TY - JOUR
T1 - Hierarchical Nyström methods for constructing Markov state models for conformational dynamics
AU - Yao, Yuan
AU - Cui, Raymond Z.
AU - Bowman, Gregory R.
AU - Silva, Daniel Adriano
AU - Sun, Jian
AU - Huang, Xuhui
PY - 2013/5/7
Y1 - 2013/5/7
N2 - 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 macrostate 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 Nyström 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 peptide.
AB - 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 macrostate 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 Nyström 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 peptide.
UR - http://www.scopus.com/inward/record.url?scp=84877781129&partnerID=8YFLogxK
U2 - 10.1063/1.4802007
DO - 10.1063/1.4802007
M3 - Article
C2 - 23656113
AN - SCOPUS:84877781129
SN - 0021-9606
VL - 138
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 17
M1 - 174106
ER -