Efficient and high-quality patterning of biological reagents for surface-based assays remains a key challenge in the life sciences. Numerous techniques have been developed to address the problem of patterning surfaces on the micrometer length scale and with chemistries suited for applications in microtechnology, bioanalytical sciences, and medical diagnostics. These techniques involve lithography, soft lithography and its numerous variants , and accurate dispensing of (bio)chemicals using spotters  and inkjet printers . Many of these techniques have been combined with self-assembly , macromolecular systems , and templated substrates  to achieve precise, complex, and robust chemical engineering of surfaces.
“Open space” microfluidics are a specific set of techniques for processing surfaces and probing biological interfaces in a liquid environment, outside of channel's walls . These techniques operate at micrometer and sub-micrometer length scales and are based on scanning probe microscopy methods [8–13], microelectrochemistry [14–19], multiphase systems [20–23], and hydrodynamic flow confinement (HFC) of liquids [24–36]. HFC generated using a microfluidic probe (MFP) is of particular interest because it can localize liquids on surfaces independently of the chemical composition of the confined liquids and without the need for electromigration of charged species [29, 30]. Using MFPs, several groups showed how to pattern arrays of proteins , detach single adherent cells from a surface , stain living cells , locally perfuse brain slices , perform pharmacological studies on single cells , and produce arbitrary chemical gradients on surfaces [29, 31].
While HFC proved to be well suited for performing a range of chemical reactions on surfaces, shaping liquids over surfaces using HFC is still in its infancy. To fully exploit the opportunities offered by HFC, it is strategic to redefine the methods for bringing/removing chemicals onto/from a surface. This chapter describes a new concept, called hierarchical HFC (hHFC), wherein multiple layers of liquids are shaped to get into contact with a surface. We illustrate how hHFC can readily address critical aspects of microscale surface chemistry through minimal dilution of chemicals in a spatially defined region of a surface, efficient retrieval of chemicals, and fast and simple switching between confined liquids. It is further shown how hHFC can be leveraged for implementing recirculation of a defined volume of liquid within the probe head for highly conservative use of reagents for patterning. Section 2.2 of this chapter is dedicated to the concept of hHFC, including the operating conditions, analytical models, experimental validation, and examples of microscale chemistry. Section 2.3 describes the implementation and an analytical model of liquid recirculation within the MFP head. Finally, Section 2.4 presents efficient and high-quality microscale protein patterning leveraging hHFC and liquid recirculation.
Creating an HFC using an MFP relies on (i) bringing two coplanar apertures into proximity of a surface in (ii) the presence of an immersion liquid and (iii) injecting a liquid from a first aperture at a flow rate Qi that is smaller than the aspiration flow rate Qa through the second aperture (Figure 2.1a). As a result, the injected liquid is confined hydrodynamically between the apex of the MFP head and the surface to be processed, with an apex-to-surface distance d. This liquid can contain critical ligands for analytes on a surface or can be used to detach and retrieve different compounds from a surface [29, 30].
In published work , stable and well-defined flow confinement was achieved for processing surfaces using Qa = 3Qi. A significant drawback of this asymmetry in the flow rates is the dilution of the liquid of interest by the immersion liquid. In the first example of hHFC, we use two extra apertures to “nest” a liquid of interest inside another shaping liquid, which is itself confined within the immersion liquid (Figure 2.1b). Therefore, the relation between the injection and aspiration flow rates can be distributed unequally between the nested liquid and the intermediate (shaping) liquid without affecting the stability of the flow confinements. In addition, dilution of chemical species retrieved from the surface can be minimized in the nested liquid. Another strategy, named “pinched HFC,” is realized by adjusting the ratio of flow rates (Qi2/Qi1 > 1, Figure 2.1c). In this case, the liquid of interest is pinched against the surface using the shaping liquid. This strategy relates to what has been demonstrated using hydrodynamic flow focusing in FACS  or pinched-flow fractionation devices [38–41], where one or multiple laminar flows are used to shape a critical liquid. Pinched HFC enables a reduction in the consumption of reagents for microscale chemistry on surfaces by excluding a volume between the MFP head and the surface that is not critical.
Finite-element modeling was used to gain insight into hHFC and the relevant operating conditions. For a given ratio Qi2/Qi1, the distance d between the apex of the MFP head and the surface defines which of the HFC modes is in operation (Figure 2.2). In nested HFC, d can of course be varied to adjust the footprint of the processing liquid on the surface. Increasing d leads to switching to pinched HFC. During the transition from nested to pinched HFC, molecules in the processing liquid may still reach the surface by diffusion through the pinched liquid (see diffusion zone in Figure 2.2). This diffusion zone was calculated for an IgG molecule (D = 4 ·10−7 cm2/s) . A strong advantage of pinched HFC is the reduction of reagent consumption for processing a surface. This reduction is ultimately limited by the lateral displacement of the processing liquid under strong pinching conditions. Using larger inner apertures can limit this expansion and can increase the operable flow conditions for pinched HFC. Interestingly, switching between nested and pinched HFCs can be achieved by simply modifying the ratio Qi2/Qi1 or by changing d. Perturbation of the shape of HFCs may occur when the apex of the MFP head and the surface are not parallel. The apex of the head can be tilted parallel or perpendicular to the flow of the processing liquid at the apex. In the scenario of a tilt parallel to the flow, the distance to surface varies for each aperture, but symmetry is conserved and the shape of the HFCs will remain unchanged, with an increased flow velocity in the vicinity of the aperture closer to the surface. In the scenario that the tilt of the head is perpendicular to the flow, the symmetry is modified and hydraulic resistance increases in the section of the apex closer to the surface, leading to a lateral shift of the HFCs. However, we found that the tilt measured after parallelism adjustment is below 0.1° or a difference between the two edges of less than 1 µm. In practice, this tilt is very small; we therefore did not investigate the effect of high tilt angles on HFC.
Based on the operating conditions of hHFC, we microfabricated an MFP head to investigate the dilution of a sample in the inner HFC. Specifically, we used a nested liquid containing a food dye and measured its concentration in the inner aspiration channel. Figure 2.3 presents the concentration of the dye (Cm) measured in the inner aspiration aperture normalized with the injected concentration Ci for different flow ratios Qi1/Qa2. The outer injection and aspiration flow rates were set to Qa2 + Qa1 = 3(Qi2 + Qi1) to ensure a stable HFC of the shaping and nested liquids. A ratio of Cm/Ci < 1 corresponds to a dilution of the dye by some of the liquid used for creating the HFC condition. This dilution is directly proportional to Qi1/Qa2 as long as the injection flow rate Qi1 remains smaller than the aspiration flow rate Qa2. In this proportional dilution regime, the confinement of the inner liquid does not take advantage of hHFC and behaves similarly to a “classical” HFC. However, when the injection flow rate Qi1 is higher than the aspiration flow rate Qa2, we observed that all of the liquid entering the inner aspiration aperture comes from the inner injection aperture. In this case, dilution of the dye is very small, and Cm converges toward Ci. This regime, which we call “minimal dilution,” becomes increasingly more efficient in preventing dilution of the dye as the apex-to-surface distance d reduces. The shaping liquid helps create a stable HFC for the inner liquid without the need for a strong asymmetry of aspiration and injection as used in classical HFC. Taking the example of d = 20 µm, the nested liquid experienced a dilution of less than 2%, whereas the dilution of an injected liquid in classical HFC is typically threefold (Qa = 3Qi). We hypothesize that diffusion of the dye out of the nested liquid accounts for the small dilution (1.4–8%) observed in Figure 2.3. This is consistent with the observation that dilution decreases with d: the envelope of the nested liquid flattens and increases its contact area with the surface at smaller d, thereby reducing the total diffusion area between the nested and shaping liquids. Nested HFC not only minimizes dilution of chemicals in a liquid of interest but can also be used for efficient retrieval of reagents/analytes from a surface.
Here we present how hHFC can be used for microscale chemistry on surfaces by means of a few examples. First, functionalized DNA was removed from a surface (Figure 2.4a,b). After deposition using microcontact printing, a solution of NaOH (0.5 M)  was injected using the inner HFC in the nested mode to denature DNA locally and remove the fluorescently labeled DNA strand from the surface (Figure 2.4a,b). This was done by positioning the MFP head at d = 20 µm with an injection-to-aspiration ratio of 1.2 (flow rates: Qi2 = 0.8 µL/min, Qi1 = 1.2 µL/min, Qa2 = 1 µL/min, Qa1 = 5 µL/min). This resulted in a 2% dilution of the denaturation solution with the immersion liquid (Figure 2.3). We calculated a sixfold increase in the concentration of the DNA retrieved from the surface using the nested HFC compared with classical HFC with the same flow rates. The local denaturation of the double-stranded DNA resulted in 90% removal of the fluorescently labeled DNA and was reversible: incubating the processed surface with the fluorescently labeled single-stranded DNA led to a recovery of the fluorescence (data not shown). This example of processing a surface and minimizing dilution during retrieval of a chemical from a surface could be important for surface analysis and for recovering precious samples, such as nucleic acids or other ligands, from specific sites on microarrays or from selected adherent cells, for example.
Another demonstration of hHFC is the simultaneous deposition of two proteins on a surface using compartmentalization of the proteins in either the inner or the outer HFC. This was done by depositing antibodies labeled with a green or a red fluorophore on an NHS-activated glass slide (Figure 2.4c,d). Here, flow rates were kept constant (Qi2 = 1 µL/min, Qi1 = 1 µL/min, Qa2 = 1 µL/min, Qa1 = 5 µL/min), but d was varied so as to select the footprint of the inner antibody pattern (shown in red) on the functionalized glass slide. For these flow conditions and aperture geometries, d = 85 µm was the critical distance at which the inner liquid stopped being nested and became lifted as in the pinched HFC configuration. Continuous patterning can also be done by varying d, while the MFP head moves over the surface (Figure 2.4d). This can be a simple method for creating complex gradients of chemicals on a surface. Moreover, switching from a nested to a pinched HFC mode enables efficient and fast switching between different processing conditions by simply changing d instead of switching between liquids using valves. We readily achieved a switching time of ∼20 ms by varying d from 10 to 100 µm (Figure 2.4c). This approach can, for example, be used for briefly stimulating cells with chemicals or retrieving factors excreted by cells .
Interestingly, the resolution of patterns created on surfaces can be increased by modulating the distance d as shown in Figure 2.4c,d. We also calculated a threefold decrease in the consumption of chemical reagents when processing a surface using the outer flow in pinched HFC mode compared with classical HFC. As an example, writing a 100 × 100 µm2 pattern of antibody only needs 16.7 nL of antibody solution using pinched HFC (1 s writing time at 1 µL/min flow rate), compared with ∼50 nL used without pinching the antibody solution, and one to a few microliters using microcontact printing .
Key parameters in the establishment and control of hHFCs are the injection and aspiration flow rates and the distance d. In addition, the HFC quickly adapts to irregular surface topographies, for example, over adherent cells and tissue sections .
For efficient use of the processing liquid, hHFC can be leveraged to circulate the liquid back and forth while ensuring homogenization through mixing in serpentine channels integrated in the MFP head . The implementation of this circulation in the device is composed of two states, in which the direction of flow is different. In state 1, liquid is injected via the two right apertures and aspirated through the two left apertures (Figure 2.5a). After switching to state 2, all flow directions of the liquids are inverted. Such liquid switching would typically be performed with 2-position valves, but they generally have a large dead volume (tens of microliters) and involve a displacement of the liquid that would disrupt the HFC temporarily. To address these two important issues, a low-dead-volume fluidic system in which the liquid reservoirs are placed close to the MFP head (Figure 2.5b) is used. The valves redirect positive and negative pressures toward the appropriate reservoirs. The advantages of using valves to switch pressure instead of liquids are (i) the absence of liquid displacement in the HFC when switching, (ii) valves can be placed away from the microfluidic system without increasing dead volumes, and (iii) switching is fast (within few milliseconds), with the pressure stabilizing within 1 s. Flow rates are monitored in real time and generated using external pressure controllers and hydrodynamic resistors (Figure 2.5b) integrated in the MFP head. Traditional syringe pump-based liquid actuation is not compatible with this device as it introduces large dead volumes and long switching times.
The operation of liquid recirculation requires a glass/silicon head comprising hydrodynamic resistors, storage and mixing zones, and fluidic vias for connection to the reservoirs (Figure 2.6). We used an HFC, with the flow rates following three rules: (i) both injections are identical, , (ii) total aspiration is sufficiently high to ensure a stable HFC, , and (iii) dilution must be minimal, . A stable and well-defined HFC was formed (Figure 2.6b, state 1). Upon switching the four pressures in the reservoirs, we observed a rapid (<1 s) establishment of the HFC with reversed flow directions (Figure 2.6b, state 2).
Two serpentine zones, of 1 µL volume each, ensure on-head storage and homogenization of the processing liquid (Figure 2.6a). Further reduction of this volume is feasible to the extent that the total volume of the recirculated liquid must be large compared with the fraction of processing liquid lost to the outer aspiration during switching, typically below 1 nL per cycle at a flow rate of 1 µL/min.
As described in Section 2.2.1, dilution of the processing liquid in a single HFC is driven primarily by aspiration of the processing liquid together with the surrounding liquid. In hHFC, because , dilution is solely due to diffusion of analytes from the processing liquid to the shaping liquid and is therefore limited. For efficient recirculation of the processing liquid, this loss of analytes should, however, be minimized. We developed a model to investigate the dilution γ of the processing liquid as a function of two key parameters, namely, the apex-to-surface distance d and the flow rate of the processing liquid Qi1.
The apex of the MFP head and the surface to be processed are considered as two parallel surfaces with an apex-to-surface distance ranging from 10 to 50 µm. Given these boundary conditions, we apply the Hele-Shaw approximation and model the liquid flow between apex and surface as a potential flow. The use of Hele-Shaw flow theory in the context of open space microfluidics is described in depth in Chapter 4. Each of the four apertures creates a static, radial velocity field of liquid flow. The resulting velocity field represents the superimposition of the radial velocity fields from the individual apertures. Due to the symmetry of the resulting velocity field, transport across the interface can be described by considering only one-half of the interface. We define a curvilinear coordinate system with χ being the coordinate axis tangential to the interface and ρ the coordinate axis perpendicular to the interface (Figure 2.7). The analyte in the processing liquid has a diffusion coefficient D, and the initial concentrations of analytes are c0 and for the processing liquid and the shaping liquid, respectively. The initial concentration profile across the interface can thus be approximated with a Heaviside step function.
We apply the advection–diffusion equation (2.1) to study the transport of analytes. Here, vχ and vρ denote the tangential and perpendicular components of the flow velocity:
The velocity field of liquid flow between the apex and the surface as well as the boundary conditions for the concentration is static; therefore Eq. (2.1) can be analyzed in steady state. As and , a further simplification of Eq. (2.1) is possible:
where is the average tangential velocity along the interface up to position χ.
As we consider the initial concentration profile to be a Heaviside step function, Eq. (2.2) is solved by 
The flux J(χ) of analytes across the interface at a specific point χ along the interface is given by the gradient of the concentration in the direction of ρ at χ:
To obtain the rate of analytes diffusing accross the interface, we integrate J(χ) along one-half of the interface and account for the apex-to-surface distance d, Avogadro's number N, and a factor two for symmetry:
The injection flow rate of processing liquid, Qi1, defines the total rate of analytes transported through the confined liquids that can be evaluated as . The dilution γ is expressed as the ratio between the rate of analytes diffusing from the processing liquid into the shaping liquid and the total rate of analytes transported through the confined liquids:
The analyte concentration in the processing liquid will decrease for each circulation cycle. To experimentally measure this reduction in concentration, we recirculated a fluorescent dye (rhodamine B) back and forth (cycles) and observed the drop in fluorescence. Using the hHFC with an injection flow rate Qi1 = 1 µL/min, we measured an average drop in fluorescence of 10.67 ± 1.05% per cycle, corresponding to 36.2% of the initial concentration after 10 cycles (Figure 2.8a, solid line and solid square block). For a second injection flow rate, Qi1 = 2 µL/min, the fluorescence reduces by 4.75 ± 0.38% per cycle, which corresponds to 64.5% of the initial concentration after 10 cycles (Figure 2.8a, solid line and solid circle block). In comparison, the use of a single flow confinement resulted in a fluorescence reduction of 66% after only one cycle and a concentration as low as 0.09% after 10 cycles (Figure 2.8a, dashed line). These results suggest that during recirculation, hHFC has the significant advantage of minimizing the dilution of the processing liquid compared with single HFC.
We also investigated the dilution of the processing liquid as a function of d for flow rates Qi1 = 1, 2 and 3 µL/min, which are commonly used when operating the MFP (Figure 2.8b), and made two important observations. First, dilution in the inner flow confinement increases with the apex-to-surface distance. Indeed, when d increases, the boundary surface between the inner and outer flow confinements increases. In addition, for a given flow rate, the apex-to-surface distance will have an impact on the flow velocity at the interface, and therefore on the amount of analytes that can diffuse through the boundary prior to being reaspirated. Second, dilution is lower at higher flow rates. Similarly, an increase of the flow rate results in an increase of the flow velocity along the boundary. This implies that both the net flux of analytes diffusing to the surface, , and the total amount of analytes injected through the aperture will increase, the former less so than the latter, resulting in increased dilution as .
Both the experimental results and the analytical model exhibit similar trends and dilution values. As an example, for Q3 = 3 µL/min, our analytical model yielded a dilution of 4.11% and our measurements a dilution of 4.24 ± 0.78% for an apex-to-surface distance d = 10 µm. The significant correlation between experiments and theory suggests that dilution is indeed primarily driven by diffusion at the liquid–liquid interface. At low flow rates, for example, Q1 = 1 µL/min and for distances below 20 µm, we observed a minor discrepancy between the model and the experimental results. This is potentially due to the change of the three-dimensional shape of the HFC, which was noticed experimentally, but not accounted for in our model.
Therefore, according to both analytical and experimental dilution values, efficient recirculation is favored at higher flow rates and when the head is in close proximity to the surface. We note, however, that the flow rate will influence the amount of processing liquid lost per circulation cycle. This implies that for a finite volume of processing liquid, there is a trade-off between the flow rate of the processing liquid and the number of circulation cycles per minute for a given volume of processing liquid. Depending on the application, parameters such as apex-to-surface distance and flow rates need to be adjusted to ensure proper surface processing and minimal loss of processing liquid.
Established biopatterning methods locally deposit analytes using minute volumes (picoliter to microliter) of reagents and can broadly be classified into two categories. The first one uses inkjet technologies, in which nanoliter volumes are spotted onto surfaces [3, 20, 48]. The second category requires a gentle contact between a pin and a substrate  to transfer a small volume of processing liquid onto a surface. Both approaches (Figure 2.9a) are in widespread use in research labs and industrial facilities as they enable high-throughput processing and precise (nanometer to micrometer accuracy) deposition of biochemicals. However, these approaches are limited by uncontrolled wetting and evaporation , which affect the homogeneity and repeatability of deposition [3, 50]. More generally, to abate evaporation, oil has been used as an immersion liquid , but, in the context of biopatterning, the surface then requires a rigorous wash step to remove the oil prior to downstream analytical tests. Such rinsing involves solvents and surfactants that will likely cause degradation of the patterned receptors. In contrast, several research groups developed microfluidic-based biopatterning techniques focusing on deposition quality  in which closed channels prevent evaporation. For example, Delamarche et al. developed microfluidic networks (MFNs) (Figure 2.9c) to deliver proteins to surfaces by placing and sealing elastomeric materials on the substrate  and, a variant thereof, a stencil-based method  to localize the processing liquid on surfaces (Figure 2.9b). These microfluidic methods resulted in high-quality biopatterns confined to specific areas on a surface, but suffered from either a large volume consumption or a low deposition rate. Moreover, MFNs are not compatible with high-density discrete unit patterns, such as microarrays, as any variations of the pattern need a redesign of the network. Other examples of contact-based microfluidic implementations, such as chemistrodes , fountain pens, [27, 56] and continuous-flow printing , also impose constraints on the type of surface and the ability to scan and are subject to cross-contamination as well. Noncontact implementations using electric fields, such as electrohydrodynamic jet printing  and scanning ion conductance microscopy , demonstrated patterns in the hundreds of nanometers range with large inter- and intra-spot variations , but required conductive substrates.
Thus, versatile and high-quality patterning of biochemicals on surfaces remains elusive, but microfluidic implementations have paved the way toward convection-enhanced deposition. In general, continuous-flow methods (Figure 2.9c–f) result in a reduction of the deposition time compared with diffusion-driven processes , but are very inefficient in terms of reagent consumption for two main reasons. First, continuous flow implies the use of larger volumes than in diffusion-based deposition, and, second, the actual use of analytes from the solution is very low. For example, a typical convection-based surface reaction in a 100-µm-deep channel would consume less than 1.5% of the sample flowing over the surface, resulting in a tremendous waste of analytes. This inefficient reagent use is problematic, particularly in biopatterning, where biochemicals such as antibodies and DNA probes are expensive. Circulating the processing liquid multiple times over the deposition zone (Figure 2.9d) provides a way to improve reagent utilization [61, 62]. In microchannels, however, laminar flows will hinder homogenization of the recirculated volume, and mixing would therefore be necessary to enable a more efficient use of the processing liquid (Figure 2.9e) [46, 63].
With this in mind, we can discern six attributes for an ideal implementation of a versatile biopatterning device (Figure 2.9f): low reagent consumption, high deposition rate, efficient reagent usage, low variation in the spots deposited, high throughput, and micrometer-scale precision in deposition. Such a device should leverage continuous-flow deposition together with mixing and recirculation of the processing liquid (Figure 2.9f). On the one hand, this ideal implementation would retain the advantages of inkjet and pin-spotting devices, namely, low reagent consumption, high throughput, and precise localization. On the other hand, processing of the surface with continuous flows would provide efficient use of analytes, reduced deposition time, and homogeneity of the pattern deposited.
To implement an MFP-based antibody/antigen assay, a standard polystyrene Petri dish was used as substrate. After incubation of IgG, we processed the surface with the MFP using a solution of fluorescently labeled anti-IgG for different durations with a constant flow rate (1 µL/min) and an apex-to-surface distance d = 30 µm. The results of these assays (n = 5 experiments per deposition time) are presented in Figure 2.10. The experiments were performed both with and without recirculation of the processing liquid, along with a reference experiment using pipette deposition. The fluorescence intensity of deposited anti-IgG was used to assess the deposition efficiency and quality. Deposition using the MFP (Figure 2.10, squares and dots) showed a higher efficiency than pipette deposition (Figure 2.10, diamonds). With an antigen concentration of 50 µg/mL, the surface was saturated in less than 3 min with the MFP and in 6 min with the pipette. Interestingly, no significant difference between deposition with and without recirculation was observed, as both methods use convection-enhanced deposition. However, the model for convective deposition predicts saturation to occur faster than what was observed in the experiments. We hypothesize that these discrepancies arise from (i) three-dimensional effects that are not accounted for in the model, resulting in a reduction of the effective flow velocity and therefore a reduction of advective transport to the surface and (ii) the fact that kon, koff, and the binding site's surface density bm were derived from the diffusion-driven deposition experiments (Figure 2.10, dotted line connecting diamonds) and may be different for the MFP-based deposition experiments.
A striking example of the benefits of recirculation using the MFP is that the total volume used after 10 min with recirculation (1 µL) was one order of magnitude lower than without recirculation (10 µL) while reaching an identical density of captured antigens. Ultimately, this approach would lead to either a drastic reduction of antigens needed for the assay or, conversely, a reduction of the assay time if a pre-concentration of the analyte is done prior to recirculation. Moreover, when using recirculation, the total volume of analyte needed is largely independent of the reaction duration. This result is particularly relevant in the case of low-concentration analytes, where the reaction time can be in the range of hours. Recirculation therefore enables enhanced kinetics as the result of convection while improving reagent use through multiple circulations of the same volume.
Most biopatterning applications require deposition on multiple zones with high spatial resolution, typically in the micrometer range. A key advantage of the MFP is its capacity to interact locally with a surface and to scan large areas rapidly . Leveraging this capacity, we investigated the recirculation of a given volume of liquid on multiple positions on a substrate. Multi-zone deposition can be used for localized capture of antigens from a sample, and, using a single microliter, recirculation allows multiple independent capture zones to be probed. Similarly, an unknown concentration of antigen can be recirculated for different lengths of times on multiple areas on an antibody-coated surface. This can be leveraged to determine the adequate deposition time on the surface to prevent over- or underexposure of the sample of interest in the capture zone. We demonstrated these two aspects by recirculating different concentrations of a fluorescently labeled IgG on an anti-IgG-coated surface (Figure 2.11a) and checked the deposition density after different deposition times (Figure 2.11b).
We also investigated the possibility of using a limited and small volume of processing liquid in the MFP head to deposit a large number of spots on the surface. We deposited 170 spots (Figure 2.11c), switching the flow direction every 10 spots, with the probe staying 10 s on top of each spot. Working close to the surface (10 µm), the dilution was limited to such an extent that only a minimal decrease in fluorescence was observed between the first and the last spots (Figure 2.11d). This decrease in fluorescence was predicted by combining the two analytical models describing dilution during recirculation and binding to the surface. The models exhibited very good correlation with the experimental values. 1.66 µL of fluorescently labeled IgG were used to perform deposition of these 170 spots, so each spot corresponds to a “consumed” volume of 9.7 nL.
Finally, we investigated the quality of the spots deposited and found intra- and inter-footprint variations of 5.8% and 3.4%, respectively (Figure 2.11e,f), confirming the advantages of “wet” methods for presenting an antibody to a surface in terms of deposition quality. We hypothesize that these relatively small deposition variations are due to the type of substrate used (standard, untreated polystyrene Petri dish) and that the deposition quality could be further increased by using engineered substrates.
This method exploits the hierarchical implementation of the HFC to efficiently present micro- to nanoliter volumes of analytes on surfaces. The analytical models we present provide guidelines on how to minimize the dilution of the processing liquid and enhance the deposition kinetics by controlling parameters such as the apex-to-surface distance, the flow rates, and the deposition time. This enables the rapid processing of areas ranging from 5 × 5 µm2 to 1 × 1 cm2 in large substrates, such as Petri dishes and glass slides, with volumes in the microliter range. As an example, 170 antibody/antigen spots were deposited with a per-spot volume of 9.7 nL and a variation in deposition homogeneity below 6%.
This section presents a model describing a metric ϵ(t) that quantifies the benefit of convective transport as compared with diffusion-driven transport for surface biopatterning. Figure 2.12 provides a graphical illustration that helps present the analytical mode. While it is clearly established  that convection will enhance the deposition rate, this gain largely depends on the working regime and parameters such as the analyte concentration in the processing liquid, the flow rates, and the surface-processing duration. We developed an analytical model that describes convection-enhanced deposition of analytes on a surface using the hHFC (Figure 2.10). This model accounts for the transport of IgG molecules from the HFC to the surface and for the kinetics of the reaction between analytes and receptors on the surface.
Binding of secondary antibodies to the surface results in the formation of a depletion zone within the HFC. This depletion zone significantly limits the flux of antibodies to the surface and is therefore of interest in this analysis. For quantitative description of the influence of the depletion zone on the transport of analyte to the surface, we adapt an analytical approach summarized by Squires et al.  The “global” Péclet number Peg is a measure of the size of the depletion zone relative to the geometrical boundaries of the HFC and is evaluated as
where WHFC is the maximum width of the HFC footprint, Qi1 is the imposed flow rate in the inner HFC, and (see Ref. ) is the diffusion coefficient of the antibodies to be deposited. We assume an inner HFC with , and an injection and aspiration flow rate . Hence, for flow conditions expected during MFP operation, , and thus the depletion zone is small compared with the size of the HFC. The “local” Péclet number Pel is a measure of the thickness of the depletion zone relative to the length of the deposition area and is given by
As , the thickness of the depletion zone is small compared with the length of the HFC footprint. While size and shape of the depletion zone conform with advective transport of analyte, solely diffusive transport enables the analyte to pass through the depletion zone and to eventually interact with the surface. With Peg and Pel being large, the dimensionless flux of analyte molecules through a thin depletion zone as described above can be calculated numerically as [60, 65]
After estimating the flux of analyte to the surface, we now focus on the interaction between the primary and secondary antibodies on the surface. We assume this interaction to obey first-order Langmuir kinetics. The Damköhler number Da represents the ratio between the consumption of analyte on the surface and transport rate of analytes. For , the deposition process is transport limited, whereas for , the process is reaction limited. For the assumed system geometry, flow conditions, and the analyte receptor system chosen, Da can be evaluated as follows:
We used a set of parameters typical of MFP operation: a surface area of 250 µm × 250 µm presenting binding sites at a density of 18 000 sites/µm2 and a processing liquid containing an antibody solution. The molar weight of the dispersed antibodies is 150 000 g/mol, and their diffusion coefficient is estimated to be 3.8 × 10−7 cm2/s. For the binding reaction, we presume first-order Langmuir kinetics with kon = 106 L/mol s and koff =10−3 s−1 (see Ref. ).
Assuming first-order Langmuir kinetics and accounting for the diffusion-limited transport to the surface, the dynamics of the surface density of bound analytes bMFP(t) can therefore be described by
where the retarding effect of the limited flux through the depletion zone is accounted for by the factor Da− 1.
When the processing liquid is pipetted onto a surface coated with a primary antibody, the growth of the depletion zone is not counterbalanced by advective transport, and the flux of analytes to the surface reduces continuously. Consequently, the Damköhler number depends on time, and thus the surface density of bound analytes for pipette-based deposition bPipette(t) can be approximated as
The metric ϵ(t) quantifies the benefit of convective transport compared with diffusion-driven transport for surface biopatterning and is the ratio of analyte bound with the MFP compared with that of pipette deposition. It can be evaluated as
Figure 2.13a shows ϵ(t) for four concentrations of IgG in the processing liquid, with standard parameters for MFP surface processing. The graph suggests that deposition using the MFP is more efficient for times shorter than 10 min and strongly depends on the analyte concentration. Once saturation of the surface with the MFP has been reached, the efficiency of pipette deposition will slowly converge to that of MFP-based deposition; thus ϵ(t) converges to 1. Interestingly, the lower the concentration, the better the MFP will perform in comparison with pipette deposition, which implies that convective deposition is particularly favorable for low concentrations. As an example, for a concentration of 50 µg/mL, the amount of analyte deposited with the MFP after 40 s will be 1.5-fold higher than with pipette deposition. Longer deposition times will result in identical deposition efficiencies for both approaches after 6 min. In contrast, for a tenfold lower concentration (5 µg/mL), the number of analytes deposited with the MFP after 5 min will be 3.5-fold higher than with pipette deposition. The pipette deposition will require more than an hour to reach the MFP-based deposition efficiency. This clearly highlights the advantage of using MFP deposition for low concentrations of analyte and also that there is an optimal range of processing durations in which the MFP is particularly relevant.
From this model, we also derived the analyte use as a function of time (Figure 2.13b), which corresponds to the ratio of analytes bound to the surface to the initial number of analytes in the processing liquid. Consequently, analyte use is first marked by a strong increase in the number of bound analytes, and we term this the deposition regime. The decrease of available free binding sites on the surface over time leads to a reduction of the association rate, and analyte use enters a plateau regime when the association rate and the dissociation rate balance each other. Through successive dilution of the processing liquid in every circulation cycle, the concentration of analytes decreases to the extent that dissociation of analytes from the surface becomes predominant in the desorption regime. Our model allows us to estimate the number of recirculation cycles (or the time) after which the processing liquid is depleted because of deposition on the surface and diffusive transport to the outer flow confinement. The processing liquid can then be replenished before the system enters the “desorption phase,” thus preventing deposition issues. Figure 2.13b further implies that analyte use depends on the initial concentration and remains below 6% for the four concentrations investigated. An important implication of this result is that a unit volume of processing liquid can be circulated multiple times for multispot deposition or for long incubation times.
The hHFC holds great promise for efficient microscale chemical processing of surfaces because it neither requires working with particular liquids nor depends on experimentally challenging conditions. This hHFC concept is therefore broadly applicable and well suited for working with biological interfaces. In addition, the outer liquid can be used for preventing the inner apertures or a surface from becoming clogged by particulates or toxic chemicals, respectively. We hypothesize that shielding the inner apertures from particles and shaping the nested HFC could lead to sub-micrometer surface processing using the MFP. hHFC can also solve the challenge of working with an immersion liquid and a processing liquid that are nonmiscible by inserting a liquid having an intermediate surface tension. Overall, hHFC is simple, flexible, interactive, and should greatly enhance methods based on HFC for shaping liquids over surfaces.
Liquid recirculation with the MFP allows a reduction of reagent consumption inherent to continuous-flow methods. This method can be scaled to form larger or smaller footprints by changing the aperture size, the aperture spacing, and the flow rates, with dimensions ranging from hundreds of nanometers to a few millimeters. The scanning capability of the probe  allows the patterning on large surfaces, typically in the centimeter range, with the possibility of creating arrays of up to 30 000 spots/cm2 with a spot size of 10 × 10 µm2. The capacity of the MFP to rapidly switch liquids  on top of the substrate makes it a relevant tool for implementing complex biochemistries requiring multiple consecutive chemicals to be dispensed on the surface and even for manufacturing protein microarrays.
Throughput, however, remains a challenge with this technique. Only one spot is patterned at a given time, but we foresee processing multiple positions on the surface in parallel by leveraging standard microfluidic channel bifurcations implemented on the probe. We believe that the MFP might not be the preferred tool when the incubation or reaction time is in the range of tens of hours. However, most surface chemistries will be accelerated by convective transport, and thus long overnight incubation will likely not be required. For specific applications, increasing the recirculated volume is readily feasible, but working with processing liquid volumes below 100 nL is challenging to implement in the current probe configuration. We believe that the microliter to milliliter range is appropriate for most biopatterning applications, as it is compatible with standard volumes used in industrial methods, such as inkjets and pinspotters. Finally, the asymmetric teardrop shape of the deposition area can be altered by using different aperture spacings and geometries. The method presented in this chapter combines five of the six attributes of an ideal biopatterning approach, namely, low reagent consumption, high deposition rate (kinetics), efficient reagent use, low variation in the spots deposited, and micrometer-scale precision in deposition. This combination of advantages creates a powerful tool for an efficient and high-quality patterning of receptors on surfaces and thus might enable quantitative assays in discovery research, point-of-care devices, large-scale surface patterning, and reverse immunoassays and will catalyze the manufacturing of protein microarrays.
This work was in part supported by the European Research Council (ERC) Starting Grant, under the 7th Framework Program (Project No. 311122, BioProbe).
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