Parameter-free prediction of DNA dynamics in planar extensional flow of semidilute solutions

The dynamics of individual DNA molecules in semidilute solutions undergoing planar extensional flow is simulated using a multi-particle Brownian dynamics algorithm, which incorporates hydrodynamic and excluded volume interactions in the context of a coarse-grained bead-spring chain model for DNA. The successive fine-graining protocol [1, 2], in which simulation data acquired for bead-spring chains with increasing values of the number of beads $N_b$, is extrapolated to the number of Kuhn steps $N_\text{K}$ in DNA (while keeping key physical parameters invariant), is used to obtain parameter-free predictions for a range of Weissenberg numbers and Hencky strain units. A systematic comparison of simulation predictions is carried out with the experimental observations of [3], who have recently used single molecule techniques to investigate the dynamics of dilute and semidilute solutions of $\lambda$-phage DNA in planar extensional flow. In particular, they examine the response of individual chains to step-strain deformation followed by cessation of flow, thereby capturing both chain stretch and relaxation in a single experiment. The successive fine-graining technique is shown to lead to quantitatively accurate predictions of the experimental observations in the stretching and relaxation phases. Additionally, the transient chain stretch following a step strain deformation is shown to be much smaller in semidilute solutions than in dilute solutions, in agreement with experimental observations.