Metastable Conformations via successive Perron-Cluster Cluster Analysis of dihedrals

Decomposition of the high dimensional conformational space of biomolecules into metastable subsets is used for data reduction of long molecular trajectories in order to facilitate chemical analysis and to improve convergence of simulations within these subsets. The metastability is identified by the Perron-Cluster Cluster Analysis of a Markov process that describes the thermodynamic distribution. A necessary prerequisite of this analysis is the discretization of the conformational space. A combinatorial approach via discretization of each degree of freedom will end in the so called ”curse of dimension”. In the following paper we analyze Hybrid Monte Carlo simulations of small, drug-like biomolecules and focus on the dihedral degrees of freedom as indicators of conformational changes. To avoid the ”curse of dimension”, the projection of the underlying Markov operator on each dihedral is analyzed according to its metastability. In each decomposition step of a recursive procedure, those significant dihedrals, which indicate high metastability, are used for further decomposition. The procedure is introduced as part of a hierarchical protocol of simulations at different temperatures. The convergence of simulations within metastable subsets is used as an ”a posteriori” criterion for a successful identification of metastability. All results are presented with the visualization program AmiraMol. K e y words . metastability, Perron-Cluster Cluster Analysis, curse of d i mension, Hybrid Monte Carlo, significant dihedrals Ma themat i cs subject classi f icat ion. 65U05, 62H30.