Lessons learned about steered molecular dynamics simulations and free energy calculations

The Jarzynski equality is routinely used to compute equilibrium free‐energy differences from a set of non‐equilibrium work values. From a computational approach, these non‐equilibrium work values are often generated using steered Molecular Dynamics, and, under certain conditions a Gaussian distribution of non‐equilibrium work values is to be anticipated. We highlight the regime in which the maximum‐likelihood estimators assuming a Gaussian distribution perform reliably.

Abstract

The calculation of free energy profiles is central in understanding differential enzymatic activity, for instance, involving chemical reactions that require QM‐MM tools, ligand migration, and conformational rearrangements that can be modeled using classical potentials. The use of steered molecular dynamics (sMD) together with the Jarzynski equality is a popular approach in calculating free energy profiles. Here, we first briefly review the application of the Jarzynski equality to sMD simulations, then revisit the so‐called stiff‐spring approximation and the consequent expectation of Gaussian work distributions and, finally, reiterate the practical utility of the second‐order cumulant expansion, as it coincides with the parametric maximum‐likelihood estimator in this scenario. We illustrate this procedure using simulations of CO, both in aqueous solution and in a carbon nanotube as a model system for biologically relevant nanoheterogeneous environments. We conclude the use of the second‐order cumulant expansion permits the use of faster pulling velocities in sMD simulations, without introducing bias due to large dispersion in the non‐equilibrium work distribution.

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