pubs.acs.org/NanoLett
Rapid Sequencing of Individual DNA Molecules in Graphene Nanogaps Henk W. Ch. Postma* Department of Physics, California State University Northridge, 18111 Nordhoff Street, Northridge, California 91330-8268 ABSTRACT I propose a technique for reading the base sequence of a single DNA molecule using a graphene nanogap to read the DNA’s transverse conductance. Because graphene is a single atom thick, single-base resolution of the conductance is readily obtained. The nonlinear current-voltage characteristic is used to determine the base type independent of nanogap-width variations that cause the current to change by 5 orders of magnitude. The expected sequencing error rate is 0% up to a nanogap width of 1.6 nm. KEYWORDS DNA, sequencing, graphene
O
limit for ssDNA translocation can be expected to be the single-nucleotide size of wNT ≈ 1 nm. When different blocking currents for different homomers were first recorded, it was suggested that this would allow for rapid sequencing of individual DNA molecules while they translocate through the pore.16,17 However, the nanopore is too deep to realize single-base resolution and the current signal is too small to allow for rapid readout of the current. Both may be addressed by using exonuclease to break up the DNA and modifying the nanopore to slow down the translocation.18 However, the individual bases enter the nanopore in a different order than they have in the DNA. In addition, biological nanopores and the lipid bilayer membrane they are embedded in are only stable within a small range of temperature, pH, chemical environments, and applied electric fields, limiting practical applications. Solid-state nanopores19 do not suffer from this. They have been fabricated in Si3 N4 membranes,20 SiO2 membranes,21 and polymer films.22 Transverse-conductance based sequencing is a particularly promising next generation sequencing technology.23-27 The idea is that different bases have different local electronic densities of states with different spatial extent owing to their different chemical composition. This idea is actively being tested by using the conducting tip of a scanning tunneling microscope (STM) over immobilized DNA on a substrate.28-31 If, instead, the bases are passing one by one through a voltage-biased tunnel gap inside a solid-state nanopore, they will alternately change the current based on how the localized base states contribute to the tunnel current. However, making nanoelectrodes that are sufficiently thin to resolve the DNA conductance with single-base resolution as well as getting the nanoelectrodes aligned with the nanopore is very challenging and has not been realized yet. Here, I propose to use graphene nanogaps for DNA sequencing, using graphene as the electrode as well as the membrane material (Figure 1). Graphene is a single-atom thick hexagonal carbon lattice that was recently discovered32
ne of the greatest challenges of biotechnology is establishing the base sequence of individual molecules of DNA without the need for PCR amplification or other modification of the molecule. The Sanger method1 has proven extremely powerful and was of crucial importance to the recent sequencing of the human genome in a monumental collaborative effort.2,3 This was accomplished with shotgun sequencing, i.e., breaking the sample into small random fragments and amplifying them, sequencing these fragments using the Sanger method, and merging these sequences by determining overlapping areas by their base sequence. There are many challenges to making this technology more accurate, comprehensive, cost-effective, and fast. DNA amplification is required which is a resourceintensive process that can also introduce errors. In addition, repetitive regions larger than the Sanger read length are hard to sequence. Numerous improvements are being developed, optimizing various aspects of the sequencing process.4,5 Singlemolecule sequencing techniques are being developed that present an alternative to the Sanger method. They promise an increase in speed, reduction in cost, reduction in error rate, and increase in read length. The potential for single-molecule sequencing with biological nanopores was first explored with naturally occurring R-hemolysin (RHL) proteins that spontaneously embed themselves in a lipid bilayer and form a nanopore.6 This RHL pore is studied using electrophysiology, in which a patch-clamp amplifier records the ion current through the protein pore while a DNA molecule translocates through it under the influence of an applied transmembrane electric field acting on the negatively-charged backbone.7-15 Both single-stranded DNA (ssDNA) and double-stranded DNA (dsDNA) have been studied. ssDNA can translocate through a pore as small as 1.5 nm,15 while 3 nm is large enough for dsDNA.14 The lower * E-mail:
[email protected]. Received for review: 09/4/2009 Published on Web: 01/04/2010 © 2010 American Chemical Society
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TABLE 1. Table of Angles and Derivatives for the Different Base Types, Derived from He et al.27 R ≡ dI/dV (nS) β ≡ d3I/dV3 (nS) ψ (deg)
T
C
G
10.4 9.10 48.7
-0.218 21.0 -0.60
6.45 -15.9 157.9
m, we can extrapolate that an applied voltage of 30 mV perpendicular to the graphene membrane with effective thickness of 0.6 nm will yield an average translocation time of 3.6 µs per nucleotide. Using the requirement of the X-prize (sequence 100 genomes in 10 days) as a benchmark for a single-device sequencing technology that will sequence all of these genomes sequentially, without any pre- or postprocessing, a required ∼3 µs read time per nucleotide is obtained, well within range of the technique proposed here. To demonstrate the single-base resolution of the proposed graphene nanogap sequencing technique, a numerical simulation is presented here based on the first-principles results of He et al.27 Since electrical transport through the bases of the DNA molecule occurs through resonant tunneling, the current depends on distance as
FIGURE 1. (a) The individual bases of a ssDNA molecule (backbone in green, bases in alternating colors) sequentially occupy a gap in graphene (hexagonal lattice) while translocating through it. Their conductance is read, revealing the sequence of the molecule. The contacting electrodes to the graphene nanogap (Au, yellow) are on the far left and right sides of this image. (b) Schematic representation of the transverse conductance technique.
and has been synthesized in a variety of manners.33-35 It is an ideal material for making nanogaps for sequencing due to (1) its single-atom thickness that enables transverse conductance measurements with single-base resolution, (2) its ability to survive large transmembrane pressures,36-38 and (3) its intrinsic conducting properties. The last property is especially advantageous because the membrane is the electrode, automatically solving the problem of having to fabricate nanoelectrodes that are exactly aligned with a nanogap. Various methods can be used to obtain graphene nanogaps. They may be fabricated by nanolithography with an STM,39 in a method similar to that used for cutting carbon nanotubes.40 Other possible fabrication methods are electromigration,41 local anodic oxidation,42 TEM nanofabrication,43 or catalytic nanocutting.44,45 The ideal nanogap width is ∼1.0-1.5 nm, allowing for ssDNA to pass through it in an unfolded state15 as well as assuring a large transverse current. To estimate the expected translocation speed and therefore the sequencing rate, the graphene nanogap can be compared to both solid-state and biological nanopores. The DNA translocation speed is typically much larger in solidstate nanopores than in biological nanopores, owing to their large difference in size, aspect ratio, and DNA-pore interaction strength.46-51 For pore sizes that are small compared to the ssDNA width, the bases stick to the side of the nanogap, lagging behind the backbone, while the molecule moves through the gap.52 The translocation speed is also influenced by the unfolding speed of the DNA into the pore.14,50 The RHL pore geometry is very similar to the graphene nanogap proposed here, since (1) the ideal nanogap width of 1.0-1.5 nm is similar and (2) the narrowest region of the RHL pore has a similar thickness to the graphene sheet. This may result in similar DNA-graphene nanogap interaction strength.53 An advantage of graphene nanogaps is that their local atomic configuration can be imaged directly with the STM after the gap has been fabricated allowing for a comprehensive comparison of measurements with theoretical calculations. Assuming an average field strength in the RHL pore of 250 mV/5.2 nm ) 48 MV/ © 2010 American Chemical Society
A 26.9 -1.22 92.6
I(V) ) I0X(V)e-2κdt
where dt is the effective tunnel distance (Figure 1b), I0X(V) is a voltage-dependent prefactor that depends on the base type X ) {A, T, C, G} (Table 1), κ ) (2mφ)1/2/p ) 1.1 × 1010 m-1 is the decay constant, m ) 9.1 × 10-31 kg is the electron mass, φ ) 4.66 eV is the graphene workfunction, and p ) 6.63 × 10-34/2π J s is the Dirac constant. For applied voltages V , φ/e, the effective tunneling distance does not depend on V. A random set of N bases Xi ) {A, T, C, G} is chosen with distances xi along the backbone. The bases are 0.33 nm apart. The current is calculated as the sum of the currents due to all bases with an effective tunnel distance dt2 ) d2 + (xi - x0)2 N
I(V, x0) )
∑ I0X (V)e-2κ√d +(x - x ) i
2
i
0
2
(1)
i)1
where x0 is the position of the center of the DNA molecule with respect to the center of the nanogap. The translocation process is simulated by varying x0. The results presented in Figure 2a show a series of current peaks that correspond to the individual nucleotides. It demonstrates that the individual bases can be resolved with this technique. To demonstrate how a change in nanogap width affects the current, the simulation is performed for different nanogap widths w ) d + wNT, where wNT ≈ 1 nm is the singlenucleotide size (Figure 2). As the nanogap becomes wider, 421
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increasing nanogap width d, which explains the observed broadening. The form used here is based on the assumption that the wave functions have a symmetry that causes the decay constant not to change when the nucleotide is moving through the nanogap, i.e., when x - xi is varied. It is expected that because these wave functions do not have this symmetry, W(x) will be more articulated with a resulting higher spatial resolution than the conservative results presented here. The actual broadening function W(x) as well as the angles ψX can be determined experimentally by measuring poly-A, -T, -C, and -G consecutively. The work function in water is typically 1.1-1.4 eV lower than that in vacuum,54 which changes κ to 9.4 × 109 m-1. This means that the peaks will be wider in water by ∼8% for tunneling distances d . 1/4κ and ∼16% for d , 1/4κ. In addition to the current peaks becoming wider, the overall current decreases exponentially with the nanogap width. A technique is required that will distinguish current changes due to base variations from changes due to nanogap-width variations. Here, I propose to use the nonlinear current-voltage characteristic to allow for base characterization independent of the nanogap width. Because the current depends exponentially on distance, the first, R ≡ dI/dV, and third derivative, β ≡ d3I/dV3, depend exponentially on distance in the same manner. Therefore, ψ ≡ Arg(β + iR) is distance independent. The simulation is performed in the same manner as above, now varying the nanogap width and calculating R and β. The angle ψ is plotted as the DNA moves through the nanogap (Figure 3a). When the bases are aligned with the nanogap, the angle becomes stable and its value is approximately the same for all nanogap widths. It is then used to determine the base type, as plotted in Figure 3b. The blue triangles indicate the actual base type while the red triangle indicates what the deduced base type is based on ψ. The histogram of recorded angles is presented in 4a and shows four well-separated peaks due to the different base types. It is clear that this method can be used to sequence an individual DNA molecule although nanogap-width variations cause the current to vary by more than 5 orders of magnitude. When the nanogap is equal to 1.7 nm, the peaks become so broad that currents due to adjacent bases start to influence the current due to the base in the center of the nanogap. This leads to a misidentification of the base type (Figure 3c). This misidentification can be remedied by deconvolving the recorded current using eq 2. This broadening is the prime source of sequencing errors, and the rate at which it occurs is indicated in Figure 4b. Current fluctuations will lower the fidelity f with which dI/dV, d3I/dV3, and ψ can be measured. To simulate this, Johnson-Nyquist current noise with a magnitude of δI ) (4kBTIB/V)1/2 is added to the current signal, where kB is Boltzmann’s constant, T is the absolute temperature, B ) 1 MHz is the measurement bandwidth, and V is the applied voltage. These current fluctuations alter the sequencing error rate slightly (Figure 4b). Initially, the errors are due to
FIGURE 2. (a-c) Current across the graphene nanogap while a singlestranded DNA molecule translocates through it for three different gap widths w and bias voltage levels as indicated. (d) For this simulation, a random sequence of CGG CGA GTA GCA TAA GCG AGT CAT GTT GT was used.
the current peaks become broader. Equation 1 can be rewritten as a convolution integral to illustrate this broadening, as
I(V, x0) )
∫∞∞ B(x)W(x0 - x) dx N
B(x) ≡
∑ I0X (V)δ(x - xi) i
(2)
i)1
W(x) ≡ exp(-2κ√d2 + x2) where B(x) is the function that describes the bases’ positions and their current and W(x) is a peak function that describes the overlap between the DNA and graphene electron wave functions. It has a width δx ) (1/κ2 + 4d/κ)1/2 at 1/e of its height. The minimum width, and therefore the highest degree of spatial resolution for transverse conductance measurements, is 1/κ ) 0.09 nm, and it increases with © 2010 American Chemical Society
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( δII ) ) arctan(
δψ ) arctan
4kBTB IV
)
(3)
which leads to a sequencing error rate 1 - f for the misidentification of A as T and vice versa of
1-f)
(
( ))
ψ 1 1 + erf 2 √2δψ
(4)
where erf(x) ≡ ∫0x e-t dt is the error function. Another source of fluctuations is thermal vibrations of the graphene membrane. The membrane is easily bent in the direction perpendicular to the membrane plane owing to its single-atom thickness. Thermal vibrations of this bending mode55 lead to a stochastic variation of the position of the nanogap with respect to the DNA longitudinal axis, and it limits the longitudinal resolution with which the base’s transverse conductance can be measured. Extrapolating using the scaling behavior δxM ∝(L/t)3/2 from recent studies of spring constant and mechanical resonator measurements of few-sheet graphene membranes,55 the thermal noise amplitude can be estimated to be 0.16 nm for a 0.6 nm thick and 500 nm long membrane. This is smaller than the 0.3 nm distance between bases, which means that single-base resolutionwillbepossibledespitethesemechanicalvibrations. Brownian motion of the ssDNA molecule will lead to a stochastic variation of the position of the nucleotides δx0 inside the nanogap. An upper limit to the magnitude of this effect can be estimated from the free diffusion of DNA when it is not inside the nanogap, as δx0 ∼ (4Dτ)1/2, where D ) 1.0 × 10-8 cm2/s is the free diffusion coefficient,56 and τ ∼ 1 µs is the average time a nucleotide spends in the nanogap. This upper limit is δx0 ∼ 2 nm, which is larger than the baseto-base distance. However, the diffusion coefficient is most likely much smaller in the confined nanogap geometry.46 In addition, it may be made smaller by functionalizing the nanogap.18 Finally, driving the DNA through the nanogap more quickly will reduce τ and, consequently, δx0 even further. To prevent a parasitic current pathway from the graphene surface through the ionic solvent that bypasses the nanogap, the graphene may be covered with a self-assembled monolayer. This will also improve the wetting properties of the graphene surface, limit electrochemical reactions of the graphene surface in contact with the solvent, and prevent adhesion of the DNA to the graphene surface.57 Residual parasitic current between the unpassivated carbon atoms at the edge of the nanogap will cause an extra contribution to the current and its first derivate dI/dV. This offset can be calibrated before and after the DNA has translocated through the nanogap and subtracted to compensate for this effect. It has been calculated that geometric fluctuations of the nucleotides while they are in the nanogap can lead to large 2
FIGURE 3. (a) Angles ψ for w ) 1.08, 1.27, 1.54, 1.72 nm. When the nucleotide is at the center of the nanogap, the angle becomes stable. (b) The angle is used to determine the base type as described in the text (blue triangles, base type; red triangles, deduced base type from ψ). For w ) 1.1-1.6 nm, the base type is deduced accurately. (c) When w ) 1.7 nm, the overlapping current peaks cause misidentification.
FIGURE 4. (a) Histogram of recorded angles ψ when the nucleotide is in the center of the nanogap with width w ) 1.54 nm. Four wellseparated peaks show that the angle can be used to identify the base type. (b) Sequence error rate with and without added JohnsonNyquist noise.
broadening of the current peaks, but later the current fluctuations become dominant. The error rate can be evaluated analytically as well. The current noise amplitude causes fluctuations in R and β that are not correlated when they are measured at different frequencies with a lock-in technique, and they in turn cause fluctuations δψ in the measured angle ψ. For a high-fidelity determination of the base type, we require that δψ is much smaller than the smallest difference between the values ψ, which for the simulation presented above is ∆ψmin ) 44° between A and T. The root mean square fluctuation amplitude in the angle is equal to © 2010 American Chemical Society
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fluctuations in the transverse conductance, limiting how well nucleotides can be distinguished.25 Rotational fluctuations can be caused by (1) rotation of the bases around the bond to the backbone δθ, and (2) overall rotation of the DNA molecule inside the nanogap θ. Due to the fact that the persistence length of the DNA molecule is much larger than the base-to-base distance, it can be expected that the second effect will lead to a similar fractional change in conductance for consecutive bases as the molecule translocates through the nanogap.25 The presence of this effect and how it changes the current can therefore be deduced from a comparison of ψ for consecutive bases. The first effect will lead to a stochastic variation of the angle δθ around the average value θ. A detailed study of how this changes the nonlinear conductance and ψ is the subject of future research. These conductance fluctuations may be reduced by stabilizing the nucleotides while they are in the nanogap, e.g., by functionalizing the nanogap with cytosine27 or by the applied bias voltage.58 As an alternative to the transverseconductance technique proposed here, the presented device can also be used to directly detect voltage fluctuations due to the local and unique dipole moments of the bases.59,60 This capacitive detection approach is not preferred, however, due to its reliance on the relatively long-range capacitive interaction, possibly limiting the spatial resolution with which individual bases can be resolved.61 For further studies of the proposed technology, the contribution of counterions31 and the unique density of states of graphene need to be taken into account. In addition, doping due to adsorbed water molecules on the graphene membrane and its reduction in the absence of an underlying SiO2 substrate needs to be considered.62 Acknowledgment. I thank Saliha Akca, Marc Bockrath, Cees Dekker, Konstantin Daskalov, Michael Dickson, Karapet Karapetyan, Hankyu Lee, George Gomes, Sandeep Sankararaman, Ralph Scheicher, Jonathan Wassei, Xiaoguang Zhang, and Michael Zwolak for discussions. This Letter is dedicated to the memory of Michael Dickson. REFERENCES AND NOTES (1)
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