  The surrogate process approximation (SPA) is applied to model the
nonequilibrium dynamics of a reaction coordinate (RC) associated with the
unfolding and refolding processes of a deca-alanine peptide at 300 K. The RC
dynamics, which correspond to the evolution of the end-to-end distance of the
polypeptide, are produced by steered molecular dynamics (SMD) simulations and
approximated using overdamped diffusion models. We show that the collection of
(estimated) SPA models contain structural information "orthogonal" to the RC
monitored in this study. Functional data analysis ideas are used to correlate
functions associated with the fitted SPA models with the work done on the
system in SMD simulations. It is demonstrated that the shape of the
nonequilibrium work distributions for the unfolding and refolding processes of
deca-alanine can be predicted with functional data analysis ideas using a
relatively small number of simulated SMD paths for calibrating the SPA
diffusion models.
