Hierarchical analysis of conformational dynamics in biomolecules: Transition networks of metastable states

Molecular dynamics simulation generates large quantities of data that must be interpreted using physically meaningful analysis. A common approach is to describe the system dynamics in terms of transitions between coarse partitions of conformational space. In contrast to previous work that partitions the space according to geometric proximity, the authors examine here clustering based on kinetics, merging configurational microstates together so as to identify long-lived, i.e., dynamically metastable, states. As test systems microsecond molecular dynamics simulations of the polyalanines $Ala8$ and $Ala12$ are analyzed. Both systems clearly exhibit metastability, with some kinetically distinct metastable states being geometrically very similar. Using the backbone torsion rotamer pattern to define the microstates, a definition is obtained of metastable states whose lifetimes considerably exceed the memory associated with interstate dynamics, thus allowing the kinetics to be described by a Markov model. This model is shown to be valid by comparison of its predictions with the kinetics obtained directly from the molecular dynamics simulations. In contrast, clustering based on the hydrogen-bonding pattern fails to identify long-lived metastable states or a reliable Markov model. Finally, an approach is proposed to generate a hierarchical model of networks, each having a different number of metastable states. The model hierarchy yields a qualitative understanding of the multiple time and length scales in the dynamics of biomolecules.