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Markov state models (MSMs) have become a popular approach for investigatingthe conformational dynamics of proteins and other biomolecules. MSMs aretypically built from numerous molecular dynamics simulations by dividing thesampled configurations into a large number of microstates based on geometriccriteria. The resulting microstate model can then be coarse-grained into a moreunderstandable macro state model by lumping together rapidly mixing microstatesinto larger, metastable aggregates. However, finite sampling often results inthe creation of many poorly sampled microstates. During coarse-graining, thesestates are mistakenly identified as being kinetically important becausetransitions to/from them appear to be slow. In this paper we propose aformalism based on an algebraic principle for matrix approximation, i.e. theNystrom method, to deal with such poorly sampled microstates. Our scheme buildsa hierarchy of microstates from high to low populations and progressivelyapplies spectral clustering on sets of microstates within each level of thehierarchy. It helps spectral clustering identify metastable aggregates withhighly populated microstates rather than being distracted by lowly populatedstates. We demonstrate the ability of this algorithm to discover the majormetastable states on two model systems, the alanine dipeptide and TrpZip2.

Hierarchical Nystrom Methods for Constructing Markov State Models for Conformational Dynamics