Nonparametric Determination of the Committor in Multimolecular Systems

A fundamental problem in analyzing large longitudinal data sets modeling dynamics in multimolecular systems is determining the underlying free-energy landscapes as a function of the committor, the optimal reaction coordinate. Here, we demonstrate that by combining a nonparametric approach with a systematic method for generating permutationally invariant collective variables, the committor can be effectively determined to describe multimolecular aggregation in a system with anisotropic interactions. The optimality of the committor is verified by a stringent validation test, and it is shown that the diffusive model along the committor yields kinetic properties identical to those derived from the original dynamics. Our method is general and relevant to the large machine learning community developing methods to determine the committor from longitudinal data sets.