Statics and Dynamics of Single DNA Molecules Confined in Nanochannels

The successful design of nanofluidic devices for the manipulation of biopolymers requires an understanding of how the predictions of soft condensed matter physics scale with device dimensions. Here we present measurements of DNA extended in nanochannels and show that below a critical width roughly twice the persistence length there is a crossover in the polymer physics.

Figure 1

(a) A confined polymer in the de Gennes regime: $D\gg P$. The molecule can be subdivided equally into a series of blobs with contour length $L_b$; the stretch arises from the mutual repulsion of the blobs. (b) A confined polymer in the Odijk regime: $D\ll P$.

Figure 2

(a) Cross-sectional scanning electron micrographs of $30\times 40\mathrm{nm}$ nanoimprinted channels and (b) $60\times 80\mathrm{nm}$ nanoimprinted channels. The channels are shown sealed to a fused silica coverslip (the sealing was accomplished via direct quartz-quartz bonding). Imprinted nanochannels are densely packed with a periodicity of 200 nm and width that can be varied from 150 to 35 nm using a novel trilayer technique (wider channels can also be fabricated with a correspondingly higher period) [18].

Figure 3

(a) Time evolution of intensity stripe for a $\lambda$-phage DNA molecule in a 60 nm channel. (b) Autocorrelated extension fluctuation extracted from the molecule shown in (a) with exponential fit. (c) Time evolution of intensity stripe for a $\lambda$-phage DNA molecule in a 180 nm channel. (d) Autocorrelated extension fluctuation for the molecule shown in (c) with exponential fit. The black dots at the stripe edges in figures (a) and (c) represent the edges of the molecules determined via an edge-finding algorithm.

Figure 4

(a) Averaged intensity of selected T2 DNA molecules in $30\times 40\mathrm{nm}$, $60\times 80\mathrm{nm}$, $80\times 80\mathrm{nm}$, $140\times 130\mathrm{nm}$, $230\times 150\mathrm{nm}$, $300\times 440\mathrm{nm}$, and $440\times 440\mathrm{nm}$ channels (left to right). (b) Averaged intensity of selected $\lambda$-DNA molecules in the same channels.

Figure 5

Log-log plot of $\lambda$-DNA extension as a function of $D_{\mathrm{av}}$, the geometric average of the channel depth and height. The DNA extension is normalized to the (dye-adjusted) total contour length of $18.63\mu \mathrm{m}$. The bold line is a best power-law fit to the data for the 440, 300, 230 , 140, 80, and 60 nm wide channels (the best fit exponent is $-0.85\pm 0.05$). The dashed line is the Odijk prediction, which fits to the three smallest channels with a persistence length of $52\pm 5\mathrm{nm}$, in agreement with the dye-adjusted persistence length of $57.5\pm 2\mathrm{nm}$.

Figure 6

Log-log plot of $\lambda$-DNA relaxation time as a function of $D_{\mathrm{av}}$, the geometric average of the channel depth and height. The data points shown are averages over all the relaxation times measured for molecules in a given width. Shown superimposed is a best power-law fit to the data taken for channels greater than 140 nm (bold curve) and a fit to the model $\tau \sim \frac{D^{\alpha }}{\log (D/w)}$ for channel widths less than 140 nm (dashed curve). The de Gennes theory underestimates the scaling exponent: the best fit exponent for the large channel widths is $-0.9\pm 0.4$. The best fit exponent for the small widths is $\alpha =1.6\pm 0.4$.