Molecule-hugging graphene nanopores - Department of Molecular ...

Fig. 1. (A) The experimental device with dsDNA translocating through a nanopore in graphene mounted on a SiN x frame. (B) Open pore currents througha series of different EM-measured graphene nanopore diameters before addition of DNA. SE bars for I o are encompassed within the area of the data points;estimated errors for D EM are discussed in Materials and Methods. (C) Solution of the Laplace equation graphically displayed for the ionic current density, j (inunits of A/m 2 ), mapped through a cross-section of (Left) a short nanopore (L = 0.6 nm, D = 2.5 nm) and (Right) a longer nanopore with the same diameter (L =5 nm, D = 2.5 nm). Note the current density is strongly localized close to the edge of the short nanopore but quite uniformly distributed throughout the entirediameter within the longer nanopore. Because of its greater electrical resistance and lesser current, nowhere in the longer nanopore will the current densityreach that seen (yellow and red colors) near the perimeter of the atomically short nanopore in graphene. Scale bar and bias voltage are identical Left andRight. (D) Typical blockades as dsDNA translocates through a SiN x nanopore and through graphene nanopores of different diameters, D EM . The open porecurrent (I o ) portion of each trace is shown on the same horizontal line even though the open pore currents varied with the pore diameters; the actual value ofeach pore’s I o is stated below each pore’s EM-measured diameter (D EM ). All of the blockade traces are drawn to the same scale (indicated on the right).Unlike those in the many solid-state nanopores in SiN x we andothers have investigated, the blockade magnitudes in atomicallyshort graphene nanopores always exhibit strong inverse nanoporediameter dependence (Fig. 1D and Fig. S1). Especially forthe smaller nanopores whose diameters approach the diameterof the translocating polymer, the observed nanoampere blockademagnitudes are significantly larger than those of the picoampereblockades obtained in other nanopores, exceeding even those ofthe large blockades observed in Mycobacterium smegmatis porinA nanopores (12, 13).The large blockade magnitudes observed in the closely fittinggraphene nanopores (Fig. 1D) are a direct consequence of themolecule blocking the ionic current except in the small regionbetween the molecule’s surface and the pore’s perimeter. Becauseof the high current density and large current density variationsin this region, small variations in the polymer’s geometryor surrounding fluid properties will be significantly reflected inthe resulting blockade.To evaluate the geometrical sensitivity of graphene nanoporesto the molecule’s blocking diameter, we investigated and analyzedmany DNA translocation events for pores of different diameters.Fig. 2 shows translocation event distributions for two pores ofdifferent diameter. We characterize each DNA translocationevent by two parameters: the event duration, which indicates thetime it takes for the molecule to fully translocate through thenanopore, and the average blockade magnitude, which reflectsthe extent to which the molecule obstructs or blocks the flowof ionic current through the nanopore.In nanopores with diameters greater than ∼4 nm, dsDNAmolecules translocate through the pore either as an extendedlinear molecule (leading to a single-dip event; Fig. 2 A and B, Left)or as a folded molecule (typically more than doubling the blockademagnitude during traversal of the folded part of the molecule;Fig. 2B, Right) (14). In nanopores with diameters < ∼4 nm (Fig.2C), only unfolded molecules were observed (single-dip events;Fig. 2D, Left), consistent with the fact that these nanopores aretoo small to easily admit folded dsDNA molecules.From the translocation time distributions observed we concludethat the dsDNA molecules are minimally retarded by strong stochasticor nonspecific chemical interactions with the graphenemembrane or the nanopore edge—i.e., they translocate freelythrough the graphene nanopore under the high-salt, high-pHconditions of our experiment (Materials and Methods). This isevident because (a) the mean translocation time (T m ∼ 100 μs) isshort, consistent with free polymer translocation theory (11, 15);(b) the translocation-time distribution is narrow, with the fullwidth at half maximum (FWHM) of ∼33% of the mean translocationtime (Fig. S2) as expected from the ensemble of initialpolymer conformations in solution (15); and (c) the distribution ofblockade magnitudes from single-file DNA translocation events isnarrow, with the FWHM of 10%, indicating well-defined poreblockinggeometry. Strong stochastic interactions are not conduciveto polymer analysis because the blockade magnitude values insuch cases can be distorted by trapping (16) and coiling up of themolecule at the pore entrance, leading to much larger blockadesignals than theoretically expected for fully extended polymers.The data in Figs. 1C and 2 and Fig. S2 show a trend towardshorter translocation times for smaller pores. This effect may bedue to a decreased electroosmotic drag on the translocating DNAin smaller pores. As noted by van Dorp et al. (17), electroosmoticdrag was minimized in their smallest nanopores. But, because vanDorp and colleagues performed their experiments with relativelylarge SiN x nanopores under different conditions than those usedhere with graphene nanopores, an explanation for the shortertranslocation times with smaller diameter graphene pores willrequire further investigation. Nevertheless, in contrast to the strongAPPLIED PHYSICALSCIENCESBIOPHYSICS ANDCOMPUTATIONAL BIOLOGYGaraj et al. PNAS | July 23, 2013 | vol. 110 | no. 30 | 12193

Fig. 2. (A and C) Event plots for different diameter nanopores. Each circle corresponds to a DNA translocation event. Each of the 309 blue circles representsthe translocation of a single extended, unfolded dsDNA molecule (pH 10); each of the 170 green circles represents partially or fully folded dsDNA translocations(pH 10); and black circles represent ssDNA translocations (pH 12.5). (B and D) Single typical event current traces corresponding to one of the eventsfrom the event plots in A and C for unfolded dsDNA (blue), partially folded dsDNA (green), and ssDNA (black) whose folding is unknown. Both of the eventplots and current traces in C and D were from an experiment performed with the same nanopore.interactions that lead to the long translocation times we andothers have observed in small diameter (∼3–4 nm) SiN x nanoporesat pH 8.5 or 8.0 with 1.0 or 1.6 M KCl (14, 18–20), our pH10 with 3 M KCl conditions minimized DNA–graphene interactions(1). These results lead us to conclude that in graphenepores under our conditions, stochastic interactions between thetranslocating polymer and the nanopore perimeter are not theprimary factor that determines the rate of polymer translocation.Raising the pH of the salt solution from 10 to 12.5 denatures thedsDNA into ssDNA molecules (18). Unfolded ssDNA translocationevents (Fig. 2 C and D, Right) showblockademagnitudesless than half those of dsDNA (Fig. 2D, Left), a reflection of thereduced diameter of ssDNA. To our knowledge this is a uniqueobservation of ssDNA translocating through a graphene nanopore.Many ssDNA event durations are widely spread, extending fromless than 100 μs toover400μs (Fig. 2C). These extended translocationtimes strongly suggest that many of the ssDNA moleculesstick to, or interact with, graphene. Because it is known thatnucleobases can form π-π stacking or van der Waals interactionswith a graphene surface (21), such interactions are not surprising.The average blockade magnitude for unfolded dsDNA translocationsin graphene nanopores was measured as a function ofnanopore diameter for a series of graphene nanopores with differentdiameters (Fig. 3A, solid blue circles). A steep increase inblockade magnitude with decreasing nanopore diameter is observed.This indicates a continuing increase in sensitivity to thedifference between the polymer’s diameter and pore diameter asthe fit between the two becomes closer. For comparison, we alsomeasured dsDNA blockades for each of two electron beam drillednanopores with electron microscope-determined diameters (D EM )of 7 nm and 4 nm in 30-nm-thick SiN x (Fig. 3A, black open circles).Note that because of their more evenly distributed ionic currentdensity even when occupied by dsDNA (Fig. 3D), neither themeasured (Fig. 3A, open circles) nor the numerically calculatedblockades in longer pores (L = 30 nm, 10 nm, or 5 nm; Fig. 3A,solidblack and solid colored lines) show very pronounced increases insensitivity or resolution as the nanopore diameter is decreased.ModelTo understand the experimental data in Fig. 3A and ascertainwhether a simple model can explain the observed results, wenumerically solved the Laplace equation to determine current flowthrough an open graphene pore (I 0 ) vs. the pore diameter (Fig. S1,dashed line) and through pores of the same diameters containinga dsDNA molecule through its center (depicted in Fig. 3B), toobtain the blockade magnitude, ΔI B .Asfitting parameters we usedD C , the ion-conducting diameter of the pore; L, the length of thenanopore [essentially the ion-insulating thickness of the graphenelayer (1)]; and d poly , the diameter of the insulating DNA moleculeat the center of the pore. The best fit to the data is given by theblack dashed line in Fig. 3A for which the diameter, D C , is smallerthan the D EM by 0.5 ± 0.3 nm, L = 0.6 ± 0.4 nm, and d poly = 2.1 ±0.2 nm. The 0.5-nm correction to each nanopore diameter mayaccount for solution ions that do not approach the hydrophobicEM-determined pore perimeter due to the energy cost of an ionshedding its hydration shell within the nanopore (22, 23) or theconsequences of chemical groups bound to the graphene nanopore’sedge (22). Although we cannot rule out error in our methodof calculating D EM (Materials and Methods), we note that similarconsiderations concerning ions approaching each of the two surfacesof the membrane may account for the value of L, 0.6 ±0.4 nm, which agrees with our previously reported value of L =0.6 [+0.9, −0.6] nm (1) as well as with theoretical predictionsfor the similar interaction distance of water on the outside of asingle-walled carbon nanotube (0.31–0.34 nm) (24). Finally, wenote that the best-fit 2.1± 0.2-nm diameter value for d poly is thegenerally accepted value for the diameter of B-DNA (25).Using the parameters given above, the modeled dependenceof the blockade magnitude vs. pore diameter (Fig. 3A, dashedblack curve) is seen to fit the data (Fig. 3A, solid circles) ratherwell and leads us to conclude that the calculation and simplemodel of dsDNA as a cylinder with a diameter of 2.1 nm capturethe essential physics with the parameters L and D C absorbing allof the molecular interaction effects (26).We define the nanopore’s sensitivity (S) as the change inblockade magnitude caused by a change in the effective blockingdiameter of the translocating polymer,S D C ; d poly= −∂ðΔI B Þ∂d poly≈− ∂ðΔI BÞ+ dI o: [1]∂D C dD C12194 | www.pnas.org/cgi/doi/10.1073/pnas.1220012110 Garaj et al.

Fig. 3. (A) Average blockade magnitude for dsDNA translocations vs. nanopore diameter. Solid blue circles are the experimentally determined mean ΔI Bsignals (±SE bars) from nanopores in single-layer graphene; open circles are measured ΔI B signals from a 30-nm-long nanopore in SiN x . Errors for the D EMvalues are discussed in Materials and Methods. Solid black and colored lines are numerically simulated values for ideal circular nanopores through membranesof the indicated thicknesses. The black dashed curve is the numerically simulated ΔI B , using the dimensions of the boundary conditions D C , L, and d polyexplained in the text. Insets are transmission electron micrographs of four sample pores to which the arrows point. The full width of each Inset image = 10 nmof the graphene sample. (B) Graphical representation of the calculated current density in a 2.5-nm diameter graphene nanopore (L = 0.6 nm) traversed bydsDNA modeled as a 2.1-nm diameter insulating cylinder. (C) Calculated sensitivity gradient (SG) (main text) along the length of a DNA molecule in a graphenenanopore as in B. (D) Graphical representation of the calculated current density in a 2.5-nm diameter SiN x nanopore (L = 5 nm) traversed by dsDNAmodeled as a 2.1-nm diameter insulating cylinder. Note that in contrast to the atomically short graphene nanopore in B, the ionic current density in a longpore remains relatively low and quite uniformly distributed throughout the small space between the nanopore’s diameter and the dsDNA’s diameter, evenwhen the nanopore is occupied by dsDNA.APPLIED PHYSICALSCIENCESBIOPHYSICS ANDCOMPUTATIONAL BIOLOGYEq. 1 is obtained by equating the Taylor expansions ofΔI B ðD C ; d poly Þ in terms of small changes in d poly to those in termsof small changes in D C (SI Text, Derivation of Eq. 1). S is thereforethe sum of the negative slope of the dashed line in Fig. 3A and theslope of the dotted line in Fig. 1B as a function of nanopore diameter.As D EM falls below ∼3.5 nm (D C < 2.8 nm), the value ofthe negative slope of the dashed line in Fig. 3A exceeds 0.3 nA/Å inour 3-M KCl medium with a bias of 160 mV. This shows that foreach 0.1-Å change in the graphene nanopore diameter of thesetightly fitting nanopores there is a 30-pA change in the ionic currentthrough the DNA-filled nanopore. On the other hand, Eq. 1shows that the sensitivity to molecule diameter change is augmentedby the slope in Fig. 1B (which exceeds 0.38 nA/Å), yieldingan S that exceeds 0.65 nA/Å. This shows that for each 0.1-Åchange in the polymer’s diameter in a tightly fitting nanopore therewould be, remarkably, a >65-pA change in the ionic currentthrough the polymer-filled nanopore. Similar results should beobtained for ssDNA (d ∼ 1.4 nm) when similarly tight-fitting nanoporesbecome available.If a graphene nanopore is used to resolve differences in thegeometrical and conductive properties of the fluid along the lengthof a translocating DNA molecule, one must also be concernedwith how the pore’s sensitivity falls off as a function of the distance,z, from the symmetry plane of the membrane. This longitudinalsensitivity gradient (SG) (Fig. 3C) is the resolution function of thenanopore molecule system that identifies where the contributionsto S come from along the molecule’s length. The nanopore sensitivitymust be the integral of this sensitivity gradient. It followsthat the resolution function is given by1SG = limδd→0 δd R dVd poly +δ ddz− dV d polydz; [2]where R is the pore resistance when occupied by a translocatingmolecule, and V d poly (z) is the electrostatic potential along thesurface and length of a molecule of diameter, d poly , as a functionof distance from the pore, z. The sensitivity gradient full width athalf maximum of ≤0.6 nm for the D EM = 3.2-nm pore (Fig. 3C)agrees with our prior estimate of a graphene nanopore’s resolution(1). This potential for both excellent resolution and highsensitivity is a consequence of the sharply peaked current densitynear the tightly fitted molecule’s surface in an atomically thinnanopore (Fig. 3B).The high sensitivity and resolution suggest that a graphenenanopore may be an ideal sensor for nanopore sequencing becauseof the large absolute values of the ionic current differencesGaraj et al. PNAS | July 23, 2013 | vol. 110 | no. 30 | 12195

that would discriminate among nucleobases along a strand ofDNA. It will therefore be important to test this potential bydemonstrating that the results shown here with dsDNA are infact also found when testing ssDNA with precisely crafted graphenenanopores that closely fit the smaller 1.2- to 1.4-nm diameterof a single DNA strand. We have not yet been able toreliably produce such small pores in graphene using electronbeam drilling but are optimistic that the recent proof-of-principledemonstration of an atom-by-atom method to grow graphenenanopores (9) will allow us to do so in the near future.Reaping the benefits of graphene for achieving improved polymercharacterization will also require solutions to several of thesame problems that have been addressed by others, using proteinnanopores (13, 27): (a) the need for a ratcheting method to controlthe rate of polymer translocation (28) and suppress Brownian molecularmotion (15) and (b) the suppression of large 1/f ionic currentnoise that can severely degrade the ionic current signal-to-noiseratio. It remains to be seen whether new approaches will be requiredto control polymer translocation through graphene pores (29) orwhether the approaches already used with biological pores (27) canalso be applied to graphene pores. Likewise, further research will berequired to determine how to optimally suppress the large 1/f ioniccurrent noise frequently observed in graphene nanopores (Fig. S3).This noise can be reduced by applying various coatings (2, 3), butbecause any coatings will increase the length of the nanopore, theyare not compatible with the high-resolution, high-sensitivity detectorstrategy reported here. We have consistently achieved noisereduction by simply reducing the free standing area of the graphenemembrane surrounding the nanopore (Fig. S3).The possibility of subnanometer resolution in graphene nanopores(1) together with the high resolution and geometrical sensitivityshown here bodes well for extending the molecular sensingcapabilities of solid-state nanopores. In particular we envision theeventual use of graphene nanopores as a robust solid-state alternativeto protein pores that have been shown capable of nanoporesequencing (13).Materials and MethodsThe graphene was grown via chemical vapor deposition (CVD) on a copperfoil (30), subsequently transferred (31) over the aperture on a free-standingSiNx film covering a silicon chip, and carefully processed to remove any residualhydrocarbon impurities from the polymer support film used duringthe transfer process (1). Individual graphene nanopores were drilled witha well-focused electron beam, using a JEOL 2010F EM operating at 200 kV aspreviously described (1). Micro-Raman measurements (model WITec CRM200) and EM imaging with atomic resolution (aberration-corrected ZeissLibra 200, operating at 80 keV electron energies) demonstrated that thetransferred graphene film was single layer and contained large areas freeof hydrocarbon contaminants. The graphene on its silicon chip was sealedin a fluidic cell to separate two chambers that were subsequently filled with3 M potassium-chloride solutions, pH 10 or pH 12.5. The graphene nanoporewas the only path through which ions and DNA molecules could pass betweenthe two chambers. Ten kilobase-pair restriction fragments of λ-DNAwere used for all experiments. Applying a constant 160-mV bias voltagebetween the chambers with Ag/AgCl electrodes, we measured the ioniccurrent during DNA translocation through the nanopore, using standardelectrophysiological methods. All translocation experiments were investigatedunder the high-salt, high-pH conditions (3 M KCl, pH 10, conductivity= 27.5 S/m), which we have found suppresses dsDNA adsorption onthe graphene surface.To estimate the EM-determined diameter of a nanopore, many of whichare not perfectly circular (Fig. 3A), the outline of each nanopore’s electronmicroscopic image was manually traced (as shown, for example, by the curvywhite line in Fig. S4). The nanopore’s area was then calculated by summingthe known sample areas represented by each of the pixels enclosed withinthe manually traced nanopore’s perimeter. Finally, D EM was equated totwice the radius of a perfect circle with that determined area (orange circlein Fig. S4). We estimate that because contrast in images of our clean, singlelayergraphene is very low, the manual tracing step may have introduced asmuch as ±5% error in our estimate of nanopore diameter whereas equatingthe radius with that of a perfectly circular area could have introduced nomore than an additional 5% systematic error.Numerical solutions of the Laplace equation using the measured electrolyteconductivity (27.5 S/m) were performed using the COMSOL Multiphysicsfinite-element solver in 3D geometry, cylindrically symmetric alongthe axis of the nanopore. The total ionic current was calculated by integratingcurrent density across the diameter of the nanopore. We also solved the fullset of Poisson–Nerst–Planck (PNP) equations, with the boundary conditionsat the graphene corresponding to idealized, uncharged membrane impermeableto ions. In our experimental regime with 3 M KCl concentration and160 mV applied bias, the PNP solution was found to differ by

Supporting InformationGaraj et al. 10.1073/pnas.1220012110SI TextDerivation of Eq. 1To avoid double subscripts and enhance legibility, the term usedto indicate the polymer diameter in the main text, d poly , is replacedhere by d without any subscript.Eq. 1 is derived by defining the difference between the poreand the molecule diameter asRecognizing thatit must be true thatδ = D − d:ΔI B = I 0 ðDÞ − I B ðD; dÞ = ΔI B ðD; dÞ;ΔI B ðD; D − δÞ = ΔI B ðd + δ; dÞ:Taylor expand both sides of this equation around δ = 0tofirstorder in δ to obtainΔI B ðD; DÞ + ∂ΔI Bð−δÞ = ΔI∂d B ðd; dÞ + ∂ΔI BðδÞ:∂D d=D−δ·D=d+δ·Noting that I B ðD; DÞ = 0; I B ðd; dÞ = 0 yields∂ΔI B= − ∂ΔI B+ I 0ðDÞ − I 0 ðdÞ:∂d ∂D δd=D−δ D=d+δHowever, I 0 ðdÞ = I 0 ðD − δÞ, which when expanded yields forsmall δ∂ΔI B= − ∂ΔI B+ dI 0∂d ∂D dD ;d=D D=dwhich is given in Eq. 1 in the main text. Note that for a shortnanopore I 0 ðDÞ ∝ D and therefore the last term in the aboveequation is a constant. Its value, 3.85 nA/nm, is approximatedby the slope of the dotted line in Fig. 1B.20I (nA)10643I 0ΔI B2 3 4 5 6 7Corrected Diameter, DC(nm)Fig. S1. Current through open nanopores or nanopores during double-stranded (ds)DNA translocation. Solid blue circles show the observed currents duringDNA translocation; dashed curve shows the calculated open pore current through graphene nanopores. The pore diameters shown here are the correctednanopore diameters, as explained in Modeling in the main text.Translocation Duration (μsec)25020015010050023 4 5 6Nanopore Diameter, DEM(nm)Fig. S2. Time duration for dsDNA to translocate through graphene nanopores. The solid circles and associated lines indicate the average blockade durationand full width at half maximum of all of the measured blockade durations for 10 kb dsDNA to translocate through nanopores of differing diameters.Garaj et al. www.pnas.org/cgi/content/short/12200121101of2

-3102PSD (nA /HZ)-51010-7SiN xgraphene 1graphene 2-910100210Frequency (Hz)410Fig. S3. Noise power spectral densities for three typical nanopores. Graphene 1, a 5-nm diameter nanopore in single-layer graphene suspended across a 200 ×200-nm SiN x aperture; graphene 2, a 5-nm diameter graphene nanopore across a 20-nm diameter SiN x aperture showing greatly reduced noise; SiN x , a 5-nmdiameter nanopore in SiN x with no graphene.Fig. S4. Estimating D EM . To estimate the diameters of nanopores that, as illustrated here, may be far from perfectly circular, the outline of the nanopore’sEMimage was manually traced (white line). D EM was then calculated as twice the radius of a perfect circle (orange circle) whose area was equal to the sum of all ofthe pixel areas enclosed within the manually traced pore outline (white line). For clarity, the white coloration of all pixels enclosed within the manually tracednanopore has been computer enhanced.Garaj et al. www.pnas.org/cgi/content/short/12200121102of2