The fundamental object for studying a (bio)chemical reaction obtained from simulations is the free energy profile, which can be directly related to experimentally determined properties. Although quite accurate hybrid quantum (DFT based)-classical methods are available, achieving statistically accurate and well converged results at a moderate computational cost is still an open challenge. Here, we present and thoroughly test a hybrid differential relaxation algorithm (HyDRA), which allows faster equilibration of the classical environment during the nonequilibrium steering of a (bio)chemical reaction. We show and discuss why (in the context of Jarzynski's Relationship) this method allows obtaining accurate free energy profiles with smaller number of independent trajectories and/or faster pulling speeds, thus reducing the overall computational cost. Moreover, due to the availability and straightforward implementation of the method, we expect that it will foster theoretical studies of key enzymatic processes.

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Heme proteins are ubiquitous in nature and perform many diverse functions in all kingdoms of life. Many of these functions are related to large-scale conformational transitions and allosteric processes. Sampling of these large conformational changes is computationally very challenging. In this context, coarse-grain simulations emerge as an efficient approach to explore the conformational landscape. In this work, we present a coarse-grained model of the heme group and thoroughly validate this model in different benchmark examples, which include the monomeric heme proteins myoglobin and neuroglobin and the tetrameric human hemoglobin where we evaluated the method's ability to explore conformational changes (as the formation of hexacoordinated species) and allosteric transitions (as the well-known R → T transition). The obtained results are compared with atomistic molecular dynamics simulations. Overall, the results indicate that this approach conserves the essential dynamical information on different allosteric processes.