Tethered DNA shear dynamics in the flow gradient plane: application to double tethering

We examine the wall contact of a $3\;{\mu}m$ tethered DNA chain's free end under shear with a focus on developing schemes for double-tethering in the application of making scaffolds for molecular wires. At this scale our results are found to be highly dependent on small length scale rigidity. Chain-end-wall contact frequency, mean fractional extension deficit upon contact, and standard deviation in extension upon contact are examined for scaling with dimensionless flow strength, Wi. Predictions made using a one dimensional approximation to the Smoluchowski equation for a dumbbell and three dimensional dumbbell simulations produce extension deficit, standard deviation, and frequency scaling exponents of -1/3, -1/3, and 2/3, respectively whereas more fine-grained Kratky-Porod (KP) simulations produce scaling exponents of -0.48, -0.42, and 0.76. The contact frequency scaling of 2/3 is derived from the known results regarding cyclic dynamics Analytical scaling predictions are in agreement with those previously proposed for ${\lambda}-DNA$. [Ladoux and Doyle, 2000, Doyle et al., 2000]. Our results suggest that the differences between the dumbbell and the KP model are associated with the addition of chain discretization and the correct bending potential in the latter. These scaling results will aide future exploration in double tethering of DNA to a surface.