On the use of local diffusion models for path ensemble averaging in potential of mean force computations

We use a constant velocity steered molecular dynamics (SMD) simulation of the stretching of deca-alanine in vacuum to demonstrate a technique that can be used to create a surrogate processes approximation (SPA) using the time series that come out of SMD simulations. In this article, the surrogate processes are constructed by first estimating a sequence of local parametric diffusion models along a SMD trajectory and then a single global model is constructed by piecing the local models together through smoothing splines (estimation is made computationally feasible by likelihood function approximations). The SPAs are then "bootstrapped" in order to obtain a plausible range of work values associated with a particular SMD realization. This information is then used to assist in estimating a potential of mean force constructed by appealing to the Jarzynski equality. When this procedure is repeated for a small number of SMD paths, it is shown that the global models appear to come from a single family of closely related diffusion processes. Possible techniques for exploiting this observation are also briefly discussed. The findings of this paper have potential relevance to computationally expensive computer simulations and experimental works involving optical tweezers where it is difficult to collect a large number of samples, but possible to sample accurately and frequently in time.