Steered Molecular Dynamics Methods Applied to Enzyme Mechanism and Energetics

One of the main goals of chemistry is to understand the underlying principles of chemical reactions, in terms of both its reaction mechanism and the thermodynamics that govern it. Using hybrid quantum mechanics/molecular mechanics (QM/MM)-based methods in combination with a biased sampling scheme, it is possible to simulate chemical reactions occurring inside complex environments such as an enzyme, or aqueous solution, and determining the corresponding free energy profile, which provides direct comparison with experimental determined kinetic and equilibrium parameters. Among the most promising biasing schemes is the multiple steered molecular dynamics method, which in combination with Jarzynski's Relationship (JR) allows obtaining the equilibrium free energy profile, from a finite set of nonequilibrium reactive trajectories by exponentially averaging the individual work profiles. However, obtaining statistically converged and accurate profiles is far from easy and may result in increased computational cost if the selected steering speed and number of trajectories are inappropriately chosen. In this small review, using the extensively studied chorismate to prephenate conversion reaction, we first present a systematic study of how key parameters such as pulling speed, number of trajectories, and reaction progress are related to the resulting work distributions and in turn the accuracy of the free energy obtained with JR. Second, and in the context of QM/MM strategies, we introduce the Hybrid Differential Relaxation Algorithm, and show how it allows obtaining more accurate free energy profiles using faster pulling speeds and smaller number of trajectories and thus smaller computational cost.