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

TL;DR

This paper introduces a multiscale bead-spring model for polymer dynamics, extending the Rouse model to allow variable spatial and temporal resolutions, enabling efficient and accurate DNA simulations with localized detail.

Contribution

It develops a generalized multiscale Rouse model with variable bead sizes and spring constants, and a dynamic resolution adjustment method using Metropolis-Hastings.

Findings

Maintains key polymer statistics with multiscale modeling.

Enables computational savings in DNA-protein binding simulations.

Allows localized high-resolution modeling within a coarser polymer framework.

Abstract

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.