Real-time reliable determination of binding kinetics of DNA hybridization using a multi-channel graphene biosensor

Reliable determination of binding kinetics and affinity of DNA hybridization and single-base mismatches plays an essential role in systems biology, personalized and precision medicine. The standard tools are optical-based sensors that are difficult to operate in low cost and to miniaturize for high-throughput measurement. Biosensors based on nanowire field-effect transistors have been developed, but reliable and cost-effective fabrication remains a challenge. Here, we demonstrate that a graphene single-crystal domain patterned into multiple channels can measure time- and concentration-dependent DNA hybridization kinetics and affinity reliably and sensitively, with a detection limit of 10 pM for DNA. It can distinguish single-base mutations quantitatively in real time. An analytical model is developed to estimate probe density, efficiency of hybridization and the maximum sensor response. The results suggest a promising future for cost-effective, high-throughput screening of drug candidates, genetic variations and disease biomarkers by using an integrated, miniaturized, all-electrical multiplexed, graphene-based DNA array.


Supplementary Methods
As shown in the schematic cross-section of G-FET and its equivalent electrical circuit (Fig. 2d), the gate capacitance of a G-FET is related to four parallel plate capacitors (C G1 , C G2 , C G3 and C Q ) connected in series. C G1 , C G2 , and C G3 denote the capacitance between graphene and solution, the capacitance of the DNA to solution, and the capacitance between Pt gate and solution, respectively. They are all formed due to electric double layers on the interfaces and called as the "geometrical" capacitances of the device. C Q denotes the quantum capacitance of graphene associated with the finite density of states. Therefore, the total gate capacitance C is given by When analytes (target DNAs) dock on the surface of the transistor channel, the additional DNAs give rise to changes in charges (∆q) at the solution-graphene interface. These capacitors will produce variations in electrostatic potential and in turn shift V cnp by The plate distance can be determined by the Debye length that is theoretically given by d = 2ce 2 /ε 0 ε r k B T, where T is the temperature, k B is Boltzmann's constant and c is the concentration of ions in the electrolyte. The Debye length is calculated to be ~7.3 nm in 0.01×PBS. From the model of the parallel plate capacitors, C G1 = S graphene ε r ε 0 /d 1 , C G2 =S graphene ε r ε 0 /d 2 , and C G3 =S Pt ε r ε 0 /d, where S Pt is the contact area between the electrolyte and the Pt electrode, S graphene is the contact area between the electrolyte and graphene monolayer, ε 0 is vacuum permittivity (8.85×10 -12 F/m) and ε r is the relative dielectric constant of water (80). The plate distance of C G1 (d 1 ) can be approximated as half height of the measured DNA pair (~3.4 nm). The plate distance of C G2 (d 2 ) can be approximated as Debye length subtracted by d 1 (~3.9 nm). The plate distance of C G3 can be estimated by the Debye length (~7.3 nm). Moreover, because the Debye length is longer than the DNA length in our case, the whole DNA can be detected without charge screening. Because S Pt (~7.85× 10 6 µm 2 ) >> S graphene (~4.05× 10 3 µm 2 ) (See the caption in Supplementary Figure 8b), the third item Δq/C G3 in Supplementary Eq. (2) (ΔV cnp due to DNA hybridization from Pt electrode) is negligible , as in previous studies (Phys. Rev. B 2015, 91, 205413 andP. Natl. Acad. Sci. USA, 2011, 108, 13002). Thus, the total geometrical capacitance (C TG ) of the electrolyte is estimated at ~3.9×10 -4 µF by The C Q of the graphene channel is estimated at ~8.1×10 -5 µF by C q S graphene . Here, C q is quantum capacitance per unit area of ~2 µF cm -2 (Nano Lett. 2009, 9, 3318 andNat. Nanotechnol. 2008, 3, 654). C Q is comparable to C TG and should be taken into account. The charge changes from T20 with 20 nucleotides can be described as ∆q =20neS graphene . Then, Supplementary Eq. (2) can be written as Using the above model and ΔV cnp of ~0.220 V with P20 addition, the probe density (n) of P20 in 0.01× PBS can be estimated to be ~1.140×10 11 cm -2 from Supplementary Eq.
(3). . Similarly, the estimated density of the hybridized DNA T20 was ~1.052×10 11 cm -2 from ΔV cnp of ~0.203 V. Thus, the hybridization efficiency of duplex formation can also be estimated to be ~92.3 %. Raman spectroscopy was employed to study the graphene film after its interaction with PBASE, subsequently with probe DNA P20 and target DNA T20. The characteristic peaks of PABSE and DNA were clearly observed after addition of respective molecules. In low-frequency regions, several intrinsic signals due to PBASE molecules appeared. The peak at 1332.7 cm -1 was from sp 3 bonding. The peak at 1611.4cm -1 can be assigned to the pyrene group resonance and the peak at 1383.2cm -1 is due to the introduction of disorder arising from orbital hybridization of the molecule with the graphene plane. After the probe DNA or the target DNA was immobilized on the Graphene/PBASE layer, more peaks appeared, which can be assigned to the modes of DNA. After the whole functionalization procedure, neither PBASE nor DNA Raman signals were observed on the Pt electrode, indicating that the Pt was not functionalized in the process of graphene functionalization.

Supplementary
is the UV light energy (21.2 eV), W is the energy at secondary electron cut-off, and ΔV is the voltage bias. Consistent with the hole doping effect, the work function is increased by ~0.3 eV. Figure 7. Transfer curves for a G-FET device in response to target DNAs of different mutation locations and probe DNAs of different sizes. a, P20 immobilization, hybridization with T20 and its mutant T20(TC01) (T to C at position 1), T20(TC04), T20(TC13) and T20(TC17). b, P26 immobilization, hybridization with T26 and its mutant T26(TC13). c, P23 immobilization, hybridization with T26 and its mutant T26(TC13). d, P19 immobilization, hybridization with T26 and T26(TC13). e, P15 immobilization, hybridization with T26 and its mutant T26 (TC13). f, P11 immobilization, hybridization with T26 and its mutant T26 (TC13). g, P7 immobilization, hybridization with T26 and its mutant T26 (TC13). In all cases, the target DNA's concentration is 5 nM. These charge neutrality point voltages (∆V cnp ) all shift in the positive gate voltage direction and the sizes of the shift depend on target DNA charges. Figure 8. a, Schematic diagram of the sensing model together with the equivalent circuit with four parallel plate capacitors (C G1 , C G2 , C G3 , and C Q ) and a resistance (R L ) connected in series. C G1 , C G2 , and C G3 denote the capacitance between graphene and solution, the capacitance of the DNA to solution, and the capacitance between Pt gate and solution, respectively. C Q denotes the quantum capacitance of graphene associated with the finite density of states due to Pauli principle. R L is the electrical resistance of the ionic solution. b, Schematic diagram of the location of Pt electrode within the channel in relation to the devices and inlet/outlet. The area of Pt (S Pt ) immersed in the buffer with a conservative estimate at ~7.85× 10 6 µm 2 (defined by πr×L=3.14×0.25×10×10 6 µm 2 , here, r is the radius of Pt wire, L is the length of the microfluidic channel; half of the Pt wire was immersed in the buffer), which is nearly 2000 times larger than the area of graphene S graphene of 4.05× 10 3 µm 2 defined by the graphene channel length of 45 µm and width of 90 µm. Supplementary Figure 11. The performance of G-FET device gated by using a non-polarizable Ag/AgCl electrode. a, Comparison of V g -I ds transfer curves of G-FETs using Ag/AgCl electrode and Pt electrode before and after target DNA adsorption. b, Transient response of I ds to V g pulsed from 0 to 50 mV. c, Real-time sensor responses to DNA hybridization and dissociation using the G-FET gated by a Ag/AgCl electrode.

Supplementary
To estimate the effect of polarizability of the Pt electrode on kinetic measurement, we performed the experiments with the same G-FET devices but gated using a non-polarizable Ag/AgCl electrode. Supplementary Figure 11a compares the transfer curves of G-FETs using Ag/AgCl and Pt electrodes, respectively, before and after target DNA adsorption. The Ag/AgCl electrode sets the solution potential about 300 mV lower than that of the Pt electrode. This difference can be attributed to the different solution-metal interfaces and different surface electrochemistry (Electrochemical Methods: Fundamentals and Applications, Wiley, New York, 2001). However, for both Ag/AgCl and Pt gated G-FETs, the shape of transfer curves are very similar, and the shift of transfer curves (or ∆V cnp ) is nearly identical after DNA hybridization. This result indicates that although the Pt electrode is polarizable, it produced little signal across the G-FET devices during DNA hybridization. Supplementary Figure 11b shows the transient response of I ds to V g pulsed from 0 to 50 mV. I ds rapidly responses to V g pulse with a characteristic fall and rise times at ~ 0.33 ms and 0.35 ms, respectively, similar to when the Pt electrode was employed (Supplementary Figure 3b). From the fit in Supplementary Figure 11c, we obtained the association rate constant, k a = 2.53× 10 5 M −1 s −1 , the dissociation rate constant, k d = 1.15× 10 −4 s −1 and the association equilibrium constant, K A = k a /k d =2.20×10 9 M −1 . These results are in excellent agreement with those obtained by using a Pt electrode.  Figure 18. Impact of the Debye screening on DNA sensing. a, Schematic (not to scale) diagram shows Debye length from the device surface. 1×, 0.1×, 0.05×, 0.01× and 0.005× lines represent Debye length values from the graphene surface in 1×, 0.1×, 0.05×, 0.01× and 0.005×PBS buffers, respectively. b, Real-time sensor response (∆V cnp ) of P20-T20 hybridization in different buffers. Here, the concentration of T20 is 5 nM.

Supplementary
The ionic strength of the solution has a strong effect on device sensitivity for DNA detection. Here, the P20 functionalized G-FET device in the corresponding buffers were used as the reference. The maximum of sensor response ∆V cnp increases as the ionic strength decreases from 1× PBS to 0.01× buffer. With further reduction of the ionic strength to 0.005× buffer, the maximum of ∆V cnp did not change much. The ionic strength of 0.01× buffer yields a Debye length of ~7.3 nm, which is slightly larger than the height of the target DNA (T20) of ~6.8 nm. Thus, all charges on T20 are unscreened at the sensor surface, resulting in a significant response. However, for the 5-fold (0.05× PBS, Debye length ~3.3 nm), 10-fold (0.1× PBS, Debye length ~2.3 nm) and 100-fold stronger (1× PBS, Debye length~0.7 nm) buffers, the Debye lengths are significantly shorter and screen DNA's intrinsic charges partially, which led to low sensitivity of the sensor.