Translocation frequency of double-stranded DNA through a solid-state nanopore

Solid-state nanopores are single-molecule sensors that measure changes in ionic current as charged polymers such as DNA pass through. Here, we present comprehensive experiments on the length, voltage, and salt dependence of the frequency of double-stranded DNA translocations through conical quartz nanopores with mean opening diameter 15 nm. We observe an entropic barrier-limited, length-dependent translocation frequency at 4M LiCl salt concentration and a drift-dominated, length-independent translocation frequency at 1M KCl salt concentration. These observations are described by a unifying convection-diffusion equation, which includes the contribution of an entropic barrier for polymer entry.

Figure 1

(a) Scanning electron microscope image of a typical quartz nanopore. (b) Finite-element analysis of the electric-field profile at a voltage of +600 mV using the geometric model given in Ref. [15]. Lines represent tangents to the electric field. (c) Typical current trace showing downward spikes due to DNA translocation interrupting the baseline. The event in the dashed area is shown at greater time resolution in (d), which also shows the event charge deficit (ECD) in blue—the integrated area of the event relative to the baseline. (e) Histograms of ECD for 1, 5, and 20 kbp DNA with $N=1119, N=764,$ and $N=456$ translocations, respectively. Each length was measured separately at +600 mV with a DNA concentration of 1.6 nM.

Figure 2

(a) Agarose gel ($1\%$) electrophoretogram of the DNA sample containing 10 lengths in the range 0.5–10 kbp. (c) ECD histogram for 5711 translocation events recorded at +600 mV. The histogram is logarithmically binned and the peaks corresponding to the shortest and longest DNA lengths are labeled. (c) Scatter plot of mean event current against event duration for same events as in (b). The dashed gray lines are fits according to $\mathrm{\Delta }{I}_{\text{Mean}}=-\frac{{\text{ECD}}_{\text{Peak}}}{\mathrm{\Delta }t}$ and the solid line shows the 3-fC threshold.

Figure 3

(a) Modeled 1D geometry with length $L$, concentration $c_0$ in the sample reservoir and zero in the opposing reservoir. (b) Triangular profile for the entropic barrier $F\left(x\right)$ with height $u_0$. $\eta$ parameterizes how far the barrier extends. (c) The electric potential ($V_m$ is the applied voltage) and (d) combined free-energy profile for the nanopore where $z$ is the effective DNA charge.

Figure 4

(a) Length dependence of DNA translocation frequency measured at five different voltages (all data from the same nanopore) in an electrolyte of 4M LiCl. The trend lines show least-squares fits to the data using Eq. (A9) [derived from Eq. (1) and the model of Fig. 3]. (b) Corresponding translocation frequency against voltage for four selected lengths. Error bars are from the standard errors of the Gaussian fits to the ECD histogram.

Figure 5

(a) Scatter plot of 1168 translocations from a sample containing 5, 10, and 20 kbp with each length at a concentration of 0.12 nM and using 1M KCl electrolyte with +600 mV applied voltage. The dashed gray lines are fits according to $\mathrm{\Delta }{I}_{\text{Mean}}=-\frac{{\text{ECD}}_{\text{Peak}}}{\mathrm{\Delta }t}$, and the solid line shows the 3-fC threshold. (b) Corresponding translocation frequency against voltage for 5, 10, and 20 kbp—the translocation frequency values are significantly higher than that observed in 4M LiCl [Fig. 4] due to the higher effective DNA charge in 1M KCl. The line shows a linear fit to all data points yielding a gradient of 0.011 ${\text{nM}}^{-1}{s}^{-1}{\text{mV}}^{-1}$. Error bars are from the standard errors of the Gaussian fits to the ECD histogram.

Figure 6

Diffusion coefficient of DNA against $N^{-0.6}$, where $N$ is in base pairs (using data from Ref. [25]). A least-squares linear fit to the data is shown.

Figure 7

(a) Typical translocation events of 10 kbp DNA showing steps due to the folding configurations of the DNA as it translocates the nanopore. (b) All points histogram of 260 events showing a baseline peak at 0 nA and successive peaks due to DNA folding states.

Figure 8

Example of least-squares fit of multiple Gaussian functions to the 10 peaks from the 10 DNA lengths present in the sample given in Table 1. The data is the same as that present in Fig. 2 but with a linear rather than logarthmic binning.

Figure 9

Histogram of time since last event for all 5711 events shown in Fig. 2. The solid line is a fit according to Eq. (B1).

Figure 10

Dependence of DNA translocation frequency on DNA concentration. Translocation frequency against DNA length measured for an individual nanopore at the concentration given in Table 1 (RC = 1) and at a three times dilution relative to Table 1 (RC = 0.33).

Figure 11

Experiment on custom ladder given in Table 2 at 4M LiCl. (a) Scatter plot of all 1066 translocations. Dashed lines indicate constant ECD with values determined from the center of Gaussian peaks fitted to each ECD histogram. (b) ECD histogram of 1066 translocation events of the DNA ladder given in Table 2. Eight peaks can be distinguished corresponding to the eight DNA lengths present in the sample.

Figure 12

Translocation frequency as a function of DNA length for the DNA sample given in Table 2 at +600 mV. The two colors represent data from two nanopores with fits yielding $\alpha =0.10{\text{ms}}^{-1},\widetilde{z_0}=0.38C{J}^{-1}$, and $\widetilde{u_0}=4.1$ (blue data) and $\alpha =0.12{\text{ms}}^{-1},\widetilde{z_0}=0.31C{J}^{-1}$, and $\widetilde{u_0}=4.6$ (brown data). Error bars represent the standard errors of the fits.

Figure 13

Repeat of Fig. 4 with a different nanopore showing the consistent behavior of increasing translocation frequency with increasing DNA length. The global least-squares fit yields $\alpha =0.073{\text{ms}}^{-1},\widetilde{z_0}=0.68C{J}^{-1}$,  $\widetilde{u_0}=4.5$.

Figure 14

Additional repeat of Fig. 4 with another nanopore with fits yielding $\alpha =0.055{\text{ms}}^{-1},\widetilde{z_0}=0.56C{J}^{-1}$,  $\widetilde{u_0}=4.3$.

Figure 15

Left column: Mean event current against event duration for all translocations. The green line shows the 3-fC threshold set in the analysis. Dashed lines indicate constant ECD with values determined from the center of Gaussian peaks fitted to each ECD histogram. $N=637$ (+300 mV), $N=3174$ (+500 mV), and $N=11661$ (+700 mV). +300 and +500 mV were recorded for approximately 20 min and +700 mV was recorded for approximately 30 min. Right column: Corresponding plots of peak current value against event duration. The threshold limits of 50 $\mu \mathrm{s}$ and 50 pA are also marked as green lines. Events cluster outside the threshold limits, indicating that nearly no translocations are missed.