Dynamic coupling between coordinates in a model for biomolecular isomerization

Abstract

To understand a complex reaction, it is necessary to project the dynamics of the system onto a low-dimensional subspace of physically meaningful coordinates. We recently introduced an automatic method for identifying coordinates that relate closely to stable-state commitment probabilities and successfully applied it to a model for biomolecularisomerization, the C 7 eq → α R transition of the alanine dipeptide [A. Ma and A. R. Dinner, J. Phys. Chem. B109, 6769 (2005)]. Here, we explore approximate means for estimating diffusiontensors for systems subject to restraints in one and two dimensions and then use the results together with an extension of Kramers theory for unimolecular reaction rates [A. Berezhkovskii and A. Szabo, J. Chem. Phys.122, 014503 (2005)] to show explicitly that both the potential of mean force and the diffusiontensor are essential for describing the dynamics of the alanine dipeptide quantitatively. In particular, the signficance of off-diagonal elements of the diffusiontensor suggests that the coordinates of interest are coupled by the hydrodynamic-like response of the bath of remaining degrees of freedom.