A benchmark for reaction coordinates in the transition path ensemble.

The molecular mechanism of a reaction is embedded in its transition path ensemble, the complete collection of reactive trajectories. Utilizing the information in the transition path ensemble alone, we developed a novel metric, which we termed the emergent potential energy, for distinguishing reaction coordinates from the bath modes. The emergent potential energy can be understood as the average energy cost for making a displacement of a coordinate in the transition path ensemble. Where displacing a bath mode invokes essentially no cost, it costs significantly to move the reaction coordinate. Based on some general assumptions of the behaviors of reaction and bath coordinates in the transition path ensemble, we proved theoretically with statistical mechanics that the emergent potential energy could serve as a benchmark of reaction coordinates and demonstrated its effectiveness by applying it to a prototypical system of biomolecular dynamics. Using the emergent potential energy as guidance, we developed a committor-free and intuition-independent method for identifying reaction coordinates in complex systems. We expect this method to be applicable to a wide range of reaction processes in complex biomolecular systems.