Giant Acceleration of DNA Diffusion in an Array of Entropic Barriers

We investigate with experiments and computer simulations the nonequilibrium dynamics of DNA polymers crossing arrays of entropic barriers in nanofluidic devices in a pressure-driven flow. With increasing driving pressure, the effective diffusivity of DNA rises and then peaks at a value that is many times higher than the equilibrium diffusivity. This is an entropic manifestation of “giant acceleration of diffusion.” The phenomenon is sensitive to the effective energy landscape; thus, it offers a unique probe of entropic barriers in a system driven away from equilibrium.

Figure 1

(a) Sketch of a tilted periodic energy landscape. (b) Illustration of a nanopit array embedded in a nanoslit, with DNA hopping from pit to pit. (c) Side view of the nanofluidic geometry indicating $h$, $H$, and $a$. A simulated polymer hops between pits under an applied drive of $v=0.05$. (d) Time-sliced fluorescence images of $\lambda$ DNA climbing a column of high-barrier pits ($h=75\mathrm{nm}$, $H=124\mathrm{nm}$) for $\mathrm{\Delta }p=400\mathrm{mbar}$. (e) DNA trajectories from the same experiment. The dashed line indicates $\mathrm{\Delta }y=v_{p}t$ ($v_p=0.7\mu \mathrm{m}{\mathrm{s}}^{-1}$).

Figure 2

Dependence of MSD on $\tau$ in (a) the device with low barriers for $\mathrm{\Delta }p=250$ (A), 140 (B), 90 (C), and 60 mbar (D). And in (b) the device with high barriers for $\mathrm{\Delta }p=750$ (i), 650 (ii), 555 (iii), and 400 mbar (iv). The corresponding $D/D_0$ and $v_s$ are indicated in (c). The dashed line has a slope of 1. (c) Dependence of $D/D_0$ on $v_s$ for low (blue dots) and high (red squares) barriers with $\tau =2\mathrm{s}$. Error bars are the standard error from a bootstrap analysis of 200 resamplings of the full data set.

Figure 3

Dependence of $D/D_0$ on $v_s/v_c-1$ in devices with high (red squares) and low (blue dots) barriers, and for simulation data (diamonds). The lines are fits of Eq. (5) to the corresponding data, with fit parameters $\mu$ and $F_c$.

Figure 4

(a) Side view of a simulated polymer inside a nanfluidic device, near the critical point, with $v=0.05$. (b) Effective force landscapes $-d\mathrm{\Psi }(y)/dy$ for $v=0.04$, 0.05, and 0.06 (labeled curves), computed from Eq. (8). The position axis is aligned with the nanofluidic geometry in (a). The inset shows an expanded view of the force landscape around the critical point. The dashed line indicates zero force.

Figure 5

Dependence of $v_p/v_0$ on $F/F_c$ in devices with high (red squares) and low (blue dots) barriers, and simulation data (black diamonds). The corresponding lines plot Eq. (9) using the fit values of $\mu$ and $F_c$. The dot-dashed line shows $v_p/v_0=1$.