A Random Force is a Force, of Course, of Coarse: Decomposing Complex Enzyme Kinetics with Surrogate Models

TL;DR

This paper introduces a surrogate modeling approach using stochastic differential equations to analyze enzyme conformational fluctuations, revealing complex relaxation behaviors and linking single-molecule experiments with simulations.

Contribution

It presents a novel ensemble surrogate model method to analyze non-Markovian enzyme dynamics from single trajectories, capturing complex relaxation phenomena.

Findings

Ensemble of surrogate models encodes unresolved conformational degrees of freedom.

Flexible models outperform simple exponentials in describing relaxation times.

Application to enzyme simulations demonstrates practical utility.

Abstract

The temporal autocorrelation (AC) function associated with monitoring order parameters characterizing conformational fluctuations of an enzyme is analyzed using a collection of surrogate models. The surrogates considered are phenomenological stochastic differential equation (SDE) models. It is demonstrated how an ensemble of such surrogate models, each surrogate being calibrated from a single trajectory, indirectly contains information about unresolved conformational degrees of freedom. This ensemble can be used to construct complex temporal ACs associated with a "non-Markovian" process. The ensemble of surrogates approach allows researchers to consider models more flexible than a mixture of exponentials to describe relaxation times and at the same time gain physical information about the system. The relevance of this type of analysis to matching single-molecule experiments to computer simulations and how more complex stochastic processes can emerge from a mixture of simpler processes is also discussed. The ideas are illustrated on a toy SDE model and on molecular dynamics simulations of the enzyme dihydrofolate reductase.