Conformation and trapping rate of DNA at a convergent stagnation point

We use a lattice-Boltzmann based Brownian dynamics simulation to investigate the elongation of DNA at a convergent stagnation point trapped by a uniform attractive potential. The trapping rate of the DNA is not sensitive to the potential and, consistent with a mean field theory, scales as the Peclet number, ${\mathrm{Pe}}^{1∕3}$. Surprisingly, we find that the coiled state is favored over the stretched state at high Pe. The final elongation is determined by conformation changes during transport to the stagnation point, rather than hydrodynamic stretching at that point.

Figure 1

Simulation setup, not to scale. Indicated are the region where the trapping force is active (trap region) and its width $\left(Y_{\mathit{\text{stick}}}\right)$, and the region used to determine the trapping rate (stagnation region).

Figure 2

Snapshot of the location of polymers for (a) $\mathrm{Pe}=3100$ and (b) $\mathrm{Pe}=370$ in the steady state. Arrows indicate the direction of fluid flow. Grayscale is used to indicate monomers of the same polymer. Insets: Mean square displacement in lattice units, $\Delta x$, of monomers in the (a) bundle and (b) fountain configuration. The time difference is normalized by ${\tau }_r$. The error in the inset curves are of the order of the linewidth.

Figure 3

Average spring extension $\Delta r_s$ normalized by the lattice spacing $\Delta x$ for different trapping conditions: $Y_{\mathit{\text{stick}}}=10\Delta x$ and circles (●): $K_{\mathit{\text{stick}}}=0.25$, squares (◼): $K_{\mathit{\text{stick}}}=0.5$, stars (⋆): $K_{\mathit{\text{stick}}}=0.75$, and diamonds (◇): specific sticking force that acts only on the chain end. The inset shows results for different $Y_{\mathit{\text{stick}}}$: diamonds (◆): $Y_{\mathit{\text{stick}}}=1\Delta x$, $K_{\mathit{\text{stick}}}=0.75$, and $N_p=5$; asterisk (∗): $Y_{\mathit{\text{stick}}}=5\Delta x$ and $K_{\mathit{\text{stick}}}=0.50$; and squares (◼): $Y_{\mathit{\text{stick}}}=10\Delta x$ and $K_{\mathit{\text{stick}}}=0.50$. The error in average extension between data subsets (two sets of ten chains) is less than 5%. The extension of an individual polymer varies between 20% and 85% of the total chain length as the chain dynamics evolve in the flow.

Figure 4

Number of monomers trapped in the initial $8.8\times {10}^{-2}\mathrm{s}$, $r$, normalized by the total number of monomers, $N_{\mathit{\text{bead}}}$, vs Pe on a log-log plot. Symbols are equivalent to those in Fig. 3. The dashed line has a slope of 0.36. The inset shows the same data on a linear plot.