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

Abstract

A multiresolution 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 updated only at integer multiples of the timesteps associated with its connecting springs. This approach extends the Rouse model to a multiresolution 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 modeling 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.