Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains

Abstract

The topic of the present paper has been motivated by a recent computational approach to identify metastable chemical conformations and patterns of conformational changes within molecular systems. After proper discretization, such conformations show up as almost invariant aggregates in reversible, nearly uncoupled Markov chains (NUMCs). Most of the former work on this subject treated the direct problem: given the aggregates, analyze the loose coupling in connection with the computation of the stationary distribution (aggregation/disaggregation techniques). In contrast to that, the present paper focuses on the inverse problem: given the system as a whole, identify the almost invariant aggregates together with the (small) probabilities of transitions between them. A robust algorithm is worked out on the basis of some detailed perturbation analysis and illustrated at a simple molecular system.