvent systems, each differing in complexity: a hard-sphere solvent, a solvent undergoing multi-particle collision dynamics, and an implicit solvent model. Finally, the configurational entropies of the intermediate and native states of crambin are predicted using two artificial neural networks: the multilayer perceptron, and the convolutional neural network.