Design principles for enhancing sensitivity in paper-based diagnostics

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Design principles for enhancing sensitivity in paperbased diagnostics via large-volume processing Eric A Miller, Yara Jabbour Al Maalouf, and Hadley D. Sikes Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b02113 • Publication Date (Web): 20 Jun 2018 Downloaded from http://pubs.acs.org on June 21, 2018

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Analytical Chemistry

Design principles for enhancing sensitivity in paper-based diagnostics via large-volume processing Eric A. Miller, Yara Jabbour Al Maalouf, and Hadley D. Sikes* Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142, USA ABSTRACT: In this work, we characterize the impact of large-volume processing upon the analytical sensitivity of flow-through paper-based immunoassays. Larger sample volumes feature greater molar quantities of available analyte, but the assay design principles which would enable the rapid collection of this dilute target are ill-defined. We developed a finite-element model to explore the operating conditions under which processing large sample volumes via pressure-driven convective flow would yield improved binding signal. Our simulation results underscore the importance of establishing a high local concentration of the analyte-binding species within the porous substrate. This elevated abundance serves to enhance the binding kinetics, matching the timescale of target capture to the period during which the sample is in contact with the test zone (i.e. the effective residence time). These findings were experimentally validated using the rcSso7d-cellulose-binding domain (CBD) fusion construct, a bifunctional binding protein which adsorbs to cellulose in high abundance. As predicted by our modeling efforts, the local concentration achieved using the rcSso7dCBD species is uniquely enabling for sensitivity enhancement through large-volume processing. The rapid analyte depletion which occurs at this high surface density also permits the processing of large sample volumes within practical timescales and flow regimes. Using these findings, we present guidance for the optimal means of processing large sample volumes for enhanced assay sensitivity.

In the field of modern medical diagnostics, microfluidic formats are increasingly employed in the design of heterogeneous immunoassays.1–4 These devices feature a variety of favorable properties, including low reagent usage, assay portability, and short analysis times. The small lateral dimensions associated with this format are also well-matched to diffusive length scales, enabling efficient analyte collection even within the laminar flow regime. Coupled with high-gain methods for signal amplification, these microfluidic systems can yield highly sensitive determinations for the accurate diagnosis of disease.5

for the greatest possible assurance of accuracy in a binary diagnostic test (e.g. when a false negative diagnosis can bear dire clinical consequences).

Typically, microfluidic devices are used to process small sample volumes - the length scales of these diagnostic systems (microns to millimeters) are often reflected in the size of the samples that they are used to handle (typically tens to hundreds of microliters). While the efficient use of small fluid volumes is desirable in cases where the patient sample is in scant supply, small volumes do place intrinsic limitations upon assay sensitivity. The signal from any immunoassay is directly dependent upon the abundance of the captured target, and thus assay sensitivity can be negatively impacted by arbitrary limits placed upon sample volume and the molar quantity of available analyte. This finding has been borne out in numerous studies which have noted an increase in diagnostic sensitivity with larger sample volumes.6–9

In order to address these use cases, heterogeneous immunoassays must be designed using multi-length scale engineering principles, allowing greater molar quantities of soluble target to be easily and efficiently combed from larger, milliliter-scale sample volumes.19 The flow-through assay format is well-suited for this application, in that it simultaneously harnesses the short diffusive length-scales of microfluidic devices while enabling the efficient delivery and processing of samples on the mesofluidic scale. This large-volume flow-through approach to sensitivity enhancement has been demonstrated using a range of protein-immobilization substrates, including divalent zinc resin, polymyxin-treated polyester cloth, and nitrocellulose.20–23

While high sample usage is often viewed as a disadvantage for immunoassays, there are distinct instances in which the capability to efficiently process large fluid volumes would be highly advantageous. For instance, this approach would be a viable means of readily boosting diagnostic sensitivity for cases in which i) the analyte is extremely scarce and high analytical sensitivity is required; ii) viscous, concentrated samples must be significantly diluted during pre-processing steps; iii) the diagnostic assay format is of limited intrinsic sensitivity, due to a low-gain amplification method or high background signal; or iv) clinicians desire high clinical sensitivity

However, the engineering design criteria for these large-volume flow-through systems have not been thoroughly explored. This multi-length scale assay format is characterized by highly incongruous timescales of analyte binding, diffusion, and convective passage through the porous substrate, and thus analyte capture is highly dependent upon operating parameters such as effective residence time and the local concentration of the immobilized capture reagent. The impact of these parameters has been explored in the context of small-volume biosensors using finite-element analysis,24–26 but this in-depth treatment has not been extended to largevolume flow-through assays.

Large-volume processing is particularly relevant for clinical instances in which the analyte is found in an abundant patient fluid (e.g. venipuncture blood, urine). Numerous serum- and urine-based disease biomarkers have been identified which fit this criterion, for a broad range of conditions including cancer, tuberculosis, and neuropsychiatric disorders.10–18

*Correspondence to [email protected]

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To probe the influence of these factors upon analyte capture from large sample volumes, we have chosen to simulate and experimentally characterize a system based on unmodified cellulose and the rcSso7d-cellulose-binding domain (CBD) affinity reagent.27 Cellulose is an ideal substrate for these flow-through assays, in that it is inexpensive, features limited biofouling, and is porous enough to permit rapid convective passage while maintaining structural integrity. In contrast, nitrocellulose features a smaller pore structure, rendering controlled transverse flow of large volumes infeasible within a practical timescale.28 Additionally, different protein species have been shown to non-specifically adsorb to nitrocellulose with variable affinity and retention of binding activity, complicating engineering analysis of these systems.29 The immobilized abundance of the rcSso7d-CBD species on unmodified cellulose has been directly quantified, and this species’ high adsorption efficiency (>90%) enables sample processing in previously inaccessible local concentration regimes. While prior studies employing antibodies in agarose beads have observed volume-averaged concentrations of up to 8,200 binding molecules µm3 (~14 µM),30 the rcSso7d-CBD species has been demonstrated to yield immobilized abundances in excess of 450,000 binding molecules µm-3 (~750 µM).27 In the context of small-volume processing, this high immobilized abundance was found to be sufficient for the near-complete depletion (92%) of the soluble analyte from 10 µL sample at a concentration of 256 nM (2.56 picomoles). When applied to mesofluidic sample processing, this high abundance serves to address two critical design constraints: 1) premature saturation of the surface-bound capture reagent (stoichiometry) and 2) low rates of analyte capture in dilute solutions undergoing rapid convective transport (kinetics).

species nor the bound complex were subject to convective transport. Model geometry was designed to represent the test zone configuration denoted in Figure S1. A non-diffusive model was produced using a two-dimensional, rectangular test zone to embody the paper substrate. A cross-sectional view of the circular test zone captures the physical three-dimensional geometry with high fidelity, due to radial symmetry. The simulated test zone was established with width w = 2r = 1.8×10-3 m, and depth L = 1.8×10-4 m (Figure S2). A multi-dimensional parameter sweep was conducted to simulate local rcSso7d-CBD concentrations ranging by orders of magnitude from 1 nM to 1 mM, and superficial flow rates ranging from 2.5×10-4 m s-1 (corresponding to a volumetric flow rate of ~1 mL min-1 and a residence time of 0.77 seconds) to 5×10-3 m s-1 (corresponding to a volumetric flow rate of ~20 mL min-1 and a residence time of 0.026 seconds). For all computational models, the analyte concentration was set at 1 nM. The time-dependent simulations were run at a time step resolution of 0.5 s for 600 seconds, in order to capture one 10-mL recirculation at the slowest volumetric flow rate. For the sake of comparison, data points were captured from time points corresponding to the completion of a single 10-mL recirculation, at each flow rate (e.g. 600 seconds at a flow rate of 1 mL min-1, 30 seconds at a flow rate off 20 mL min-1, etc.).

In this study, we use finite-element analysis to demonstrate that operating within this local concentration regime is uniquely enabling for sensitivity enhancement via large-sample processing. We also conduct experiments to characterize the determinants of analyte capture and assay sensitivity, and explore critical design choices for this flow-through format, providing guidance for the optimization of key performance parameters in consideration of reasonable operating constraints.

A separate finite-element model was used to simulate lateral diffusion within the test zone pores and its effect upon analyte capture. This two-dimensional model focuses upon an idealized, circular pore (r = 5.5 μm) containing soluble analyte at a concentration of 1 nM (Figure S3). The pore is surrounded by a continuous fiber network, which features immobilized rcSso7d-CBD at a concentration of 40 mM, in order to simulate operation in the limit of instantaneous analyte capture. Because the system is operated in a low Reynolds number/high Peclet number regime, fluid flow and axial dispersion effects are not included in this model set-up. The system was allowed to equilibrate over the course of two seconds, with a time-step of 0.0001 seconds. The integrated quantity of soluble analyte remaining in the pore was captured at all time points, as was the concentration profile of the target across the pore diameter.

Materials and Methods

Cellulose test zone preparation

Modeling and assay simulation

All samples were processed using Whatman No. 1 Chromatography Paper (VWR, Radnor, PA). Circular test zones for large-volume processing studies were prepared using a solid ink printer.33 A series of 1.3-cm diameter circles were printed on unmodified paper, each containing a bare 0.3-cm diameter test zone at the center. These devices were heated in an oven (Binder, Tuttlingen, Germany) at 150°C for two minutes in order to melt the wax through the full paper depth (0.18 mm). The resulting assays featured central hydrophilic test zones with an average area of 2.5 ± 0.1 mm2 and an average volume of 0.45 µL. The cross-sectional area of the fluid flow, delineated by the diameter of the filter holder O-ring, was 71.2 mm2, yielding a total flow volume of 12.81 µL (Figure S1). Prior to sample processing, test zones were cut out of the array using a 0.5-inch EK Tools Circle Punch.

Computational simulations were produced using the COMSOL Multiphysics 5.3 finite-element modeling software package (Comsol, Inc., Burlington, MA, USA). Finite-element models were solved on a dual-core Dell Latitude E6330 with 16GB of RAM. Information regarding the microscopic topology of the fibrous cellulose network is lacking, but under all flow conditions, flow within this system is incompressible and within the laminar regime (Re = 1.78×10-3 –3.56×10-2), and thus the system was modeled by assuming a constant superficial velocity throughout the test substrate. Physical parameters are listed in Table S1. In instances where these parameters are mathematically derived (dynamic viscosity, diffusivity, and fluid density), these derivations can be found in the Supporting Information (SI). All governing equations and model assumptions are also detailed in the SI. The association constant was set at kon = 1×105 M-1 s-1, in keeping with standard findings of diffusion-limited on-rates.31 The analyte dissociation constant was set at koff = 5.5×10-5 s-1, corresponding to a measured rcSso7d-streptavidin affinity of Kd = 5.5×10-10 mol L-1.32 In order to simulate the immobilization of the substrate-bound rcSso7d-CBD, the diffusion coefficient of the binder was set to 0 m2 s-1, and neither this

The bifunctional, streptavidin-binding rcSso7d-CBD species was produced as previously described (see SI).27 Unless otherwise noted, test zones were contacted with 6 μL of rcSso7d-CBD solution at a concentration of 30 μM (0.83 mg mL-1) for a minimum of 30 seconds. Following this primary incubation, test zones were blotted and washed twice with 20 μL of 1x PBS. Samples were not permitted to dry between the primary incubation and sample processing steps.


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Analytical Chemistry Large-volume sample processing Solutions of streptavidin AlexaFluor-647 (SA-AF647) were prepared via serial dilution, precision pipetting large volumes in 1-mL aliquots in order to ensure accuracy. Samples were mixed for ten seconds via moderate vortexing following analyte addition. For all samples, 0.22-µm sterile-filtered 1x PBS (pH 7.4) with 1% w/v bovine serum albumin (BSA; 10 mg mL-1) was used as the diluent. rcSso7d-CBD-functionalized test zones were placed face-up into a Swinnex 13mm filter holder (Millipore Sigma; Billerica, MA, USA), and connected to a 10-mL Luer-Lok syringe (BD Medical; Franklin Lakes, NJ, USA) which had been pre-filled to the desired volume with analyte solution. One milliliter of excess analyte solution was added to the syringe in order to fill the headspace in the filter holder. The syringe and filter holder were connected to a second syringe via a Qosina Female-to-Female Luer-Lok Connector (Ronkonkoma, NY, USA), and any air in the system was bled off in order to form an incompressible fluid column. Parafilm was wrapped around both the Swinnex filter holder and the junction between the connector and the second syringe, to prevent air leakage. This dual-syringe device was then secured in a Harvard Apparatus PHD 4400 programmable syringe pump (Holliston, MA, USA). The syringe pump was set to the specific syringe diameter of 14.5 mm, and programmed to repeatedly inject and withdraw the sample volume across the rcSso7d-CBD-coated test zone at a given volumetric flow rate. Following the prescribed assay time or number of recirculations, the test zone was removed and washed twice with 20 μL of 1x PBS. All samples were blotted dry and placed face-up in an empty culture tube box, and were allowed to dry in the dark under ambient conditions for at least 16 hours prior to imaging. Fluorescence microscopy The top side of each sample (to which the binder was originally applied) was imaged using an Olympus Ix81 Microscope. Unless otherwise noted, samples involving the SA-AF647 conjugate were exposed for 80ms, using the Semrock Cy5-4040C filter set. The resulting data files were processed as previously described (see Supporting Information).32 Three technical replicates were generated for each large-volume experimental condition, and four technical replicates were produced for all small-volume experimental conditions. The MFI values were averaged for all technical replicates for a given experimental condition, and for all figures, error bars represent one standard deviation from this mean intensity.

Results and Discussion Dimensionless number analysis In order to gain insight into the binding performance of paper-based assays operating in the mesofluidic regime, it is useful to assess whether analyte capture is theoretically limited by the rate of i) reaction, ii) diffusive transport, or iii) convective sample delivery. By identifying the rate-limiting process, we can rationally tune the operating conditions (within reasonable physical and logistical constraints) in order to optimize analyte capture. The first Damköhler number (DaI) allows direct comparison of the characteristic rate of binding (rb) and the rate of convection (rc):

Da I 

rb rc

 kon CB rt

(Eq. 1)

Here, τrt represents the average residence time of a fluid bolus within the test zone, determined by calculating the ratio of the approximate volume through which the fluid bolus flows (Figure S4) and the volumetric flow rate. If this average residence time is longer than the characteristic timescale of analyte capture (i.e. DaI ≫ 1), then in a well-mixed system, the analyte should be depleted from the bolus within a single pass through the test zone. Using this measure, we find that for the standard local concentrations observed with the rcSso7d-CBD binding protein (CB = ~400 µM), the system is primarily within the convection-limited regime (DaI > 1) for all volumetric flow rates used in this study (Table 1). In contrast, a system featuring the low local concentration of rcSso7d-CBD (~40 µM) would be within the reaction-limited regime (DaI < 1) for a broader range of volumetric flow rates. Analogously, the second Damköhler number (DaII) enables the comparison of the analyte binding rate and the rate of diffusion:

Da II 

rb



kon CB r

2

(Eq. 2)

D

rd

For values of DaII ≫ 1, the system is operating within the diffusionlimited regime, where the rate of target binding is rapid relative to diffusion. For an estimated diffusion coefficient of D = 2.22×10-11 m2 s-1, and a reported pore radius of r = 5.5 µm within the fibrous cellulose network, the characteristic timescale for diffusion is 1.36 seconds. Given a reactive timescale of 0.025 seconds (CB = 400 µM), this system is fully within the diffusion-limited regime (DaII = 54.5). However, at lower concentrations, DaII begins to transition into the reaction-limited regime (DaII = 1 at CB = 7.4 µM), indicating that the high immobilized abundance of rcSso7d-CBD fundamentally changes the operating regime. Lastly, we can calculate the Graetz number34 in order to compare the timescales of radial diffusion and convective passage through a cylindrical cellulose pore of length L at a superficial velocity vavg:

Gz 

rc rd

2



 rporevavg

(Eq. 3)

LD

For the observed values of Gz >> 1, the timescale of diffusion is longer than that of convection, and thus analyte diffusion is the most rate-limiting transport process. Taken together, these findings indicate that for maximal binding efficiency, higher concentrations of the immobilized binder should be used for a greater rate of capture, and a slower volumetric flow rate should be used to provide sufficient time for the analyte to diffuse to the fiber surface. However, real-world constraints on total processing time dictate that a balance be struck between capture efficiency and flow rate, requiring a more quantitative treatment of this system. Table 1. Dimensionless numbers for varying processing conditions Parameter Superficial velocity (m s-1) Single-pass residence time (s) DaI C = 400 µM DaI C = 40 µM Gz


1

Volumetric flow rate (mL min-1) 5 10 20

0.00023

0.0012

0.0023

0.0047

0.77

0.15

0.077

0.038

30.8 3.1 5.57

6.2 0.62 27.83

3.1 0.31 55.67

1.5 0.15 111.34


to saturate approximately 4-6% of the available binder, despite an analyte capture rate of less than 50%. This depletion of available binder will progressively reduce the binding rate in future recirculations. In contrast, the predicted binder saturation at a local concentration of 400 µM is at most 0.25% at a low volumetric flow rate of 1 mL min-1, despite the complete capture of the soluble analyte. Thus, operating in this high concentration regime ensures that analyte capture does not deplete the pool of available binder, and maintains favorable binding kinetics across multiple recirculations. Finite-element model: Instantaneous capture

Figure 1. Finite-element modeling data demonstrating proportional analyte breakthrough at varying volumetric flow rates and with varying concentrations of binding reagents. These curves depict how analyte capture is influenced by the relationship between the kinetics of the binding reaction and the rates of transport processes within cellulose. Each curve represents a single 10-mL recirculation at a different local binder concentration (mol L-1; denoted in the legend). The inlet analyte concentration is 1 nM. Finite-element model: Instantaneous transport In order to determine the optimal operating conditions for this system, we sought to establish bounds on theoretical assay performance using two distinct finite-element models. The first model operates within the idealized non-diffusive limit, wherein the immobilized binder is distributed homogeneously throughout the test volume and there are no lateral diffusive gradients of the soluble target (Figure S2). The second model operates within the diffusionlimited regime, assuming instantaneous analyte collection at the surface of the cellulose fibers, and measuring the time required for the soluble target to diffuse outward from the pore interior (Figure S3). These models serve to place upper and lower bounds upon proportional analyte capture as a function of effective residence time. In the first scenario, we used finite-element analysis to predict assay performance for a range of volumetric flow rates and binder concentrations. Using a two-dimensional representation of the test zone in COMSOL, we simulated the passage of a 10-mL sample at a molar analyte concentration of 1 nM, over the period of a single recirculation. Using this approach, we can assess the proportion of unbound soluble analyte following a single pass (Figure 1). As expected, we see that this proportional breakthrough increases both with increasing volumetric flow rate and with decreasing binder concentration. Interestingly, the breakthrough profile appears to shift dynamically from a high-capture regime to a low-capture regime as the binder concentration transitions from 400 µM to 10 µM. This underscores the uniquely enabling nature of operation within the concentration regime achieved with the rcSso7d-CBD binding species. By ratcheting up the immobilized binder concentration, we are better able to match the timescale of analyte capture to the convective timescales required for mesofluidic processing. Operating at high local concentrations also enables rapid analyte capture without depleting the pool of available binder or diminishing the kinetic performance of the assay (Figure S5). For low binder concentrations (10 µM and below), a single 10-mL pass through the test zone at low volumetric flow rates (1 mL min-1) is sufficient

The approximations of this non-diffusive treatment of the binding system, which posit the homogeneous distribution of the immobilized binder throughout the test zone volume, are imperfect. The pores within Whatman No. 1 chromatography paper are 11 µm in diameter, and since the immobilized binder is localized to the surface of the cellulose fibers, a considerable proportion of the test zone is dead volume across which the soluble target must diffuse prior to capture. Thus, while the instantaneous transport model can establish an upper bound on the quantity of analyte which can be captured for a given set of operating conditions, we must also account for the opposite instance, in which we see perfect collection but target capture is limited by the rate of analyte diffusion. This allows us to establish informative bounds on assay performance, even with incomplete information about the physical system. To approximate the proportion of soluble target that would diffuse across the 5.5 µm radius of a pore within a given residence time, we produced a simple two-dimensional model simulating an idealized pore structure (Figure S3). Under these diffusion-limited conditions, we see that the rate of analyte capture is significantly diminished relative to the instantaneous capture model (Figure 2).

Figure 2. Proportional binding curves predicted by the finite-element model in the diffusive limit. In this scenario, the rate of diffusion to the cellulose fibers is the rate-limiting process, as the immobilized binder is localized to the pore walls and the rate of analyte capture is assumed to be rapid relative to diffusion. The dashed curve (ND) represents the binding performance predicted by the non-diffusive, homogeneous distribution model at standard rcSso7d-CBD concentrations (400 µM). Solid curves represent binding in the diffusion-limited case at varying local concentrations of the immobilized binder (mol L-1). The leftmost diffusive curve (black), corresponding to a local surface concentration of 40 mM, was used to simulate instantaneous capture; no appreciable increase in the binding proportion is seen for higher local concentrations.


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Analytical Chemistry This model confirms that within the concentration regime achieved with the rcSso7d-CBD species, the system may be diffusion-limited (i.e. the concentration of the binder is sufficiently high that the non-diffusive binding curve saturates at lower residence times than the diffusive binding curve). Under these conditions, analyte capture can only be improved by reducing the convective rate, in order to provide sufficient residence time for the target to diffuse to the fiber surface. However, this treatment may overestimate the impact of diffusion upon analyte capture. Due to the interwoven nature of the fibrous cellulose substrate, there is likely stream-splitting which occurs as the fluid flows across downstream fibers. While this flow is laminar and will not undergo turbulent mixing, this effect is expected to reduce the average diffusion length-scale, diminishing the rate-limiting impact of diffusive transport. In summary, these modeling efforts resulted in several insights. Firstly, the high immobilized abundance of rcSso7d-CBD makes analyte binding kinetically feasible within the flow regimes required for large-sample processing. The concentration regime associated with rcSso7d-CBD may be uniquely enabling for this application (Figure 1a). Due to this high abundance of rcSso7d-CBD on the paper surface, the complete depletion of analyte from large solutions is stoichiometrically feasible (Figure S5). This large excess of immobilized binder also permits the theoretical treatment of this large-volume system using a pseudo first-order rate constant model (Figures S6-S9). Finally, the binding kinetics within the high local concentration regime are sufficiently rapid that the system falls within the diffusion-limited regime (Figure 2). Sensitivity enhancement via large-volume processing To experimentally assess whether the processing of large sample volumes yields enhanced analyte capture relative to a small sample volume, paper samples were treated with 180 picomoles of rcSso7d-CBD. These samples were used to process either 10 µL or 10 mL of SA-AF647 solution across a range of soluble analyte concentrations. The 10-mL samples yield significantly higher binding signal than the 10-µL samples, suggesting that the immobilized binder is still available in significant abundance following the analyte depletion in the small sample volumes (Figure 3).

We note that discernible signal onset occurs at a much lower concentration for the large sample volumes. Taking the mean intensity of a bare paper test zone treated with 10 mL of analyte solution at 2 nM as a conservative signal floor for both data sets (IBG = MFI + 3σ = 6.11), we find that the point of signal onset for the large sample is 3.5 pM (Figure S10). In contrast, the small-volume samples only yield discernible signal at a much higher analyte concentration of 171 pM. Thus, even though the molar analyte concentration may be equivalent for a given data point, the larger volume sample features a greater molar quantity of analyte that is available for capture, and thus yields a more intense fluorescent signal. Concentration dependence of analyte capture We next sought to explore how this sensitivity enhancement is influenced by binder abundance. If the molar abundance of the binder is too low, the capture species may be saturated by the soluble analyte, or may reach binding equilibrium prior to complete analyte depletion. Additionally, low local concentrations of immobilized binder will result in diminished kinetic performance. This consideration is particularly important within mesofluidic flow systems, as the timescale for target capture must be shorter than the fluid residence time within the test zone. Thus, under conditions of low binder abundance there will be minimal differential diagnostic benefit to processing larger patient samples. Only in instances where the binding species is immobilized in high molar excess will rapid analyte depletion from large sample volumes be feasible. To test these hypotheses, we conducted titration experiments varying the soluble concentrations of rcSso7d-CBD applied to the paper substrates. At a high applied soluble concentration of 30 µM (180 picomoles; CB = ~400 µM), we observe significant differential benefit to processing a larger sample volume (Figure 4). At this high immobilized abundance, a 10-mL sample can yield up to 70x higher signal than a 10-uL sample at an equivalent analyte concentration. In contrast, assays prepared using rcSso7d-CBD at a low soluble concentration of 3 µM (18 picomoles; CB = ~40 µM) demonstrate greatly diminished benefit when used to process large-volume samples. At this lower immobilized abundance, processing a 10-mL sample yields at most a 10x higher signal, relative to a 10-uL sample at an equivalent analyte concentration. Given the local binder concentrations often attained in cellulose-based diagnostic tests (estimated to be ~1 µM; see SI and Figure S11), the molar quantities of surface-bound capture protein have previously been insufficient for the efficient processing of large sample volumes. We note that the two small-volume sample sets perform nearly identically, despite a ten-fold difference in the molar abundance of the immobilized rcSso7d-CBD (Figure S12). This suggests that in either case, there is enough binding protein present for the complete depletion of analyte from the small sample volumes, even at the highest analyte concentration (20 femtomoles; 2 nM).

Figure 3. Sensitivity enhancement through large-volume processing. Mean fluorescence intensity (MFI) observed at varying analyte concentrations for large- (10 mL; 5 mL min-1; 20 recirculations) and small-volume (10 µL; 40 minutes) samples. Lines of best fit were generated using a five-point sigmoidal curve (Eq. S10). Error bars represent the standard deviation of three (large-volume) or four (small-volume) independent replicates.

At this highest concentration, the molar quantity of analyte in the 10-mL sample (2 nM) is 20 picomoles. Thus, there should be sufficient binder present for complete analyte depletion for all samples with a local rcSso7d-CBD concentration of 400 µM (180 picomoles), and the same should be true for nearly all samples featuring a local rcSso7d-CBD concentration of 40 µM (18 picomoles). Thus, the varying performance between the applied concentrations is due to binding kinetics, rather than stoichiometric limits. Additionally, under conditions of ideal collection and total analyte depletion the expected signal ratio would reflect the 1000x difference in available analyte. That there is at most a 70x signal difference for the high-concentration samples indicates that sample delivery may also be limiting under these assay conditions.



Figure 4. Comparison between analyte titration curves for rcSso7d-CBD at varying local concentrations. (a) Mean fluorescence intensity (MFI) observed at varying analyte concentrations for large- (10 mL) and small-volume (10 µL) samples, using test zones with local rcSso7dCBD concentrations of 400 µM and 40 µM. Data points corresponding to the 400 µM/10 µL samples directly overlap with those corresponding to the 40 µM/10 µL samples (Figure S12). (b) Fluorescence ratios comparing the corresponding large- and small-volume samples at local rcSso7d-CBD concentrations of 400 µM and 40 µM. Large-volume samples consist of 10 mL of analyte solution (5 mL min-1, 20 recirculations). Small-volume samples consisted of 10 µL incubated on the test zones for an equivalent 40-minute period. Error bars represent the standard deviation of three (large-volume) or four (small-volume) independent replicates. Integrated guidance for large-volume processing In order to characterize the relevant operating regimes for this system, we conducted binding experiments wherein 10 mL volumes of 1 nM SA-AF647 were driven across the test substrate for 10, 20, or 40 minutes, at varying flow rates (Figure 5). As expected, longer processing times generally result in a greater degree of analyte capture. The binding curves shift upward as the total processing time increases from 10 to 40 minutes, indicating that analyte depletion has not yet occurred on the shorter time scales (Figure 5a). The system also transitions between distinct binding regimes, from fast flow rates being more favorable at short times to slow flow rates yielding greater signal at long times (Figure 5b). However, we see that the efficiency of signal development declines with longer incubation times (Figure 5c), indicating that diminishing molar quantities of analyte are captured over time. An optimal balance between assay speed and diagnostic sensitivity might be struck by combining these strategies, using a fast flow rate in an initial depletion phase, followed by a slow flow rate for a diffusive capture phase. This two-phase loading approach has previously been demonstrated in the context of protein purification.35 For samples processed at a given flow rate, the number of recirculations is generally positively correlated with signal development (Figure 5d). Additionally, in virtually all cases where two samples are processed for the same number of recirculations, higher signal is observed for the sample treated with the lower flow rate. This supports the model predictions that slow flow rates result in a closer match between the timescales of convection and analyte diffusion. Notably, however, the positive impact of additional fluid recirculations is diminished with increasing volumetric flow rate, as evidenced by the declining trendline slopes (Figure S13). While this finding may seem to suggest rapid analyte depletion at fast flow rates, signal development for these fast flow rate samples saturates at a lower point than is observed at slow flow rates. This suggests that neither analyte depletion nor binder saturation have occurred.

Rather, this reduced capture may be due to the slight test zone perforation which can occur under these fast flow conditions (20-30 mL min-1). Whereas slow flow rates force the sample evenly across the test zone, resulting in micron-scale diffusion lengths, a perforated test zone may permit flow channeling, which would result in reduced contact between the analyte and the test zone. However, if this is the case, it does not significantly impact absolute binding signal, and it has negligible impact upon the efficiency of signal development at these fast flow rates. This finding is promising for large-volume processing in limited-infrastructure settings where syringe pumps are unavailable, suggesting that manual processing of large volumes may likewise boost assay sensitivity (Figure S14).

Conclusions In this study, we have investigated the use of flow-through paperbased diagnostics for the processing of large-volume samples. Finite-element analysis was used to predict general performance regimes and trends for these assays. These models suggest that the local concentration regime accessed using the rcSso7d-CBD binding scaffold is uniquely enabling for the rapid processing of samples on the mesofluidic scale. Experimentation in this model system demonstrated that large-volume processing can yield significant sensitivity enhancement, due to the greater molar quantities of available analyte. The observed signal increase was enabled by the high immobilized abundance of the rcSso7d-CBD species, which yields analyte capture within the short residence times required for mesofluidic sample processing. Lastly, we empirically identified critical design criteria for the efficient processing of large diagnostic samples, offering guidance for optimizing analyte binding on a basis of both a) assay efficiency and b) proportional target capture. While the processing of large patient samples may pose a logistical burden in low-infrastructure clinical contexts, the experimental results of this study demonstrate the feasibility of this approach at high flow rates characteristic of manual processing. Additionally, a number of low-cost devices have been produced for the facile handling of large fluid volumes. These include spring-loaded syringes


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Figure 5. Assay performance for varying flow rates and total processing times. a) Absolute mean fluorescence intensity (MFI), b) proportional MFI (relative to samples processed for the same period of time at 1 mL min-1), and c) signal development efficiency (MFI min-1) for varying single-pass residence times and total processing times. d) Signal development as a function of the number of recirculations. Linear trend-lines indicate the performance of samples produced using a common volumetric flow rate (denoted in the legend). Sample specifications: 10 mL, 1 nM SA-AF647. Error bars represent the standard deviation of three independent replicates. for controlled sample delivery36 and urinary hygiene devices, which can be adapted for the in-line analyte collection.37 The findings of this study have been applied in the context of immunoassay development, but these principles are valid for any application involving the handling of large fluid volumes for target detection (e.g. environmental sensors, diaphoresis-based assays for the detection of rare cell types, in-line sensors for biopharmaceutical manufacturing, etc.). By carefully considering critical design criteria such as the concentration of the binding molecule, the fluid flow rate and processing strategy, and the assay configuration, any bio-sensing application can be rendered more sensitive via largevolume processing.

ASSOCIATED CONTENT Abbreviations CBD cellulose-binding domain; SA-AF647 streptavidin Alexa Fluor 647; MFI mean fluorescence intensity

The following files are available free of charge. Model details, pseudo first-order rate analysis, estimation of immobilized protein on functionalized paper, manual titration curve

AUTHOR INFORMATION Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. *Correspondence to [email protected] Funding sources The Charles E. Reed Faculty Initiatives Fund, the MIT Tata Center for Technology and Design, and the Singapore-MIT Alliance for Research and Technology (AMR IRG) supported this work. YJAM acknowledges support from MIT's UROP Program. Competing interests The authors declare that they have no competing interests.

Supporting Information



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Design principles for enhancing sensitivity in paper-based diagnostics

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