Markov state models (MSMs) have been used to describe ensembles of pathways connecting metastable states when sufficient overlap of unbiased sampling is attainable. In the cases where multiple ensembles are separated by large free-energy barriers, a chain-of-states method can be used to estimate the rate of transitioning between these sets, though these approaches often consider a single state representing each endpoint. We have developed a Markov state model of Markov state models which we call the Hierarchical-MSM where chain-of-states simulations are used to model the transitions between each local MSM. We have demonstrated that this approach outperforms the conventional string method where only a single pathway is considered for two test cases, a toy model and the alanine dipeptide. In this method, there is no need for sufficient overlap between ensembles, which becomes less likely as the complexity of the system increases. It also provides the additional insights of multiple pathways between ensembles. We now extend this approach to investigate an enzyme, chorismate pyruvate-lyase. We utilize classical simulations to populate kinetically distinct metastable states in the reactants and products ensembles and utilize a QM/MM implementation of the finite-temperature string method to obtain the free-energy barrier of paths connecting these ensembles. With this approach, we aim to predict the rate of the enzyme-catalyzed reaction while considering multiple pathways and their relative contributions to the process.

Identifying multiple pathways in enzyme catalysis using a QM/MM hierarchical Markov state model

ACS Fall 2021

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