Multiscale simulations of dilute-solution macromolecular dynamics in macroscopic and microscopic geometries

A Brownian model of DNA is developed and shown to give results in quantitative agreement with available equilibrium and non-equilibrium experimental data. A fast, accurate method of calculating the Langevin forces on the molecule is presented, as well as a semi-implicit stochastic integration scheme which allows for the use of reasonable time steps.; A new method is developed for the simulation of polymer dynamics in macroscopic devices. The method involves a splitting of the diffusion equation into internal configuration and convective fluxes. The internal configuration of the microstructure is evolved via stochastic simulation to give a δ-function representation of the distribution function. The convective update of the distribution function is performed in an orthogonal polynomial representation, taking advantage of the natural hierarchy of length scales present in the problem. We find that convective update can performed accurately by considering only the large length scale contributions.; A general method is developed for dynamic simulations of macromolecules in confined geometries. At equilibrium, we examine the stretch, diffusivity and relaxation time of DNA as a function of channel width and molecular weight. The ratio of these properties to their free-solution values form master curves when plotted against S_b/H. Scaling laws are obtained for highly confined chains. In pressure-driven flow, the DNA chains migrate toward the channel centerline in agreement with well-known experimental observations. The thickness of the resulting hydrodynamic depletion layer increases with molecular weight at constant flow strength; higher molecular weight chains therefore move with a higher average axial velocity than lower molecular weight chains. A simple kinetic theory dumbbell model of a confined flexible polymer correctly predicts the trends observed in the detailed simulations. We also examine the steady-state stretch of DNA chains as a function of channel width and flow strength. The flow strength needed to stretch a highly confined chain away from its equilibrium length is shown to increase with decreasing channel width, independent of molecular weight; this is fairly well-explained using a simple blob picture.