Mixing Crowded Biological Solutions in Milliseconds - Analytical

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Anal. Chem. 2005, 77, 7618-7625

Mixing Crowded Biological Solutions in Milliseconds Albert Liau,†,‡ Rohit Karnik,‡,§ Arun Majumdar,§,| and Jamie H. Doudna Cate*,⊥,#

Biophysics Program, Department of Mechanical Engineering, and Departments of Molecular and Cell Biology and Chemistry, University of California, Berkeley, California 94720, and Materials Sciences Division and Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720

In vitro studies of biological reactions are rarely performed in conditions that reflect their native intracellular environments where macromolecular crowding can drastically change reaction rates. Kinetics experiments require reactants to be mixed on a time scale faster than that of the reaction. Unfortunately, highly concentrated solutions of crowding agents such as bovine serum albumin and hemoglobin that are viscous and sticky are extremely difficult to mix rapidly. We demonstrate a new dropletbased microfluidic mixer that induces chaotic mixing of crowded solutions in milliseconds due to protrusions of the microchannel walls that generate oscillating interfacial shear within the droplets. Mixing in the microfluidic mixer is characterized, mechanisms underlying mixing are discussed, and evidence of biocompatibility is presented. This microfluidic platform will allow for the first kinetic studies of biological reactions with millisecond time resolution under conditions of macromolecular crowding similar to those within cells. Biological macromolecules are rarely studied under in vitro conditions that accurately emulate in vivo environments. In particular, the important intracellular effects of macromolecular crowding are seldom addressed by biologists. Molecular crowding can be crucial in modeling the behavior and interactions of macromolecules inside the cell, where 20-30% of the total volume is occupied by macromolecules.1-3 By decreasing the configurational entropy or the diffusion constant of various proteins or nucleic acids, crowding can have dramatic productive and destructive consequences. It can promote the formation of large molecular complexes, yet it can also accelerate the formation of nonfunctional aggregates.1 The effect of crowding on reaction equilibria and kinetics is experimentally well-established.2,3 Probing kinetics faster than the * Corresponding author. Phone: (510) 486 4033. Fax: (510) 486 6240. E-mail: [email protected]. † Biophysics Program, University of California, Berkeley. ‡ These authors contributed equally to this paper. § Department of Mechanical Engineering, University of California, Berkeley. | Materials Sciences Division, Lawrence Berkeley National Laboratory. ⊥ Departments of Molecular and Cell Biology and Chemistry, University of California, Berkeley. # Physical Biosciences Division, Lawrence Berkeley National Laboratory. (1) Ellis, R. J. Trends Biochem. Sci. 2001, 26, 597-604. (2) Hall, D.; Minton, A. P. Biochim. Biophys. Acta 2003, 1649, 127-139. (3) Minton, A. P. J. Biol. Chem. 2001, 276, 10577-10580.

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minute or hour time scale, however, has not been possible. A requirement for studying reaction kinetics is that the reactants must be mixed to homogeneity on a time scale faster than that of the reaction. Therein lies the major obstacle to studying kinetics in a crowded system: the rapid mixing of reactants contained within a highly concentrated solution of crowding agent. At high concentrations emulating intracellular conditions (typically1 200400 mg/mL), commonly used crowding agents such as bovine serum albumin (BSA) and hemoglobin (Hb) exhibit high viscosity and adsorb to surfaces, making rapid mixing very difficult. For example, standard stop-flow fluorometers widely used to study kinetics in dilute solutions on the millisecond time scale cannot be used with sticky, highly viscous crowded solutions. A robust microfluidic system has been developed by Song et al.4,5 to rapidly mix dilute solutions within aqueous droplets suspended in an oil carrier fluid (Figure 1a). In this micromixer, three separate aqueous streams converge in a single microchannel where they pinch off into droplets called plugs that are suspended in a perfluorinated oil containing a surfactant. As the plugs move through a serpentine microchannel, alternating asymmetric flow patterns are induced as the plug traverses each half-cycle of the serpentine channel (Figure 1a). This leads to chaotic advection that rapidly mixes the contents of the plugs.4 The critical advantage of this system is that the reaction time coordinate is directly related to the distance along the microchannel. The plugs move steadily down the channel and reactants are confined in each plug, which prevents axial dispersion. Thus, the progress of reactions occurring within the plugs is amenable to kinetic analysis (Figure 1b). Biological reactions in dilute aqueous solutions in which the time required for full mixing, or dead time, is on the order of 1 ms have been studied in this mixer.5 Our experiments, however, indicate that this system is ineffective for mixing crowded solutions. We, therefore, redesigned the microfluidic system by introducing protrusions along the channel walls (Figure 1c) that induce rapid mixing of highly concentrated protein solutions. This work will facilitate the kinetic study of biological reactions in crowded systems on a millisecond time scale. We characterize mixing in the system and discuss the underlying mechanisms of rapid mixing in these kinds of crowded solutions. (4) Song, H.; Tice, J.; Ismagilov, R. F. Angew. Chem., Int. Ed. 2003, 42, 768772. (5) Song, H.; Ismagilov, R. F. J. Am. Chem. Soc. 2003, 125, 14613-14619. 10.1021/ac050827h CCC: $30.25

© 2005 American Chemical Society Published on Web 11/03/2005

Figure 1. Fast mixing of reactants and the study of subsequent reaction kinetics. (a) A microfluidic system for the rapid mixing of aqueous solutions. In this micromixer designed by Song et al.,4,5 three separate aqueous streams converge, then intersect with an oil stream, and pinch off into droplets (plugs) suspended in the oil carrier fluid. Alternating asymmetric flow patterns are induced as the plug traverses each half-cycle of the serpentine channel (inset). (b) General scheme for studying reaction kinetics. Reactants X and Y must mix on a time scale faster than the time of the reaction. Once mixed, the kinetics can be extrapolated from the observation of a signal (i.e., fluorescence) produced by the reaction. (c) Schematic of the bumpy serpentine mixer. Two streams of crowded solutions (CS) containing reactants X and Y separated by a third stream of crowded solution intersect with two oil streams to form droplets suspended in oil (plugs). The plugs then proceed through n cycles of the bumpy serpentine channel until the plug contents are fully mixed.

EXPERIMENTAL SECTION Fabrication. The micromixer devices were fabricated with poly(dimethylsiloxane) (PDMS) (Sylgard 184, Dow Corning), using a micromolding process.6 To fabricate the PDMS component, a microchannel mold was made by patterning a silicon wafer with photoresist and etching the silicon ∼20 µm deep in a DRIE system (Surface Technology Systems Advanced Silicon Etch system) to leave a positive relief of channels with a 1:1 aspect ratio. The silicon mold was then placed in a desiccator with a few drops of tridecafluoro-1,1,2,2-tetrahydrooctyl-1-trichlorosilane (United Chemical Technologies, Bristol, PA) to aid in the future removal of PDMS. PDMS was mixed in a 10:1 ratio of monomer and curing agent, poured over the mold, degassed, cured at 90 °C for 30 min, and then removed from the mold. Inlet and outlet holes were (6) Duffy, D. C.; McDonald, J. C.; Schueller, O. J. A.; Whitesides, G. M. Anal. Chem. 1998, 70, 4974-4984.

drilled in the PDMS component using a drill (model 395, Dremel) and 300-400-µm-diameter drill bits. The molded component was then bonded to a previously prepared PDMS-coated glass slide using a transfer bonding technique7 to obtain the device. Microscopy. Fluidic connections were made by inserting 0.016-in.-o.d. PTFE tubing (Cole-Parmer) that was connected to 27G needles via 0.012-in.-i.d. PTFE tubing. Glass syringes (Hamilton) were mounted on a syringe pump (SP200I, World Precision Instruments) to control flow through the device. The device was mounted on an inverted epifluorescence microscope (TE2000-U, Nikon) for experiments. Images were acquired with an ORCAER camera (Hamamatsu Photonics) controlled by Wasabi software (Hamamatsu Photonics). Image analysis was performed using ImageJ8 and Wasabi. Fluid Folding Experiments. Both bovine Hb (Sigma) and BSA (Equitech-Bio) were dissolved in phosphate-buffered saline (Invitrogen). The 200 mg/mL BSA solutions were loaded into three 100-µL fixed-needle glass syringes (Hamilton). One BSA solution contained 5 mM calcein dye (Molecular Probes). In experiments mixing Hb and BSA, 300 mg/mL Hb solutions were loaded into two of the three 100-µL syringes, and the remaining syringe was filled with 260 mg/mL BSA containing 5 mM calcein dye. In all experiments, a 1:2 v/v mixture of EGC-1702 (3M) and Fluorinert (FC-70, Sigma) with a 1:10 v/v dilution of perfluorinated surfactant (C6F11C2H4OH, Acros) served as the oil carrier stream and was loaded into two 1-mL removable-needle glass syringes (Hamilton). The three 100-µL syringes were driven by syringe pump at flow rates ranging from of 0.02 to 4 µL/min, and the 1-mL syringes were driven by an identical syringe pump at flow rates ranging from 0.2 to 8 µL/min. For the sucrose experiments, a 1.8 M sucrose solution (Sigma) was prepared in deionized water. The fluorescent stream consisted of 5 mM calcein in 1.8 M sucrose solution. For the Hb folding experiments, one of the 300 mg/mL Hb streams contained ∼5 mM Alexa Fluor 647 (Molecular Probes), the other two streams being 300 mg/mL Hb. Mixing Time-Scale Measurements. Calcium ion binding experiments were performed with 1 mM calcium ion indicator Fluo-4FF (Molecular Probes) with 1 mM EDTA (Sigma) in 270 mg/mL Hb in one stream, a 270 mg/mL Hb solution containing 1 mM EDTA in the separator stream, and a 270 mg/mL Hb solution containing 10 mM CaCl2 in the third stream. Viscometry and Tensiometry. Viscosities of Fluorinert, 300 mg/mL Hb, 200 mg/mL BSA, 1.8 M sucrose, and the Fluorinert, EGC-1702, surfactant mixture (oil carrier fluid) were measured using a falling ball viscometer (Gilmont). Interfacial tensions of the oil carrier fluid with 200 mg/mL BSA, 270 mg/mL Hb, and the 1:2 v/v mixture of 260 mg/mL BSA and 300 mg/mL Hb solutions were measured by an inverted pendant drop technique. Pendant drop images were captured using a drop shape analysis system (Kruss, DSA-10). Interfacial tensions were extracted using the method of a selected plane and tables listed by Andreas et al.9 and Stauffer.10 (7) Satyanarayana, S.; Karnik, R.; Majumdar, A. J. Microelectromech. Syst. 2005, 14, 392-399. (8) Abramoff, M. D.; Magelhaes, P. J.; Ram, S. J. Biophotonics Int.. 2004, 11, 36-42. (9) Andreas, J. M.; Hauser, E. A.; Tucker, W. B. J. Phys. Chem. 1938, 42, 10011019. (10) Stauffer, C. E. J. Phys. Chem. 1965, 69, 1933-1938.

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Biocompatibility Tests. To determine whether proteins adsorbed to the droplet-oil interface, emulsions of aqueous protein solutions in the oil carrier fluid were prepared by vortexing a 1:10 v/v mixture of the aqueous and oil phases. Aqueous protein solutions of 500 ng/mL Alexa Fluor 647-conjugated BSA (Molecular Probes) were prepared with and without a background of either 130 mg/mL BSA or 150 mg/mL Hb. Assuming an adsorption density of 1 mg/m2 protein11 at the aqueous solutioncarrier oil interface, one would expect adsorption to significantly affect bulk concentration of labeled BSA in droplets up to 1 mm in diameter, which is much larger than the plug size. The resulting droplets, comparable in size with plugs in our mixer, were imaged using an epifluorescence microscope with a 10× objective. Luminescence experiments were performed with 2 mg/mL QuantiLum recombinant firefly luciferase (Promega) and 12 mM beetle luciferin (Promega) in a 230 mg/mL Hb solution containing reaction buffer from an ATP Determination Kit (Molecular Probes) in one stream and 30 mM ATP in 230 mg/mL Hb in another stream with a separator stream of 300 mg/mL Hb. RESULTS AND DISCUSSION Plug Formation. We first tested the microfluidic mixing system developed by Song et al.4 with crowded solutions of BSA. When crowded solutions of 200 mg/mL BSA were used in place of aqueous solutions in this micromixer, the most immediate and detrimental problem was the irreversible sticking of BSA or Hb (presumably denatured)12 to the microchannel walls, which not only disrupted plug formation but also quickly rendered the micromixer unusable (Figure S-1, Supporting Information). One possible solution to the denaturation problem has been to use a perfluorinated silane pretreatment of the microchannels to limit sticking of proteins on the walls.5 In the present experiments, the inclusion of a perfluorinated coating fluid EGC-1702 in the oil stream alleviated the sticking and served as an effective substitute for the perfluorinated silane pretreatment of the microchannel walls. We continued to use the nonionic surfactant C6F11C2H4OH used in the original micromixer at 10% bulk concentration4 since plug formation was not as robust at surfactant concentrations of 0-1% (data not shown). In addition, slight narrowing of the channel just after plug formation improved the stable formation of longer plugs. The inclusion of two symmetrically converging oil streams instead of one asymmetrical oil stream significantly reduced sticking problems and also minimized premixing due to swirling at the point of plug formation13 (Figure S-1, Supporting Information). In addition, the two symmetric oil streams assist the formation of plugs in a manner similar to the “droplet fission” process in Tan et al.14 These modifications facilitated the robust formation of 200 mg/mL BSA plugs, 300 mg/mL hemoglobin plugs, and plugs composed of a mixture of BSA and hemoglobin, with the plug length 2-5 times the plug width to facilitate mixing.15 Mixing. The serpentine microchannel mixer designed by Song et al. enables millisecond mixing while using two-phase fluid flows (11) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 415-426. (12) Beverung, C. J.; Radke, C. J.; Blanch, H. W. Biophys. Chem. 1999, 81, 5980. (13) Tice, J. D.; Song, H.; Lyon, A. D.; Ismagilov, R. F. Langmuir 2003, 19, 9127-9133. (14) Tan, Y.; Fisher, J. S.; Lee, A. I.; Cristini, V.; Lee, P. A. Lab Chip 2004, 4, 292-298. (15) Olbricht, W. L. Annu. Rev. Fluid. Mech. 1996, 28, 187-213.

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Figure 2. Bumpy channels inducing circulation in plugs of crowded solutions. (a) The contents of dilute aqueous plugs mixed rapidly in a smooth serpentine mixer. Calcein dye initially confined to a third of the plug quickly redistributed to homogeneity within the plug. In contrast, neither plugs of two-thirds 300 mg/mL Hb and one-third 260 mg/mL BSA (b) nor plugs composed entirely of 200 mg/mL BSA (c) mixed in the smooth serpentine mixer. In straight channels, bumps induced circulation within a 200 mg/mL BSA plug (d), whereas the absence of bumps resulted in no discernible circulation within such plugs (e). Plugs of 200 mg/mL BSA (f) and plugs of two-thirds 300 mg/mL Hb and one-third 260 mg/mL BSA (g) exhibited rapid fluid folding in the bumpy serpentine mixer as shown by the redistribution of calcein dye within the plug. All channels shown are 20 µm wide and 20 µm deep.

at low Reynolds numbers (Figure 2a). Such mixing requires significant fluid flow within the plugs, which in the absence of surfactants is a function of three parameters:15 (a) viscosity ratio λ, defined as the viscosity µp of fluid inside the plugs relative to oil viscosity µo, (b) the capillary number Ca ) µoV/γ, where V is the average velocity and γ is the plug-oil surface tension, and (c) k, the ratio of undeformed plug diameter d to channel width w. The capillary number reflects the relative strengths of shear and surface tension forces.

For rapid mixing, a high flow speed (V) is desirable. However, at high Ca, plugs break up into smaller droplets due to shear forces, whereas at low Ca, surface tension keeps plugs intact. Thus, Ca limits the flow speed of the plugs. With crowding solutions of BSA or HB, the microchannel size had to be reduced to a 20 µm × 20 µm cross section, to allow the plugs to traverse a greater number of cycles while maintaining the flow rate and Ca such that the plugs remained intact. At flow rates exceeding ∼10 µL/min, plugs with sizes k ≈ 1 remained intact. At slower flow rates, plugs tended to be longer. It is important to note that, with smaller microchannel sizes, the pressure that the device must withstand increased and fabrication became more difficult, making miniaturization beyond the current size impractical. The viscosity ratio for the water-oil system employed by Song et al.4 is ∼0.2 (viscosities of 5.1 mPa‚s for perfluorodecalin and 1 mPa‚s for water). With crowded solutions, the viscosity ratio was found to be much higher, even with substitution of the oil carrier stream. The viscosities of the crowding solutions were measured to be 6.8 ( 0.2 mPa‚s for 300 mg/mL Hb and 3.9 ( 0.14 mPa‚s for 200 mg/mL BSA. While Hb solutions are reported to be Newtonian fluids,16,17 BSA solutions are shear thinning, with viscosity of 10% w/w BSA ranging from over 100 to less than 10 mPa‚s depending on shear rate.18,19 The measured viscosity of Fluorinert was 26.4 ( 1.1 mPa‚s while the viscosity of the carrier oil used in our system (mixture of Fluorinert, EGC-1702, and surfactant) was 4.88 ( 0.06 mPa‚s. The viscosity ratio was thus 1.4 for 300 mg/mL Hb and could range approximately from 20 to 1 for 200 mg/mL BSA, depending on the shear rate. Plugs flowing in the microchannel are separated from the channel walls by a lubricating oil film. For large viscosity ratios, the thickness of this oil film must be sufficiently small to achieve the maximum fluid velocity within the plugs. When k < 1, which corresponds to droplets smaller than the channel size, the thickness of the carrier oil layer between the droplet and the channel wall is large, which would reduce flow in the case of high viscosity ratios. However, the thickness of the oil film is minimized when k > 1 and Ca is kept as low as possible.15 In the serpentine mixers, the thickness of the oil film is small compared with the channel size for k > 1, indicating that the viscosity of Hb solutions would be unlikely to impede flow in plugs. However, whether viscosity would impede flow in plugs of BSA is not clear, since viscosity could vary over a wide range due to possible shear thinning. Another factor that may impede flow within plugs is the presence of surfactants. When the surface Peclet number Pe ) Vw/Ds, where Ds, the surfactant interface diffusivity, is large, surfactant gradients may develop and reduce flow in plugs.15 The rapid adsorption and desorption of the nonionic surfactant used here and in the original mixer4 likely decreases surfactant gradients,20 thus remobilizing the plug-oil interface and aiding flow within plugs of dilute solutions. However, when the dilute solution in the plugs is replaced by a crowded solution, proteins in the crowded solution adsorb onto the plug-oil interface and (16) Artmann, G. M.; Kelemen, C.; Porst, D.; Bu ¨ldt, G.; Chien, S. Biophys. J. 1998, 75, 3179-3183. (17) Monkos, K. Int. J. Biol. Macromol. 1994, 16, 31-35. (18) Ikeda, S.; Nishinari, K. Biomacromolecules 2000, 1, 757-763. (19) Inoue, H.; Matsumoto, T. J. Rheol. 1994, 38, 973-984. (20) Stebe, K. J.; Lin, S. Y.; Maldarelli, C. Phys. Fluids A 1991, 3, 3-20.

act as surfactants.12,20-22 In the present case, the interfacial tension of the water-oil carrier interface was measured to be 17.4 mN/ m. However, the interfacial tensions of the crowded solution-oil interfaces were in the range of 4.5-6.0 mN/m, indicating protein adsorption at the interface.23 These adsorbed proteins have very slow desorption kinetics,20 which may result in Marangoni stresses that severely impede flow in plugs. Consistent with this model, plugs of crowded solutions failed to mix in the original serpentine mixer (Figure 2b,c). While exaggerating the curvature of the serpentine did not appreciably enhance flow in plugs, this exaggerated curvature allowed for the most important alteration in the present devices: protrusions, or “bumps”, along the outer wall of the serpentine channel. The importance of the bumps was demonstrated in experiments with straight channels, where the bumps alone were capable of inducing appreciable circulation in plugs (Figure 2d,e). In contrast to the original serpentine mixer, the new “bumpy serpentine mixer” (Figure 1c) creates oscillatory flows that fold and refold the flow very rapidly within plugs of 200 mg/mL BSA and 300 mg/mL Hb producing fine fluid striations. As the plug travels down the channel, the striations thin exponentially such that complete mixing can be achieved after the plug has traversed only a few cycles (Figure 2f,g). Fluid folding is readily apparent in experiments where one stream contains a fluorescent dye. The dye distribution quickly changed from confinement to a part of the plug to the formation of distinct bands. This folding is highly reproducible and robust. Varying the flow rates of the oil and BSA/ Hb streams yielded plugs of different sizes, which fold at different rates but all exhibit similar striation patterns (not shown). Striation Length and Mixing Time-Scale Measurements. We characterized the mixer performance by (a) observation of fluid folding using a fluorescent dye (calcein) incorporated in one of the mixing streams and (b) observation of the fluorescence intensity of the Ca2+ binding dye, Fluo-4FF. Striations were readily visible in BSA plugs (Figure 2f), but were not as clear in Hb plugs due to the opacity of Hb. Striations were most clearly visible in hybrid plugs consisting of a mixture of Hb and BSA with calcein dye (Figure 2g). Striations in the BSA and hybrid BSA/Hb plugs revealed that the flow within the plugs is notably two-dimensional and qualitatively different from that in aqueous plugs. With the large depth of focus in our optical setup, three-dimensional flow would not yield such distinct striated patterns. Striations were not clearly visible in aqueous plugs (Figure 2a), probably due to the three-dimensional nature of flow, with perturbations due to the serpentine channel superposed on a steady circulation corresponding to circulating flow in a straight channel. The hybrid plugs described above underwent steady folding as they traversed the microchannel, and striation length decreased with each cycle of the mixer (Figure 3a). Successive micrographs of plugs taken a half-cycle apart (Figure 3b) suggest that striation length halves after each cycle of the mixer. The first plug shows the initial dye distribution, where the striation length may be taken to be 10 µm, which is half the channel size. Folding is visible after just half a cycle (second plug), and the plug appears to be folded once after one cycle (two bands, third plug) and twice after another cycle (four bands, fifth plug). This folding is similar to (21) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 403-414. (22) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 427-439. (23) Roach, L. S.; Song, H.; Ismagilov, R. F. Anal. Chem. 2005, 77, 785-796.

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the horseshoe map24 and suggests a simple model to account for the variation of striation length with time. Assuming that τ is the time taken per cycle and that striation length halves every cycle, the striation length lst at time t is given as

lst ) l0/2t/τ

(1)

where l0 ) 10 µm is the initial striation length. The time per cycle is inversely proportional to the flow rate. For a flow rate of 1 µL/ min, τ ) 5 ms. In time t, molecules will diffuse a distance of the order of the diffusion length scale, ld.

ld ) xDt

(2)

Given the diffusivity of the molecular species being mixed in the plugs, the time scale tm for mixing can be estimated from eqs 1 and 2 by equating the diffusion length with the striation length.

2

Figure 3. Mixing time characterized by fluid folding and ion binding reactions. (a) Striation length (lst) decreased exponentially along the bumpy serpentine mixer. (b) Images of plugs after every half-cycle along the bumpy serpentine channel reveal fluid folding in greater detail. (c) The mixing of the calcium ion indicator Fluo-4FF and calcium ions in 300 mg/mL Hb yielded increasing fluorescence until full mixing was achieved. The numbers above each curve correspond to the oil and Hb flow rates (µL/min), respectively. (d) Time and number of cycles required for the Ca2+/Fluo4FF reaction to reach 50% of maximum intensity plotted for different flow rates (triangles). Mixing time for Ca2+ (solid line) was calculated from eq 3 assuming a diffusivity of 8 × 10-10 m2/s. The mixing time for macromolecules (dashed line) was also calculated from eq 3, assuming a diffusivity of 10-11m2/s. The number of cycles required for 50% mixing (squares) is shown on the scale to the right. 7622

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l0 tm/τ

) xDtm

(3)

This well-known scaling relationship is characteristic of exponential stretching and folding and has been observed in the case of mixing dilute solutions in the original system.25 The scaling of mixing time can be compared with quantitative mixing time obtained by measuring the fluorescence intensity of Fluo-4FF dye. The fluorescence intensity increases when the dye molecules bind Ca2+ ions. Since the binding process is diffusionlimited, this reaction provides a way to quantify mixing in plugs when solutions containing the dye and Ca2+ ions are mixed. Normalized fluorescence intensities of the dye in Hb plugs at various flow rates are shown in Figure 3c. Mixing time decreased as flow rate increased, with the fastest mixing occurring within 2 ms at the highest flow rate of 16.3 µL/min. Mixing time was found to vary only slightly with flow ratio of oil and crowded solutions, as long as plugs were larger than the channel size (k > 1). The scaling of mixing time suggested in eq 3 was tested by comparing the time taken to reach 50% of the maximum fluorescence intensity in the Ca2+-dye binding experiments with tm predicted by eq 3 (Figure 3d). The observed mixing time and the calculated mixing time agree, suggesting the validity of our model. Equation 3 clearly suggests that, at slower flow rates, mixing time for species with different diffusivities are markedly different, whereas this difference is much smaller at higher flow rates. At flow rates up to 9 µL/min, while the mixing time decreased, the number of cycles required for mixing increased and the striation length at the point of mixing decreased, in accordance with eqs 1-3 (Figure 3d). In the dye binding experiments, Ca2+ and Fluo-4FF were mixed in an 8:1 ratio instead of a 1:1 stoichiometric ratio because of the presence of near-millimolar Ca2+ in the hemoglobin solution. This should lead to a slight underestimation of the mixing time at lower flow rates. However, the underestimation is likely to be small since (24) Ottino, J. M. The kinematics of mixing: stretching, chaos and transport. Cambridge University Press: New York, 1997. (25) Song, H.; Bringer, M. R.; Tice, J. D.; Gerdts, C. J.; Ismagilov, R. F. Appl. Phys. Lett. 2003, 83, 4664-4666.

the mixing time depends only weakly (i.e., logarithmically) on the diffusion time scale. Consistent with this model, the dye binding data agree well with mixing rates determined from fluid folding experiments. Notably, the behavior at the flow rate of 16.3 µL/min deviated from that at lower flow rates. The mixing time is relatively shorter, and the number of cycles required for mixing decreases (Figure 3d). This suggests that the folding mechanism differs in some way at the highest flow rates. Future experiments may be able to exploit these differences to further reduce the mixing time scales in these devices. Mechanism of Mixing. In dilute aqueous plugs, mixing is achieved by the alternation between two asymmetric flow patterns within the plugs, induced as the plug traverses each half-cycle of the serpentine channel4,26 (Figure 1a). Each flow pattern consists of two countercirculating flows. The curvature of the serpentine channel causes one circulating flow to be stronger than the other, leading to flow asymmetry.4 Because the Reynolds number is small, the flow patterns are established rapidly relative to the time required for traversing a half-cycle when the boundary conditions near the plug change, i.e., when the plug switches from one curve to another. Each asymmetric flow pattern lasts half a cycle, and thus efficient mixing requires sufficient fluid displacement along the streamlines of the flow pattern within each half-cycle. It is also important that the flow patterns superposed show significant regions of streamlines with transverse intersections. This facilitates the stretching and folding characteristic of chaotic mixing.26 However, for plugs of crowded solutions, our experiments showed that there is insufficient circulation within the plugs in a half-cycle of the serpentine channel (Figure 2b,c), leading to poor mixing. With bumps only on one side of the channel, fluid circulation within plugs of crowded solutions was significantly enhanced and the circulation asymmetry was exaggerated (Figure 4). Fluid folding experiments revealed that the bumps influenced the flow pattern to such an extent that the circulating flow opposite to the bumps almost vanished (Figure 4a). In addition, an increased half-cycle length including several bumps increased the fluid displacement in each half-cycle resulting in more rapid mixing. Furthermore, the appearance of distinct striations indicates that the flow is predominantly two-dimensional, given the large depth of field. It can be argued that bumps lead to enhanced circulation within plugs primarily due to two effects, thinning the lubrication layer of outer fluid below the bumps (Figure 4b) and as a consequence of interfacial stresses induced by bumps (Figure 4c). For large λ, the oil layer between the plug and the channel wall acts as a lubrication layer. A channel with constrictions requires a higher pressure to drive the flow of plugs than can be accounted for by a uniform channel with diameter equal to that at the constriction.27 Moreover, it is a simple matter to show via a form of the Reynolds lubrication equation that the bumps thin the lubrication layer. Because the lubrication layer thins at the bumps, this increases the shear stress experienced by the plugs. This thinning of the lubrication layer may thus be expected to result in enhanced flow in cases where the viscosity ratio is high enough to impede flow in plugs. (26) Wiggins, S.; Ottino, J. M. Philos. Trans. R. Soc. London A 2004, 362, 937970. (27) Olbricht, W. L.; Leal, L. G. J. Fluid Mech. 1983, 134, 329-355.

Figure 4. Mechanism of mixing. (a) Two-dimensional representation of flow patterns in plugs of crowded solutions in the bumpy serpentine mixer. Mixing is achieved by periodically alternating between the two asymmetric flow patterns (left and right) as the plug traverses each half-cycle of the serpentine channel. Bumps may drive flow in plugs of crowded solutions via two mechanisms. (b) Bumps can decrease the lubrication (oil) layer thickness and exert higher shear on one side of the plug. (c) Symmetric Marangoni stresses (light arrows) that oppose flow in plugs may be perturbed at the plug-oil interface below the bumps and the subsequent redistribution of surfactant. The resulting asymmetric Marangoni stresses may facilitate flow in plugs. (d) In the original (smooth serpentine) mixer, plugs of 1.8 M sucrose with fluorescent dye mixed rapidly. The lack of clear striations indicates a three-dimensional circulation of fluid in these plugs. Total flow rates were 1 µL/min oil and 0.3 µL/min sucrose solution. (e) Plugs of 300 mg/mL Hb, with one-fourth the viscosity of sucrose, did not show rapid fluid folding in the smooth serpentine mixer. Total flow rates were 2 µL/min oil and 0.6 µL/min sucrose solution. (f) Rapid mixing of sucrose solutions in the bumpy serpentine mixer, also with three-dimensional flows. Total flow rates were 1 and 0.15 µL/min for the oil and sucrose solutions, respectively.

However, thinning of the lubrication layer is unlikely to be the sole requirement for mixing of crowding solutions of Hb or BSA when k > 1. In experiments with concentrated solutions of sucrose with viscosity 29.5 ( 0.9 mPa‚s, plugs mixed in the Analytical Chemistry, Vol. 77, No. 23, December 1, 2005

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original mixer design lacking bumps, albeit more slowly. Folding is clearly visible in the smooth serpentine mixer for plugs of sucrose solutions (Figure 4d) but not in the case of plugs of 300 mg/mL Hb solutions (Figure 4e) or 100 mg/mL BSA (Figure S-2, Supporting Information), although the viscosity of the Hb solution is approximately one-fourth of that of the sucrose solution. Moreover, the absence of distinct striations even in the bumpy serpentine mixer (Figure 4f) indicates that mixing of sucrose solutions was three-dimensional, as observed for dilute aqueous plugs (Figure 2a). These results suggest that mixing in plugs of crowded solutions is dominated by interfacial properties. As a plug traverses the constriction due to the presence of a bump, the interfacial area increases, leading to a change in surfactant concentration at the interface. The enhanced shear stress experienced by the plug due to thinning of the lubrication layer may further affect the distribution of surfactant, the surfactant being protein in the present case. The extension and contraction that the plug-oil interface undergoes when the plug traverses a bump is also likely to result in interfacial stresses. In the absence of bumps, symmetric Marangoni stresses due to static surfactant concentration gradients work to oppose flow within plugs.15 Bumps break the symmetry of the Marangoni stresses and thus seem to facilitate flow within plugs. Finally, in the case of BSA (which is non-Newtonian), deformation of the plugs and the resulting shear thinning may further affect the flow. In summary, the above experiments strongly suggest that adsorption of proteins at the plug-oil interface impedes mixing in the smooth serpentine mixer. The introduction of bumps affects the interfacial stresses and further introduces flow asymmetry, facilitating rapid mixing in plugs of crowded solutions. A more comprehensive understanding of how bumps affect the interface and flow within the plugs will likely require in-depth analyses and specialized experiments. Biocompatibility. Several lines of evidence indicate that the bumpy serpentine mixer is biocompatible. Inclusion of a perfluorinated surface coating (EGC-1702) was essential to keep the BSA or Hb from sticking to the microchannels. This provides one measure of the biocompatibility of the new microfluidic devices. A further measure of biocompatibility is provided by the crowded solution itself. Biocompatibility is a problem in plugs of dilute aqueous solutions, where the analyte protein molecules are directly exposed to the plug-oil interface. When the analyte protein is at a low concentration, a significant fraction of the analyte can adsorb onto the interface, interfering with the analysis. This problem has been addressed elsewhere by the inclusion of specialized surfactants in the oil,23 which effectively decreased the adsorption of protein on the plug-oil interface. In the case of crowded solutions, the excess of the crowding protein (BSA or Hb) should compete with the analyte for adsorption onto the interface, since the adsorbed layer is populated by the protein that presents itself first to the interface.28 The behavior of fluorescently labeled BSA in the presence of excess of unlabeled crowding proteins (BSA or Hb) indicated that indeed the crowding agents prevent the adsorption of the analyte protein to the interface (Figure 5a). Therefore, the crowding agent itself is likely to adsorb on the interface, further ensuring biocompatibility of our system. (28) Dickinson, E. Colloids Surf. B 1999, 15, 161-176.

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Figure 5. Demonstration of biocompatibility of the micromixer. (a) Emulsions of protein solutions in the oil carrier fluid revealed protein adsorption to the plug-oil interface. The droplets of 500 ng/mL fluorescently labeled BSA (left) had a bright periphery indicative of BSA adsorption to the interface. Droplets of 500 ng/mL fluorescently labeled BSA with 130 mg/mL unlabeled BSA (center) or 150 mg/mL unlabeled Hb (right), showed a bright center that, with the microscope’s depth of field, corresponds to a uniform distribution of fluorescently labeled BSA in the droplet. This distribution did not change over the time scale of minutes, which is well over the time required for the proteins to diffuse across the diameter of the droplet. (b) Luminescence of luciferase activity is consistent among different flow rates. Numbers for each series of data points correspond to oil and Hb flow rates, respectively (in µL/min). The inset shows a micrograph of the luminescence at oil and Hb flow rates of 0.4 and 0.06 µL/min, respectively.

To assess the biocompatibility of our system in an enzymological context, we tested whether the enzyme luciferase retains its activity in the micromixer. In the presence of ATP and oxygen, luciferase catalyzes the conversion of luciferin to oxyluciferin, producing bioluminescence.29 When a Hb stream containing luciferase and luciferin, a separator Hb stream, and a Hb stream containing ATP are mixed in our system, the observed luminescence is consistent among different flow rates (Figure 5b). This experiment demonstrates the feasibility of studying enzymatic reactions in crowded solutions with such a mixing system, and thorough kinetic characterization of luciferase and other enzymes in crowded solutions can now be pursued. CONCLUSION The accurate characterization of the in vivo behaviors of biological processes requires the ability to rapidly mix crowded solutions. We have developed a micromixer and demonstrated for the first time the capability of reproducibly and robustly mixing crowded solutions in milliseconds. The mixer was characterized with the observation of fluid folding and a Ca2+ ion binding (29) DeLuca, M.; McElroy, W. D. Biochemistry 1974, 13, 921-925.

reaction. With the demonstration of biocompatibility in this mixing system via protein adsorption studies and luciferase-catalyzed luminescence, the possibility of studying the kinetics of biological reactions in crowded solutions is now tractable. ACKNOWLEDGMENT The authors are indebted to Andrew Szeri (University of California, Berkeley) for helpful discussions and guidance during the development and characterization of the micromixer. The authors thank Rustem Ismagilov (University of Chicago) for providing the initial mixer design and for valuable input on experimental practicalities and Srinath Satyanarayana for help with surface tension measurements. The authors also thank one reviewer for suggesting the sucrose solution mixing experiments. The devices were fabricated at the Microfabrication Laboratory

at the University of California, Berkeley. Funding for this project was provided by NSF (MCB-0417261). SUPPORTING INFORMATION AVAILABLE Micrographs showing sticking and swirling in the mixer, summary of viscosity and tensiometry results, calculations of flow speed and Ca, fluid folding in 100 mg/mL BSA, and observations suggesting dynamically changing interfacial properties. This material is available free of charge via the Internet at http:// pubs.acs.org.

Received for review May 12, 2005. Accepted September 29, 2005. AC050827H

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