Anal. Chem. 2003, 75, 5775-5782
Fabrication of Patterned Multicomponent Protein Gradients and Gradient Arrays Using Microfluidic Depletion Kari A. Fosser and Ralph G. Nuzzo*
Department of Chemistry and Frederick Seitz Materials Research Laboratory, University of Illinois at UrbanasChampaign, Urbana, Illinois 61801
We demonstrate that depletion effects in the fluids used to fill a poly(dimethylsiloxane) microfluidic device can be used in conjunction with its design rules to generate patterned protein gradients. The linear portions of these structures can be designed to present gradients of bound protein coveragesvarying from near-saturation to effectively zerosover distances ranging from a few hundred micrometers to more than 1 cm by design. Such patterns can be developed in a simple, single-channel form as well as in a multichannel gradient array of more complex design. The patterning protocols also support the use of multiple protein sources, and we demonstrate an assembly process mediated by a protein that inhibits adsorption to generate a gradient array in pixel form. We describe examples of multiple protein gradient patterns along with simple immunoassays to illustrate the scope of the methodology, the activity of the patterned proteins, and their recognition in gradient form on a surface. These gradients should prove useful to studies in biosensor and bioassay development and as substrates for cell culture to study growth and motility. The development of methods to form well-controlled gradients of surface-adsorbed speciessmolecular adsorbates, proteins, etc.s has been the focus of many studies.1-7 Studies in biology have been motivated primarily by the interesting opportunities that gradient structures afford to model, in vitro, the types of complex phenomena that occur in vivosexamples include biological processes such as chemotaxis8 and axon guidance.9,10 The effects * Corresponding author. E-mail:
[email protected]. Telephone: (217) 2440809. Fax: (217) 244-2278. (1) Caelen, I.; Bernard, A.; Juncker, D.; Michel, B.; Heinzelmann, H.; Delamarche, E. Langmuir 2000, 16, 9125-9130. (2) Caelen, I.; Gao, H.; Sigrist, H. Langmuir 2002, 18, 2463-2467. (3) Dertinger, S. K. W.; Chiu, D. T.; Jeon, N. L.; Whitesides, G. M. Anal. Chem. 2001, 73, 1240-46. (4) Jeon, N. L.; Dertinger, S. K. W.; Chiu, D. T.; Choi, I. S.; Stroock, A. D.; Whitesides, G. M. Langmuir 2000, 16, 8311-8316. (5) Liedberg, B.; Wirde, M.; Tao, Y.-T.; Tengvall, P.; Gelius, U. Langmuir 1997, 13, 5329-5334. (6) Terrill, R. H.; Balss, K. M.; Zhang, Y.; Bohn, P. W. J. Am. Chem. Soc. 2000, 122, 988-989. (7) Plummer, S. T.; Wang, Q.; Bohn, P. W. Langmuir 2003, 19, 7528-7536. (8) Knapp, D. M.; Helou, E. F.; Tranquillo, R. T. Exp. Cell Res. 1999, 247, 543553. (9) Baier, H.; Bonhoeffer, F. Science 1992, 255, 472-475. (10) Halfter, W. J. Neuroscience 1996, 16, 4389-4401. 10.1021/ac034634a CCC: $25.00 Published on Web 09/23/2003
© 2003 American Chemical Society
of ligand/receptor density on biological recognition in assays11 and polyvalency12 are also amendable to study using gradient structures. Many different approaches to forming gradients have been reported. A standard technique exploited to study the biology of cell migration involves the introduction of a test analyte at one end of a chamber and noting its effects on cell growth. A related technique is the use of a Boyden chamber, a device that forms a gradient in a permeant by its diffusion through a membrane.13 A more pattern-focused approach centers on the use of the technologies of photolithographic patterning.2 Such methods typically involve directed processes that pattern the surface chemistry of a substrate in gradient form and allow proteins to adsorb subsequently in a complementary fashion. Self-assembled monolayers have found broad applications in studies of gradient systems, and several groups have demonstrated their fabrication (e.g., in studies of wettability using diffusion5 or electrochemical protocols6,7,14). A more recent general approach has centered on use of microfluidic devices. Microfluidic patterning of proteins using poly(dimethylsiloxane) (PDMS)-based devices was first described by Delamarche and co-workers.15 The techniques of soft lithography that formed the basis of this report are now well developed,16,17 and the use of microfabricated PDMS tools to form bioresponsive patterns (e.g., using microcontact printing, (µCP)18-21) is now quite common.22 The use of microfluidicssthe focus of the current reportshas some advantages over other soft-lithographic patterning methods. First, it embeds a class of patterning procedures that naturally (11) Butler, J. E.; Ni, L.; Nessler, R.; Joshi, K. S.; Suter, M.; Rosenberg, B.; Chang, J.; Brown, W. R.; Cantarero, L. A. J. Immunol. Methods 1992, 150, 77. (12) Cairo, C. V.; Gestwicki, J. E.; Kanai, M.; Kiessling, L. L. J. Am. Chem. Soc. 2002, 124, 1615-1619. (13) Zantek, N. D.; Kinch, M. S. Methods Cell Biol. 2001, 63, 549-559. (14) Plummer, S. T.; Bohn, P. W. Langmuir 2002, 18, 4142-4149. (15) Delamarche, E.; Bernard, A.; Schmid, H.; Michel, B.; Biebuyck, H. Science 1997, 276, 779-781. (16) Xia, Y.; Whitesides, G. M. Angew. Chem., Int. Ed. 1998, 37, 550-575. (17) Whitesides, G. M.; Ostuni, E.; Takayama, S.; Jiang, X.; Ingber, D. E. Annu. Rev. Biomed. Eng. 2001, 3, 335-373. (18) Inerowicz, H. D.; Howell, S.; Regnier, F. E.; Reifenberger, R. Langmuir 2002, 18, 5263-5268. (19) Tan, J. L.; Tien, J.; Chen, C. S. Langmuir 2002, 18, 519-523. (20) Bernard, A.; Renault, J. P.; Michel, B.; Bosshard, H. R.; Delamarche, E. Adv. Mater. 2000, 12, 1067-1070. (21) Bernard, A.; Delamarche, E.; Schmid, H.; Michel, B.; Bosshard, H. R.; Biebuyck, H. Langmuir 1998, 14, 2225-2229. (22) Kane, R. S.; Takayama, S.; Ostuni, E.; Ingber, D. E.; Whitesides, G. M. Biomaterials 1999, 20, 2363-2376.
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leads to the patterning of proteins in gradient form. Second, it allows for a minimization of the amounts of protein required to form a gradient. Third, it results in deposition directly from solution and avoids the drying of proteins that is required in a method such as µCP.23 Gradient patterning using microfluidic methods has also been described in an early report by Delamarche and co-workers. The procedure used was somewhat unusual in that they utilized PDMS as a substrate sealed to a Si microchannel device to pattern gradients via capillary action-mediated flow. This method yielded protein gradients that ranged in length from 30 µm to as much as a few millimeters.1 Whitesides and co-workers described a more directed design approach that utilizes a mixing tree to generate gradients across a wide channel. The shape of the gradient is controlled by the solution concentration in the input channels, the design rules of the arrayed network, and the mass-transfer influences that attend diffusion in laminar flow systems.3,4 The cross-channel gradients developed in this way have found significant applications in the study of cells in microculture.24,25 Patel and co-workers studied protein patterning using protocols similar to those of Delamarche; they also noted depletion effects that resulted from the nonspecific adsorption of proteins on the PDMS.26 In this paper, we present a developed procedure for generating protein gradients of varied structure and form on substrate surfaces commonly employed for bioassay and cell-based studies. The protocol exploits depletion effects and protein-mediated assembly to generate the gray scale (i.e., gradient) patterns. We use unmodified microfluidic devices fabricated in PDMS to generate these gradient profiles. The hydrophobic nature of PDMS (water contact angle ∼105°27) strongly promotes the nonspecific adsorption of proteins21 with only a minimal amount of desorption over the time scale utilized in these experiments.28 This depletion of protein in the solution used to fill the device, along with the system’s design rules, allows for a general form of gray scale patterning. Using the highly developed techniques of soft lithography,29,30 the design rules can be adapted easily to generate patterning tools for a wide variety of gray scale forms. Since these gradients are formed along the linear direction of flow of the protein solution, the gradients obtained are ones that complement those derived from laminar flow mixing trees24,25 and might allow an additional degree of control for studies involving cells. Driven fluid flows critically underpin the patterning method described in this work. Filling hydrophobic PDMS channels with aqueous solutions is both difficult and subject to adverse impacts (23) Delamarche, E.; Bernard, A.; Schmid, H.; Bietsch, A.; Michel, B.; Biebuyck, H. J. Am. Chem. Soc. 1998, 120, 500-508. (24) Jeon, N. L.; Baskaran, H.; Dertinger, S. K. W.; Whitesides, G. M.; Water, L. V. d.; Toner, M. Nat. Biotechnol. 2002, 20, 826-830. (25) Dertinger, S. K. W.; Jiang, X.; Li, Z.; Murthy, V. N.; Whitesides, G. M. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12542-12547. (26) Patel, N.; Sanders, G. H. W.; Shakesheff, K. M.; Cannizzaro, S. M.; Davies, M. C.; Langer, R.; Roberts, C. J.; Tendler, S. J. B.; Williams, P. M. Langmuir 1999, 15, 7252-7257. (27) Ocvirk, G.; Munroe, M.; Tang, T.; Oleschuk, R.; Westra, K.; Harrison, D. J. Electrophoresis 2000, 21, 107-115. (28) Lok, B. K.; Cheng, Y.-L.; Robertson, C. R. J. Colloid Interface Sci. 1983, 91, 104-116. (29) McDonald, J. C.; Duffy, D. C.; Anderson, J. R.; Chiu, D. T.; Wu, H.; Schueller, O. J. A.; Whitesides, G. M. Electrophoresis 2000, 21, 27-40. (30) Duffy, D. C.; McDonald, J. C.; Schueller, O. J. A.; Whitesides, G. M. Anal. Chem. 1998, 70, 4974-4987.
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due to bubbles, arrested filling, dewetting, and other defects. Plasma oxidation, which renders it hydrophilic for a short period of time, and in some cases imparts a nonreversible seal to the substrate upon contact, has been used as one strategy to partially overcome these difficulties.29 Our own results with this approach have been somewhat inconsistent, and thus, we adopt a driven fill method that can accommodate PDMS channel systems of varied complexity and dimensions with lessened impacts due to defects. We previously described a filling method, the channel outgas technique (COT), that allows us to rapidly fill complex PDMS channel designs with an aqueous solutions.31 The abilities engendered by the COT method provide a critical underpinning to the development of gradient protein patterns based on the depletion effects that arise during the flow of solution through the microchannels of the device. Perhaps of most importance to future work, the gray scale patterns can be developed using very small volumes of protein solutions; volumes of 20-25 µL containing 1-10 µg/mL are typical of the work described here. These minimal quantities of material can be used to generate gray scale patterns on substrates such as polystyrene and glass that are quite large as to the dimensions embedded in the gradient and the area they cover. Together with the device design rules, protein patterns showing gradient profiles can be formed over distances ranging from a few hundred micrometers to more than 1 cm or in arrays that cover more than 1 cm2 of substrate surface area. The focus in this report centers largely on the development of gradients of protein molecules of interest in cell growth and bioassay. We describe the parameters (experimental and device design) that affect and proscribe the nature of the gradient formation process. As a simple first demonstration, we highlight patterns produced on either unmodified polystyrene (cell culture grade) or glass surfaces. The latter substrates were first modified with amine-terminated silane and glutaraldehyde to impart an aldehyde functionality to the surface that leads to covalent bonding of the protein to the surface via its reaction with amine (lysine) side chains of the protein.32,33 The gradients produced in this way were characterized first using fluorescently labeled proteins, an easy and straightforward method to visualize areas of varying protein coverage. We also highlight characterizations made using immunoassays, ones that demonstrate the recognition of the gray scale pattern. This report includes descriptions of the design rules that dictate the slope, length, and profile of a gradient formed in a single-channel system. Additionally we show that counterpropagating two-protein gradients can be fabricated. Simple patterns that allow the production of multiple gradients to be produced using one fill point and microarrays of proteins of various coverages are also illustrated. EXPERIMENTAL SECTION Materials. Poly(dimethylsiloxane) was obtained from Dow Corning (Sylgard 184). Silicon wafers (p-type, 100 orientation) were obtained from Silicon Sense. The photoresist, SU-8 5, and developer were obtained from Microchem. Glass coverslips, No. 2 thickness, were obtained from Fisher. Polystyrene Petri dishes (31) Monahan, J.; Gewirth, A. A.; Nuzzo, R. G. Anal. Chem. 2001, 73, 31933197. (32) Robinson, P. J.; Dunnill, D.; Lilly, M. D. Biochim. Biophys. Acta 1971, 242, 659-661. (33) Walt, D. R.; Agayn, V. I. TRAC, Trends Anal. Chem. 1994, 13, 425-430.
were obtained from Falcon. The coupling agent, (3-aminopropyl)triethoxysilane was obtained from Aldrich. Glutaraldehyde (grade I 50%), IgG-FITC, anti-IgG-TRITC, and IgG-free bovine serum albumin (BSA) were obtained from Sigma. Collagen IV-Oregon Green 488 and BSA-TRITC were obtained from Molecular Probes. Phosphate-buffered saline, cell culture grade, was obtained from BioWhittaker. Device Fabrication. The fabrication of PDMS microfluidic devices via rapid prototyping is described in detail elsewhere.29,30 Briefly recounted, a master pattern of SU-8 5 photoresist on Si was formed by photolithography using a transparency mask. We used a photoresist layer to give resist features with a height of ∼5-15 µm and width and length dictated by mask pattern. The heights of masters’ features were varied by adjusting the spin speed for photoresist coverage. All master feature heights were measured using a Sloan Dektak 3ST profilometer. The master was modified by vapor exposure to tridecafluoro-1,1,2,2-tetrahydrooctyl1-trichlorosilane (Gelest) before pouring a PDMS prepolymer over it to an average thickness of 2 mm. After the polymer was cured (>2 h at 65 °C), the device was cut and peeled from the master. Reservoir holes were punched through the PDMS channel outlets using a 3-mm-diameter dermal biopsy punch (Miltex). Substrate Modification. Glass coverslips or cut microscope slides were cleaned with piranha solution (3:1 H2SO4/H2O2), rinsed, and dried with N2. The glass was then immersed in a 2% solution of (3-aminopropyl)triethoxysilane for 30 min, rinsed, and dried with N2. The treated glass was then cured by heating for 1 h at 110 °C. The glass was allowed to cool and then was placed in a 2% solution of glutaraldehyde for 30 min, removed, rinsed, and dried. Polystyrene substrates were rinsed with 2-propanol and water and then dried. Protein Patterning. PDMS devices were washed with streams of acetone, 2-propanol, and water and dried before sealing reversibly to the modified substrate via conformal contact. Protein solutions were made in pH 7.4 phosphate-buffered saline and introduced to the reservoir hole (∼25 µL). The outlet reservoir was sealed closed by placing a PDMS or glass piece over it (Figure 1). The entire device was placed under vacuum (∼125 Torr) for ∼5 min and then vented back to 1 atm over a period of 40 s to fill using this embodiment of the COT protocol.31 The device was removed and visually examined. If the blocked area was sealed correctly, we found that even the most complex systems could be filled with high reproducibility during the venting step. When desired, the filled device was allowed to sit for a specified adsorption time. Hydrodynamic flow due to the height difference of the two reservoirs was observed during this time, a factor that also impacts the gradient structures obtained. After filling, the protein solution was removed from the reservoir using a micropipet and replaced with H2O or buffer and exposed to vacuum to dilute the solution in the microchannels. Following several rinses, the PDMS was quickly peeled away and the substrate was rinsed with buffer, H2O, or both and dried with N2. If the device was used for two-component patterning, after rinsing, the blocked reservoir was unsealed and a second protein solution was introduced to the reservoir. The device was COT filled in the opposite direction to the initial protein pattern. Assays. Following pattern formation, the entire substrate was exposed to a solution (0.1 mg/mL) of BSA for a minimum of 30
Figure 1. Schematic of the channel outgas filling process and formation of protein gradient.
min in order to block the unpatterned areas. For immunoassays using IgG-FITC, the sample was then exposed to a 1:300 dilution of anti-IgG TRITC for 30 min. Imaging. Fluorescent patterns were imaged using an Olympus AX-70 epifluorescent upright microscope and an appropriate dichroic mirror assembly. Images were collected with an Optronics MagnaFire digital camera and analyzed using ImagePro software. Intensity profiles collected over long lengths for singlechannel experiments were completed using multiple images. A simultaneous transmission picture of an underlying calibrated field finder slide was used to determine the length scales of these analyses. Each data point represents the intensity of a specific pixel of an individual image. RESULTS AND DISCUSSION The protocol used for protein patterning and gradient formation is presented schematically in Figure 1. Figure 2 shows typical single-channel protein patterns of collagen labeled with an Oregon Green dyesone with a uniform coverage and the other in a gradient formsthat were patterned in this way. The procedures used were identical with the exception of the protein concentration used in each case. The surfaces of glass substrates were first modified using sequential exposures to (3-aminopropyl)triethoxysilane and glutaraldehyde following procedures described in the literature.32,33 No modifications were used in the case of polystyrene. A PDMS device, one typically containing two holes to define channel inlets/outlets, was placed in conformal contact with the substrate (PDMS forms autoadherent seals with these materials). The filling method used, COT,31 was optimized to enable the use of minimal volumes and one-directional flow, factors important to the development of gradient substrate patterns of proteins (such as growth factors) that are not available in large quantities. The amount of analyte solution required is dictated by the size of the reservoir hole. We have found that, with a 3-mm-diameter hole produced with a dermal biopsy punch, less than 25 µL of solution was required to generate large surface area patterns. We believe it can be optimized further by adjustment of the reservoir Analytical Chemistry, Vol. 75, No. 21, November 1, 2003
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Figure 3. Fluorescent intensity profiles with sigmoid curve fit for gradients of BSA-TRITC formed in a single 2.5-cm-length channel. See Table 1 for information for specific sample channel dimensions and gradient measurements.
Figure 2. Example of protein concentration effects on gradient formation. Pattern of 0.1 mg/mL collagen-Oregon Green in a singlechannel, 60-µm-width device (upper). The same pattern used with collagen-Oregon Green concentration of 0.01 mg/mL (lower).
dimensions and PDMS thickness. The loaded device was placed in a vacuum chamber, which was evacuated to ∼125 Torr. This step removes the air in the microchannel which is then filled subsequently (after venting) by the solution in contact with it. This proceduresone that achieves great economies in the use of protein solutionssis remarkably general and can be used to form complex patterns, including ones with multiple channels and intersecting lines of flow. We have found that as long as the protein solution reservoir is completely filled and a good seal is present at other outlets, the channel will fill. Any introduction of air to the channel during venting through poor sealing will hinder this process. Because the channel volumes are still on the order of nanoliters, approximately half or more of the solution can be reserved for further analysis or use with other techniques. The rinsing procedure is critical to the success of the patterning process. Unless carried out properly, diffusion and gravity-driven flows both tend to diminish the depth and spatial range of the gray scale embedded in the pattern. We found rinsing was best carried out by removing the solution from the fill reservoir and subsequently refilling it with buffer, as well as removing the sealing plate and excess solution from the channel outlet and resealing. When the device is placed under vacuum for a second time, the solution in the microchannel is pulled to the filled reservoir (where it is extensively diluted); venting refills the microchannel system with the buffer rinse solution. The microfluidic device, when removed with concurrent rinsing, reveals a pattern on the substrate that matches that of the 5778 Analytical Chemistry, Vol. 75, No. 21, November 1, 2003
microchannel system. We found that the areas of the substrate contacted by the PDMS device were still highly active toward protein adsorption and that a deposition step with a second protein by flood exposure could be carried out selectively with a nearly perfect orthogonal registry to the microfluidically deposited pattern. BSA is a protein widely used in studies of biopolymer and cellular patterning. BSA’s utility derives in part from its pronounced ability to hinder nonspecific adsorption of proteins, a property that is quite useful in cell growth and bioassay.34 This orthogonal adsorption and formation of multicomponent patterns is illustrated in many of the experiments described below. The data shown in Figure 2 clearly demonstrate that microfluidic systems can be used to pattern proteins on surfaces in gray scale form. The data further suggest that, in addition to whatever experimental sensitivities are inherent in the procedure, the protein concentration of the fill solution is one critical determinant of the nature of the gradient obtained. This implicitly suggests depletion effectssconcentration changes that result from the irreversible protein adsorption along the channel lengthsis one critical scaling parameter that mediates this aspect of the patterning. To better understand the characteristics underlying this behavior, several parameterssnotably the size of the microchannel and concentration of protein solutionswere varied in a simple, single-channel system. Because gradient formation is dependent on depletion effects, the protein concentrations must be low enough to preclude adsorption to saturation throughout the device. Concentration, though, does work in tandem with the channel system design rules to determine the nature of the gray scale pattern obtained. Figure 3 shows measured gradient profiles of BSA-TRITC patterned with an initial concentration of 1 µg/mL for single-channel lengths of 2.5 cm and various channel widths and heights. These data were obtained from independent onecolor intensity measurements made at different locations along the pattern. The channel design and gradient parameters are listed in summary form in Table 1. The line shape of the intensity profile is fit well by a four-parameter sigmoid curve. A more quantitative analysis can be made as illustrated by the data given in the (34) Nimeri, G.; Lassen, B.; Golander, C. G.; Nilsson, U.; Elwing, H. J. Biomater. Sci. 1994, 6, 573-83.
Q ) ∆P/R
Table 1. Channel Parameters and Gradient Measurements for Data in Figure 3 sample
length (cm) width (µm) height (µm) surface area (cm2) volume (nL) S/V (cm-1) L/wh3 (1011 cm-3) {∝ R} saturation distancea (µm) gradient center (µm) gradient slopeb (µm-1) gradient lengthc (µm)
1
2
3
4
5
2.5 95 9.8 0.052 23 2251 2.80 4855 8110 -7.73 5491
2.5 95 8.6 0.052 20 2536 4.14 3734 5657 -13.79 3182
2.5 95 6.7 0.051 16 3196 8.75 1118 1776 -35.59 1088
2.5 190 8.4 0.099 40 2486 2.22 1437 2294 -22.47 1970
2.5 190 6.7 0.098 32 3090 4.37 387 788 -60.15 716
a Calculated from distance at which intensity is 90%. b Maximum of first derivative for four-parameter sigmoid fit. c fwhm of first-derivative plot.
Supporting Information, which includes the first-derivative plot of the sigmoid fit. This latter representation demonstrates the various gradient slopes (heights in the first-derivative plots) and lengths (as measured by the fwhm of the first derivative14) seen in this comparative series (parameters listed in Table 1). As is evident in the data, the gradients formed extend from surface coverages that all have essentially the same saturation value to essentially zero. The gradients in this example form over linear displacement distances (from the fill point origin) ranging from 1 mm to more than 1.5 cm. The dimensional scalings also are correlated with a specific displacement point of the gradient onset from the fill point origin. The general trends seen in the gradient profiles present in Figure 3sin terms of the shapes and slopes of the profile curves can be qualitatively correlated with aspects of the device design rulessnotably with the relative rankings in the surface-to-volume ratios (S/V) of the devices. A saturation adsorption region is seen at the beginning of each profile. We refer to these regions as one bearing a monolayer coverage of the protein. As the protein is adsorbed in the moving fluid front, its concentration at any length down the channel is decreased relative to its initial value. These depletion effects yield the gradient profiles of protein coverage that eventually decrease to zero given an initial protein concentration that is low enough for this to occur. Most notably, the general trends show (and visual observations confirm) that as S/V increases, the flow changes (smaller cross-sectional area channels fill more slowly) and this, in conjunction with the concentration sensitivities, affects both the saturation length and profile parameters of the gradients (Table 1). In general, the data presented in Figure 3 and Table 1 reveal that an increase in S/V results in an increase in gradient slope, a decrease in its length, and a decrease in the saturation distance (i.e., the point at which the intensity decreases to 90% of the initial value). The COT method is a form of pressure-driven flow. Its main benefit is the significant improvement it yields in the elimination of bubbles and other defects. With our current system design, we were not able to measure quantitatively the flow rates developed in the filling process. Flow in microfluidic channels is dictated by the pressure gradient and fluidic resistance as described by
(1)
In devices of the type used in this work, R, the fluidic resistance, is modeled for a rectangular channel with high aspect ratio and is described by the relation
R ) (12 µL)/wh3
(2)
where µ is the fluid viscosity and L, w, and h are the channel’s length, width, and height, respectively.35 Because this describes a more direct relation between flow rate and channel dimensions, the dimension variables of R are listed in Table 1 (L/wh3) for the data shown in Figure 3. Typically, we found that the channel systems begin to fill during the venting process. For single-channel devices with cross-sectional areas of 1000 µm2, we found that head pressures of ∼500 Torr frequently served to initiate these pressure-driven flows. Assuming that the pressure inside the microchannel reaches 125 Torr, the critical pressure difference to fill these channels appears to be ∼375 Torr. An estimation of flow rate based on channel parameters and this pressure difference, using the relations in eqs 1 and 2, suggests a flow velocity on the order of 5-20 nL/s and gives fill times of
