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Total Capture, Convection Limited Nanofluidic Immunoassays Exhibiting Nanoconfinement Effects Casey J. Galvin, Kentaro Shirai, Ali Rahmani, Kakuta Masaya, and Amy Q Shen Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b04664 • Publication Date (Web): 15 Feb 2018 Downloaded from http://pubs.acs.org on February 16, 2018

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Analytical Chemistry

Total Capture, Convection Limited Nanofluidic Immunoassays Exhibiting Nanoconfinement Effects Casey J. Galvin,∗,† Kentaro Shirai,‡ Ali Rahmani,† Kakuta Masaya,‡ and Amy Q. Shen∗,† †Micro/Bio/Nanofluidics Unit, Okinawa Institute of Science and Technology Graduate School, 1919-1 Tancha, Onna-son, Okinawa, 904-0495, Japan ‡Sysmex Corporation, 4-4-2 Takatsukadai, Kobe-shi, Hyogo, 651-2271, Japan E-mail: [email protected]; [email protected] Abstract Understanding nanoconfinement phenomena is necessary to develop nanofluidic technology platforms. One example of nanoconfinement phenomena are shifts in reaction equilibria toward reaction products in nanoconfined systems, which have been predicted theoretically and observed experimentally in DNA hybridization. Here we demonstrate a convection limited nanofluidic immunoassay that achieves total capture of a target analyte, and an apparent shift in the antibody-antigen reaction equilibrium due to nanoconfinement. The system exhibits wavefronts of the target analyte that propagate along the length of the nanochannel at a velocity much slower than that of the carrier fluid. We apply an analytical model describing the propagation of these wavefronts to determine the density of capture antibody binding sites in the enclosed nanochannel for a known concentration of the target analyte. We then use this binding site density to estimate the concentration of solutions with 5x and 10x

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less analyte. Our analysis suggests that nanoconfinement results in a preference toward binding of the target analyte with the surface-grafted capture antibody, as evidenced by an apparent reduction in the equilibrium dissociation constant. Our findings motivate the advancement of new biomedical and chemical synthesis technologies by leveraging nanoconfinement effects, and demonstrate a useful platform for studying the effect of nanoconfinement on chemical systems.

1

Introduction

Highly confined, nanofluidic systems offer a rich set of physical phenomena, 1–8 which have been used in a number of technology platforms, including surface chemistry patterning, 9 ion concentration platforms, 10 and measurement of reaction kinetcs, 11,12 among others. Implementation of heterogeneous immunoassays (i.e., a capture antibody tethered to the device surface binds with a target analyte in solution) in nanofluidic systems also offers the potential to transform immunoassay technology by achieving 100% capture of a target analyte. 13,14 Of particular interest to nanofluidic immunoassay technology are the predicted and reported changes in reaction rates and reaction equilibria due to nanoconfinement. 15–19 Recently, Shon and Cohen have shown experimentally a shift in the equilibrium of bimolecular reactions toward the hybridized state (i.e., toward reaction products) between single-stranded DNA in nanoreactors with dimensions ranging from 150 nm to 500 nm. 20 These dimensions are similar to typical heights of nanofluidic channels, suggesting the possibility this phenomenon may also occur in a heterogeneous nanofluidic immunoassay. The reason for this shift in the equilibrium has been explained either as an effect of the increased effective concentration in nanoscale reaction volumes 20 or as a shift in the value of the debinding reaction rate, kof f , as a result of a reduction in mixing entropy due to a reduction of possible mixed microstates of the reactants. 21 Observing this effect in an alternative system may provide insight into the most appropriate explanation. Heterogeneous immunoassay devices can operate in diffusion limited, reaction limited

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or convection limited regimes depending on which characteristic time scale of the device is the longest. 22–25 Diffusion limited and reaction limited systems are governed by the time it takes for a target analyte to diffuse to or react with the reaction surface, respectively. In a convection limited system, the longest time scale is the residence time of the target analyte in the device. Convection limited regimes generally occur in nanofluidic systems, in which case analyte molecules can easily diffuse to and bind with the reactive surface sites within the residence time in the nanochannel due to the reduced channel height. Therefore, we sought to understand if a convection limited immunoassay demonstrates observable nanoconfinement phenomena. In convection limited heterogeneous immunoassays, numerical simulations have predicted a propagating wavefront regime. 23,26,27 In this regime, a target analyte is totally depleted from the bulk solution by binding sites at the beginning of the reaction zone. The gradual saturation of these initial binding sites leads to propagation of the target analyte as a wavefront along the axial flow direction of the nanochannel at an effective velocity (Ueff ) that is significantly slower than the velocity of the fluid carrying the analyte through the channel (Ufluid). A continuum based model characterizing this propagating wavefront regime (the wavefront propagation model) provides an expression relating Ueff and Ufluid to key parameters of a convection limited immunoassay system in a long, shallow, broad rectangular channel with fully developed flow: nw Cs,0 1 Ufluid =1+ , Ueff h Cb,0 + KD

(1)

where h is the height of the nanochannel, nw indicates the number of walls modified with capture antibody (= 1 or 2), Cb,0 is the initial bulk analyte concentration, Cs,0 is the initial density of binding sites, and KD is the equilibrium dissociation constant of the immunochemical reaction, where KD = koff /kon , which are the dissociation and binding rate constants of the immunochemical reaction, respectively.

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Since the wavefront propagation regime is most likely to appear in nanoscale channels, this regime offers a versatile platform for analyzing the effect of nanoconfinement on reactions in the nanochannel. We analyze data obtained for solutions with varying concentrations of green fluorescent protein (GFP) in 200 nm and 580 nm tall, fused silica rectangular nanochannels modified with anti-GFP capture antibody on the channels’ surfaces. By directly visualizing and determining Ueff of the propagating GFP wavefronts, we are able to estimate the concentration of GFP solutions of known concentrations on the order of a previously estimated value of KD , and find a reduction in the apparent value of KD consistent with previous reports on nanoconfined biomolecular reactions. Moreover, our work demonstrates a total capture nanofluidic immunoassay and accompanied analytical framework that can provide information on antigen binding site density and solution concentration, antibody-antigen reaction equilibria, and multiscale phenomena in nanoconfined systems.

2 2.1

Experiments Materials

Coupling agent bis(sulfosuccinimidyl)suberate (BS3 ; # 21580)) was obtained from ThermoFisher Scientific. Enhanced green fluorescent protein (GFP; # TX 65520) was obtained from GeneTex (Irvine, CA). Anti-GFP mouse monoclonal antibody (Abcam 1218) was obtained from Abcam (Cambridge, MA).

2.2

Device Fabrication

Nanofluidic devices were fabricated following a previously described protocol. 13,30 Briefly, a combination of electron beam lithography and reactive ion etching was used to fabricate 20 parallel nanochannels in a fused silica glass substrate. The nanochannels were 2 mm long, 3 µm wide and 200 nm or 580 nm tall. In a separate fused silica glass substrate, two microchannels 500 µm wide and 4.5 µm deep were fabricated by conventional UV pho-

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tolithography techniques. The two slides were then bonded to seal the device using a fluorine containing O2 gas plasma as described previously, with the exception that the bonding was performed at 100◦ C for 1 hour. 13,36 Following bonding, an aqueous solution of 2% APTES was passed through the device from the right microchannel to the left microchannel via the nanochannels (i.e., in the opposite direction of the flow of the GFP solutions during experiments) to coat the nanochannel walls with APTES. Next, a 10 mM solution of BS3 crosslinking agent in phosphate buffer saline (PBS), followed by a 25 µg/mL solution of anti-GFP antibodies in PBS was passed through the device to tether the anti-GFP antibodies to the nanochannel surface. Next, 0.1 M Tris buffer was passed through the device to quench residual BS3 binding functionalities.

2.3

Experimental Procedure

Immunoassay experiments involved passing solutions of GFP with 2% BSA and 0.05% Tween20 in PBS buffer through the left microchannel to the right microchannel via the nanochannels using a pressured controlled pumping system (Fluigent MCFS-EZ, France). The BSA and Tween-20 were used to prevent non-specific adsorption of the GFP to the channel walls. Note that BSA and Tween-20 were present in all solutions used in these experiments, so that any effect of these additives on the reaction system is consistent across the different channel heights used in the experiments. The fluorescence intensity in the nanochannel was monitored using an inverted fluorescence microscope (Olympus IX71) equipped with an sCMOS camera (Andor, Belfast). A fluorescence micrograph was recorded every second over 160 seconds. Following GFP capture, the initial anti-GFP antibody layer could be regenerated by passing an acidic solution of Gly-HCl (pH 2.4) through the device, resulting in debinding of the GFP from the anti-GFP antibody. This strategy enabled the evaluation of multiple GFP solution concentration in the same channels with approximately the same binding site density profile.

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2.4

Data Analysis

The pixel intensity of raw fluorescence microscope images were determined along the centerline of individual nanochannels using ImageJ for each time point. These pixel intensity profiles were then processed in Matlab R2017 (The MathWorks Inc., Natwick, MA) by the following operations using custom scripts. The background was subtracted from these intensity profiles by subtracting the first profile (i.e., t = 0) from the rest of the time points. The data were then corrected for photobleaching using the algorithm described below. Finally, the data were normalized by the saturated intensity profile for each channel. Data for the 580 nm channels and the 305 nM solution in the 200 nm channels were normalized by the final time point of their respective data sets. Data for the 60 nM and 6 nM solutions in the 200 nm channels, which did not fully saturate along the length of the nanochannel, were normalized by the final time point of the 305 nM solution in the same channel. Finally, the normalized intensity profiles were fit to Equation 2 to yield the wavefront midpoint position, x0 , as a function of time. These data were imported into Origin (OriginLab, Northhampton, MA), and the derivative of x0 with respect to time determined using the included analysis scheme.

2.5

Photobleaching Correction Scheme

The photobleaching correction scheme must account for the time-dependent concentration of GFP during saturation of the binding sites as the GFP wavefront propagates along the nanochannel. To achieve this requirement and determine the photobleaching corrected intensity at a given point and time, Icorr (t), we separate the measured GFP fluorescence intensity at the same point and time, I(t), into two components: (1) the GFP intensity due to previously captured GFP molecules, I0 (t), and (2) the incremental increase of GFP intensity during the time interval between fluorescence microscope images, Iinc (t), such that I(t) = I0 (t) + Iinc (t). We assume that Iinc (t) does not undergo photobleaching in the given time interval since it comprises fresh GFP molecules that have not experienced sig-

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nificant fluorescence exposure, yet. We further assume that I0 (t) has undergone photobleaching following an exponential decay, and is equal to Icorr (t − 1) × e−at , where a is the rate of photobleaching and t is the time interval of photobleaching (i.e., 1 second). The value of a was determined by saturating the GFP binding sites along the nanochannel and fitting the decay in fluorescence intensity with time to the exponential decay function by varying a.

This fitting was done at each pixel along the entire length of the

nanochannel, and the average value of a used to the correct the experimental data. We can then calculate the incremental intensity increase as Iinc = I(t) − Icorr (t − 1) × e−at and we can calculate Icorr (t) = I0 (t)/e−at + I(t) − Icorr (t − 1) × e−at . This simplifies to Icorr (t) = I0 (t) × (1/e−at − 1) + I(t).

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Results and Discussion

3.1

Direct Visualization of Propagating Wavefronts

Experimental reports have presented evidence of the propagating wavefront regime’s existence in micro- and nanofluidic channels, 14,28 however a direct visualization and analysis of the wavefront profile and propagation has not been reported. Gervais, et al, observed a reduced propagation velocity of streptavidin (SA) flowing through a 1 µm square channel coated with biotinylated bovine serum albumin (BSA), and the authors calculated Cs,0 for two concentrations of streptavidin. Leïchlé and Chou note the presence of a depletion zone that propagates along a reaction site contained in a 600 nm channel for a DNA hybridization reaction. However, no quantitative analysis is provided. Figure 1a shows the integrated micro/nanofluidic device used in our experiments, and is based on the design used in previous work. 13 The device contains an array of 20 nanochannels (height h = 200 nm or 580 nm, width w = 3 µm and length L = 2 mm) that span microfluidic channels with heights of 4.5 µm on each side of the nanochannel arrays. The walls of the nanochannels were first coated with APTES (red layer in Figure 1a), followed by anti-GFP

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Figure 1: a, Schematic of the device design used in nanofluidic immunoassay experiments. An array of twenty nanochannels spans and connects two microchannels in fused silica glass. A GFP solution is pumped from the left side microchannels, resulting in flow of the solution through the nanochannels. The zoomed-in view of the nanochannels illustrates that the nanochannels are coated with a layer of antiGFP capture antibodies (blue Y’s) through covalent bonds with a layer of APTES (red layer) tethered to the nanochannels walls. The inset of the APTES layer illustrates the BS3 coupling chemistry used to tether the anti-GFP antibodies to the nanochannel surface. (b-f), Normalized fluorescence intensity wave profiles plotted as a function of position in the nanochannel for different combinations of channel height, h, GFP solution concentrations, Cb,0 , and convection Damkohler number, Dac (see text for definition). The values for each experiment are listed in the upper right corner of each panel.

capture antibodies (blue Y’s in Figure 1a) using BS3 coupling chemistry. Green fluorescent protein (GFP) with various initial concentration values, Cb,0 , were pumped through the microchannels at pressures of 300 kPa or 200 kPa, which resulted in the passage of the solutions from the left to the right side of the microchannel through the nanochannels. An inverted fluorescent microscope (Olympus IX71) equipped with an sCMOS camera (Andor) was used to record GFP fluorescence in 1 second intervals over 160 seconds while the GFP solution passes through the nanochannels. The field of view of the microscope was ≈ 400µm. A set of signal processing steps (cf. Experimental Section) transformed

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Table 1: Dimensionless parameters and relevant time scales of reported experimental systems

Ref.

h (nm) Nominal Effectivea

Cb,0 (nM)

580

540

60

200

160

700

660 1000 1000 600

This work

Shirai28 Gervais26

Leïchlé13

305 60 6 various 3600 400 1000

Peh e

DaD f

Dac

td (s)

tr d (s)

tc (s)

20 13

4.8E-3

0.9 1.4

1.5E-3

1.2

1.1

174c

0.6

1.4E-3

32

1.3E-4

0.4

11.5

878 120 120 300

12

5.8E-3

0.2

2

7.2E-2

72

1.2

2.7E-1

37

2.2E-3 1.6E-2 1.6E-2 2.4E-3

1.5 0.2 0.2 9.0E-3

2.3 16.7 16.7 0.3

P (kPa) 300 200

Ufluidb (µm/s) 1820c 1210d

300

300 N/A

a) See text for determination of effective heights b) Calculated assuming Hagen-Pouiselle flow in a rectangular, shallow channel c) Pressure = 150 kPa at entrance of nanochannels d) Pressure = 100 kPa at entrance of nanochannels e) D = 5×10−11 m2 /s for this work; 6×10−11 m2 /s for Gervais, et al.; 1.5×10−10 m2 /s for Leïchlé, et al. f) Assumed Cs,0 = 10−9 mol/m2 for this work; 36×10−9 mol/m2 for Gervais, et al; 16×10−9 mol/m2 for Leïchlé, et al.

the raw fluorescence intensity data for each channel visible in the microscope viewing field into the normalized wave profiles shown in Figure 1b-f, plotted from 0 to 160 seconds in 10 second intervals for all panels. The data in panels b and c are normalized by the intensity profile at 160 seconds for their respective data set. The data in panels d-f are normalized by the saturated fluorescence intensity profile of the 305 nM data set at 160 seconds since they were performed in the same set of channels (cf. Experimental Section). We estimate that the unbound GFP flowing through the channels contributes ≈ 1 to 5% of the overall fluorescence (see Supporting Information for details). Although Figure 1b-f shows data from only one nanochannel, these results are representative of additional, adjacent nanochannels. A representative micrograph of all the nanochannels visible under the microscope is shown in the Supporting Information (cf. Figure S1), and shows some channels were clogged for at least one of the GFP solutions. These channels were not considered in further analyses. Although breakdown of continuum models in aqueous-based nanofluidic systems is expected in channels with dimensions on the order of 1–10 nm, 5,6,29 our channels greatly exceed 9 ACS Paragon Plus Environment


these limiting heights. In order to confirm that the requirements necessary to apply the wavefront propagation model are satisfied, relevant time scales and dimensionless parameters of the nanofluidic systems used in this work and prior work are listed in Table 1. The dimensionless numbers are defined as: Peclet number in the transversal direction, P eh = Uf luid h/D, where D is the diffusion coefficient, and diffusional Damkohler number, DaD = kon Cs,0 h/D, and the convection Damkohler number, Dac = kon Cs,0 L/(Uf luidh), where L is the length of the nanochannel. P eh compares the relative rates of convection and diffusion, Dah compares the rate of reaction to diffusion, and Dac compares the rate of reaction to convection. Time scales are defined as the diffusion time scale, td = h2 /4D for channels with capture antibody on both top and bottom surfaces (our system); reaction time scale, tr = h/(kon Cs,0 ); and convection time scale, tc = L/Uf luid. The criteria for achieving a convection limited system are Dac » 1, tc » tr , and tc » td . Only the 200 nm nanochannels in our experiments satisfy these criteria, as well as the previously reported convection limited systems. 14,28 We confirmed this point by simulating a 200 nm heterogeneous immunoassay in COMSOL, finding good agreement between simulations results and Equation 1 (cf. Figure S2). A cursory examination of the wave profiles in Figure 1 reveals that increasing Dac and tc (i.e., moving from b to d) results in an increasingly wave-like profile of the GFP fluorescence intensity along the nanochannel. Only panels d-f at Dac = 32 show clear wave profiles propagating in the axial direction with increasing time, illustrating the benefit of reducing channel height in the nanofluidic immunoassay. Furthermore, reducing the GFP solution concentration (Cb,0 ) at constant Dac (i.e. going from d to f) results in a reduced propagation of the wavefront into the channel, which is consistent with the wavefront propagation model. Since the data for Dac = 0.8 and 1.2 are in a transition region between reaction and convection limited regimes, we focus on the data for Dac = 32 (i.e., 200 nm tall nanochannels) in further analyses with the wavefront propagation model.

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3.2

Binding Site Density Profile Determination

In order to assess the validity of the wavefront propagation model for our system, we first estimate the binding site density (BSD, Cs,0 ) profile along the nanochannels using the wavefront propagation model, and compare it to a BSD profile estimated independently from fluorescence intensity. The first step of the analysis is to determine Ueff by fitting the wave profile data, I(x), in Figure 1d-f to: x −x0 I(x) = 1 − 0.5 erfc √ , 2σ

(2)

where x0 is the wavefront midpoint position (i.e., I(x0 ) = 0.5) and σ is the width of the wavefront (cf. Supporting Information for values of σ in Figure S3). Taking the derivative of x0 with respect to time yields Ueff along the length of the nanochannel. The results of this analysis are plotted in Figure 2a for all three GFP concentrations in the 200 nm tall channels. As observed previously, reducing Cb,0 results in a slower wave propagation speed. Since the 305 nM data achieves saturation along the entire length of the nanochannel, only those data are used to calculate a BSD profile along the nanochannel using the wavefront model. The BSD profile estimated from the wavefront propagation model is compared to a BSD profile obtained from the experimental saturated fluorescence intensity in Figure 2b. The fluorescence intensity BSD profile is obtained using a calibration curve derived by plotting fluorescence in the microchannel adjacent to the nanochannel inlets against the number of GFP molecules in a unit area for the three different GFP concentrations used in the experiments (cf. Supporting Information). This calibration curve was then applied to correlate the fluorescence intensity along the nanochannels. The BSD determined by fluorescence intensity is shown in Figure 2b as the solid, green line. The black lines decorated with symbols indicate the BSD determined by the wavefront model for different effective heights of the nanochannel. Although the nominal height of the nanochannels is 200 nm, the APTES and

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Figure 2: a, Wavefront propagation speed, Uef f , in a 200 nm tall nanochannel for GFP concentrations, Cb,0 , of 305 nM (black squares), 60 nM (red squares), and 6 nM (blue squares). b, Binding site density, Cs,0 , profiles for GFP molecules along the channel walls obtained either by calibration of the fluorescene intensity (solid green line) or by calculation from the wavefront propagation model (grey lines) for nanochannel height, h, of 200 nm (circles), 180 nm (up triangles), 170 nm (down triangles) and 160 nm (squares).

anti-GFP capture antibody layers coating the nanochannels will reduce the effective height of the nanochannel. Since measuring film thicknesses inside of an enclosed nanochannel remains a significant experimental challenge, we assume a range of effective thicknesses of the combined APTES and capture antibody layers on the nanochannel (0, 10, 15 and 20 nm), and calculate the resulting BSD profile with the wavefront propagation model for effective nanochannel heights h of 200 nm (grey circles), 180 nm (grey up triangles), 170 nm (grey down triangles) and 160 nm (grey squares). The values for Ufluid at the different effective h values were calculated using the Hagen-Pouseille equation in a rectangular channel. 31 The value of Cb,0 was set at 305 nM. The value of KD = 17 nM was taken from analysis of the same anti-GFP antibody in 700 nm tall channels under reaction-limited conditions 30 (cf. Table 1). This value was determined by assuming first order Langmuir reaction kinetics and fitting the GFP fluorescence intensity data to the resulting rate equation by varying KD . A brief description of this analysis is contained in the Supporting Information. This value of KD is consistent with typical values of KD for protein-antibody pairs, and the magnitude of KD relative to Cb,0 = 305 nM results in a weak dependence on KD in this BSD profile

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analysis. Comparison of the BSD profiles obtained from the wavefront propagation model with the fluorescence intensity BSD profile reveals good agreement for the h = 160 nm data. Although results from only one nanochannel are shown here, the results are representative of four adjacent nanochannels. Since both sides of the nanochannel are coated with anti-GFP capture antibody, this value of h corresponds to a thickness of the capture antibody and tethering chemistry films of 20 nm, consistent with the typical height of 15 nm for an antibody oriented perpendicular to the channel wall. 32,33 Moreover, the BSD in the nanochannel derived from the fluorescence intensity is likely a lower bound due to scattered intensity from regions out of the focal plane in the microchannel not present in the nanochannel. The deviation between the wavefront model and fluorescence profiles at positions from 0 to ≈ 100 µm (i.e., close to the entrance of the nanochannel) may originate from the wavefront not yet reaching its fully developed profile (cf. Figure 1d). In this case, the wavefront model is not valid. Similarly, the wave profiles close to 400 µm tend to have insufficient data to fit properly because a portion of the wavefront falls outside of the microscope viewing area. From the BSD profile, we can estimate the average spacing between binding sites. Based on Figure 2b, taking 600 sites/µm2 (≈ 1 × 10−9 mol/m2 ) as a characteristic value yields an area of ≈ 1660 nm2 /site, which is in accord with a value of 1500 nm2 /site that assumes 10% of capture antibodies on the surface act as binding sites, 22 suggesting most of the capture antibodies do not bind a GFP. Assuming this area is either a square or a circle yields a diameter or edge length of 40–46 nm, respectively. This size is capable of accommodating a typical antibody with dimension of 10–15 nm across the two Fab regions. 32,33 Accounting for steric hindrance during grafting and thermal fluctuations of the grafted antibodies, these results are physically realistic. GFP is cylindrically shaped with a diameter of ≈ 2.4 nm and length of ≈ 4.2 nm. 34 Therefore, GFP will readily fit into the available binding site. Gervais, et al, reported 23 a calculated value of Cs,0 of ≈ 36 × 10−9 mol/m2 using the wavefront propagation model for the streptavidin-biotin assay used in their experiments.

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This higher value is consistent with the 7–10 biotin molecules per biotinylated-BSA molecule (i.e., a larger number of binding sites per capture molecule) used in their experiments, and the observation of secondary binding in their fluorescence data. Interestingly, the value of Cs,0 obtained by Gervais, et al, is also well below their estimated surface concentration of a close packed monolayer of biotinylated-BSA of ≈ 100 × 10−9 mol/m2 . This observation highlights the difficulty and importance of determining the actual BSD, and not just the concentration of total capture antibodies on the surface.

3.3

Observation of Apparent Change in Equilibrium Dissociation Coefficient

The previous section applied the wavefront propagation model to determine the BSD profile along the nanochannel for a known solution concentration, Cb,0 . Alternatively, if the BSD profile of the nanochannel is known, the wavefront propagation model can be used to estimate Cb,0 of the GFP solution. A value of Cb,0 = 305 nM results in a weak dependence on KD for the wavefront propagation model, since 305 nM » 17 nM. Values of Cb,0 = 60 nM and 6 nM, however, results in Cb,0 ∼ KD . By using Equation 1 to estimate values of Cb,0 on the order of KD , the analysis will become sensitive to changes in the apparent value of KD as a result of nanoconfinement. We used the BSD profile determined independently by the fluorescence calibration curve to calculate the Cb,0 values of the 60 nM and 6 nM GFP solutions. Since the Ueff data for the 6 nM solution barely reaches the entrance of the nanochannel, we used the BSD value at the very entrance of nanochannel for the entire range of Ueff values for the 6 nM data. The 60 nM data used the fluorescence intensity BSD profile without any modification. A value of h = 160 nm was used for both concentrations. For each data point, Cb,0 is estimated for four different, adjacent nanochannels using the BSD profiles as determined previously in those nanochannels (cf. Experimental Section). Although a value of KD = 17 nM was estimated previously for this antibody-antigen pair, we also computed results by setting KD

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= 0. This value of KD represents a theoretical lower limit of KD , which must be positive or equal to zero. The resulting values of Cb,0 for both KD = 17 nM and 0 nM were then plotted in Figure 3 as a function of the wavefront midpoint position, x0 .

Figure 3: a-b, GFP solution concentration, Cb,0 , values obtained using the propagating wavefront model for four adjacent nanochannels (indicated by symbol type), plotted as a function of wavefront midpoint position for 60 nM (a) and 6 nM (b) solutions. The blue data correspond to a value of KD = 0 nM, and the red data correspond to a value of KD = 17 nM. The solid lines of each color are exponential decay functions fit to all of the data of that corresponding color. The fits to blue data yield plateau values of 53 nM (a) and 6.9 nM (b), as written at the end of the fitting line. The fits to red data yield plateau values of 36 nM (a) and -10.1 nM (b). The green lines indicate the known values of the GFP concentration in the solution.

An exponential decay function fit to these data yielded plateau values of Cb,0 = 53 nM and 6.9 nM for KD = 0 nM, while setting KD = 17 nM resulted in plateau values of Cb,0 of 36 nM and -10.1 nM. A negative concentration is physically impossible, and the estimated values of Cb,0 when KD = 17 nM differ significantly from the expected value. Since the BSD analysis resulted in reasonable agreement between the wavefront propagation model and fluorescence intensity profiles, we speculate that a change in the value of KD is the most likely explanation. Furthermore, both the 60 nM and 6 nM estimations differed from the expected values of Cb,0 by approximately the value of KD determined in the 700 nm channels. This result suggests strongly an effect of nanoconfinement on the apparent KD of our system, and the resulting shift toward products (i.e., analyte bound to capture antibody)

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is consistent with the findings of Shon and Cohen. 20 It is important to note that koff is not necessarily equal to exactly zero; rather, koff is reduced significantly relative to the value of kon . A reduction in koff would prove beneficial for immunoassay platforms, as koff has been identified as a significant parameter in both heterogeneous immunoassays 24 and digital immunoassays. 37

Figure 4: Schematic of the antibody-antigen system under nanoconfinement. When the antigen (green circle) dissociates from the antibody (blue Y), the effective antigen concentration (Cb,eff ) inside the dashed box is on the order of µM. The volume of the dashed box is estimated from the surface density of binding sites. The effective concentration Cb,eff is much greater than the value of KD , possibly leading to rapid rebinding of the antigen. The figure is not drawn to scale.

As noted previously, the average area afforded to each binding site is ≈ 40 nm × 40 nm. The space above the binding site in the enclosed channel is on the order of 100 nm, yielding an effective binding site volume of ≈ 1.6 × 10−19 L. A single GFP molecule in this volume yields an effective concentration of 10 µM. Therefore, when a bound GFP molecule dissociates from a capture antibody, its effective concentration is ≈ 10–100× the nominal value of Cb,0 , with Cb,eff ≈ 1000 × KD . This concept is illustrated in Figure 4. Thus, the increased effective concentration due to nanoconfinement 20 is a reasonable explanation for the observations of our system. The alternative explanation that kof f is reduced due to a reduced entropy of mixing is not as well suited to our system. Multiplying Cb,0 by the volumetric flow rate of the 200 nm nanochannels yields a molecular flux of approximately 300 to 3000 GFP molecules for the 6 nM and 60 nM GFP solutions, respectively. Although these numbers are relatively

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small, they are two to three orders of magnitude larger than the values at which koff is predicted to be affected. 21 For that reason, we speculate that the increase in the effective concentration in the nanochannel best explains our observations. We estimated kon using the wavefront width, σ, data obtained while fitting to equation 2 (cf. Figure S3). The wavefront width can be described as: / σ=

2

1

Uf luid h

Cs,0 Cb,0

π nw kon Cs,0 −

,

(3)

z(Cb,0 +KD )

where the terms in equation 3 have the same meaning as for equation 1. Setting KD = 0 and solving for kon using data for Cb,0 = 305 nM and 60 nM yields values in the range of 3.5– 6.5 ×105 M−1 s−1 . These values are consistent with typical protein-antibody kon values, 35 and agree with the value of kon = 4.4 ×105 M−1 s−1 determined previously for this antibody under reaction limited conditions. 30 The reasonableness of these values supports the implication that the shape of the wave profile is determined entirely by the value of kon . The notion that the effective concentration inside of the nanochannel is several orders of magnitude higher than the bulk concentration, Cb,0 , raises a paradox: if the effective concentration in the nanochannel is so high, why does the wavefront propagation model obtain Cb,0 values consistent with the concentration in the bulk solution? This paradox is resolved by recalling that the nanofluidic immunoassay in these experiments operates in the convective limited regime. The rate of propagation of the wavefront is dictated by the flux of GFP into the nanochannel, which depends on Cb,0 . At the same time, the reaction equilibrium is sensitive to the effective concentration in the nanochannel, which is remarkably higher than the nominal value of Cb,0 . Thus, Ueff is sensitive to macroscopic parameters (e.g., Cb,0 ), and KD is sensitive to nanoconfinement effects. For these reasons, convection limited nanofluidic reaction systems, including immunoassays, make appealing experimental platforms for investigating multiscale phenomena.

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3.4

Practical Application of a Convection Limited Immunoassay

The results of the previous section suggest the ability to use a mediocre antibody with a relatively high value of KD to achieve a highly sensitive assay. However, developing the convection limited immunoassay and the wavefront propagation model into an actual technology platform raises a number of practical issues. Of course, any nanoconfinement effects that lead to deviation from the behavior described by the wavefront propagation model must be understood and incorporated into the model. Although we provide evidence of one example of nanoconfinement here, other unexpected phenomena may arise under further experimentation. Setting this point aside, there are other design challenges due to the convection limited regime in which the device operates. First, the sensitivity of the wavefront propagation model will depend on the tolerances achieved in the manufactured device. The high-aspect nanochannels required to achieve the wavefront propagation regime remain a challenge to manufacture and perform quality control. For example, glass capillaries are one platform consistent with inexpensive, mass produced devices. 38 Capillaries with inner diameters of 20 µm to 200 nm have expected tolerances from 5% to 50%. 39 This tolerance would need to tighten significantly for capillaries being used in a clinical setting. There are also challenges associated with the step of coating the channel walls with capture antibody. Indeed, in our experiments we observed heterogeneous, saturated fluorescence intensity along the nanochannels. Interestingly, this variation occurs in adjacent channels in approximately the same location, which suggests that the source of this variation does not arise from channel coating defects specific to a given channel. Instead, there appears to be some systematic variation across channels. As a result, we speculated that the variation stems from the manufacturing process of the channels. Since the channels are only 200 nm in height, even slight variations in the depth of the channels can result in significant proportional variation (e.g., 10 nm = 5%). This variation could arise during the initial resist coating step, etching step, bonding step, etc., and may be the accumulated result of sev-

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eral contributions. If there is a variation in channel thickness, then the flow velocity at the thinner regions will be faster compared to the taller regions. This could have two effects: (1) naturally changing flow velocity, as observed in the data, and (2) affecting the grafting of molecules during the grafting step due to shorter residence times and higher shear rates. Resolving these manufacturing challenges is critical to implementing any technology, and doing so at the nanoscale amplifies the effect of these imperfections. Propagating even small variations in channel height and binding site density would result in unsatisfactory variation in the final antigen concentration estimation. A more subtle issue concerns detecting very low antigen concentrations. In order to apply the wavefront propagation model, the antigen wave must advance far enough along the nanochannel to achieve its steady state wavefront speed. This issue is apparent in the 6 nM data set, where the wavefront barely propagates into the nanochannel. Since the system is convection limited, solutions with lower concentrations of antigen will require longer time to propagate along the nanochannel. Since the antigen concentration is an unknown quantity during the immunoassay, so then is the time required to achieve sufficient signal for analysis. One approach to solve this issue is to choose a set time (e.g., 5 minutes) to monitor the system based on the lowest concentration of the specified sensitivity range. The rest of the operating parameters can then be chosen to achieve the wavefront propagation regime. An interesting engineering design challenge arises at this point, since the operating parameters that satisfy the time requirements for the lowest concentration may not achieve the wavefront propagation regime for the highest concentrations of the sensitivty range. We suggest that demonstrating experimentally a solution to this technical issue is a worthwhile experimental pursuit.

4

Conclusion

We have demonstrated the behavior of a convection limited nanofluidic, heterogeneous immunoassay operating in the wavefront propagation regime. The wavefront propagation model

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shows promise for determining analyte binding site density in enclosed channels, and estimating solution concentrations of a target analyte without the need for a calibration curve. However, as part of our investigation we observed an apparent effect of nanoconfinement on the reaction equilibrium. The resulting apparent shift in the reaction equilibrium promises to enable the use of mediocre antibodies to conduct highly sensitive assays. However, failure to take these perturbations to macroscale behavior into account in the wavefront propagation model will inevitably lead to incorrect results. To that end, incorporating molecular scale phenomena (e.g., surface charge and polarization) may enable deeper insights into the rich physics that occur under nanoconfinement by analyzing wave propagation in nanofluidic surface reaction systems. Heterogeneous immunoassays and other biomolecular reactions confined to nanofluidic channels are an attractive platform for testing these updated models.

Acknowledgement We gratefully acknowledge support from OIST Graduate University with subsidy funding from the Cabinet Office, Government of Japan. A. Q. S. also acknowledges funding from the Japan Society for the Promotion of Science (Grants-in-Aid for Scientific Research (C), #17K06173). We also thank Ms. Kara Brower for an insightful suggestion during discussions about our experiments.

Supporting Information Available • Estimation of KD of immunochemical reaction in 700 nm tall channels (reaction limited) is provided in Section S1 in the Supporting Information. • Estimation of the contribution of unbound GFP in nanochannels to overall fluorescence intensity is provided in Section S2 in the Supporting Information. • Unprocessed fluorescence images of 305 nM GFP solution after 160 seconds are pro-

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cessed to determine the fluorescence intensity used in constructing the fluoresce-based calibration curve (Figure S1). • Comparison of Ueff /Ufluid values obtained by COMSOL Multiphysic and calculated from the wavefront propagation model are compared to show that the wavefront propagation model agrees well with numerical simulations of the nanofluidic hetereogeneous immunoassay system (Figure S2). • Wavefront width, σ from the wavefront propagation model , determined by fitting the normalized fluorescence intensity wave profiles to an error function, is plotted as a function of wavefront midpoint position (Figure S3). This material is available free of charge via the Internet at http://pubs.acs.org/.

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