Molecular Sieving in Periodic Free-Energy Landscapes Created by Patterned Nanofilter Arrays

We present an experimental study of Ogston-like sieving process of rodlike DNA in patterned periodic nanofluidic filter arrays. The electrophoretic motion of DNA through the array is described as a biased Brownian motion overcoming periodically modulated free-energy landscape. A kinetic model, constructed based on the equilibrium partitioning theory and the Kramers theory, explains the field-dependent mobility well. We further show experimental evidence of the crossover from Ogston-like sieving to entropic trapping, depending on the ratio between nanofilter constriction size and DNA size.

Figure 1

(a) Partitioning of rigid, rodlike DNA across a nanofilter that consists of a deep region ($d_{\mathrm{d}}$) and a shallow region ($d_{\mathrm{s}}$) of equal length. The period and width of one nanofilter is $p$ and $w$, respectively. (b) Free-energy landscapes experienced by DNA while crossing a nanofilter (the black curve shows $E=0$, and the gray curve, $E_{\mathrm{av}}>0$). $E_{\mathrm{s}}$, $E_{\mathrm{d}}$ are electric fields in shallow and deep regions, respectively. $E_{\mathrm{av}}$ is the average electric field over the nanofilter. DNA preserve the free draining property in the shallow and deep region, resulting in the slopes for both regions proportional solely to the local electric field. (c) SEM images of alternating deep (300 nm) and shallow (55 nm) regions. $p=2\mu \mathrm{m}$.

Figure 2

(a) 100-bp DNA ladder separated in a nanofilter array ($d_{\mathrm{s}}=80\mathrm{nm}$, $d_{\mathrm{d}}=580\mathrm{nm}$, and $p=4\mu \mathrm{m}$). Electropherograms (jagged gray line) were taken 1 cm from the injection point. Gaussian functions [smooth gray line (red online)] were used for fitting and the black bars label the peak widths [$\pm$ standard deviation (SD)]. (b) Relative mobility ${\mu }^{*}$ of 100-bp DNA ladder with solid fitting curves. The $\pm \mathrm{SD}$ of ${\mu }^{*}$ derived from the half peak width are all less than 4%, so statistical error bars for ${\mu }^{*}$ are not plotted. The inset shows the best fitting constant $\alpha$ for different field strengths. $\alpha$ has a mean about 8684 and a $\pm \mathrm{SD}$ about 3%. Mean trapping time ${\tau }_{\mathrm{trap}}$ (c) and relative mobility ${\mu }^{*}$ (d) with the best fitting curves; ${\tau }_{\mathrm{trap}}$ and ${\mu }^{*}$ were measured for low molecular weight DNA ladder in a nanofilter array with $d_{\mathrm{s}}=55\mathrm{nm}$, $d_{\mathrm{d}}=300\mathrm{nm}$, and $p=1\mu \mathrm{m}$. Separation length was 5 mm and ${\tau }_{\mathrm{trap}}=T_{\mathrm{travel}}/5000-{\tau }_{\mathrm{travel}}$. The $\pm \mathrm{SD}$ of ${\mu }^{*}$ are all less than 6%, so statistical error bars for ${\mu }^{*}$ are not plotted. The inset shows $\alpha$ with a mean about 1990 and a $\pm \mathrm{SD}$ about 13%. All the fitting curves in (b), (c), (d) are calculated with $q=2.49\times {10}^{-21}\mathrm{J}/\mathrm{V}\mathrm{bp}$, $l_p=53\mathrm{nm}$, and $l=0.36N\mathrm{nm}$.

Figure 3

Mobility $\mu$ as a function of DNA length. DNA fragments were extracted after agarose gel separation. The nanofilter array has $d_{\mathrm{s}}=73\mathrm{nm}$, $d_{\mathrm{d}}=325\mathrm{nm}$, $p=1\mu \mathrm{m}$. The relative large statistical error bars (drawn if larger than the symbol) are likely due to the low DNA concentrations. The left and right shaded (gray and yellow online) areas indicate Ogston sieving and entropic trapping, respectively. The transition points are marked with the vertical dashed line drawn for DNA $\mathrm{\text{length}}=1.5\mathrm{kbp}$.