Vertically sheathing laminar flow-based immunoassay using simultaneous diffusion-driven immune reactions

We present that enhanced simultaneous incubation of multiple antibodies (Abs) can be achieved by exploiting microfluidic laminar flows and difference in diffusivity between primary Ab (pAb) and secondary Ab (sAb). We demonstrate that injecting Ab of larger and smaller diffusivity (DAb) in an upper and lower laminar flow over the analyte-coated bottom surface, respectively, would result in enhanced signal intensity in the given reaction time. To prove this, we simultaneously infused anti-prostate specific antigen (PSA) pAb (upper laminar flow) and quantum dot (QD) labeled secondary Ab (QD-sAb) (lower laminar flow) to generate two Ab laminar flows vertically sheathing each other in the microfluidic device in which PSA was immobilized on the glass bottom surface. Because of the larger DAb of pAb than that of QD-sAb due to the heavy metal components of QD, anti-PSA pAb diffuses more rapidly toward the bottom surface where the immune reaction between PSA, pAb, and QD-sAb instantaneously occurs. We corroborated our principle by switching the position of the two Ab laminar flows (QD-sAb in upper and pAb in lower laminar flows) in the channel, which resulted in significantly lower intensity of QD signals than the previous method. Moreover, when we adjusted the interface of pAb and QD-sAb in upper and lower laminar flows, respectively, closer toward the bottom surface, the fluorescence signal was even more intensified. This is attributed to the increased flux of anti-PSA pAb more adjacent to the reaction site, which, in turn, enhances the binding efficiency of pAb to PSA on the surface.


Introduction
Conventional immunoassay methods, including enzyme-linked immunosorbent assays (ELISA), have become primary tools for the biochemical analysis of clinically important biomolecules, such as biomarkers for various diseases, hormones, viruses, and bacteria due to their high sensitivity and specicity. 1,2 However, despite its wide use as a gold standard for a modern immunological assay platform, the overall ELISA process remains time-consuming and labour-intensive, which oen requires multiple serial mixing and washing steps. 3 These drawbacks of the conventional immunoassay platforms are attributed to the prolonged incubation steps, which are due to the inefficient mass transport imposed by slow and infrequent delivery of antibody molecules to analytes immobilized on the solid matrix surface. 4,5 Leveraging microuidic principles for delivering reagents to the immunoreaction sites has alleviated this issue by considerably reducing the diffusion distances and allowing constant replenishment of the antibody molecules at the reaction site. [6][7][8] The additional utility of the microuidic immunoassays was to reduce the reagent volumes consumed, to incorporate multiple processes in a single device, and to signicantly lower overall analysis time. 9,10 To quantify the presence of the target molecules in liquid samples, the conventional microuidic devices oen deliver antibody molecules in a stepwise-owing manner for a multistep immunoassay. 11,12 For uorescence immunoassay, the intensity of the detection signals emitted in this case not only indicates the rate of immunoreaction that occurs between the analyte and antibody molecules but also highly correlates with the rate of mass transport of the antibody molecules from bulk solutions to the reaction site. 13 In fact, for the vast majority of the known immunoassay mechanisms, immunoreactions between antigens and antibodies occur "instantaneously", which implies that the rate-limiting step of the immunoassay is the diffusion of antibody molecules to the reaction site. 14 Various microuidics-based immunoassay methods have been developed to address the limitations of conventional assay platforms. They exploited a variety of different approaches, such as the automated lab-on-a-disc devices, 15,16 integration of an optical system in the microuidic devices, 17-19 a quantum dot (QD) "barcoding" system, 20,21 and the three-dimensional microuidic connement. 22,23 Despite considerable efforts in the microuidic immunoassay platforms in the past decades, most researches have focused on automation, 24-26 increased surface areas, 27,28 improved reporter probes, 29,30 and distinctive detection principles; 31,32 however, the efficient delivery of antibody reagents to the reaction sites has been rarely explored.
In this work, we report that a signicantly improved immune reaction can be achieved by using simultaneous infusion of primary and secondary antibodies by exploiting the difference in diffusivity between antibody reagents owing in the vertically sheathing laminar streams in a microuidic channel. We also demonstrate the more preferable experimental conditions when primary antibody (pAb) and secondary antibody (sAb) are simultaneously infused into a microuidic channel where analytes are immobilized.
All computational simulations were completed with the commercially available nite element method soware, COMSOL® (COMSOL, Inc., Burlington, MA, USA). The parameters provided to the numerical analysis included diffusion coefficients of antibodies (D 1 ¼ 6.3 Â 10 À11 m 2 s À1 for anti-PSA pAb; D 2 ¼ 2.4 Â 10 À11 m 2 s À1 for QD-sAb), their concentrations (20 nM for QD-sAb; 30 nM for anti-PSA pAb), dimensions of the microuidic channel (width ¼ 40 mm, length ¼ 15 mm), and the ow rates at which the solutions were infused (50 mL h À1 for both anti-PSA pAb and QD-sAb solutions). The diffusion coef-cients for anti-PSA pAb and QD-sAb were estimated using the Stokes-Einstein equation, 33 based on molecular weight (150 kDa) and hydrodynamic radius (10 nm), respectively.

Fabrication of the microuidic device and reversible bonding strategy
Polydimethylsiloxane (PDMS) devices were fabricated by a standard so lithography process using a Sylgard 184 silicone elastomer kit purchased from Dow-Corning (Midland, MI, USA) and a mold fabricated with SU-8 negative photoresist (Micro-Chem Corp., Newton, MA, USA). For an immunoassay in a Tshaped device, the analyte (PSA) was rst immobilized on an aldehyde glass slide by infusion of the PSA solution (20 mg mL À1 ) at a ow rate of 10 mL h À1 through a straight channel using the Device A (1 mm Â 40 mm Â 15 mm; width Â height Â length) (Fig. 1a). The T-shaped device also contains a straight channel with a rectangular cross-section (40 mm Â 40 mm Â 15 mm; width Â height Â length) that has two inlets and one outlet ports (Fig. 1a). To demonstrate the principle of the immunoassay we proposed, we immobilized the analyte (PSA) on the aldehyde-coated glass slide substrate using the Device B of the serpentine microuidic channel (100 mm Â 40 mm Â 212 mm; width Â height Â length) (Fig. 1b). We then simultaneously injected two antibody reagents solutions (pAb and sAb) using the Device C that contains a straight rectangular channel (400 mm Â 40 mm Â 37 mm; width Â height Â length) with two inlets and a single outlet. A metallic pressing device (0.35 kg) was placed onto the PDMS device to ensure secure reversible sealing between the PDMS channel and the glass slide surface (Fig. S1 †). The design of the pressing device and its operation principle were adopted from the previous research. 34

Immunoassay procedures
Lateral diffusion-based immunoassay experiment for evaluating and visualizing the difference in diffusion rates of the antibodies was carried out by infusing the solutions of anti-PSA pAb (30 nM) and QD-sAb (20 nM) through the channel of the microuidic T-shaped device that is placed over the PSApatterned area on the aldehyde glass slide. Both solutions were infused at a ow rate of 50 mL h À1 for 20 min. Since the channel of the T-shaped device (width ¼ 40 mm) is signicantly narrower than the channel of Device A (width ¼ 1 mm), it can be easily aligned with the PSA-patterned area without employing the serpentine-shaped channel (Device B).
Vertically sheathing laminar ow-based immunoassay that we propose in this work begins with owing the PSA solution (20 mg mL À1 ) at a ow rate of 10 mL h À1 for 2 h through a serpentine microuidic channel of the Device B (Fig. 1b) to immobilize PSA on the glass slide. By using a serpentine channel, we were able to immobilize PSA on a wide area of the aldehyde glass slide surface, which facilitated subsequent alignment of the microuidic channel of Device C for injecting primary and secondary antibody solutions. We then removed the PDMS device and thoroughly washed the analyte-patterned area of the substrate using 1Â PBS. Aer this, non-specic binding sites on the PSA patterns were quenched with 3% BSA for 15 min. Aer another PBS washing, the microuidic Device C (Fig. 1b) with two inlets and one outlet was placed onto the target area (PSA patterned) and was reversibly sealed using the pressing device to infuse the pAb and QD-sAb solutions for subsequent immunoreactions. To implement the vertically sheathing laminar ow-based immunoassay, anti-PSA pAb solution (30 nM) and QD-sAb solution (20 nM) were infused into the inlet 1 and inlet 2 of the Device C, respectively, at a ow rate of 50 mL h À1 for 20 min. At low Reynolds number (0.14), the pAb and QD-sAb solutions in an upper and lower laminar stream, respectively, are owing through the microuidic channel without convective mixing (the experimental condition 1). To validate our proposed principle, we switched the inlets of the pAb and QD-sAb solutions (the experimental condition 2) and infused QD-sAb and pAb solutions in an upper and lower laminar ow, respectively, in the channel. In each experiment, about 17 mL of each antibody solution (pAb and QD-sAb) was consumed for one round of immunoassay. Furthermore, to position the interface of pAb and QD-sAb solutions closer to the bottom surface of Device C, we changed the ow rates to 20 mL h À1 and 80 mL h À1 for QD-sAb (lower laminar ow) and pAb (upper laminar ow), respectively. For comparison, we also owed the solution of pAb and QD-sAb solutions, mixed at a ratio of 1 : 1 and 1 : 4, at a ow rate of 100 mL h À1 for 20 min (the experimental condition 3). The amount of the antibody reagents (pAb and QD-sAb) for each experiment was consistently retained throughout all experiments.
We measured the uorescence signals of QD-sAb immobilized on the glass slides aer removing the PDMS devices from the glass slide to completely exclude the signals that could have been emitted from QD-sAb non-specically bound to the surface of the PDMS channel. A uorescent microscope (CKX53; Olympus, Japan) and a long pass lter were used to assess uorescent signals emitted from Qdot 625 conjugated with the secondary Ab. All images were captured using a CMOS camera (DigiRetina 16, Tucsen, China) and analyzed using ImageJ (NIH, USA).
Signicant differences in all experimental data were determined by the ANOVA test, as dened P values < 0.05. The results were presented as an average of at least triplicate samples AE standard error of the mean depicted by error bars in all graphs.

Results and discussion
Computational simulation of interdiffusion of antibody reagents in a microuidic channel We predicted that the immunouorescence signals on the bottom surface would be signicantly enhanced when simultaneously injecting pAb (D 1 ¼ 6.3 Â 10 À11 m 2 s À1 ) in the upper laminar ow and QD-sAb (D 2 ¼ 2.4 Â 10 À11 m 2 s À1 ) in the lower laminar ow because pAbs diffuse more rapidly toward the reaction site on the bottom surface and achieve instantaneous immune reactions of PSA, anti-PSA pAb, and QD-sAb (Fig. 2). We set out to validate our prediction by switching the position of the pAb and QD-sAb in the vertical laminar ows, which was predicted to result in much-reduced signal intensity because QD-sAb with D 2 smaller than D 1 more slowly diffuses toward the bottom surface while owing in the laminar ows. Moreover, the uorescence signals are predicted to be even more augmented when we adjust the vertical position of the laminar ow interface between pAb and QD-sAb closer toward the bottom surface where the PSA molecules are immobilized. This is attributed to that the utmost ux of pAb is formed in the interface between two laminar ows because the ux is proportional to the concentration gradients.
To validate our theoretical prediction, we carried out computational simulation using COMSOL Multiphysics soware. We simulated the two laminar ows owing through the T-shaped microuidic channel with two inlets and one outlet to visualize the molecular mass transport across the channel in a lateral direction. The width of the T-shaped channel corresponds to the height of the channel in Device C, and this T- Fig. 2 The principle of the proposed microfluidic immunoassay based on vertically sheathing laminar flows of pAb and QD-sAb using Device C. When pAb and QD-sAb are flowing in the upper and lower laminar flows, respectively, pAb diffuses more rapidly to the reaction site where the immunoreactions between PSA, pAb, and QD-sAb instantaneously occur.
shaped model allows us to simply visualize and quantitate the diffusion between the laminar ows, which occurs in Device C in a vertical direction. Thus, the concentration proles of antibodies across the width of the T-shaped microchannel approximate their actual diffusion in a vertical direction toward the reaction site on the bottom surface in Device C. The interpretation of our proposed diffusion in the T-shaped device is valid because the mass transport is mainly determined by diffusion, not by the gravitational force, in this microscale regime, and thus, the axis along which the diffusion takes places can be assumed negligible.
We rst calculated the concentration prole of anti-PSA pAb and QD-sAb solutions when they were injected into the Tchannel device at a ow rate of 50 mL h À1 (the ow rate ratio ¼ 1 : 1). The simulation results (Fig. 3a) indicate that the initial concentration prole of anti-PSA pAb at 1.5 mm downstream from the inlet undergoes considerable changes at 5.5 mm and 9.5 mm due to rapid diffusion of pAb molecules across the channel while that of QD-sAb presents insignicant changes at 5.5 mm and 9.5 mm along the microuidic channel due to their relatively larger molecular weight (Fig. 3b). If we change the ratio of the ow rate between the QD-sAb and pAb solutions from 1 : 1 to 1 : 4, the interface was shied toward the le side of the channel and the change in the concentration prole between the two positions along the channel (1.5 mm and 5.5 mm) became even more signicant (Fig. 3c and d), which is most likely due to the slower ow rate near the channel wall. 35 In this case, because the concentration gradients of pAb became closer toward the surface of the right side in the T-channel device, which corresponds to the bottom surface of Device C, we predicted that the higher ux of pAb to the reaction sites could be achieved in Device C.

Lateral diffusion-based immunoassays in a microuidic Tshaped device
To conrm that our theoretical prediction is valid, we carried out the experiment using pAb and QD-sAb solutions (the ow rate ratio ¼ 1 : 1) in the T-shaped microuidic device. Because PSA was immobilized on the bottom surface of the glass slides, we assessed the immunoreaction of pAb and QD-sAb on the PSA molecules by measuring the QD signal intensity emitted from QD-sAb ( Fig. 4a and b). Although the uorescence images obtained at each position (1.5 mm, 5.5 mm, and 9.5 mm) along the T-shaped channel did not reveal the real-time concentration prole of each reagent (pAb and QD-Ab), we indirectly assessed the relative interdiffusion of pAb and QD-sAb by assessing the uorescence intensity, which is proportional to the reaction rate dominated by diffusion of each molecule to PSA on the surface. The uorescence signals were formed symmetrically across the channel when the pAb and QD-sAb owed for a relatively short distance from the inlet (1.5 mm and 5.5 mm) because the interdiffusion in a lateral direction across the channel between pAb and QD-sAb did not have enough time to result in signicant differences of the uxes of each reagent (Fig. 4b top and  middle). However, as they owed for a distance over 9.5 mm, we observed apparently asymmetric uorescence signal distributions across the channel (Fig. 4b, bottom), which is attributed to the more rapid diffusion of pAb toward the right side of the channel in comparison to diffusion of QD-sAb toward the le side of the channel. With this experimental validation, we predicted that we could enhance the uorescence signals if we inject antibody reagent solutions with larger D pAb and smaller D QD-sAb in the upper and lower laminar ow, respectively, in Device C.

The simultaneous infusion of antibody reagents for immunoassay
We experimentally validated our proposed principle by infusing pAb (sheathing in the upper laminar ow) and QD-sAb over the PSA-immobilized surface in Device C. According to Fick's rst law, the rate of immune reactions in mass-transport limited circumstances is determined by the ux of antibody reagents. 36 In this case, delivering pAb to the reaction site is a rate-limiting factor because pAb needs to bind to the PSA molecules on the bottom surface prior to being recognized by QD-sAb. Thus, the concentration gradients of pAb proportionate to the pAb ux toward the surface are a determinant in the sequential immune reactions between PSA, pAb, and QD-sAb, and the uorescence signals are predicted to be signicantly enhanced as we position the interface of pAb and QD-sAb closer to the PSA-immobilized bottom surface. In contrast, if the QD-sAb and pAb solutions are injected in the upper and the lower laminar ows, respectively, into Device C, this would lead to a considerable reduction in the uorescence signals because QD-sAb inefficiently diffuses to the Fig. 3 The concentration profiles across the T-shaped microfluidic channel at each longitudinal position were predicted by COMSOL®. When pAb and QD-sAb were infused into the device at a flow rate ratio of 1 : 1, we obtained the concentration profiles of (a) anti-PSA pAb and (b) QD-sAb. The concentration profiles were also predicted when (c) anti-PSA pAb and (d) QD-sAb were injected at a ratio of 4 : 1. The interface between two reagent solutions was shifted toward the right side of the channel due to the asymmetric input flow rates.
bottom surface due to its relatively smaller diffusion coefficient (D 2 ).
As we predicted, the signicantly enhanced uorescence signals were obtained in the experimental condition 1 in comparison to the experimental condition 2 ( Fig. 4c and d), and it became even more intensied when we adjusted the position of the interface between pAb and QD-Ab closer toward the bottom surface ( Fig. 4e and f). We normalized the uorescence signal to the highest uorescence signals (the experimental condition 1) as we compared the relative uorescence intensity.
We also infused a pre-mixed solution of pAb and QD-sAb into Device C (the experimental condition 3), however the uorescence signals were much lower (0.333 AE 0.063) than that we obtained with the experimental condition 1, which is due to the higher molecular weight of the pAb-QD sAb complexes compared to that of individual antibody molecules and the Fab domains of QD-sAb already occupied by pAb molecules while mixing.

Conclusions
Most immunoassays involve pAb and reporter probe-conjugated sAb to quantitate the target molecules immobilized on a solid matrix. Because the reporter-probes oen include catalytic enzymes, uorescence dyes, and QDs, the diffusion coefficient of the sAb tends to be smaller than that of pAb. Thus, exploiting the difference of diffusivity of antibody reagents owing in parallel in laminar ows, we can signicantly improve the efficiency of immune reactions with pAb and sAb by simultaneously infusing those antibody solutions in a microuidic channel. The pAb solution with larger D pAb is more desirable to be injected in the upper laminar ow, sheathing sAb of smaller D sAb in the lower laminar ow, to enhance the signals that are gained from the reporter probes conjugated with secondary Ab. This strategy allows us to exclude the washing steps in the immunoassay procedure, which are commonly required in the conventional microuidic immunoassays. While pAb diffuses through the laminar ows to the reaction surface, the antigenbinding domains of pAb interact with QD-sAb, which could reduce the accessibility of the binding domain to PSA due to steric hindrance. However, this effect was not signicant in our experiment due to the continuous replenishment of unbound pAbs from the upper laminar ow. Moreover, the signal intensity could be further improved when adjusting the interface of pAb and sAb closer to the surface where analytes are immobilized and consequent immunoreactions take place. For example, we could employ the additional third laminar ow on top of the two laminar ows of pAb and QD-sAb, which would push the interface between pAb and QD-sAb even closer to the substrate surface. This would enhance the mass transport of pAb toward the reaction surface, resulting in the improved rate of immune reactions in a given condition.

Conflicts of interest
There are no conicts to declare. and (e). All data are expressed as the average AE S.E.M. from three independent experiments. The P value was calculated from the ANOVA test. *, P < 0.0005; **, P < 0.005; ***, P < 0.05.