Markov State Models for Rare Events in Molecular Dynamics

Rare but important transition events between long lived states are a key feature 1 of many molecular systems. In many cases the computation of rare event statistics by direct 2 molecular dynamics (MD) simulations is infeasible even on the most powerful computers 3 because of the immensely long simulation timescales needed. Recently a technique for 4 spatial discretization of the molecular state space designed to help overcome such problems, 5 so-called Markov State Models (MSMs), has attracted a lot of attention. We review the 6 theoretical background and algorithmic realization of MSMs and illustrate their use by some 7 numerical examples. Furthermore we introduce a novel approach to using MSMs for the 8 efficient solution of optimal control problems that appear in applications where one desires 9 to optimize molecular properties by means of external controls. 10