DNA Volume, Topology, and Flexibility Dictate Nanopore Current Signals

Nanopores have developed into powerful single-molecule sensors capable of identifying and characterizing small polymers, such as DNA, by electrophoretically driving them through a nanoscale pore and monitoring temporary blockades in the ionic pore current. However, the relationship between nanopore signals and the physical properties of DNA remains only partly understood. Herein, we introduce a programmable DNA carrier platform to capture carefully designed DNA nanostructures. Controlled translocation experiments through our glass nanopores allowed us to disentangle this relationship. We vary DNA topology by changing the length, strand duplications, sequence, unpaired nucleotides, and rigidity of the analyte DNA and find that the ionic current drop is mainly determined by the volume and flexibility of the DNA nanostructure in the nanopore. Finally, we use our understanding of the role of DNA topology to discriminate circular single-stranded DNA molecules from linear ones with the same number of nucleotides using the nanopore signal.


S2.1 Principle of DNA carrier-based nanopore sensing
It is necessary to illustrate how our designs of DNA carrier can result in multi-level drops in the nanopore current trace. The current response of a nanopore sensor, usually called a resistive pulse, is induced when a translocation event temporarily blocks the pathway of ions through the nanopore thereby changing the nanopore resistance. The side containing analyte molecules is defined as the cis side of the nanopore, and the side at which the analytes finally arrive after translocation is the trans side. In general, the nanopore resistance can be divided into that of the open pore region and that of the access region ( Figure S11a). For a conical nanopore, the inherent resistance generated by the movement of ion molecules in solution through the nanometric aperture can be written as below 1 .
where is the resistivity of the electrolyte solution, is the length of the nanopore, and are respectively the diameters of the trans opening and the cis opening of the nanopore. If we simplify the local analyte to a nanosphere with a diameter of , and is the distance of its center from the cis opening of the nanopore, then the change in nanopore resistance due to its presence can be calculated as the following formula 1 .
Accordingly, for a particular nanopore, the diameter and position of the analyte are essential parameters that affect ∆ under constant solution conditions. As shown in Figure S8b, when the DNA carrier backbone enters the access region, is defined by the diameter of the characteristic double-helix structure of ds DNA and remains basically the same. The nanopore current drops as becomes smaller until the backbone occupies the whole response area and the current trace arrives at the first-level platform. At the point when the secondary DNA nanostructure on the carrier reaches the access region, significantly increases, resulting in a further decrease of nanopore current. The current drops to its lowest point when the synergistic effect of and reaches its maximum. Then as the DNA carrier comes out of the response area, the nanopore resistance changes in reverse until the current trace returns to the original baseline. Based on this principle, the magnitude, duration, and frequency of the multi-level resistance pulses can reveal much useful information about properties of the DNA carrier and the secondary nanostructures on it, such as size, shape, charge, and many more. In Figure S9a, we show ∆ /∆ 0 as a function of the number of poly-dT overhangs on Carrier 1 and find a linear relationship, as expected. We force the trendline to cross the origin of coordinates because no signal is expected when there's no nanostructure. In contrast, a cubic polynomial can fit the relationship between peak depth and the length of poly-dT overhangs on Carrier 2 ( Figure S12b). One explanation is that the overhangs are with one end anchored to the carrier backbone and the other end moving flexibly in the solution in all directions, so the maximum range of space that an overhang may occupy in the solution around the anchor point can be seen as a ball with the length of the overhang as the radius. The success of both the linear ( Figure S12a) and cubic ( Figure S12b) fits demonstrate that nanopore current signals are related to the volume of secondary nanostructures in DNA carriers. This opens the pathway to the systematic study of more complex DNA sequences.

S2.3 Worm-like chain (WLC) model
The WLC model 2-4 describes polymers whose successive segments are orientationally cooperative and the flexibility is brought by fluctuations of the contour rather than large-angle bond rotations. For a polymer of maximum length 0 (for dsDNA, 0 = 0.34 × 5 ; for ssDNA, 0 = 0.43 × 6 ), parametrize its path as ∈ (0, 0 ). Allow ⃗( ) to be the position vector along the DNA chain at point ( Figure S13), then the energy associated with the bending of the DNA can be written as: where is the Boltzmann constant, is the absolute temperature, and is the polymer's characteristic persistent length which is usually within a few orders of magnitude of the chain length ( of 30 nm and 2.4 nm are estimated for dsDNA and ssDNA in this work 7 ).

Figure S13
Illustration of the WLC model, with position and its unit vector ⃗( ) as shown.
At finite temperatures, a coiled and random configuration of the undisturbed polymer is often caused by thermal fluctuations, so the end-to-end distance ( ) of the polymer is significantly shorter than 0 . When 0 < , the average value of under minimum can be calculated as:

S3.1 Influence of attachment position on nanopore current signal
Our design has four functional attachment positions along the carrier. Since the sequence of M13 is different at these four positions, the staples and overhangs designed accordingly also have different sequences and thus have different tendency to self-fold or interact with each other. In order to make a more convincing comparison of the nanopore current signals generated by different structures bound to different positions on the same carrier, a preliminary experiment studying the influence of attachment position on the significance of ion current drop is required. On Carrier 10, there are four repeats of 30 nt poly-dT overhangs at position A, B, C, and D respectively. Nanopore measurement result is shown below.

Figure S14
Schematic and nanopore measurement result of Carrier 10 with four repeats of 30 nt poly-dT overhangs at position A, B, C, and D respectively.
From the boxplot, we can see that although the peak depth of 4x30 nt poly-dT at the four positions is a little bit different from each other, the difference is not huge compared to the difference resulting from the different structures we designed on the same carrier, thus can be neglected when we do the analysis. However, we admit that in cases where we need to do careful comparison, it is necessary to take into account the influence of staple sequences at different positions, and make better choices at the design stage.

S3.2 More repeats or extended length
It may be interested to some readers If we bind a long structure with the same length at one position, for example replacing 4x20 bp dsDNA with 1x80 bp dsDNA, would it create the same signal or even higher due to the flexibility.
Accordingly, we synthesized Carrier 11 and got the following result ( Figure S15). From the boxplot, we can see that the 80 bp dsDNA generated a similar signal to the 4x20 bp structure on average, especially the range of peak depth of these two structures is almost the same. But the average peak depth of the 80 bp dsDNA is smaller than the 4x20 bp structure. We calculated the end-to-end lengths ( ) of 80 bp and 20 bp dsDNA and got 23.64 nm and 6.55 nm respectively. The of 80 bp dsDNA is a bit smaller than four times the of 20 bp dsDNA (26.20 nm), so it is reasonable to think that the 80 bp dsDNA overhang is not as extended and flexible as four repeats of 20 bp dsDNA, thus leading to slightly weaker nanopore signals. Another possible explanation is that the length of 80 bp dsDNA is larger than the diameter of our glass nanopore (about 10 nm), and long overhangs are more likely to lie down when the carrier translocates through the nanopore. From the results of Carrier 6, such "lying down" could also result in lower peak depth.

S3.3 Dependence on sequence
Besides Carrier 3 containing poly-dC and poly-dT structures, and Carrier 4 containing poly-dA and dG-rich structures, a third carrier is required to make all categories of nucleotides interrelated. From the nanopore measurement result of Carrier 12 with poly-dT and dG-rich structures ( Figure S16a), we find a wider range of peak depths resulted from dG-rich than poly-dT though the current signals they generate are both generally more intense than poly-dA and poly-dC, as indicated in the results of Carrier 3 and Carrier 4. When we scrutinize the events from Carrier 12 one by one, we find some event traces with considerably high or low dG-rich peaks, while the peak depths of poly-dT are always within rational bounds ( Figure S16b). This helps verify our hypothesis that dG-rich overhangs can interact with each other and form unexpected complex 3D structures under our experimental conditions. Therefore, they are not as ideal as poly-dT strands as candidates for ssDNA nanopore study. Scatterplots of peak depth in relation to the location of these secondary structures on Carriers 3, 4, and 12 are presented in Figure S16c as adminicular evidence. We also demonstrate the better flexibility of poly-dT than randomly sequenced overhangs of the same length on Carrier 13 ( Figure S17).

S3.4 Dependence on nanopore size
Although we fabricated the nanopores following a consistent protocol, it was quite hard for us to get ones with exactly the same size. To investigate whether the size of nanopore might influence the current signals we got, we made both smaller and larger nanopores by setting the HEAT of the puller 20 higher or lower (than 470) while keeping all the other parameters unchanged, and measured Carrier 5 with them. From results shown in Figure S18, we find that the relative significance of the three DNA nanostructures on Carrier 5 remains the same as the size of the nanopore increases, but the absolute current drops they bring about gradually decrease since these structures appear smaller compared to the cross-sectional area of a larger nanopore. The almost overlapping trend lines of the two identical reference structures in Figure S18d demonstrate the reliability of our measurement results.  2.8 μL TM buffer (10 mM Tris-HCl, 10 mM MgCl2, pH=7.5) 1 μL MgCl2 (100 mM) 24.2 μL deionized water followed by heating to 70°C and then linearly cooling to 25°C in a thermocycler over 50 minutes. The staples were at 5 times excess to the scaffold.
For carriers containing double-stranded structures, 16 μL of 1 μM additional strands other than the customized staples (cAD in Carrier 5; cB20 in Carrier 11; circular B60 and D60 in Carrier 8) were added to the annealed mixture and incubated at room temperature for an hour. For carriers containing stem-loop or junction structures, the additional strands (HA4, HB12, HC20, and HD28 in Carrier 7; HC20 and (DWT10a+DWT10b) in Carrier 8; DE1, DE2, and DE3 in Carrier 11) were individually heated to 88°C followed by a linear cooling ramp to 25°C over 40 minutes before being added to the carrier solution. Sketched designs of carriers 1 to 10 and detailed staple sets of each carrier are given in S3. After the annealing and incubation procedures, excess oligonucleotides were then removed with washing buffer (10 mM Tris-HCl, 0.5 mM MgCl2, pH=8) by centrifuging at 9000g for 10 minutes using Amicon Ultra 100kDa filters for successive two times. Typically, we could collect about 30 μL solution of purified DNA carriers after washing, which was then quantified with NanoDrop 2000 spectrophotometer. All the carrier solutions were frozen in a refrigerator at -20°C for later use.

S4.2 Preparation of circular DNA
The hybrid (BS) of linear 5'-phosphorylated oligonucleotide (B60) and its corresponding splint strand (Sp) was obtained by mixing 10 μL B60 (100 μM) 15 μL Sp (100 μM) 75 μL TM buffer and then heating to 95°C for 5 minutes, followed by slowly cooling down to room temperature. Details are listed in the below table. The electrophoresis was conducted in 1 × TBE buffer (pH=8.0) with 10 mM MgCl2 at a constant voltage of 110V (10 V/cm) for one hour. Then the gel was stained by GelRed for 15 minutes before visualization on a UV transilluminator. After cutting the corresponding bands out of lanes 7 to 10 of the gel with a razor blade under a UV light, the slices were chopped into fine pieces and transferred into a 1.5 mL microcentrifuge tube. TM buffer was added to the tube until it was just above the gel and kept at room temperature overnight to elute circular B60. The supernatant was collected using a pipette and quantified with NanoDrop 2000 spectrophotometer. Ag/AgCl electrodes prepared by curing 1-mm Ag wires in a 10% solution of NaClO were separately inserted into the central reservoir and the outer chamber to create an electrical circuit across the nanopore. The one connecting the central reservoir served as the ground, while the other could be moved between outer chambers to address different nanopores. Current-voltage characteristic curves from -600 mV to 600 mV were recorded to indicate the estimated sizes of nanopores. Those with a maximum current of around 10 nA and a root-mean-square (RMS) noise below 7.5 pA were selected for further measurements. Based on a simplified equation for conical nanopores 9 : where the electrical conductivity of 4 M LiCl solution is approximated to 15 S/m 10 in this work, and the inner taper angle is around 4º, we had the diameters of nanopores (nm) ≈ 600 (nA). Parameters of all the nanopores used in this work are listed in Table S9. with LabVIEW software developed by senior students in our group 8 and self-written python programs. Folded events, as exemplified in Figure S19a, b, were left out to avoid additional affecting factors. From the current trace of unfolded events, as instantiated in Figure S19c, d, the six peaks indicating two references and positions A to D could be easily discriminated according to the distances between peaks and the ends of current drops. However, a small slope was often observed at the baseline, possibly due to the slight change in buffer concentrations as the measurement was carried out. Additionally, the absolute values of the first-level plateau and secondary drops were found somewhat related to the nanopore size. Hence in this work, the current baseline of each measurement was linearly fitted, and the slope was corrected (Figure S19e where ∆ 0 refers to the average value of the first-level current drop, which was mostly within the range of 0.1-0.2 nA. ∆ refers to the difference between the minimum current output within a second drop and ∆ 0 . ∆ 0 refers to the time scale between the two peaks generated by reference structures, typically lasting for 0.8-1.6 ms. ∆ refers to the interval between any target peak and the peak suggesting reference S, namely the one nearer to the end of the DNA carrier.

Figure S19
Current trace of (a, b) representative folded events, (c, d) representative unfolded events before correction of the baseline slope, and (e, f) the same unfolded events after slope correction.