Graphene Sculpturene Nanopores for DNA Nucleobase Sensing

Article pubs.acs.org/JPCB

Graphene Sculpturene Nanopores for DNA Nucleobase Sensing Hatef Sadeghi, L. Algaragholy, T. Pope, S. Bailey, D. Visontai, D. Manrique, J. Ferrer, V. Garcia-Suarez, Sara Sangtarash, and Colin J. Lambert* Physics Department, Lancaster University, Lancaster LA1 4YB, U.K. S Supporting Information *

ABSTRACT: To demonstrate the potential of nanopores in bilayer graphene for DNA sequencing, we computed the current−voltage characteristics of a bilayer graphene junction containing a nanopore and found that they change significantly when nucleobases are transported through the pore. To demonstrate the sensitivity and selectivity of example devices, we computed the probability distribution PX(β) of the quantity β representing the change in the logarithmic current through the pore due to the presence of a nucleobase X (X = adenine, thymine, guanine, or cytosine). We quantified the selectivity of the bilayer-graphene nanopores by showing that PX(β) exhibits distinct peaks for each base X. To demonstrate that such discriminating sensing is a general feature of bilayer nanopores, the well-separated positions of these peaks were shown to be present for different pores, with alternative examples of electrical contacts.

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INTRODUCTION A single strand of deoxyribonucleic acid (DNA) is constructed from a deoxyribose sugar and phosphate backbone with sequences of four nucleic acid bases, adenine (A), thymine (T), guanine (G), and cytosine (C) (see Figure 1) attached along its length. Apart from well-established biological functionalities,1 DNA also exhibits interesting electrical characteristics, including a range of superconducting, conducting, semiconducting, and insulating properties.2 Sequencing of nucleobases within single-stranded DNA is the focus of a great deal of research aimed at developing efficient and cost-effective personalized medicine.3 Established technologies, such as chain-termination and single-molecule sequencing methods,4−6 are time-consuming and costly,7 and the search for alternative fourth-generation sequencing methods is attracting huge scientific interest.8,9 All molecular-based biosensors rely on a molecular recognition layer and a signal transducer that reports specific recognition events. Electrochemical or electrical methods are well-suited for DNA sequencing, because there is no need for separate transduction to an electrical signal and, therefore, detection can be accomplished with an inexpensive electrochemical analyzer.10 Furthermore, recent developments in device miniaturization provide electrical transduction capabilities at the nano- and molecular scales, leading to low-cost and low-power requirements compared to conventional methods. One implementation of this approach is based on measurement of the variation in the ionic current through a solid-state11−15 or biological16,17 nanopore, due to the translocation of a DNA strand through the pore. However, the current leakage through such pores, low signal-to-noise ratios, and poor control of the speed of the strand through the pore create significant obstacles.18,19 To overcome the key technical problems © 2014 American Chemical Society

associated with real-time, high-resolution nucleoside monophosphate detection, biological nanopores MspA and αhemolysin have been employed as recognition sites inside the pore.16 However, the sensitivity of biological nanopores to experimental conditions, the integration of biological systems into large-scale arrays, the small (approximately picoampere) ionic currents, and the mechanical instability of the lipid bilayer that supports the nanopore still need to be improved.19−22 In this article, we examine an alternative strategy that involves measuring changes in the electrical conductance of the membrane containing the pore, rather than variations in an ionic current passing through the pore. In particular, we demonstrate the potential of this approach for sequencing nucleobases passing through nanopores in bilayer graphene. For sensing applications, graphene has a number of potential advantages, such as a wide electrochemical potential window, low electrical resistance, and well-defined redox peaks, which can lead to increased sensitivity.23 It also offers superior performance for future biosensing applications24 and high sensitivity toward the detection of a range of molecules and ions.25−34 In addition, current technologies such as transmission electron microscopy (TEM) allow the drilling of nanopores with different diameters, down to subangstrom precision.35−38 Some of the first graphene nanopores for DNA sequencing were realized experimentally by Schneider et al.39 and Merchant et al.,40 who measured the change in ionic currents through graphene nanopores on top of silicon nitride due to single-molecule DNA translocation. However, the responses of devices to changes in the ionic current upon Received: April 9, 2014 Revised: May 21, 2014 Published: May 21, 2014 6908

dx.doi.org/10.1021/jp5034917 | J. Phys. Chem. B 2014, 118, 6908−6914

The Journal of Physical Chemistry B

Article

Figure 1. Schematics of the four DNA bases: adenine (A), thymine (T), guanine (G), and cytosine (C).1

Figure 2. (a) Relaxed atomic structure of a sculpted bilayer graphene nanopore with monolayer graphene leads and (b) transmission coefficient T(E). The inset in panel b shows the logarithm of the transmission coefficient T(E). The Fermi energy is set to EF = 0.0 eV.

SIESTA, the top and bottom graphene layers adjust their positions to achieve a more locally energetically stable AA stacking in the vicinity of the pore. This type of relaxation was recently reported elsewhere.48 The width of the graphene nanoribbon and the diameter of the pore in Figure 2 are ∼3 and ∼1.5 nm, respectively, with an intersheet separation of 0.34 nm. Because the distance between two bases in a DNA strand is also ∼0.34 nm,49 the proposed bilayer graphene nanopore (BLGNP) is optimized for base detection. Specifically, on one hand, a membrane of thickness more than 0.34 nm would contain more than one base at a time inside the pore, thereby reducing its ability to discriminate,50 whereas on the other hand, a monolayer pore is less stable structurally. Furthermore, the method should be easier to implement than an alternative nanopore technique that relies on locating electrodes on an insulating pore-containing substrate and passing a tunnelling current through individual nucleobases.51 To further optimize the device, we also propose that the pore be contacted to the outer current source through monolayer graphene leads, as shown in Figure 2. As shown in the side view at the bottom of Figure 2a, for the electrical current to flow from left to right through the monolayer graphene current-carrying leads, it must pass through the orbitals of the carbon atoms on the inner surface of the pore, which increases the sensitivity of the device to the presence of nucleobases. After relaxation, the surface carbon atoms are mainly sp2-bonded, although there is also a small number of unsaturated bonds. In the structure of Figure 2, these are passivated by adding hydrogen to form C−H bonds.52 In what follows, we compute the current I as a function of the voltage V between the left and right leads (i.e., between the source and drain) and show that, through appropriate data analysis, this device can be used to discriminate between nucleobases passing through the pore.

translocation of DNA bases are slow (on the scale of milliseconds)41 compared with much faster response available to direct electrical measurement (on the scale of micro- to nanoseconds).42 The first ab initio density functional theory (DFT) study of the interaction of nucleobases with a monolayer graphene nanopore device was reported by Nelson et al., where the variation of the electrical current upon translocation of DNA bases inside the pore was proposed as a detection method.43 Saha et al. also calculated the conductance of a monolayer graphene nanopore containing nucleobases and showed that the conductance depended on the orientation of the nucleobases within the pore.3 However, they did not propose a clear method of distinguishing between different bases. Furthermore, nanopores in monolayer graphene are unstable and change their shape over time.44 For DNA sequencing, it might be necessary to calibrate individual pores, and such instabilities would lead to a progressive loss of calibration. On the other hand, our calculations in refs 45 and 46 show that bilayer pores are stable, and experiments such as those reported in ref 47 show that the edge reconstruction that stabilizes such pores is persistent. For this reason, we examine in this work the potential of nanopores in bilayer graphene, which are more stable than their monolayer counterparts. An example platform consists of a bilayer graphene nanoribbon containing a reconstructed, stable nanopore, as shown in Figure 2. This structure is an example of a class of sp2bonded carbon structures known as sculpturenes.45 They are formed by sculpting selected shapes from AB-stacked bilayer graphene and allowing the shapes to spontaneously reconstruct to form stable structures of sp2-bonded carbon that remain stable over time. For the structure in Figure 2, after structure relaxation is performed using the density-functional theory code 6909



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Figure 3. (Left) Example of each nucleobase base (a) A, (b) C, (c) G, and (d) T located inside the nanopore. (Center) Logarithmic transmission log10 TX,m(E) and (right) its deviation αX,m(E) from that of the bare (unoccupied) pore.

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METHODS

positions of nucleobases within the pore, molecular dynamics simulations of the nucleobases were carried out using the LAMMPS package.55 The atoms were treated in the DREIDING force field model, a Langevin thermostat at 300 K was employed, and the atomic positions were updated in 0.02-fs time steps. During the simulation, a number of snapshots were taken, and for each frozen snapshot, the electronic structure of the combined nucleobase and nanopore was obtained self-consistently using the SIESTA-based implementation of DFT described above. From the converged

To find the optimized geometry and ground-state Hamiltonian of the structure of Figure 2, we followed the procedure described in ref 45 and employed the SIESTA53 implementation of DFT using the generalized gradient approximation (GGA) of the exchange and correlation functional with the Perdew−Burke−Ernzerhof (PBE) parametrization,54 a doubleζ polarized basis set, a real-space grid defined with a plane-wave cutoff energy of 250 Ry, and a maximum force tolerance of 40 meV/Å. To describe the many possible orientations and 6910



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should be noted that, for the purpose of this proof of principle, the effect of water was not included in the calculations, because the H−π interactions between water molecules and graphene are weak and, in a recent article,57 the effect of water was found to be insignificant. To study the sensing properties of the nanopore platform and the effect of the orientation of the bases inside the pore on the transmission, we chose 54 different configurations for each of the four nucleobases and calculated the transmission for all 4 × 54 = 216 possibilities. These configurations were obtained using molecular dynamics simulations, in which each base was allowed to move inside the pore (see the movies in the Supporting Information). Fiftyfour different snapshots were taken, and a full NEGF calculation was performed for each configuration. As examples, the left-hand side in Figure 3a−d shows one configuration for each of the A, C, G, and T bases located inside the nanopore. The resulting logarithmic transmission coefficients [log10 TX,m(E)] and their deviations from those of the bare pore [αX,m(E)] are shown at the center and right-hand side, respectively, of Figure 3. Figure 4 shows all 216 plots of log10 TX,m(E) superposed on the same graph, for each of the A, C, G, and T bases and 54

DFT calculation, the underlying mean-field Hamiltonian was combined with the SMEAGOL56 implementation of the nonequilibrium Green’s function (NEGF) method. This yields the transmission coefficient T(E) for electrons of energy E (passing from the source to the drain) through the relation T (E) = Trace{ΓR (E) GR (E) ΓL(E) GR †(E)}

(1)

Σ†L,R(E)]

In this expression, ΓL,R(E) = i[ΣL,R(E) − describes the level broadening due to the coupling between the left (L) and right (R) electrodes and the central scattering region associated with the pore; ΣL,R(E) represents the retarded self-energies associated with this coupling; and GR = (ES − H − ΣL − ΣR)−1 is the retarded Green’s function, where H is the Hamiltonian and S is the overlap matrix (both of which were obtained from SIESTA). To highlight the underlying changes in transport properties due to the presence of a nucleobase X = [A, C, G, T], with orientation m, within the pore, we computed the transmission coefficient TX,m(E) and defined the quantity αX, m(E) = log10[TX, m(E)] − log10[Tbare(E)]

(2)

where Tbare(E) is the transmission coefficient for electrons of energy E passing from left to right in the presence of a “bare” (i.e., unoccupied) pore. αX,m(E) is a measure of the difference between TX,m(E) and the transmission Tbare(E) in the absence of a base. To differentiate between different bases, we analyzed the set of all values of αX,m(E) for Emin < E < Emax and configuration m = 1, ..., M, belonging to a given base X. The probability distribution of the set {αX,m(E)}for a given base X is then defined as PX(α) =

1 M(Emax − Emin)

M

∑∫ n=1

Emax

Emin

dE δ[α − αX, m(E)] (3)

where δ[α − αX,m(E)] is a Dirac delta function, which has the property that the fraction of values of αX,m(E) between α = a and α = b is given by ∫ badα PX(α). From an experimental point of view, αX,m(E) is not directly accessible in a two-terminal device such as that shown in Figure 2; therefore, for the purpose of analyzing experimentally accessible two-terminal data, we also examined the quantity βX,m(V) defined as βX, m(V ) = log10[IX, m(V )] − log10[Ibare(V )]

Figure 4. Logarithm of the transmission coefficient versus energy for each base with 54 different configurations (a total of 216 curves).

different configurations for each base. This shows that the lowvoltage conductance alone [which is proportional to the transmission coefficient TX,m(E) evaluated at the Fermi energy E = 0] does not provide enough information to discriminate between different nucleotides and, therefore, a more comprehensive analysis based on measurement of αX or βX is required. Figure 4 also shows that the energy dependence of TX,m(E) reflects a complex interference pattern that arises from quantum interference in the vicinity of the pore surface. In this sense, the pore acts like a chaotic quantum dot, whose properties were well-studied by the mesoscopic physics community in the late 1980s.58 From the plots in Figure 4, the probability distributions PX(α) were obtained by sampling the curves at a uniformly spaced set of energies and creating histograms of the associated values of αX,m(E). The resulting probability distributions are shown in Figure 5. The presence of distinct peaks in Figure 5 demonstrates the potential of this bilayer nanopore for the discriminating sensing of nucleobases. Figure 6a shows corresponding plots of the experimentally accessible quantities βX,m(E), whose probability distributions are shown in Figure 6b. Again, the presence of distinct peaks demonstrates the excellent sensing potential of the proposed bilayer nanopore for sequencing DNA.

(4)

where IX, m(V ) =

2e h

E F + eV /2

∫E −eV /2

dE TX, m(E)

F

(5)

is the finite-bias current evaluated for bias voltage V for each orientation m = 1, ..., M, of a given base X within the pore. The probability distribution of the set {βX,m(E)} for a given base X is then defined as PX(β) =

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1 M(eVmax − eVmin)

M

∑∫ n=1

Vmax

Vmin

dV δ[β − βX, m(V )] (6)

RESULTS AND DISCUSSION Figure 2b shows the transmission coefficient Tbare(E) versus energy (where the energy origin is chosen such that Fermi energy is EF = 0.0 eV) in the absence of any nucleobase. It 6911



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calibrated prior to use. Furthermore, the ordering of the peaks also depends on sample preparation. To demonstrate this feature, the inset of Figure 7c shows the probability distributions arising when the phosphate deoxyribose backbone remains attached to the bases as they pass through the pore, as shown in the bottom structure of Figure 7a and in the Supporting Information (Figure S1). Again, the peaks in PX(β) remain well-separated, but their ordering is changed.

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CONCLUSIONS In conclusion, we have demonstrated the discriminating sensing properties of new bilayer-graphene, sculpturene-based nanopore devices by calculating the electrical current−voltage characteristics of two-terminal devices in the absence and presence of given nucleobases for many different positions and orientations of bases within the pore. The resulting fingerprint probability distribution PX(β) shows distinct peaks for different nucleobases. The proposed method is based on direct electricalcurrent measurements and potentially has clear advantages compared with conventional DNA sequencing methods based on ionic-current measurements. One of these is a higher signalto-noise ratio, because the current through the graphene is on the order of microamps, whereas the currents measured in ioncurrent-based methods are on the order of picoamps and there is no reason to suppose the noise would be greater. Another is the potential for a faster response, because conventional nanoelectronics can complete a current−voltage cycle on the scale of micro- or even nanoseconds, whereas ionic-currentbased methods require milliseconds or longer. By comparing bilayer and toroidal pores within different geometries and electrical contacts and by sensing bases in the absence and presence of the phosphate deoxyribose backbone, we have demonstrated that discriminating sensing is resilient. However, the ordering of the peaks in PX(β) depends on both the shape of the pore and the presence of phosphate deoxyribose, and therefore, it is likely that nanopores will need to be calibrated individually before use. This calibration is feasible, because bilayer nanopores are much more stable than their monolayer counterparts and graphene-based nanostructures can be interfaced with complementary metal−oxide−semiconductor (CMOS) electronics, thereby allowing them to be individually addressed and replicated many times in a single chip. Therefore, the proposed method could open new routes for label-free, fast, and inexpensive DNA sequencing.

Figure 5. Probability distribution [PX(α)] of the set {αX,m(E)} for a given base X where X = A (black), C (red), G (blue), and T (green).

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NUCLEOBASE SENSING USING ALTERNATIVE SCULPTURENES To demonstrate that discriminating sensing is a general feature of other sculpturene-based nanopores, with alternative electrical contacts, we next investigated the effects of varying the structures of both the pore and the electrical contacts. As discussed in ref 45, a range of stable nanopore-containing sculpturenes can be created by sculpting shapes from bilayer graphene and allowing the shapes to relax. Figure 7a (top) shows one such structure, obtained by cutting bilayer graphene into a torus-containing nanoribbon and allowing it to reconstruct to form a two-terminal hollow torus connected to carbon nanotube (CNT) leads. In Figure 7a, the pore is approximately 1.6 nm in diameter, and it is linked to (6,6) armchair CNTs with a thickness of approximately 0.5 nm. For the bare, unoccupied pore, Figure 6b shows the transmission coefficients for electrons of energy E. By introducing structurally optimized nucleobases into the cavity of the torus and calculating the I−V characteristics for four different orientations of each base, we obtained the probability distributions PX(β) shown in Figure 7c. Despite the more limited data set, this figure again demonstrates the potential of this nanopore for discriminating nucleobase sensing and suggests that nanopores formed from bilayer graphene provide a basic technology platform for discriminating sensing. The fact that the ordering of the peaks in Figure 7c differs from that in Figure 6b suggests that the size and shape of the pores is poorly controlled, so each pore would need to be

Figure 6. (a) Differences between the logarithm of the current in the presence of each base for 54 different configurations (βX,m). (b) Probability distribution [PX(β)] of the set {βX,m} for a given base X, where X = A (black), C (red), G (blue), and T (green). 6912



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Figure 7. (a) Atomic structure of a two-terminal hollow torus connected to carbon nanotube (CNT) leads. (b) Transmission coefficient Tbare(E) calculated for single-electron transport from the left to the right lead. (c) Probability distribution [PX(β)] of the set {βX,m} for a given base X with backbone (inset: without backbone).

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ASSOCIATED CONTENT

S Supporting Information *

Movies showing the bases inside the pore and the reconstruction of bilayer graphene in the pore side. Also, the sequence of methods operations that describes the applied computational methods in detail, as well as schematics of the four DNA bases attached to phosphate deoxyribose. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the European Union Marie-Curie Network MOLESCO. Funding was also provided by the UK EPSRC and the Spanish MINECO through Grant FIS201234858. V.G.-S. thanks the Spanish Ministerio de Economiá y Competitividad for a Ramón y Cajal fellowship (RYC-201006053).

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Graphene Sculpturene Nanopores for DNA Nucleobase Sensing

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