DNA Adsorption on hBN Surfaces
To investigate the interaction between DNA molecules and the hBN surface at single molecule resolution, we prepared 35 nt-long ssDNA molecules labelled with a Cy3 fluorophore. The hBN surface was prepared on a borosilicate coverslip via the mechanical exfoliation technique (Methods). Since the flakes on the coverslip were freshly cleaved, the topmost hBN surface was nearly contaminant-free. Figure 1a illustrates the wide-field epifluorescence single-molecule microscope used to capture fluorescence images of a hBN flake immersed in a buffer solution carrying the ssDNA molecules.
We first measured the background signal of the pristine hBN surface by applying a 5 µl droplet of blank buffer solution. We observed ~ 1 emitting spot per 1,000 µm2 on the hBN surface (Figs. 1b and 1c). When we added a 5 µl droplet containing 1 pM ssDNA, we observed that the number of fluorescence spots increase at a constant rate. A higher rate was observed when an additional droplet of 10 pM ssDNA was added, providing evidence that the fluorescence spots correspond to ssDNA molecules.
The ability to conduct studies at ultra-low concentrations, down to the low picomolar range, highlights the promise of hBN surfaces for single-molecule research. However, our experiments initially often showed significantly larger numbers of emission spots than expected at these low biomolecule concentrations. These observations indicated that the freshly exfoliated hBN surfaces could easily become contaminated by other fluorescent emitters during sample preparation, which may explain why only a limited number of experimental studies have successfully explored the binding and diffusion of biomolecules on vdWMs including hBN42. Therefore, we sought to pinpoint the exact sources of contamination and develop robust protocols for maintaining the purity of surfaces during sample preparation.
We noted that conducting experiments in aqueous environments presents a unique challenge compared to employing vdWMs in air and vacuum conditions. In the latter cases, ensuring the cleanliness of the vdWM surface during fabrication is sufficient for imaging. However, working in aqueous conditions demands a high level of cleanliness extending to both the vdWM surface and the fluidic environment, as contaminants transported by the liquid medium can contaminate initially clean surfaces. We suspected that this issue is compounded by the unavoidable contamination of the borosilicate substrate by residuals from the adhesives used for mechanical exfoliation (Figure S1).
The key to resolving this issue was to coat the surface with a polymer anti-stiction layer. We anticipated that the less adhesive polymer layer would prevent residuals from sticking to the surface or even the polymer itself may be broken and removed together with the sticky tape during the exfoliation, leaving no residual adhesives on the surface. To test this idea, we coated the glass surface with polyethyleneglycol (PEG) and carried out the hBN deposition and exfoliation (Methods). Indeed, this PEG coating was proven to be effective in preventing any adhesive residues from contaminating the glass surface, as depicted in Figure S2. Consequently, this approach allows hBN surfaces to be utilized as a highly reliable and sensitive single-molecule detection platform, capable of working with sub-picomolar concentrations.
2D Diffusion of DNA
During the single-molecule fluorescence measurements using the PEG-coated surface, it became apparent that the adhered ssDNA molecules moved over the surface, exhibiting substantial surface mobility (Movies S1-S4), as predicted by previous molecular dynamics (MD) simulations20,22–24,27,28. The motion of the adsorbed ssDNA was notably faster when we used a shorter 7 nt (nucleotide)-long ssDNA instead of the long 35 nt ssDNA (Movies S1 and S3). For a quantitative analysis, we extracted trajectories of individual ssDNA molecules by using a single-molecule tracking algorithm (Fig. 2a and Methods). Figure 2b shows the trajectories recorded over 400 s, and Fig. 2c shows all the trajectories located within the square area. The 2D diffusion motion of ssDNA molecules on the hBN surface implies the surface binding energy of ssDNA is high enough to localize the molecule near the surface for a prolonged time. Additionally, this suggests a uniform binding energy per atom, allowing the molecules to diffuse along the surface without any energy penalty.
The trajectory maps revealed that there were boundaries on the hBN surface that ssDNA molecules were unable to traverse. Most boundaries were straight lines that run parallel to the lattice angles derived from the edge of the hBN flake (Fig. 2b inset and Figure S3). This confinement effect aligns well with recent MD simulations on ssDNA movement on graphene27. These simulations showed that the rate at which ssDNA moves across an atomic step is much lower than the rate at which it moves over a flat 2D plane since ssDNA molecules encounter resistance when they attempt to traverse the atomic step. This resistance exists not only at the up-steps but also at the down-steps, confining ssDNA effectively within the boundaries of a flat terrace on the hBN crystal.
Closer analysis of single-molecule trajectories reveals that the diffusive motion of ssDNA molecules is occasionally arrested or slowed down over varying periods of time (red traces in Fig. 2b). These stoppages and slow movements were identified based on whether the apparent temporal diffusion coefficient (DA,temp) fell below a certain threshold value of 0.031 µm2/s. These stoppage events occur not only at step edges but also in the middle of a domain. This is more clearly illustrated in Figs. 2d and 2e, where DA,temp and jump distances were derived from the trajectory data. Figure 2d presents DA,temp plotted over time as well as the corresponding trajectories, with blue and red colours indicating values that are above and below the threshold, respectively. The graphs from top to bottom display four molecules as representative examples, each demonstrating different types of motion: fast continuous diffusion, fast diffusion followed by stoppage, linear diffusion along a straight line and long-term anchoring at a single position. In Fig. 2e, the jump distances, the distance that a ssDNA molecule travels during a certain lag time τ, calculated for different values of τ = nΔt, with n = 1, 2, 4, 8, 16 and Δt = 0.1 s are shown. The histograms show two peaks, suggesting that the motion can be categorized into two states, slow (red line) and fast (blue line) diffusion. As the slow peak does not change its position with increasing lag times, we attribute it as a stationary state of molecules. We note that the jump distances measured from the stationary phase are ~ 0.1 µm (red lines in Fig. 2e), which is below the optical diffraction limit. Thus, the jump distances from the stationary phase probably merely reflect the uncertainty in the position determination from the single molecule images and do not necessarily correspond to motion of the molecule.
Further experiments using ssDNA strands of different lengths, specifically 7, 15, 35, and 100 nt, show a decrease in both the apparent diffusion coefficient DA and the diffusion exponent α values as the length of the DNA strand increases. Three datasets, all of which were measured from different hBN surfaces and are plotted separately in Fig. 2g, were collected per length of ssDNA. DA and α were determined by fitting the average mean squared displacement (MSD) with the function \(⟨{r}^{2}\left(\tau \right)⟩ = 4{D}_{A}{\tau }^{\alpha }\), where \(⟨{r}^{2}\left(\tau \right)⟩\)and τ denote ensemble average of the displacement and the lag time, respectively (Fig. 2f)58. Longer ssDNA molecules exhibit lower mobility DA and more pronounced sub-diffusive behaviour, i.e. α < 1, indicating anomalous diffusion. Interestingly, DA has a clear trend with length with no significant differences between the datasets, while α has a wide margin of error across the different datasets (Fig. 2g). This indicates that DNA mobility is primarily affected by its length, while subdiffusivity is influenced not only by the DNA length but also by the local character of the hBN surface, which is sample dependent, e.g. due to variations in the configuration of step edges and the domains they define on the hBN surface.
Computational Study of DNA Diffusion over hBN Surfaces
To elucidate the diffusion mechanism of DNA on the hBN surface, we performed MD simulations using the same parameters used in the experiments, i.e. the same buffer, salts, and the length of the ssDNA. As depicted in Fig. 3, three types of hBN surfaces were simulated: a perfect planar surface (Fig. 3a), a surface with a step edge (Fig. 3b), and a surface containing 0.1% of B and N vacancies (Fig. 3c).
On the perfect planar hBN surface, the ssDNA molecule slid freely as visualized in the snapshot images in Fig. 3a and Movie S5. The ssDNA molecules with lengths of 7, 15, 35, and 64 nt exhibited normal 2D diffusion with diffusion coefficients of 749, 228, 111, and 65 µm2/s, respectively, as presented in Figure S4. Notably, these values were significantly higher than the experimental values in Fig. 2g by a factor of 103 – 104. The simulation results suggested that the diffusion coefficients are independent of the nucleotide type, as supported by the comparison of 25 nt polyA with polyT ssDNA (Figure S5). The MD simulation in Figs. 3b and S6 and Movie S6 also provides evidence supporting the possibility of linear movement of a ssDNA molecule along a step edge, similarly to the observation in the third row of Fig. 2d. The displacement maps clearly illustrate the differences in DNA dynamics between a perfect planar surface and a surface with a step edge. On the perfect planar surface, high displacements occurred almost continuously in both the x and y directions. In contrast, on the surface with a step edge, displacements were not only reduced but also predominantly occurred along the y-axis, parallel to the step edge.
On the hBN surface containing 0.1% of atomic defects, the motions of ssDNA molecule experienced transient arrests, as illustrated in Figs. 3c and S7 as well as Movies S7 and S8. When the ssDNA molecule was bound to multiple atomic defects, it exhibited limited mobility within the group of defects. However, it was also observed that ssDNA was not permanently bound to the defects, and some segments of the molecule could escape from the defects, as depicted in the displacement map.
Our MD simulation revealed how ssDNA molecules interacted with hBN surface at the nanoseconds timescale, yet the large differences in the diffusion coefficients between the experiments and simulations remained to be explained. The MD simulations were limited to the (sub-)microsecond range, whereas the experimental timescale was several hundreds of seconds. To bridge this timescale gap, we investigated the defect-controlled motion observed in our MD simulations using the Monte Carlo (MC) simulation method. We assumed that a freely diffusing molecule could be temporarily trapped on the surface when it encountered a defect site. As illustrated in Fig. 4a, the 2D diffusion was modelled with the following conditions: the DNA molecules diffuse on a finite square surface with area Ld2, with a free-diffusion coefficient (D0) obtained from MD simulations of a perfectly flat hBN surface (Methods).
The apparent diffusion coefficient DA remained constant regardless of Δt when Ptr = 0, which is the ideal case for normal diffusion with no trapping. In contrast, when Ptr was greater than zero, DA decreased as τ increased. For instance, at Ptr values between 0.02% and 0.2%, DA drastically reduced from 749 µm2/s at Δt = 1 ns and then saturated to less than 1 µm2/s at Δt = 0.1 s, as depicted in Fig. 4b. This implies that transient trapping at atomic defect sites could be responsible for the discrepancy between the MD simulation and experimental results. The diffusion exponent (α) showed two regimes of subdiffusivity, 1 ns < Δt < 10 µs and Δt > 0.1 ms (Fig. 4b). While the first regime originates from the trapping rate since it is comparable to Δt/Ptr, the second regime is attributed to the confinement effect from the step edges at domain boundaries.
We find that for 7 nt and 15 nt ssDNAs, the Ptr values that match the experiment results are 0.12% and 0.04%, respectively (blue and red lines in Fig. 4c). The Ptr can also be estimated based on the speed of ssDNA diffusion and the density of defects on the hBN surface so that the reliability of the MC simulation results can be verified. For instance, with Ptr = 0.12%, the 7 nt ssDNA diffusion lifetime is calculated to be τd = 1 ns/0.0012 = 0.83 µs. Using this lifetime and the MD diffusion coefficient we can estimate the typical diffusion length ld of the molecules with the 2D random walk equation \({l}_{d}=\sqrt{4D{\tau }_{d}}\). If this length is limited by trapping by defects, then it should be an estimate for the defect density. In the case of 7 nt ssDNA, we obtained the typical diffusion length ld = 50 nm with D0 = 749 µm2/s. For 15 nt ssDNA, we obtained τd = 2.5 µs and ld = 47.7 nm using D0 = 228 µm2/s. The diffusion lengths of the two ssDNA with different lengths were similar to each other, suggesting that it is limited by surface defects. We can estimate the defect density to be approximately (1 cm/50 nm)2 cm-2 = 4 \(\times\) 1010 cm-2, which is consistent with expected values for high-pressure grown hBN flakes59,60.
We conclude that the diffusion of ssDNA on the hBN surface has two phases. On a defect-free, flat hBN surface, ssDNA moves with a high diffusion coefficient of e.g. 749 µm2/s for 7 nt-long DNA. On a surface with atomic defects, the ssDNA can be intermittently trapped at defect locations. The trapping probability is estimated from MC simulations, from which we estimate a trap density of 4 \(\times\) 1010 cm-2 with an average trap time τt,avg = τ0 exp(-µ) = ~ 335 µs. The existence of these trapping sites can thus account for the experimentally observed apparent diffusion rates DA.
Confinement of ssDNA molecules in a hBN nanochannel
In Fig. 2b, we discussed the confinement effects induced by step edges by limiting the motion of the ssDNA molecules within a single hBN terrace. This characteristic offers the opportunity to develop highly localized nanochannels that can guide DNA in a pseudo-one-dimensional manner. Notably, vdWMs like hBN possess an inherent property of cleaving along the crystal orientation, facilitating the preparation of clean ribbon-shaped crystalline surfaces. To demonstrate the feasibility of guiding molecules, we show in Fig. 5 and Movies S9 the motion of a 16-nt ssDNA on a narrow, elongated hBN nanochannel extending from a larger region of the crystal. Figure 5a represents a superposition of 3,500 images recorded during 350 s, where the letters c-f indicate the motion of a ssDNA molecule, shown in more detail in Figs. 5c-5f. As seen in Fig. 5b, while the apparent diffusion coefficient (DA = 0.039 µm2/s) value is comparable to that on a large 2D surface, we observe pronounced subdiffusivity (α = 0.64). Figures 5c-5f highlight various characteristic ssDNA movements on the hBN nanochannel, demonstrating ssDNA entering through an inlet (Fig. 5c), moving linearly along the channel (Fig. 5d), and navigating through y-junction branches (Figs. 5e and 5f). These observations open the possibility of using hBN surfaces as 2D fluidic devices that can actively transport biomolecules on demand.