Quantifying the Affinities and Kinetics of Protein Interactions Using Silicon Nanowire Biosensors

Transcription

1 SUPPLEMENTARY INFORMATION DOI: /NNANO Quantifying the Affinities and Kinetics of Protein Interactions Using Silicon Nanowire Biosensors Xuexin Duan, Yue Li, Nitin K. Rajan, David A. Routenberg, Yorgo Modis and Mark A. Reed 1. Sensing mechanism and analytical models Detection using Si NW-FETs is based on a conductivity change in response to variations in the field or potential at their surface. In the case of our p-channel silicon, applying a negative gate voltage leads to an accumulation of carriers and thus increases the conductance, whereas applying a positive gate voltage depletes carriers and reduces the conductance. The FET biosensor is commonly operated in the linear response regime where the drain-source current (I ds ) is increasing linearly with the changing of the gate voltage (V g ) and it can be described by conventional MOSFET response (Eq S1), (S1) where e is the elementary charge, μ is the carrier mobility, ε is the permittivity of vacuum, ε r is the permittivity of the SiO 2 gate dielectric, A is the area of the channel, d is the thickness of the capacitive coupling, V ds is the drain to source voltage, L is the NATURE NANOTECHNOLOGY 1

2 channel length, V T is the threshold voltage, and g m is the device solution transconductance. We use a liquid gate V g throughout our measurements, varied when performing device characterization, and fixed while performing sensing measurements. A back gate is also fabricated on the device, but is not used during sensing measurements (floating). The backgate is used for device characterization during processing or when dry. V ds is kept fixed (at ~0.1V) during sensing measurements. This configuration is ideally suited for affinity-based detection, whereby the receptor is immobilized on the Si-NW surface. When analytes dock on the surface of the transistor channel with the receptor, the changes in surface charge density (Δq), induced by the adsorbent, produce variations in the surface potential and in turn shift the threshold voltage (ΔV T ) which can be detected as changes in the drain-source current (ΔI ds ). This can be described by Eq S2 (S2) Here C 0 is the capacitive coupling between the analyte molecules and Si channel. Eq S2 is important since it defines a direct relation between the absolute sensor output ΔI ds with the device surface charge density changes Δq. This equation holds true when the device transconductance g m doesn t change after the analytes bind to the Si surface, as has been observed in our experiments. It should be noted that g m is not necessarily a constant between different Si NW-FETs due to potential variations in threshold voltage (V T ). g m can be easily determined through I ds - V g measurement for each devices without performing actual sensing experiments (g m = ). Thus, ΔI ds /g m S2

3 is no longer a function of the device performance, and it only depends on the equivalent gate potential induced by the absorbent (ΔV T ). In the case of a surface based biomolecule specific binding, the fraction of adsorbed molecules with respect to the concentration in solution can be described following a Langmuir isotherm (assuming that the analyte is both monovalent and homogenous, the ligand is homogeneous, and that all binding events are independent ) as (S3) Here, [A], [B] max, and [AB] represent the concentration of analytes in bulk solution, the maximum surface density of functional binding sites on the Si-NW, and the surface density of adsorbed analyte molecules, respectively. K D is the equilibrium (dissociation) constant. The physical meaning of K D is important because its value indicates the strength of the binding energy between protein and receptor. A higher K D means a weaker interaction. The amount of surface charges (Δq) due to the absorbents is proportional to the surface density of adsorbed analytes as q A [AB], where q A is the electric charge contributed by the unit surface density of the adsorbed analytes to the Si NW. Thus, Eq S2 can be combined with Eq S3 to give Eq S4 (Eq 1 main text) (S4) It is worth mentioning from Eq S4, (q A /C 0 )[B] max and K D represent the maximum sensor response and the affinity properties of the biomolecule interactions on Si NW surfaces. Both can be derived through sensing measurement from a series of analyte S3

4 concentrations [A]; thus the affinity of the biomolecule interactions and the maximum response of the sensor can be determined. 2. Kinetic binding model and data fitting The binding kinetics of a surface immobilized ligand to capture an analyte in solution is typically modeled as a two-compartment reaction (Supplementary Figure 1). Since the analyte and the surface ligands are initially located physically at different points, this brings about the necessity to transport the analyte to the surface in the association phase, and to transport it away from the surface in the dissociation phase. In the association phase a depletion zone will be caused, where the local concentration of the analyte is lower than in the bulk, whereas in the dissociation phase a retention zone is present close to the surface sites that allow dissociated analyte molecules to rebind to empty surface sites before they can escape into the bulk. These concentration gradients (relative from surface to bulk) diminish continuously with time as steady state is attained. Unless the lifetime of these gradients is much faster than the timescale of the chemical kinetics, they will have a profound influence on the observed binding kinetics. For the binding kinetics on the Si nanowire FETs, [A], [A] S, [B]max, and [AB] represent the concentration of analytes in bulk solution, in the surface reaction compartment, the maximum surface density of binding sites on Si-NW, and the surface density of adsorbed analyte molecules. [A] is assumed to be constant, while the ligand concentration in the surface compartment, [A] S, is depleted due to the binding reaction, but is replenished by both diffusion of bulk analyte and by S4

5 dissociation of surface bound complexes. This two-compartment reaction can be described as follows:, (S5) k M is a diffusion-limiting rate constant, k 1 and k -1 are the association and dissociation rate constants. The net reaction rates of [A] S and [AB] can be defined by the following set of equations: (S6a) (S6b) Since kinetics were analyzed both in volume and at the surface, we must be aware of the different dimensions of each; [B] max and [AB] are expressed in mol m -2 whereas [A] S and [A] are expressed in mol m -3. By multiplying the solution rates by the volume of the reaction zone, V, and the surface rates by the area of the sensor, S, we can present each equation in the same units (mol/s). The initial conditions at time t = 0 are [A] S = [A] 0 and [AB] = 0. During desorption measurements, all reactants are washed away so [A] 0 = 0. As no analytical solutions are known for Eq S6, we solved such differential equations by numerical integration. Because the model does not specify the height of the inner compartment, there are four unknown parameters that enter Eq S6, k 1, k -1, k M, and h = V/S. However, the solutions to Eq S6 are insensitive to the value of h, and we take h = 1 to avoid having to divide the data values by h before fitting the data. 1 Consistency of S5

6 the fits is improved by fitting the binding curves recorded from different concentrations of analytes with the same kinetic parameters. In the fast mixing model, the replenishing of the analyte from the bulk is always faster than its consumption on the sensor surface, thus the analyte surface concentration [A] s can be regarded as equal to the bulk concentration [A]. Thus Eq S6 can be simplified as a first order Langmuir absorption equation, (S7) Then Eq S7 can be solved analytically: 1 (S8) Combined with, we define V eq = (q A /C 0 ) /, and the association dynamic of a sensor responses can be described as: 1 (S9a) According to Eq S9a, both k 1 and k -1 can be determined from the association phase; however, due to the rather small value of k -1, a more precise estimation of k -1 is from the direct measurement of the dissociation phase. Under the conditions of fast-mixing, in the dissociation phase, the rebinding of released analyte (dissociated analyte rebinds to ligand before leaving the sensor surface) can be ignored, thus the dissociation phase can be described by a simple first order exponential decay: (S9b) S6

7 Here V r represents small populations of bound molecules residues after the analyte desorption which can be read directly from the binding curve. Materials. 3-aminopropyltriethoxysilane (APTS), p-phenylene diisothiocyanate (PDC), and 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES) were purchased from Aldrich. EZ-Link NHS-PEG 4 -Biotin, and D(+)-Biotin were purchased from FISHER SCIENTIFIC COMPANY LLC. All materials were used as received without further purification. Streptavidin-unconjugated was purchased from ROCKLAND IMMUNOCHEMICAL. The lyophilized Streptavidin was restored with deionized water and diluted to the desired concentrations with buffers before using. DNA Oligonucleotide (5 -TCGACGTTGACGTTGACGTT) with phosphorothiate backbones was synthesized at the W.M. Keck Biotechnology Resource Laboratory at Yale University. Mouse hmgb1 was cloned into the pet28a vector (Novagen) using the Nco I and Bam HI restriction sites. HMGB1 was expressed in Escherichia coli strain Rosetta (DE3) (Novagen) by induction at OD 600 = with 1.0 mm isopropyl-β-d-thiogalactoside (IPTG) for 4 h at 37 ºC. The protein was purified by anion exchange chromatography on a Hitrap Q column (GE Healthcare), followed by size-exclusion chromatography on a Superdex /300 GL column in 50 mm Tris, ph 8.0, 50 mm NaCl, 3 mm mercaptoethanol. The HMGB1 was dialyzed against MES buffer before used. Buffer preparation g of HEPES free acid was dissolved in approx. 900 ml of pure water g NaCl was added. The solution was then titrated to ph 7.5 at room S7

8 temperature with monovalent strong base. The buffer was then made up volume to 1000 ml with pure water. For MES buffer, 1.95g of MES free acid was dissolved in approx. 900 ml of pure water g NaCl was added. The solution was then titrated to ph 5.6 at room temperature with monovalent strong acid. The buffer was then made up volume to 1000 ml with pure water. S8

9 Supplementary Figures Figure S1. Schematic representation of a two-compartment model. S9

10 Figure S2. (a) Optical image of Si-NW FET die. (b) Optical image of a single Si-NW FET device. The purple layer is the Si nanoribbon mesa, on top of the green SiO 2 BOX (buried oxide layer). The yellow regions are metal interconnects. S10

11 Figure S3. Schematic of the experimental approach for HMGB1 immobilization. S11

12 Figure S4. Real-time sensor response of HMGB1 immobilization. After the current becomes stabilized, a solution of 20 µm HMGB1 (10 mm MES ph 5.6) is passed over the p-phenylene diisothiocynate (PDC) functionalized Si NW at 30 µl/min. It clearly shows that the positively charged HMGB1 decreases the current I ds, and after a 10 min reaction, the sensor response is saturated. S12

13 . Figure S5. Control experiment of DNA binding to PDC functionalized Si NW without HMGB1immoblization. (1) Myszka, D. G.; He, X.; Dembo, M.; Morton, T. A.; Goldstein, B. Biophys. J. 1998, 75, 583. S13