An experimental study of Ogston-like sieving process of rod-like DNA in patterned periodic nanofilter arrays is performed in this project. 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' rate 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.

The electrophoretic drift of DNA across the nanofilter is essentially an electric-field-driven partitioning process. Compared with the high-entropy deep region, the limited DNA configurational space inside the shallow region creates a configurational entropic barrier for DNA passage at the abrupt interface between the deep and shallow regions. This configurational entropic barrier originates from the steric constraints that prevent a partial overlap of DNA with the wall, and is different from the conformational entropic barrier associated with deformation and entropic elasticity. The configurational entropic barrier can be calculated analytically with the equilibrium partitioning theory, by assuming short DNA molecules as rigid, thin rod-like molecules.

The motion of DNA through the nanofilter array can be further described as a biased thermally activated process overcoming periodically modulated free energy barriers [see Fig. 1 in the section of Patterned one-dimensional periodic nanofilter array for size-separation of biomolecules]. The free energy landscape U tilted by the electric field Eav contains local maxima (barriers) and minima (traps), similar to a double well potential. From a simplified version of the Kramers' rate theory, we can calculate the escape transition rate for DNA to surmount the barrier kesc and the mean trapping time ttrap. Therefore, we can further compare measured DNA mobility through the nanofilter array with our theoretical calculation (Fig. 1).

Fig. 1 (a) 100-bp DNA ladder separated in a nanofilter array (ds = 80 nm, dd = 580 nm, and p = 4 µm). Electropherograms (grey) were taken 1 cm from the injection point. Gaussian functions (red) were used for fitting and the black bars label the peak widths (±s.d.). (b) Relative mobility µ * of 100 bp DNA ladder with solid fitting curves. (c-d) Mean trapping time ttrap (c) and relative mobility µ* (d) with the best fitting curves. ttrap and µ* were measured for low molecular weight DNA ladder in a nanofilter array with ds = 55 nm, dd = 300 nm, and p = 1 µm. Separation length was 5 mm.

The experimental data in Fig. 1 deviated slightly from the theoretical curves as the DNA length increases to several persistence lengths. This is expected since for long DNA, other degrees of entropic freedom, such as internal conformation, become non-negligible in the kinetics of crossing the nanofilter barriers. The (conformational) entropic trapping mechanism was used to explain s eparation of long DNA (>5 kbp) in similar intervening entropic barriers where longer DNA were found to advance faster than shorter ones because of their greater hernia nucleation possibility. We demonstrate the crossover from Ogston sieving to entropic trapping by measuring mobility of DNA of a size ranging from 0.5 - 8 kbp in a 73 nm nanofilter array. T he radius of gyration Rg of these DNA, estimated from the Kratky-Porod model, span a range of 40 - 220 nm, covering the region around Rg/ds ~ 1. Figure 2 clearly shows two distinct sieving regimes as evidenced by the valleys existing on the mobility curves. The left side of the valley is Ogston sieving, and mobility decreases as DNA length increases. The right side shows evidence of entropic trapping, and mobility increases with DNA length.

Fig. 2 Mobility as a function of DNA length. DNA fragments were extracted after agarose gel separation. The nanofilter array has ds = 73 nm, dd = 325 nm, p = 1 µm. The relative large statistical error bars (drawn if larger than the symbol) is likely due to the low DNA concentrations. The grey and yellow areas indicate Ogston sieving and entropic trapping, respectively. The transition points are marked with the vertical dashed line drawn for DNA length = 1.5 kbp.

References

1. Fu, J., Yoo, J. & Han, J. Phys. Rev. Lett. 97, 018103.1-3 (2006). (pdf‡)
2. Fu, J. & Han, 2005 Gordon Research Conf. on the Physics and Chemistry of Microfluidics, Oxford, UK.
3. Fu, J. & Han, J. American Physical Society National March Meeting 2006, Baltimore, Maryland.

‡ Copyright by the American Physical Society.