Evaluation of Blob Theory for the Diffusion of DNA in Nanochannels

Abstract

We have measured the diffusivity of λ-DNA molecules in approximately square nanochannels with effective sizes ranging from 117 nm to 260 nm at moderate ionic strength. The experimental results do not agree with the non-draining scaling predicted by blob theory. Rather, the data are consistent with the predictions of previous simulations of the Kirkwood diffusivity of a discrete wormlike chain model, without the need for any fitting parameters.

Figure 1

Snapshots of λ-DNA obtained from two movies in the D_eff = 143 nm nanochannel. (a) Movie where |β − 1| < 0.1. The movie contains a sheared molecule (arrow in the t = 0 s image), a molecule that diffuses out of the field of view (arrow in the t = 400 s image), two molecules that merge in the nanochannel (arrow in the t = 1000 s image). These molecules are not included in the analysis. The arrow in the image at t = 150 s indicates a typical molecule included in the analysis. (b) Movie with net upward drift of all molecules, leading to |β − 1| > 0.1 for their ensemble-averaged mean-squared displacement. Such a movie is excluded from the calculation of the diffusion coefficient for this channel. The movies used to generate this figure are available as Supporting Information.

Figure 2

Mean squared displacement of 57 λ-DNA molecules inside a 137 × 118 nm² nanochannel as a function of time lag from different segments of recorded images. The power law fit to the data from the complete movie (blue ×) for δt ∈ [150 s, 400 s] yields an exponent 0.98, indicating normal diffusive behavior. The inset shows the dynamic diffusion coefficient, MSD/2δt, as a function of time lag. After an initial decay till δt ~ 150 s, the MSD/2δt value is reasonably constant. A linear fit to MSD for δt ∈ [150 s, 400 s] in this nanochannel gives the diffusion coefficient D_t = 0.0550 μm²/s. Similar plots for the other channel sizes are included as Supplementary Information.

Figure 3

(a) Average fractional extension, X/L and (b) normalized variance in extension, σ²/Ll_p, from the current contribution (red ■) and previous experimental studies^, (black ○, ▲, ▼). The experimental results are compared to the extended de Gennes theory (black solid line). The standard errors for our experiments are smaller than the size of data points.

Figure 4

Log-log plot of diffusion constant, D_t, as a function of the average fractional extension, X/L. (a) Power law fit (solid black line) to the experimental data (red ■) yields an exponent −0.85 ± 0.15 at a 95% confidence level. (b) The simulation and theoretical predictions (Eqs. 3 and 7) were computed with Rouse diffusivity, D_R = 0.0129 μm²/s for λ-DNA (L = 19 μm) in water (η = 0.89 cP) at room temperature (T = 25 °C). The line calculated from Eq. 7 gives c₁ = 0.86±0.79 and c₂ = 1.2±0.19 at a 95% confidence level. The error bars for the standard error of the mean experiments are calculated from uncertainty in linear fit to uncorrelated MSD vs δt and are smaller than symbol size.