Foldamer dynamics expressed via Markov state models. II. State space decomposition.

Sidney Elmer, Sanghyun Park, & Vijay S. Pande.
Journal of Chemical Physics (2005)

SUMMARY: Here, we lay out some new methodology for simulation for future FAH calculations. This new method, Markovian State Models (MSM), allows FAH to solve some important limitations of previous methods. Since these limitations are most relevant for larger and more complex systems than what has been done in FAH so far, this does not affect the work in the past. However, it lays the foundation for FAH to tackle even more complex and challenging problems.

TECHNICAL ABSTRACT: The structural landscape of poly-phenylacetylene (pPA), otherwise known as m-phenylene ethynylene oligomers, has been shown to consist of a very diverse set of conformations, including helices, turns, and knots. Defining a state space decomposition to classify these conformations into easily identifiable states is an important step in understanding the dynamics in relation to Markov state models. We define the state decomposition of pPA oligomers in terms of the sequence of discretized dihedral angles between adjacent phenyl rings along the oligomer backbone. Furthermore, we derive in mathematical detail an approach to further reduce the number of states by grouping symmetrically equivalent states into a single parent state. A more challenging problem requires a formal definition for knotted states in the structural landscape. Assuming that the oligomer chain can only cross the ideal helix path once, we propose a technique to define a knotted state derived from a helical state determined by the position along the helical nucleus where the chain crosses the ideal helix path. Several examples of helical states and knotted states from the pPA 12-mer illustrate the principles outlined in this article.