  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.
