Measuring the wall depletion length of nanoconfined DNA

Abstract

Efforts to study the polymer physics of DNA confined in nanochannels have been stymied by a lack of consensus regarding its wall depletion length. We have measured this quantity in 38 nm wide, square silicon dioxide nanochannels for five different ionic strengths between 15 mM and 75 mM. Experiments used the Bionano Genomics Irys platform for massively parallel data acquisition, attenuating the effect of the sequence-dependent persistence length and finite-length effects by using nick-labeled E. coli genomic DNA with contour length separations of at least 30 µm (88 325 base pairs) between nick pairs. Over 5 × 10⁶ measurements of the fractional extension were obtained from 39 291 labeled DNA molecules. Analyzing the stretching via Odijk's theory for a strongly confined wormlike chain yielded a linear relationship between the depletion length and the Debye length. This simple linear fit to the experimental data exhibits the same qualitative trend as previously defined analytical models for the depletion length but now quantitatively captures the experimental data.

FIG. 1.

A DNA molecule confined in an electrolyte-filled nanochannel. Both the DNA molecule and the surface of the nanochannel are negatively charged. The difference between the effective channel size D_eff available to the DNA molecule and the actual channel size D is the depletion length δ.

FIG. 2.

The logarithmic terms in Eq. (2) (dashed green line), Eq. (6) (solid orange line), and Eq. (7) (dotted-dashed blue line) versus ionic strength. The shaded region indicates the ionic strengths used in our experiments.

FIG. 3.

False-color image of DNA in the nanochannels. The blue-colored backbone is labeled with YOYO-1, while the green dots within the backbone are the Nt.BspQI nick sites. An image processing algorithm further processes the image to select the molecules which correspond to a blue line and choose the nick sites based on a minimum intensity of the green channel. Green labels with a very low intensity blue backbone (arrow in the bottom left), indicative of molecules that have not been stained properly or free labels, are discarded by the algorithm. The scale bar is representative of the minimum allowed separation between any two nick pairs on the same molecule—nick pairs shorter than this length were not included for further analysis to avoid finite-length effects and the sequence-dependent persistence length effect.

FIG. 4.

Probability density of fractional extensions obtained for the five different ionic strengths listed in Table I for nick pairs with L > 30 µm.

FIG. 5.

% GC content for all adjacent nick pairs in the E. coli genome separated by at least 2500 bp (•) and those separated by the minimum distance L = 30 µm used in our analysis (▾).

FIG. 6.

Depletion length as a function of ionic strength from experiments (red squares), semiflexible chain model [Eq. (6), solid blue line], rod-like model [Eq. (7), dash-dotted orange line], and the approximation δ = $w$ (dashed green line). The dashed black line is Eq. (13). The inset shows the experimental data and Eq. (13) as a function of the Debye length. The error bars correspond to maximum errors.

FIG. 7.

The residual between the experimentally measured fractional extension and Eq. (14) for the experiments in Ref. (I = 28 mM, ■), Ref. (I = 7.2 mM, $○$), and Ref. for l_p/w = 3.0 (I = 3.8 mM, ▴) and l_p/w = 5.8 (I = 78.4 mM, ▾). The residuals are largely unchanged for most of the experiments while points in the shaded region represent data with reduced agreement with theory after correcting for δ.