Umbrella sampling is a biased molecular dynamics (MD) based method for the calculation of one- or more-dimensional free energy profiles associated to chemical processes . In one of the versions of this method, intermediate steps between two thermodynamic states are covered by a series of windows, at each of which a biased MD simulation is performed. In chemical reactions, free energy differences between two states that differ in geometry (like reactants complex, transition state and products complex) are usually of interest since free energy barriers, for instance, can be used to calculate rate constants by means of the transition state theory. Moreover, mechanistic information can be assessed through free energy profiles calculation. In this way, in the study of chemical reactions by the umbrella sampling method, the windows are located at different values of an order parameter that is often a combination of geometric grounds that describe the progress of the process. In this context, this order parameter is generally referred to as ‘reaction coordinate’ even though it might not be the exact reaction coordinate of the system (i.e. the one-dimensional coordinate that connects reactants and products by the minimum energy pathway).

In this work, we present an improved sampling protocol for obtaining free energy profiles of biochemical reactions in solution using umbrella sampling in a quantum mechanics-molecular mechanics (QM-MM) scheme.

One of the most important assumptions in umbrella sampling calculations is that the selected reaction coordinate is the only slow degree of freedom. This is usually true if all the important events of the reaction are included in the definition of the reaction coordinate. However, in QM-MM MD, time simulations longer than tens of ps are rarely computed because of their computational cost and some degrees of freedom might not be well-sampled even if they are supposed to be equilibrated. Our results suggest that solvent pattern rearrangements related to charges redistribution during the reaction are not well-sampled in the ps scale and this might lead to an overestimation of the computed free energy barriers.