  Markov state models (MSMs) have become a popular approach for investigating
the conformational dynamics of proteins and other biomolecules. MSMs are
typically built from numerous molecular dynamics simulations by dividing the
sampled configurations into a large number of microstates based on geometric
criteria. The resulting microstate model can then be coarse-grained into a more
understandable macro state model by lumping together rapidly mixing microstates
into larger, metastable aggregates. However, finite sampling often results in
the creation of many poorly sampled microstates. During coarse-graining, these
states are mistakenly identified as being kinetically important because
transitions to/from them appear to be slow. In this paper we propose a
formalism based on an algebraic principle for matrix approximation, i.e. the
Nystrom method, to deal with such poorly sampled microstates. Our scheme builds
a hierarchy of microstates from high to low populations and progressively
applies spectral clustering on sets of microstates within each level of the
hierarchy. It helps spectral clustering identify metastable aggregates with
highly populated microstates rather than being distracted by lowly populated
states. We demonstrate the ability of this algorithm to discover the major
metastable states on two model systems, the alanine dipeptide and TrpZip2.

Biomolecules;Applications