A coarse graining method for the identification of transition rates between molecular conformations

The coarse graining method to be advocated in this paper consists of two main steps. First, the propagation of an ensemble of molecular states is described as a Markov chain by a transition probability matrix in a finite state space. Second, we obtain metastable conformations by an aggregation of variables via Robust Perron Cluster Analysis (PCCA+). Up to now, it has been an open question as to how this coarse graining in space can be transformed to a coarse graining of the Markov chain while preserving the essential dynamic information. In this article, we construct a coarse matrix that is the correct propagator in the space of conformations. This coarse graining procedure carries over to rate matrices and allows to extract transition rates between molecular conformations. This approach is based on the fact that PCCA+ computes molecular conformations as linear combinations of the dominant eigenvectors of the transition matrix.