One-dimensional reaction coordinate and the corresponding potential of mean force from commitment probability distribution

In general, finding a one-dimensional representation of the kinetics of a high-dimensional system is a great simplification for the study of complex systems. Here, we propose a method to obtain a reaction coordinate whose potential of the mean force can reproduce the commitment probability distribution from the multidimensional surface. We prove that such a relevant one-dimensional representation can be readily calculated from the equilibrium distribution of commitment probabilities, which can be obtained with simulations. Also, it is shown that this representation is complementary to a previously proposed one-dimensional representation based on a quadratic approximation of the potential energy surface. The usefulness of the method is examined with dynamics in a two-dimensional system, showing that the one-dimensional surface thus obtained can predict the existence of an intermediate and the occurrence of path switching without a priori knowledge of the morphology of the original surface. The applicability of the method to more complex and realistic reactions such as protein folding is also discussed.