Graphene Nanopores for Electronic Recognition of DNA Methylation

Dec 30, 2016 - We investigate theoretically the ability of graphene nanopore membranes to detect methylated sites along a DNA molecule by electronic s...
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Graphene Nanopores for Electronic Recognition of DNA Methylation Aditya Sarathy,†,‡ Hu Qiu,† and Jean-Pierre Leburton*,†,‡,§ †

Beckman Institute for Advanced Science and Technology, ‡Department of Electrical and Computer Engineering, and §Department of Physics, University of Illinois, Urbana, Illinois 61801, United States ABSTRACT: We investigate theoretically the ability of graphene nanopore membranes to detect methylated sites along a DNA molecule by electronic sheet current along the two-dimensional (2D) materials. Special emphasis is placed on the detection sensitivity changes due to pore size, shape, position, and the presence of defects around the nanopore in a membrane with constricted geometry. Enhanced sensitivity for detecting methylated CpG sites, labeled by methyl-CpG binding domain (MBD) proteins along a DNA molecule, is obtained for electronic transport through graphene midgap states caused by the constriction. A large square deviation from the graphene conductance with respect to the open nanopore is observed during the translocation of MBD proteins. This approach exhibits superior resolution in the detection of multiple methylated sites along the DNA compared to conventional ionic current blockade techniques.

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INTRODUCTION Hyper- and hypo-methylation of cytosines (known as methylated CpG dinucleotides) in the promoter sequences of genes in DNA are considered to be the causes of various cancers.1 One such example is the observation of hypermethylation of CpG dinucleotides in the promoter sequences of the GSTP1 gene in prostate cancer patients.2 Aberrant methylation patterns, compared to those found in normal tissues, have been associated with other cancers such as breast, liver, etc.3 There is also accumulating evidence that the epigenetic modifications of genes, determining their expression and eventual control on biological processes, change during an organism’s lifetime due to their exposure to the environment.4 In this context, it has previously been demonstrated that biological nanopores (such as α-hemolysin5 and MspA6,7) and solid state nanopores (such as silicon nitride)2,8 can be utilized to detect methylated CpG dinucleotides in DNA, providing significant insights into the development and progress of diseases.9 Ultimately, this low-cost methodology compared to current methods such as polymerase chain reaction and fluorescence-based techniques10 is expected to have a nonnegligible impact on clinical diagnosis. Graphene structures have received much attention due to their superior mechanical and electronic properties11,12 in terms of structural stability and electronic transport,11 respectively. Moreover, the electrical properties of graphene enable the use of in-plane transverse electronic current to sense the presence of biomolecules in the nanopore in addition to ionic current detection.13,14 Finally, graphene layers can be physically tailored into constricted nanoribbons to confine the electronic current around the nanopore, and assembled into a field-effect transistor membrane to tune their electrical conductivity for superior biomolecular detection sensitivity.13,15 Technological advances in the developments of experimental techniques such © XXXX American Chemical Society

as focused ion beam (FIB), lithography, and chemical vapor deposition (CVD) have enabled the fabrication of graphene based devices such as field effect transistors (FETs)16 and their eventual integration into electronics applications. Apart from electronics applications, there has also been a growing interest in utilizing graphene for biomolecular (in particular, DNA) detection13,17−21 due to its monatomic thickness enabling single base resolution sensing. Recent simulations19,20,22−25 and experimental works21,26,27 have shown that monolayer and multilayer graphene membranes containing nanopores are capable of detecting translocation of biomolecules such as DNA and proteins by ionic current blockade. While ionic current blockade measurements can also be achieved in conventional thick nanopores made from insulating materials such as SiNx and SiO2,28 the electrically active nature of graphene enables the recognition of translocating biomolecules in a nanopore based FET configuration, whereby detection is accomplished via transverse sheet current measurements.13,15,29,30 An experimental demonstration of DNA translocation through graphene nanopores via ionic and sheet currents was performed by Traversi et al.14 whereby detected events from the two measurement modalities (ionic and sheet currents) were correlated with each other. Similarly, Puster et al.31,32 demonstrated that measurements of ionic current through the nanopore along with the simultaneous response of graphene sheet currents could capture the translocation of ds-DNA through a pore neighboring a graphene nanoribbon. In both of the experiments, the variations in sheet currents were Special Issue: Klaus Schulten Memorial Issue Received: November 2, 2016 Revised: December 15, 2016

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DOI: 10.1021/acs.jpcb.6b11040 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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MEMBRANE DEVICE STRUCTURE AND SIMULATION SCHEME Figure 1a depicts the schematic of a DNA−MBD complex being threaded through a 5 nm diameter nanopore device consisting of a graphene nanoribbon as the sensing membrane. A metal gate placed below the membrane (bottom gate setup) controls the carrier concentration and thereby the electrical conductivity in the graphene membrane for high detection sensitivity.13 The graphene nanoribbon measures 11 and 16 nm along the width and length, respectively, and is shaped as a constriction or quantum point contact (QPC). This membrane is physically characterized by its dimensions, pore position, and the pore’s vicinity to membrane constriction, as shown in Figure 1b where the atomicity of a constricted membrane consisting of a pore with a diameter of 5 nm is depicted. The thickness of the membrane near the neck, denoted as Wneck, is set to 1 nm. The edges of the graphene membranes are passivated with hydrogen.15 The device is embedded in an ionic water solution, connected between source and drain electrodes to set up the sheet current. A DNA molecule with single or multiple methylated CpG sites, labeled by methyl CpG binding domain proteins (such as MBD1, MBD2, MeCP2, etc.), is translocated via electrophoresis caused by a voltage bias VTC applied across the graphene nanopore membrane. Here, we utilize MBD1 to label the methylated CpG sites due to its small thickness of ∼6 bps compared to that of MBD2 or MeCP2 (∼14 bps).2 Molecular Dynamics Simulations. The trajectories of DNA/protein translocation through graphene nanopore devices were simulated by molecular dynamics (MD) simulations. The device was solvated in a water box, with K+ and Cl− ions added to achieve a neutral system at a concentration of 1 M.34 Periodic boundary conditions were employed in all directions of the box. All MD simulations were carried out with the program NAMD 2.9,35 and visualized and analyzed with VMD. The protein and DNA were described by the CHARMM22 force field with CMAP corrections and the CHMARMM27 force field, respectively. Water was modeled by the TIP3P water model.36 A particle-mesh Ewald (PME) method was used to treat long-range electrostatics.37 A time step of 2 fs was used. van der Waals energies were calculated using a 12 Å cutoff. A constant temperature at 300 K was maintained by a Langevin thermostat.38 The nanopore system was minimized for 5000 steps, followed by a 2 ns equilibration simulation as a NPT ensemble. Subsequently, each system was further equilibrated as a NVT ensemble for 4 ns. An external electric field E = V/Lz was then applied to the system along the +z direction to drive the DNA/protein transport through graphene nanopores, where V is the voltage bias and Lz is the length of the box in the z direction. Poisson−Boltzmann Equation. In order to evaluate the effect of DNA−MBD complex translocation through a graphene nanopore on the sheet current, we extract snapshots from the DNA translocation trajectory at 100 ps intervals. For each snapshot, the electrostatic potential induced by the charge distribution of DNA was determined by means of the selfconsistent Poisson equation.13,39 Given the MD trajectory snapshots of the translocating DNA−MBD complex defining the charge density ρDNA−MBD(r) through the coordinates of all atoms and their partial charges, the electric potential φ(r) was calculated using the Poisson equation13,39

correlated to changes in the surrounding electric potential induced by the DNA translocation. Experimental demonstrations with thick solid state nanopores (SiNx)2,8 have also shown that methylated CpG sites, labeled by MBD proteins, can be detected with ionic currents. In this paper, we investigate by simulation techniques the possibility of achieving a high resolution sensing of methylated CpG sites (labeled by MBD proteins) using the transverse sheet conductance of graphene membranes with constricted geometries (depicted in Figure 1). In our approach, we use

Figure 1. (a) Schematic of the simulated nanopore device. A DNA consisting of a methylated CpG site, labeled by an MBD1 protein, is electrophoretically translocated through a 5 nm graphene nanopore. The sheet current flows along the graphene membrane due to a bias VDS applied between source and drain electrodes. (b) A typical graphene membrane containing a constriction and nanopore connected between two leads. The membrane is characterized by the diameter of the nanopore (d) and the width of the constriction (Wneck) apart from its overall length and breadth.

molecular dynamics simulations to obtain the trajectory of methylated DNA33 through the graphene nanopore. Within the Poisson−Boltzmann formalism, the variations of the electrostatic potential around the pore caused by the DNA translocation are used to calculate the electronic current variations in the graphene layer by the nonequilibrium Green’s function (NEGF) technique.13 With this coupled molecular dynamics−electronic transport scheme, we investigate the effect of lattice defects, edge irregularities, and pore design on the electronic current detection sensitivity. From the data obtained with this sensitivity analysis, we propose a graphene nanopore membrane geometry with a high transverse conductance responsiveness to the electrostatic potential variations around the pore induced by the translocating methylated DNA− protein complex. We show that the detection of methylated sites along the DNA strand via transverse electronic sheet conductance is corroborated by the ionic current blockage data. The technique of transverse sheet conductance sensing also has the ability to detect multiple methylated sites on the DNA molecule. B

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Figure 2. Sensitivity tuning of a constricted graphene nanopore membrane. The schematics of different structural variations in the graphene membrane are shown in the left column along with the corresponding transmission coefficient (T(E)) and sensitivity (dG/dEF) in the middle and right columns. The changes in the sensitivity by varying (a) pore diameter (2.4, 5.2, and 6 nm), (b) pore shape (transverse and longitudinal ellipse), (c) pore position (center located at 25, 40, 60, and 75% of the membrane length along the source−drain axis for a 5 nm diameter pore), and (d) edge conditions via defects (with 5 nm pore diameter) are considered.

Here, K+ and Cl− are the local electrolyte concentrations and C0 is the nominal concentration in the solution which we have set to 1 M. The above two equations are solved numerically until convergence criteria are met. Transverse Sheet Current Detection. The electronic transport across the membrane is based on the tight-binding Hamiltonian,13 that computes the electronic properties of the graphene sheet in the presence of external potentials φ(rn) on each carbon atom. This Hamiltonian reads

∇·[ϵ(r)∇ϕ(r)] = −e[K+(r) − Cl−(r)] − ρDNA − MBD (r) (1)

where ϵ(r) is the local permittivity and r = (x, y, z). The electrolytes in the solution (K+(r) and Cl−(r)) are also taken into account and are assumed to obey the Poisson−Boltzmann statistics ⎡ −eϕ(r) ⎤ K+(r) = C0 exp⎢ ⎥ ⎣ kBT ⎦

⎡ eϕ(r) ⎤ Cl (r) = C0 exp⎢ ⎥ ⎣ kBT ⎦

(2)

H=

∑ (ϵ − eφ(rn)) + ∑ [tijci†cj + hc] n

−

⟨i , j⟩

(4)

where the on-site energy on each carbon atom is denoted by ϵ and the electrostatic potential at the same position is given by

(3) C

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The Journal of Physical Chemistry B φ(rn). The index n denotes every carbon atom in the membrane. The second term of the Hamiltonian describes neighbor interactions with index j running over all nearest neighbor carbon atoms of site i, with the interaction between site i and j given by tij. We utilize the third nearest neighbor and three orbital interaction Hamiltonian in our calculations.13 The edges of the graphene membrane are passivated with hydrogen.40 The electrostatic potentials (φ(rn)) coupled to the molecular dynamics (MD) simulations are calculated using a self-consistent Poisson−Boltzmann approach.13,41 The transmission coefficient of a given graphene nanopore membrane geometry is given by T12̅ = −Tr[(Σs − Σ†s )GC(Σd − Σ†d)GC†]

higher than that of the 5.2 nm pore is caused by the larger membrane constriction width of the former being favored over the narrower one as electrons flow from source to drain. Due to the absence of midgap states, the 6 nm pore is not sensitive to translocating molecules within the chosen Fermi energy window. By using a field-effect transistor membrane as shown in Figure 1a, the Fermi energy of the graphene nanoribbons can then be tuned within the vicinity of the midgap states for higher detection sensitivity. Generally, a device geometry and Fermi energy are sought such that there is a high conductance variation to changing membrane-co-planar potential distributions. In experimental setups, perfectly circular nanopores within a graphene membrane (as illustrated in Figure 2a) are not easily fabricated due to the difficulty in controlling ambient device growth environments. In this context, we show in Figure 2b the transmission coefficient and sensitivity of a membrane containing an elliptical pore with the pore’s major axis aligned along either the transverse or longitudinal direction to the source−drain axis. The major axis of the pore has a length of 2.5 nm, while the minor axis is 1.5 nm long. While according to our quantum mechanical calculations (Transverse Sheet Current Detection section) mid-gap states are present in both alignments, the transverse elliptical pore consists of mid gap states with wider energy ranges. The wider mid-gap states in the transverse elliptical nanopore, contribute significantly to a higher sensitivity as shown in Figure 2b. Hence, one observes a complex interplay between the constriction width and pore geometry resulting in tunable sensitivity. In Figure 2c, we illustrate the effects of pore position on the transmission coefficients and corresponding sensitivity. Here, the graphene membrane geometries consist of a 5 nm circular nanopore at four different positions with their centers located at 25, 40, 60, and 75% of the membrane length along the source− drain axis, as denoted by pores 1, 2, 3, and 4, respectively. The transmission coefficient and corresponding sensitivity are found to be almost identical for pores 1 and 4 on one hand and pores 2 and 3 on the other hand. This behavior indicates the transmission characteristic is symmetric about the membrane axes; i.e., the transmission coefficient and conductance profile are invariant with respect to a particular direction of current flow.13 There is however some mismatch in the detection sensitivity due to the imperfect lattice symmetry between pores 2 and 3. The device sensitivity also appears to vary symmetrically with respect to pore position, hence enabling the electronic conductivity to be tuned with maximum sensitivity by adjusting the gate voltage of the field effect membrane to position the Fermi energy in the midgap state window. Apart from imperfections induced in the pore shape, position, and dimension, another possible imperfection that might occur during the experimental fabrication of the nanopore devices are defects at the graphene nanoribbon edges. Figure 2d depicts four different graphene membranes denoted 1, 2, 3, and 4, with different random distributions of defects around a nanopore of 5 nm diameter. A striking feature of these geometries is the detection sensitivity dependence on the defect positional distribution and size through the formation of midgap states in graphene as seen in the transmission coefficient. Although these defects add scattering centers for charge carriers, the membrane exhibits a similar detection sensitivity around the Fermi energy of −0.1 eV as with the 5.2 nm pore in Figure 2a in the absence of defects,

(5)

where GC is the Green’s function of the graphene membrane and Σs/d describe the self-energies of the source and drain leads, respectively.42 The total conductance at a given source drain bias of VDS is given by G=

2e VDSh

∞

∫−∞ T̅(E)[f (E) − f (E + eVDS)]dE

(6)

where f(E) is the Fermi−Dirac distribution at 300 K. The source−drain voltage is given by (μs − μd)/e = VDS. The Fermi energy is EF, and the corresponding carrier concentration can be adjusted by an external gate.

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RESULTS AND DISCUSSION Graphene nanoribbon devices with QPC geometries usually have complex energy band profiles due to the presence of the pore and irregular atomic arrangement along the edges that introduce scattering with a rich conductance spectrum.15 Figure 2 displays the effects of structural variations in graphene nanopore geometries, positions, and edge defects (left column) on transmission coefficients (middle column) and detection sensitivities (right column). The transmission coefficient (denoted as T(E)) of the QPC describes the rate at which electrons with specific energy flow from source to drain through the membrane,42 while the sensitivity is defined as the variation of conductance (G), with respect to the Fermi energy (EF) in the graphene layer, i.e., dG/dEF.13 In Figure 2a, we consider pore diameters (D) of 2.4, 5.2, and 6 nm, respectively, with their centers coinciding with the graphene membrane’s center. In the middle plot, we show the transmission coefficient for an energy range of 0.5 eV around the midgap (zero energy) of graphene, which displays a series of peaks for the 2.4 and 5.2 nm diameter nanopores, due to the presence of localized energy states caused by the pore, and depending on its size. The quantum mechanical calculations (see Transverse Sheet Current Detection section) show that the 6 nm pore does not have any midgap states, and consequently does not display any transmission peak. This is due to 2.4 and 5.2 nm pore graphene nanoribbons with increased constriction widths between the pore and the nanoribbon edge compared to the 6 nm pore configuration admit more electronic states within a particular carrier energy window.13 Hence, the conductance sensitivity (Figure 2a, right) resulting from a thermal average of the transmission coefficient over the charge carrier distribution (eq 6), exhibits broad extrema that correlate to the corresponding presence of the midgap states. The 2.4 nm nanopore membrane displays extrema of sensitivity at four distinct Fermi energies, while the 5.2 nm nanopore geometry shows only two distinct extrema. The magnitude of extrema for the 2.4 nm pore also D

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location (red dotted curve) depicts three distinct regions corresponding to the translocation of the DNA fragment above and below the protein, as well as the MBD protein itself. The duration of translocation of the DNA−MBD complex is ∼38 ns, while that of the pristine DNA is ∼19 ns, the difference likely due to the different masses of the two molecules. The snapshots of the DNA−MBD complex at different time instants are shown in the insets of Figure 3c. The conductance trace is seen to initially fluctuate slightly around ∼0.4 μS within the time window from 0 to 11 ns when the pore is occupied by only DNA. In contrast, when the MBD protein is present in the pore, a sudden drop in sheet conductance, from ∼0.24 to ∼ − 0.15 μS, is observed between the time interval from 17 to 21 ns. This large deviation of conductance within a small time window is due to the changing charge configuration along different regions of the protein. These results suggest that the translocation of MBD1 proteins could be more efficiently detected by computing the square deviation of the conductance profile in successive time windows, whereby a large deviation within a time window corresponds to translocation of the protein, as will be shown in Figure 4. Figure 4a shows the square deviations of the sheet conductance (blue) and the total charge inside the nanopore (red) within successive time intervals of 3.5 ns at the chosen Fermi energy of 0.05 eV for DNA containing a single labeled methylation site translocating through a 5 nm graphene nanopore. The plot displays a clear peak (blue) between the time interval from ∼17 to 20 ns, coinciding with the peak of the square deviation of the total charge in the pore (red). There is a slight shift between the two peaks, presumably because the graphene conductance depends not only on the total charge but also on the inhomogeneous charge distribution of MBD1 protein, making this protein a natural marker for methylation detection with transverse conductance. In order to validate this conjecture, we show a representative ionic conductance trace (defined as the ratio of ionic current to the applied translocation bias VTC) in Figure 4b, along with the number of atoms residing in the pore within a thin slice of −0.175 Å < z < 0.175 Å. It is seen that, after the protein enters the pore, a sudden reduction in ionic current leads to a conductance dip with a minimum of ∼16.2 nS while the atom number jumps to the range of 120−270, suggesting that the reduction in ionic current is caused by blockade of the MBD1 protein bound to the DNA. For an unmethylated DNA, no significant dip was seen in the current profile, validating the crucial role of the MBD1 protein in methylation detection with solid state nanopores.2 One can clearly correlate the time durations containing the largest square deviations of the transverse sheet current with that for the minimum value of ionic currents, confirming the validity of transverse sheet current detection. Apart from a large variation in conductance during the translocation of the protein, our simulations also indicate that the conductance values due to the backbone before and after the protein translocation are different. This is due to the high sensitivity of the membrane nanopore to external charges and angular conformations of the translocating DNA.13 We also observe the end of DNA adhering to the graphene pore rim (see insets of Figure 3c) after translocation which is induced by strong hydrophobic interaction between them. Such adhesion can be minimized by the use of larger voltage biases or a less hydrophobic membrane material such as MoS2.43 Figure 4c depicts the square deviation of the transverse conductance trace for the translocation of a DNA strand

except for defect 2, for which the membrane is a little less sensitive. Hence, the detection sensitivity of a given graphene nanopore membrane does not seem to be influenced by the presence of such defects. All of these observations indicate that the graphene electronic sensitivity to local electric potential variations around the nanopore can be tuned by the membrane gate voltage so that the Fermi level lies among the midgap states, where a large response of conductance to change in membrane-co-planar potential distributions is expected. Figure 3 shows the transmission coefficients, sensitivity, and a sample conductance trace during a methylated DNA

Figure 3. Electronic detection of DNA methylation with graphene nanopores. The transmission coefficient (a) and sensitivity (b) show the presence of a midgap state and corresponding high sensitivity of detection in the energy window of −0.1 to 0.05 eV, respectively. (c) A typical conductance current trace (plotted with respect to open pore conductance) during the translocation of the MBD−DNA complex through the graphene nanopore. (c, inset) Successive snapshots of the MD simulation trajectory showing the translocation of the mDBA− MBD complex through the pore.

translocation through the nanopore, simulated by molecular dynamics, under a driving voltage of VTC = 0.5 V. The transverse sheet current in graphene was calculated using quantum mechanical nonequilibrium Green’s function based transport. Figure 3a shows that the transmission coefficient consists of sharp midgap states spreading over an energy window from −0.2 to 0.1 eV, well suited for sensing the methylated sites as indicated in Figure 3b, where DNA detection is most sensitive. Representative traces of the conductance obtained from the translocation of DNA−MBD complex (red) and a pristine DNA (unmethylated DNA without MBD complexes attached, blue) are shown in Figure 3c, for which the Fermi energy of the graphene membrane is chosen to be positioned at 0.05 eV, where high detection sensitivity is achieved. The conductance trace (plotted with respect to the open pore conductance) for the translocation of pristine DNA, depicted in Figure 3c (blue), shows two slightly different levels corresponding to the presence of DNA and open pore, before and after the first 19 ns, respectively. This small conductance difference between the two situations is due to the fact that the influence of the potential on graphene membrane edges is effectively screened out by the solute. One also observes a small peak in the conductance trace of the pristine DNA translocation which is attributed to the stochastic fluctuations of the biomolecule extremity while exiting the nanopore. In contrast, the conductance trace for the DNA−MBD complex transE

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Figure 4. (a) The square deviation of the sheet conductance (SD(G − Gopen)) at a Fermi energy of 0.05 eV (blue) and the square deviation of total charge (SD(charge)) present inside the pore (red) computed within successive time windows of 3.5 ns. A peak corresponding to the square deviation denotes the translocation of the protein. (b) The calculated ionic conductance (Gionic) (blue) and the number of atoms present within the pore (red) during the translocation of a methylated DNA complexed by a single protein. A large dip in the ionic conductance denotes the translocation of the protein, validated by the maximum number of atoms within the pore during the same time window. (c) The square deviation of the sheet conductance trace (blue) at a Fermi energy of 0.05 eV calculated within successive time windows of ∼3.5 ns and the number of atoms within the pore (red) during the translocation of a DNA with two methylated sites separated by 10 base-pair distance and complexed by MBD proteins. We see two clear peaks in the square deviation corresponding to the two peaks in the number of atoms in the pore which in turn correlates to translocation of the two proteins.

successive methylated CpG sites separated by about 10 base pairs.

consisting of two methylation sites separated by 10 base pairs. The square deviation of the conductance (blue) is calculated in intervals of 3.5 ns and shows two distinct peaks, identifying the two proteins during their translocation through the pore. This is evident from the number of atoms profile, calculated within a thin slice of −0.175 Å < z < 0.175 Å, shown in red which exhibits the two peaks denoting the presence of both proteins in the pore. We also note that the magnitudes of the conductance square deviations calculated for the single and double site detection is different due to the fact that the conductance calculated at a given time instant is dependent on the angular position of the DNA backbone and the protein within the pore. Changes in these positional conformations at a given Fermi energy can strongly affect the magnitude of the measured current and electrical sensitivity of the device. Nonetheless, the peaks corresponding to the translocation of the proteins are always visible in the trace of the conductance squared deviation trace at a fixed Fermi energy.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +001 (0)217 3336813. ORCID

Jean-Pierre Leburton: 0000-0002-8183-5581 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by grants from Oxford Nanopore Technologies, the Seeding Novel Interdisciplinary Research Program of the Beckman Institute at the University of Illinois, Urbana−Champaign, and National Institutes of Health grant P41GM104601. The authors also gratefully acknowledge supercomputer time provided through the Extreme Science and Engineering Discovery Environment (XSEDE) grants MCA93S028 and TG-ECS150006 and also by the University of Illinois at Urbana−Champaign on the TAUB cluster.

SUMMARY

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In conclusion, we showed that the electronic detection sensitivity of biomolecules by a graphene nanopore membrane can be enhanced by the presence of midgap energy states in the 2D material shaped as a QPC. While the sensitivity is strongly dependent on the position of the Fermi energy and lattice defects in the graphene membrane, single and multiple methylated sites labeled by MBD proteins along the DNA are clearly identified by calculating the square deviations of the sheet conductance within successive time windows. Our methodology based on biomolecule detection by transverse sheet conductance anticipates the possibility of distinguishing

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DOI: 10.1021/acs.jpcb.6b11040 J. Phys. Chem. B XXXX, XXX, XXX−XXX