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Spontaneous Transport of Single-Stranded DNA through Graphene−MoS2 Heterostructure Nanopores Binquan Luan* and Ruhong Zhou Computational Biological Center, IBM Thomas J. Watson Research, Yorktown Heights, New York 10598, United States S Supporting Information *
ABSTRACT: The effective transport of a single-stranded DNA (ssDNA) molecule through a solid-state nanopore is essential to the future success of high-throughput and lowcost DNA sequencing. Compatible with current electric sensing technologies, here, we propose and demonstrate by molecular dynamics simulations the ssDNA transport through a quasi-two-dimensional nanopore in a heterostructure stacked together with different 2D materials, such as graphene and molybdenum disulfide (MoS2). Due to different chemical potentials, U, of DNA bases on different 2D materials, it is energetically favorable for a ssDNA molecule to move from the low-U MoS2 surface to the high-U graphene surface through a nanopore. With the proper attraction between the negatively charged phosphate group in each nucleotide and the positively charged Mo atoms exposed on the pore surface, the ssDNA molecule can be temporarily seized and released thereafter through a thermal activation, that is, a slow and possible nucleotide-by-nucleotide transport. A theoretical formulation is then developed for the free energy of the ssDNA transiting a heterostructure nanopore to properly characterize the non-equilibrium stick−slip-like motion of a ssDNA molecule. KEYWORDS: heterostructure, DNA sequencing, nanopore, graphene, MoS2, ratcheting, nucleotide-by-nucleotide
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a solid-state nanopore can be advantageous and are highly sought after currently. Recently, nanopores in a two-dimensional (2D) material have been extensively studied due to the atomically thin nanopore whose thickness is comparable to the spacing between two neighboring nucleotides in a ssDNA molecule, spatially limiting only one nucleotide inside a pore for sensing. For example, with a biasing electric field, graphene nanopores have been demonstrated for DNA transport in experiments,15−17 and their applications for nucleotide sensing were studied theoretically;18,19 nanopores in a single-layer molybdenum disulfide (MoS2) sheet have also been proven in experiment to be capable of both DNA translocation and sensing;20−22 additionally, DNA transport through nanopores in a 2D hexagonal boron nitride23,24 and in a 2D tungsten disulfide (WS2)25 sheet was demonstrated in experiments, as well. Remarkably, recent advances in nanofabrication allow researchers to integrate distinct 2D materials into van der Waals (vdW) heterostructures.26 A plethora of combinations of 2D
ccompanied and prompted by the success of proteinpore-based DNA sequencing,1−3 tremendous efforts have been devoted to develop a biomimetic solid-state nanopore platform with merit of robustness and scalability.4−9 Current research works have been focused either on the transport of DNA through a solid-state nanopore or on the sensing of each type of DNA nucleotides; however, their integration to form a coherent sequencing device has remained challenging. Typically, a sinle-stranded DNA (ssDNA) molecule can be driven through a nanometer-sized hole in a thin solid film that separates cis and trans solution reservoirs, by a biasing electric field created by a pair of electrodes inserted in the two reservoirs. For the sensing purpose, a large electric field is beneficial for differentiating ionic currents blocked by different nucleotides inside a nanopore, but it may permit the DNA transport at an ultrahigh speed not matched by the one for accurate sensing. An additional pair of electrodes built around a nanopore was proposed to measure transversal electronic tunneling currents for sensing a nucleotide between the two electrodes,10−14 which raises another challenge of avoiding the cross-talking among multiple pairs of electrodes in a device. Given that the nucleotide sensing has to be electric (via ionic or electronic currents), methods that allow a controlled and nonelectrically driven transport of DNA through © XXXX American Chemical Society
Received: February 16, 2018 Accepted: April 5, 2018
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DOI: 10.1021/acsnano.8b01297 ACS Nano XXXX, XXX, XXX−XXX
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water molecules, 542 K+, and 523 Cl−. A 20-mer ssDNA molecule with a random sequence was initially placed around the pore, mainly residing on the MoS2 side of the heterostructure. Atoms in the heterostructure were fixed at their initial lattice positions during the equilibration and following production runs. With one nucleotide in the 3′-end of the ssDNA molecule restrained slightly above the graphene surface, the remaining nucleotides extended through the pore and were adsorbed on the MoS2 surface during the equilibration process (Figure 1b). Note that the adsorption of ssDNA on the MoS2 surface is consistent with findings from a previous study.33 The methods that allow an initial entry of ssDNA into the heterostructure nanopore are discussed in the Supporting Information. After the restraint on the nucleotide in the 3′-end was released during production runs, the base of that nucleotide was quickly (within several nanoseconds) adsorbed on the graphene surface (see the red nucleotide in Figure 1a,b). Detailed simulation methods are provided in the Methods section. At an increased temperature of 350 K, it was observed during the 1.7 μs MD simulation that nucleotides in the ssDNA molecule moved spontaneously and consecutively through the heterostructure nanopore. Figure 1c shows the time-dependent centers of mass (COM) of the entire ssDNA molecule, ZCOM, projected on the z-axis (perpendicular to the heterostructure surfaces). Starting from mainly being adsorbed on the MoS2 surface (ZCOM ∼ −15 Å), the ssDNA molecule underwent stepwise motions through the pore and toward the graphene surface. At ∼1.62 μs, all nucleotides in the ssDNA molecule were on the graphene surface (ZCOM = 0 Å) and remained there for the rest of the simulation time. To qualitatively understand the key force that consistently drives the transport of the ssDNA molecule from the MoS2 surface to the graphene surface, we analyzed the potential energy change of the ssDNA molecule from the simulation trajectory (more below with adsorption free energy analyses). Figure 1c shows that the pairwise vdW energies between the ssDNA molecule and the heterostructure were gradually reduced when more nucleotides in the ssDNA molecule moved from the MoS2 surface to the graphene surface. Thus, the transport was mainly driven by the difference of adsorption energies for the ssDNA molecule on two types of surfaces. From the simulation trajectory, we took some representative (total nine) snapshots of ssDNA heterostructure complex at various times to highlight the transport process (Figure 2; also see the movie in the Supporting Information). Starting with the first nucleotide above the graphene surface (Figure 2a), it took about 0.1 μs for the second nucleotide to move out of the pore and be adsorbed on the graphene surface (Figure 2b). During the next 0.3 μs or so, about two nucleotides moved onto the graphene surface every 0.1 μs (Figure 2c,d). During the following transport (Figure 2e−g), a total of 11, 12, and 13 nucleotides were adsorbed onto the graphene surface at 0.68, 0.85, and 1.13 μs, respectively. Strikingly, the last few nucleotides (from 16th to 20th) flew through the nanopore within 0.1 μs (Figure 2h,i). At about 1.7 μs, all nucleotides in the ssDNA molecule were transported through the pore and diffused freely thereafter on the graphene surface. It is worth emphasizing that all nucleotides, once being adsorbed onto the graphene surface, formed the strong π−π base stacking with the graphene sheet, accounting for the stronger vdW interaction between the ssDNA molecule and the graphene sheet (Figure 1c).
materials into one vertical stack, held together by vdW forces, have yielded many functional materials with wide applications, such as unusual electronic properties of germanene on MoS2,27 field-effect transistors (FETs),28 and photoresponsive memory devices29 formed by graphene−MoS2 heterostructures. Here, we propose and investigate nanopores in a quasi-2D heterostructure stacked by two different 2D materials, which may drive the ssDNA transport through a built-in nanopore without a biasing electric field. Due to the strong van der Waals interaction, bases of a ssDNA molecule are normally adsorbed on a 2D material such as graphene.30 Therefore, two distinct vdW surfaces of a heterostructure result in different chemical potentials for an adsorbed DNA nucleotide, and the difference provides the driving force for a continuous transport of a ssDNA molecule through the nanopore nucleotide-by-nucleotide, which is different from the Brownian ratchet. To prove the principle, we used the molecular dynamics method to illustrate the transport of a ssDNA molecule through the nanopore in a graphene−MoS2 heterostructure and analyzed theoretically the free energy landscape for the ssDNA transport.
RESULTS To model the transport process of a ssDNA molecule through the heterostructure pore, we carried out all-atom molecular dynamics simulations using the program NAMD.31 Figure 1a
Figure 1. MD simulation of ssDNA transport through a graphene− MoS2 heterostructure nanopore. (a) Perspective top view of the simulation system. Atoms in the MoS2 sheet are shown as vdW spheres (Mo, gray; S, yellow); the graphene sheet (cyan) is in the bond representation; ssDNA is in the stick representation with each nucleotide type colored differently (A, blue; T, green; C, red; G, black); water is shown transparently; and K+ and Cl− ions are colored in tan and cyan. (b) Side view of the simulation system. (c) Time-dependent centers of mass (ZCOM, projected on the z-axis) of the entire ssDNA and time-dependent interaction energies between ssDNA and the heterostructure.
illustrates the nanoscopic simulation system. The graphene sheet and the monolayer MoS2 sheet (measured about 9.88 × 9.22 nm2) are stacked on top of each other, with a binding distance of 3.4 Å.32 Any atoms in the heterostructure that are within 1 nm from the origin point (0,0) were removed to form a 2 nm diameter nanopore. The heterostructure nanopore was further solvated with a 1 M KCl electrolyte, containing 26 895 B
DOI: 10.1021/acsnano.8b01297 ACS Nano XXXX, XXX, XXX−XXX
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Table 1. Adsorption Free Energies ΔF (kcal/mol) for Four Types of DNA Bases on Graphene and MoS2 ΔF
adenine
thymine
cytosine
guanine
on Gph. on MoS2
−11.2 ± 0.4 −7.5 ± 0.3
−9.9 ± 0.2 −7.2 ± 0.4
−8.9 ± 0.3 −6.0 ± 0.3
−12.1 ± 0.3 −8.4 ± 0.4
even the weakest binding for a base on the graphene surface (C: −8.9 kcal/mol) is stronger than the strongest binding for a base on the MoS2 surface (G: −8.4 kcal/mol). Therefore, it is energetically advantageous (ΔU = UGph. − UMoS2 < 0) for desorbing a nucleotide from the MoS2 surface and adsorbing a nucleotide on the graphene surface simultaneously, resulting in the continuous transport of the ssDNA molecule from the MoS2 surface to the graphene surface through the pore. Figure 3 shows the time-dependent number m of nucleotides in the ssDNA molecule that were transported through the pore
Figure 2. Snapshots of a progressive transport of the ssDNA molecule through the heterostructure pore: (a) 0, (b) 0.10, (c) 0.23, (d) 0.38, (e) 0.68, (f) 0.85, (g) 1.13, (h) 1.60, and (i) 1.69 μs.
For a homopolymeric ssDNA molecule (e.g., poly(dA)), one nucleotide moving from the MoS2 surface into the pore is accompanied by a same type of nucleotide moving from the pore region to the graphene surface. Thus, the above analysis for different adsorption energies qualitatively accounts for the transport process. However, for the ssDNA molecule with a random sequence (containing all four nucleotide types: adenine (A), thymine (T), cytosine (C), and guanine (G)), the nucleotide moving into the pore could be different from the one moving out of the pore. Therefore, more quantitative analyses of adsorption energies of all four types of nucleotides are of interest. To obtain the adsorption free energy ΔF of each type of DNA base (without the sugar ring and phosphate group) on both sides of the heterostructure, we used the free energy perturbation method34 that allows the calculation of free energy change during the annihilation process of a molecule. We calculated free energy changes F1 and F2 for two annihilation processes in our MD system: (1) the annihilation of a DNA base on a heterostructure surface (either MoS2 or graphene) and (2) the annihilation of a DNA base that is far away from the heterostructure surface. Because water molecules fill the space originally occupied by the DNA base, the end states of the above two annihilation processes are equivalent. Note that the free energy difference between two initial states is the adsorption free energy (or chemical potential), U. Thus, according to the above thermodynamic cycle, U = F2 − F1. Theoretically, F1,2 can be obtained from the following ensemble (NPT) average,34 F1,2 = −kBTln⟨exp((Vf − Vi)/kBT)⟩, where Vi and Vf are potential energies at the initial (i) and the final (f) stages; kB is the Boltzmann constant; T is the temperature. The calculated binding free energies for the four types of DNA bases on either the MoS2 or the graphene surface of the heterostructure are summarized in Table 1. According to these results, the ranking of binding affinities of four base types on either MoS2 or graphene surface is G > A > T > C, which is consistent with previous findings.35 It is important to note that
Figure 3. Number (m) of transported nucleotides in the ssDNA molecule vs time at various temperatures: 300 K (cyan), 350 K (orange), and 400 K (red for sim-1 and brown for sim-2). Inset: Theoretical predictions of free energies F of the ssDNA molecule (N = 20) during its translocation through the pore, without considering the ssDNA−pore interaction; Δu = |ΔU|/kBT.
and resided on the graphene surface. Here, m was obtained from the integer part of N·nB/nT, where nB is the number of backbone atoms in ssDNA that are above the graphene surface, nT is the total number of the backbone atoms in ssDNA, and N (=20) is the number of nucleotides in ssDNA. When T = 350 K, interestingly, m increases in a stepwise fashion and remains at each value for a finite amount of time, which suggests that, at each step, the ssDNA molecule was temporarily trapped in a potential well. The large variation of trapping times at different steps (besides various ΔU) indicates that the forward stepwise motion is a thermally activated process. When the temperature was changed to 400 K (with two independent simulations labeled as sim-1 and sim-2) and 300 K, the transport process can speed up and slow down, respectively (Figure 3), confirming that the stepwise transport was thermally activated. Fluctuations in the number of transported nucleotides in Figure 3 indicate that one nucleotide at the border of the pore and the graphene surface can quickly move back and forth, or be in and out of a potential well. During the ssDNA transport through the heterostructure pore, there are two factors that can impose wells in the free energy landscape. One is the entropy of the ssDNA molecule, and the other is the nucleotide−pore attraction. C
DOI: 10.1021/acsnano.8b01297 ACS Nano XXXX, XXX, XXX−XXX
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ACS Nano Considering the chain entropy of the ssDNA molecule,36,37 the free energy F of the ssDNA molecule of N nucleotides with m of them being transported to the graphene surface can be written as F = (1 − γ )kBT ln[m(N − m)] + mΔU
(1)
where the surface entropic exponent γ = 0.6938 and 0.9239 for a self-avoiding 3D and 2D (considered here) polymer chain near a wall, respectively. The second term in the above equation is due to the chemical potential difference. For simplicity, here, ΔU is assumed to be constant, with a value of −6.1 kcal/mol < ΔU < −0.5 kcal/mol according to Table 1. As shown in the inset of Figure 3, when Δu = (|ΔU|/kBT) = 0, the entropy term of the ssDNA free energy leads to a barrier in the middle. Thus, the entropy force (−dF/dm) slows down the initial entry of the ssDNA molecule into the pore, but it also speeds up the exit of the ssDNA molecule (see Figure 3, red and orange lines). However, considering many trapped steps of the ssDNA molecule when 1 < m < N, the entropy alone cannot account for the observed transport behavior. Additionally, when Δu = 0.1, the barrier begins to disappear (Figure 3, inset). For the ssDNA molecule, Δu > 0.85. Therefore, the chemical potential difference dominates the entropy contribution. Note that the entropy barrier only increases slightly for a long (e.g., N = 20 000) ssDNA molecule and thus will not affect the transport (see Supporting Information). From the simulation trajectories, a detailed analysis of the transport process of each nucleotide revealed that a nucleotide can interact strongly with the nanopore surface. Figure 4a highlights detailed atomic interactions between a nucleotide and the pore. On the pore surface, positively charged Mo (+0.78e) atoms40 are exposed and attract the negatively charged phosphate group PO−4 in a nucleotide. This interaction without involving the base in a nucleotide is therefore nonspecific (or sequence-independent). Meanwhile, potential energy analysis on a single nucleotide in Figure 4b shows that while the vdW energy decreases monotonically, the electrostatic one has minimums when the nucleotide is inside the pore, confirming the importance of the Mo−PO−4 electrostatic interaction. Because of the energy well, a nucleotide is trapped inside the pore for some time before it can move or be thermally activated to the graphene surface. In Figure 4c, we show time-dependent COMs (z-component) of seven different nucleotides in the ssDNA molecule. Except for the first nucleotide that started above the pore already, for all the remaining six, their COMs were nearly constant for some time when these nucleotides were inside the pore, suggesting that they were temporarily trapped. Due to the thermal activation at 350 K, some residues have very small residence time inside the pore, which might be resolved using a smaller nanopore (with an enhanced nucleotide−pore interaction) and a reduced temperature of 300 K. Including the consecutive trapping of nucleotides on the pore surface during ssDNA transport, the free energy can be rewritten in terms of the length l of a transported ssDNA as
Figure 4. Transport dynamics of a single-nucleotide (in ssDNA) through the pore (T = 350 K). (a) Snapshot of a nucleotide inside the pore, highlighting the electrostatic interaction between the phosphate group (PO−4 ) in DNA and positively charged Mo atoms exposed on the pore surface (see the arrow). (b) Pairwise interaction energies between the ssDNA molecule and the heterostructure during the transport process. (c) Centers of mass ZCOM (projected on z-axis) of various nucleotides in the ssDNA molecules vs time.
Connecting with the discrete variable m in eq 1, the integer part of l/d is m. Here, the ssDNA transport through the pore can be alternatively viewed as nanopores sliding along the ssDNA molecule; thus for the pore being periodically trapped at each nucleotide, one can approximate the periodic free energy wells with U0 cos(2πl/d). On the free energy landscape, the contribution of the adsorption free energy difference lΔU/d is to tilt the periodic trapping potential wells U0 cos(2πl/d). It is worth noting that the tilt of periodic potential wells allows the observed unidirectional stepwise transport of ssDNA, distinguished from the Brownian ratchet (no tilting). Locally, the effective well depth decreases to |U0| − |ΔU|. When |U0| < |ΔU|, the local trapping well is not present, and the nucleotide inside the pore can quickly move through the pore. In Figure 2, there are several events where trapping times for particular nucleotides are negligible. On the contrary, when |U0| > |ΔU|, the finite potential well can trap a nucleotide for some time until being thermally activated. Therefore, it is possible to transport a ssDNA molecule nucleotide-by-nucleotide through a designed heterostructure pore (with properly chosen |U0| and |ΔU|), which is extremely important for realizing the nanopore-based DNA sequencing technology. More generally, the abovedescribed ssDNA transport belongs to the broad category of non-equilibrium processes (governed by equations similar to eq 2), such as the stick−slip motion of an AFM (atomic force microscope) tip on a solid surface,41 earthquakes along fault lines,42 overstretching transitions of a dsDNA molecule,43 and tunneling currents through Josephson Junctions.44
⎡ l(L − l) ⎤ ⎛ l⎞ l F = (1 − γ )kBT ln⎢ ⎥ + ΔU + U0 cos⎝⎜2π ⎟⎠ 2 ⎣ d ⎦ d d (2)
where L is the contour length of the ssDNA molecule; d is the spacing between two neighboring nucleotides, and U0 (
