The mechanism of the self-assembly of associating DNA molecules under shear flow: Brownian dynamics simulation

A shear flow induces the assembly of DNAs with the sticky spots. In order to strictly interpret the mechanism of shear-induced DNA assembly, Brownian dynamics simulations with the bead-spring model were carried out for these molecules at various ranges of the Weissenberg numbers (We). We calculate a formation time and analyze the radial distribution function of end beads and the probability distribution of fractional extension at the formation time to understand the mechanism of shear-induced assembly. At low Weissenberg number the formation time, which is defined as an elapsed time until a multimer forms for the first time, decreases rapidly, reaching a plateau at We = 1000. A shear flow changes the radial distribution of end beads, which is almost the same regardless of the Weissenberg number. A shear flow deforms and stretches the molecules and generates different distributions between end beads with a stickly spot. The fractional extension progresses rapidly in shear flow from a Gaussian-like distribution to a uniform distribution. The progress of the distribution of fractional extension increases the possibility of meeting of end beads. In shear flow, the inducement of the assembly mainly results from the progress of the probability distribution of fractional extension. We also calculate properties such as the radius of gyration, stretch, and so on. As the Weissenberg number increases, the radius of gyration at the formation time also increases rapidly, reaching a plateau at We = 1000.