Polymer reversal rate calculated via locally scaled diffusion map

A recent study on the dynamics of polymer reversal inside a nanopore by Huang and Makarov [J. Chem. Phys. 128, 114903 (2008)] demonstrated that the reaction rate cannot be reproduced by projecting the dynamics onto a single empirical reaction coordinate, a result suggesting the dynamics of this system cannot be correctly described by using a single collective coordinate. To further investigate this possibility we have applied our recently developed multiscale framework, locally scaled diffusion map (LSDMap), to obtain collective reaction coordinates for this system. Using a single diffusion coordinate, we obtain a reversal rate via Kramers expression that is in good agreement with the exact rate obtained from the simulations. Our mathematically rigorous approach accounts for the local heterogeneity of molecular configuration space in constructing a diffusion map, from which collective coordinates emerge. We believe this approach can be applied in general to characterize complex macromolecular dynamics by providing an accurate definition of the collective coordinates associated with processes at different time scales.