Varying the resolution of the Rouse model on temporal and spatial
scales: application to multiscale modelling of DNA dynamics

A multi-resolution bead-spring model for polymer dynamics is developed as a
generalization of the Rouse model. A polymer chain is described using beads of
variable sizes connected by springs with variable spring constants. A numerical
scheme which can use different timesteps to advance the positions of different
beads is presented and analyzed. The position of a particular bead is only
updated at integer multiples of the timesteps associated with its connecting
springs. This approach extends the Rouse model to a multiscale model on both
spatial and temporal scales, allowing simulations of localized regions of a
polymer chain with high spatial and temporal resolution, while using a coarser
modelling approach to describe the rest of the polymer chain. A method for
changing the model resolution on-the-fly is developed using the
Metropolis-Hastings algorithm. It is shown that this approach maintains key
statistics of the end-to-end distance and diffusion of the polymer filament and
makes computational savings when applied to a model for the binding of a
protein to the DNA filament.