Stretching DNA using the Electric Field in a Synthetic Nanopore

Abstract

The mechanical properties of DNA over segments comparable to the size of a protein-binding site (3–10nm) are examined using an electric field-induced translocation of single molecules through a nanometer diameter pore. DNA, immersed in an electrolyte, is forced through synthetic pores ranging from 0.5 to 1.5nm in radius in a 10nm thick Si₃N₄ membrane using an electric field. To account for the stretching and bending, we use molecular dynamics to simulate the translocation. We have found a threshold for translocation that depends on both the dimensions of the pore and the applied transmembrane bias. The voltage threshold coincides precisely with the stretching transition that occurs in dsDNA near 60pN.

The encyclopedic information encoded in the genome is packaged, copied, and transcribed through protein mechanisms that exploit the distinctive physical properties of DNA. Recently, single molecule spectroscopies have been developed to infer the average elastic properties of long (48kbp~16.3μm) molecules from force-extension measurements. Bustamente et al.^1,2 have successfully fit this data over a range of forces (from 10fN to 100pN) using a simple worm-like chain model with the link length and extension modulus as parameters. When subjected to a force >10pN, DNA deforms, stretching the double helix. It is remarkable that near 60pN a dramatic transition occurs—the double helix stretches from 107% to nearly 170% of the length of B-DNA over a few picoNewtons.^3,4 The distance between bases in the stretched DNA is 0.7nm; over 200% of the normal length.

Despite the success of this model, to capture the microscopic physics required to understand DNA-protein interactions, measurements of the mechanical properties of DNA over segments comparable to the size of a protein-binding site, which is about 10–30 base-pairs(bp) long (3–10nm), are required. We propose to test the elastic properties of DNA on this length scale by using the field-induced translocation of DNA across a membrane through a nanopore. ^5–8 When an electric field is applied across the membrane with a pore in it, DNA immersed in electrolyte is attracted to the pore, blocks the current through it, and eventually permeates the membrane through the pore.^5–8 The forces acting on single nucleotides in a DNA strand during the translocation are approximately F~qZΔV/a, where qZ is the effective charge per nucleotide, and ΔV is the electrostatic potential drop over the nucleotide separation a. Assuming, that Z≈ 1 and a=0.34nm, the force corresponding to the applied voltage can range from 0<F<1nN. As a result of this force, it has already been shown that folds and bends can occur in DNA during translocation through a 10nm diameter pore, which affects the current and the translocation kinetics.⁹

In this letter, we report the results of a stringent test of the nanometer-scale mechanical properties of single DNA molecules. Single molecules of double-stranded DNA (dsDNA) and single-stranded DNA (ssDNA), immersed in electrolyte, were forced through synthetic nanopores, ranging from 0.5 to 1.5nm in radius, in a 10nm thick Si₃N₄ membrane using an electric field. Molecular dynamics (MD) simulations provide a comprehensive account of the bending and stretching that accompanies a translocation. MD has identified a threshold for permeation of dsDNA through the pore that depends on the radius and the field. These predictions have been confirmed experimentally. The stretching transition that occurs near 60pN tension was found to determine the voltage threshold.

We formed membranes using conventional semiconductor fabrication practices described elsewhere.¹⁰ Subsequently, a single nanopore is created in the membrane by electron beam stimulated decomposition and sputtering using a JEOL 2010F transmission electron microscope (TEM) operating at 200keV. Fig. 1(a) represents an array of TEM images taken at a tilt angle of 0° of pores with apparent radii of 0.5 ± 0.1nm, 0.95 ± 0.1nm and 1.5 ± 0.1nm in a Si₃N₄ membrane nominally 10nm thick. (To account for elliptical shape, the radius R_p is taken to be the geometric mean of the major and minor axis of the pore.) The thickness of similarly processed membranes was determined to be 10±2nm using scanning electron microscopy and 11±3nm using electron energy loss spectroscopy. The TEM images represent a two-dimensional projection through the membrane. The shot noise observed in the central area identified with the pore indicates perfect transmission of electrons through the membrane in that area. To investigate the three-dimensional structure, we tilted the membrane in the TEM about the pore axis and explored various defocus conditions. A model of the pore geometry that is consistent with this data is shown in Ho et al.¹⁰, and Heng et al.¹¹ - two intersecting cones with a 10° cone angle - is represented schematically in the inset in Fig. 1(d).

Figure 1.

(Top) TEM images of pores with apparent radii of 0.5 ± 0.1 (a), 0.95 ± 0.1 (b), and 1.5 ± 0.1 nm (c) in a 10 nm thick Si₃N₄ membrane at 0° tilt. (Middle) Gel arrays showing five horizontal lanes with fluorescent bands that identify 58-mer ssDNA and 58bp dsDNA at the positive (+) and negative (−) electrodes separated by 0.5nm (e), 1.0nm (f), and 1.5nm (g) pores (with 100bp ladder as a reference). The applied voltage was 200 mV. (Bottom) I-V characteristics in 1M KCl solution of the same three pores. Line fits yield slopes of 0.63 ± 0.03 nS, 1.09 ± 0.03 nS, and 1.24 ± 0.03 nS for the three pores, respectively.

To characterize molecular transport, we measured the electrolytic current through a pore as a function of the applied electrochemical potential at 23.5±1°C. The currents were measured using an Axopatch 200B amplifier in resistive feedback mode with a 100kHz bandwidth. All experiments were carried out in a membrane transport bi-cell made of either acrylic or PDMS, where the membrane separates two identical compartments each containing ≈ 40μL-1mL of 1M KCl electrolyte and a Ag/AgCl electrode. Fig. 1(d) shows the current-voltage (I-V) characteristics of the pores shown in Figs. 1(a–c), measured over a range of ±1V in 1M KCl after > 55 hours of immersion in de-ionized water. In all cases the I-Vs are approximately linear. A line fit to the data yields the conductance 0.63 ± 0.03nS, 1.09 ± 0.03nS and 1.24 ± 0.03nS. It is apparent that the conductance does not scale linearly with the radius derived from TEM. We attribute the observed variations in conductance to a fixed (negative) charge in the pore.¹⁰

Following the conductance measurements, DNA in 10mM TRIS-Cl buffer at pH 8.5 was injected at the negative electrode. A voltage was applied across the membrane and the current through the nanopore was measured. We have previously shown that under these conditions voltage-driven translocations of single molecules of DNA across the membrane temporary block the electrolytic current through the pore.⁷ Using the pore as a stochastic sensor, we have also shown that the duration of the current transients can be used to discriminate between ssDNA and dsDNA, as well as dsDNA of various length.⁷ Molecular dynamics simulations of DNA translocations through a synthetic nanopore¹² predict a translocation velocity of 400nucleotides/μsec for an electric field of 1.4V/5.2nm (much faster than that observed in proteinaceous pore like alpha-hemolysin which shows a velocity of 10nucleotides/μsec at a similar field.¹³ The narrow bandwidth (100kHz) of the measurement apparatus used in these experiments limits the observation to transients longer than 10–100 μseconds. And even if the transient can be measured, it cannot be used to unambiguously discriminate between a translocation of DNA across the membrane and a temporary occlusion of the pore without a subsequent translocation.¹⁰ Therefore, to establish unequivocally that DNA permeates a pore and to count the number of copies, the minute amount of the DNA near the positive electrode was amplified using PCR and analyzed by gel electrophoresis or by quantitative PCR. This same methodology was used by Kasianowicz⁵ to first establish the correspondence between the number of current transients through an alpha-hemolysin pore and the number of ssDNA molecules translocating through the pore.

We tested the permeability of ssDNA(58-mer) and dsDNA(58bp) through the pores shown in Figs. 1(a–c) using an applied voltage of 200mV across the membrane. Typical gel arrays are shown in Figs. 1(e,f,g) along with a molecular weight (MW) reference denoted as “100bp ladder,” which contains a spread of DNA MW. After staining, the DNA in each lane can be seen as bands spread according to the length (or MW). Notice that the ssDNA collected at the positive electrode, denoted by (+)58-mer, is observed to permeate through all three pores and gives the same amplified pattern as the ssDNA injected at the negative electrode, denoted by (−)58-mer. On the other hand, dsDNA only permeates the R_p=1.5nm±0.1nm pore at 200mV.

We constructed a microscopic model of the experiment and carried out MD simulations of electrophoretic transport through pores. A crystalline Si₃N₄ membrane was built by replicating a unit cell of β-Si₃N₄ crystal along the unit cell vectors, producing a hexagonal patch of 10.3 nm thickness and 4.6 nm sides. By removing atoms from the Si₃N₄ patches we produced pores of symmetric double-conical (hourglass) shapes with radii that correspond to our experiments. A DNA double helix with the same sequence used in our experiments was built from individual base pairs in the geometry suggested by Quanta.¹⁴ First, the DNA was placed in front of the pore, normal to the membrane, and then the Si₃N₄ DNA complex was solvated in pre-equilibrated TIP3P water molecules. K⁺ and Cl⁻ ions were added corresponding to a 1M concentration. The final system measured about 30.3 nm in the direction normal to the membrane and included about 160,000 atoms. In order to simulate the system, the molecular force field describing water, ions and nucleic acids¹⁴ was combined with the MSXX molecular force field for Si₃N₄.¹⁵ The protocols are described elsewhere.¹²

At first, we simulated the 0.7nm-, 1.0nm- and 1.5nm-radii pores combined with one 58-bp dsDNA helix. To shorten the translocation times to a practical duration, the simulations were done at 1.3V. We applied a uniform electric field across a 10.3nm thick Si₃N₄ membrane to drive a 58bp dsDNA through 0.7nm- and 1.0nm-radius pores. The field induced a rearrangement of the ions and water that, in turn, focused the field to the vicinity of the membrane abolishing the gradient in the bulk, and producing a 1.3V transmembrane bias. Fig. 2(a) shows the position of the dsDNA center of mass (CoM) relative to the center of the Si₃N₄ membrane against time. Within the first few nanoseconds, the electric field drove dsDNA into the pores; the wider pore facilitated faster translocation. Due to their conical shapes, both pores narrow towards the center of the membrane, which slowed down DNA translocation. After about 4.5ns, the translocation halted in both simulations before the DNA arrived at the narrowest part of the pores. The snapshots included in the inset illustrate the conformations of dsDNA at the end of these simulations. Noticed that dsDNA traveled a longer path inside the wider pore suggesting that the translocation halts at a particular cross-section. To ascertain if the translocation halted at the same cross-section in both pores, we plot in the insert of Fig. 2(a) the local diameter of the pore around the first DNA base pair. In both simulations, the translocation of dsDNA halted when the pore narrowed to 1.25±0.1nm-radius. So, we conclude that pores with R_p<1.25nm are impermeable to dsDNA for fields <1.3V/10nm, in agreement with the experiments.

Figure 2.

(a) 1.3 V was applied to drive dsDNA into 0.7-nm-radius (circles) and 1.0-nm-radius (squares) pores. After about 4.5 ns, the translocation of DNA halted in both. The snapshots show the conformations of DNA at the end of these simulations. The inset to (a) shows the radius of the pore cross-section near the first base inside the 0.7nm and 1.0nm pores. The translocation of dsDNA halts when the pore narrows to 1.25±0.1nm. (b) Translocations of 58bp dsDNA through 0.7nm(circle), 1.0nm(square), and 1.5nm(triangle) radius pores. Black (1.3V) and red (6.5V) symbols reflect the applied bias. The snapshot on the left illustrates dsDNA permeating the 1.0-nm radius pore at 6.5V bias. This pore was not observed to conduct dsDNA at 1.3V bias. The middle snapshot shows the final conformation of dsDNA after passing through the narrowest part of the 1.5nm radius pore at 1.3 V. The right illustrates the unzipping of the dsDNA inside the 0.7nm pore at 6.5 V. The snapshots are each of different scale. (c) dsDNA permeates a 1.0nm radius pore for voltages >3.2V. The snapshot illustrates the conformation of dsDNA at 3.2 V after 12ns.

To determine if a higher field could drive dsDNA through the same pores, we continued our simulations from the conformations shown in Fig. 2(a), applying a 6.5V transmembrane bias. In Fig. 2(b), we plot the position of the dsDNA CoM against the simulation time. The results of these simulations suggest that dsDNA can permeate both pores at a sufficiently high voltage. In the case of a 1.0nm-radius, the 6.5V bias deformed the DNA helix, shifting one of the strands relative to the other by approximately one nucleotide, while preserving the hydrogen bonds between strands. Such stretching and shifting reduces the effective diameter of a double helix, allowing it to pass through the constriction of the pore without unzipping. In the case of the 0.7nm pore, 6.5V unzipped dsDNA before it reached the narrowest part of the pore. After denaturing, one of the two strands passed through the 0.7nm constriction, while the other strand remained at the same place where the unzipping occurred. In contrast, we found that dsDNA permeates a 1.5nm-radius pore at 1.3 V. In Fig. 2(b), the dsDNA CoM is plotted against time. Within the first 5ns, the field drove dsDNA into the 1.5nm-radius pore with a speed comparable to that inside the 0.7nm-and 1.0nm- pores. In the 1.5nm pore simulation, however, the translocation of DNA did not halt before reaching the center of the membrane. Instead, after about 11ns, one end of the DNA helix passed through the 1.5nm constriction. Shortly following that, this end adhered to the surface of Si₃N₄ on the other side of the pore (z<0). Such surface adhesion of nucleosides has been described in depth in Aksimentiev et al.¹² and Yeh and Hummer¹⁷. Driven by the field, the rest of the DNA helix continued the move through the pore, deforming the double helix of DNA into a loop, as shown in Fig. 2(b). A translocation like this was reported earlier.¹²

To establish the threshold field and the force required to drive dsDNA through the pore, we restarted our simulation of the 1.0nm-radius pore from the conformation shown in the inset of Fig. 2(a). In Fig. 2(c) we plot the dsDNA center-of-mass against time for biases ranging from 1.3 to 6.5V. These results indicate that dsDNA permeates a 1.0nm-radius pore for voltages ≥3.2V. At 3.9V, the DNA strands unzipped when entering the pore, which resulted in transient slow down of the translocation. The predicted thresholds were tested experimentally using two pores with 1.0±0.1nm- and 1.1±0.1nm-radii. The gel array in Fig. 3(a) indicates that 58bp dsDNA can be forced through a 1nm-radius pore if the applied voltage is >2.75V. Notice that we only observe a fluorescent band in the lane corresponding to the positive electrode, (+)58bp, for an applied bias of 3V. We obtained a similar result for a 1.1nm-radius pore, but the observed threshold voltage was lower: 58bp dsDNA permeates the pore for V> 2.25V.

Figure 3.

(a) Gel arrays containing 3 horizontal lanes with fluorescent bands indicating 58bp dsDNA found at the negative (−) and positive (+) electrodes in a bi-cell with a 1nm radius pore (along with a 100bp ladder.) The 58bp permeates the pore only for V>2.75V. (b) Similar to (a) but instead using a 1.1nm radius pore. The 58bp permeates this pore only for V>2.25V. (c) qPCR results obtained for the same pores showing the copy number versus voltage. Upper left insets TEM micrograph taken at 0° tilt for 1nm radius (blue) and 1.1nm radius(red). 622bp dsDNA permeates the 1nm pore for V>2.5V, and the 1.1nm pore for V>2.25V. Lower right inset Expanded view of the data near threshold.

We also measured the number of DNA copies translocating near threshold by quantitative real-time PCR. Two PCR primers were designed to amplify a 72bp region within a 622 base target sequence. A TaqMan^® probe was designed, mapping to this 72bp target sequence and labeled with an FAM reporter dye at the 5′-end and with a TAMRA quencher dye at the 3′-end. During amplification, the primers and the probe hybridize to the target sequence. Subsequently, during polymerization, the 5′ exonuclease activity of the DNA polymerase cleaves the probe releasing the reporter dye and resulting in increased fluorescence, which is proportional to the amount of target. Figs. 3(b,c) represent the results of qPCR analyses showing the number of copies found to permeate through the 1.0nm and 1.1nm-radius pores as a function of the applied potential. In correspondence with the 2.75V threshold obtained from the gel array for 58bp, the 1.0nm pore exhibits a threshold voltage of 2.5V for 622bp dsDNA. Similarly, the 1.1nm-radius pore shows a threshold voltage of 2V. The 0.25V discrepancy observed between the gel array and qPCR data may be attributed to the difficulties associated with capturing and handling such a small number of DNA copies.

To elucidate the origin of the sharp voltage threshold for permeation of dsDNA, we used MD to examine the potential inside a 1.0nm-radius pore. The distribution corresponding to 2.6V is shown in Fig. 4(b). The potential drops abruptly near the constriction and the corresponding force increases rapidly near the pore center, as illustrated in Fig. 4(a). At 2.6V, we estimate the average force acting on a nucleotide at the leading edge of the DNA at about 45pN, while above threshold at 3.2V this force exceeded 60pN, sufficient to stretch the helix and allow the molecule to pass.

Figure 4.

(a) The force versus distance from the center of the pore. Inset Expanded view of the same data near threshold. The vertical bands indicated the location of the leading DNA base pair. (b) Electrostatic potential contours inside a 1.0nm-radius pore at 2.6 V.