Open Access

Han Cheng Lie, Konstantin Fackeldey, Marcus Weber

• Trajectory- or mesh-based methods for analyzing the dynamical behavior of large molecules tend to be impractical due to the curse of dimensionality - their computational cost increases exponentially with the size of the molecule. We propose a method to break the curse by a novel square root approximation of transition rates, Monte Carlo quadrature and a discretization approach based on solving linear programs. With randomly sampled points on the molecular energy landscape and randomly generated discretizations of the molecular con� guration space as our initial data, we construct a matrix describing the transition rates between adjacent discretization regions. This transition rate matrix yields a Markov State Model of the molecular dynamics. We use Perron cluster analysis and coarse-graining techniques in order to identify metastable sets in con� guration space and approximate the transition rates between the metastable sets. Application of our method to a simple energy landscape on a two-dimensional con� guration space provides proof of concept and an example for which we compare the performance of di� erent discretizations. We show that the computational cost of our method grows only polynomially with the size of the molecule. However, � nding discretizations of higher-dimensional con� guration spaces in which metastable sets can be identi� ed remains a challenge.