Hydrodynamic Tweezers: 1. Noncontact Trapping of Single Cells

Jul 7, 2006 - Noncontact Trapping of Single Cells Using Steady Streaming Microeddies ... Citation data is made available by participants in Crossref's...
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Anal. Chem. 2006, 78, 5429-5435

Hydrodynamic Tweezers: 1. Noncontact Trapping of Single Cells Using Steady Streaming Microeddies Barry R. Lutz, Jian Chen, and Daniel T. Schwartz*

Electrochemical Materials and Interfaces Laboratory, Department of Chemical Engineering, University of Washington, Box 351750, Seattle, Washington 98195-1750

A key need for dynamic single-cell measurements is the ability to gently position cells for repeated measurements without perturbing their behavior. We describe a new method that uses a gentle secondary flow to trap and suspend single cells, including motile cells, at predictable locations in 3-D. Trapped cells can be more dense or less dense than the surrounding medium. The cells are suspended without surface contact in one of four steady streaming eddies created by audible-frequency fluid oscillation (e1000 Hz) in a microchannel containing a single fixed cylinder (radius ) 125 µm). Comparison of measured trap locations to computations of the eddy flow show that each trap is located near the eddy center, and the location is controlled via the oscillation frequency. We use the motile phytoplankton cell (Prorocentrum micans) to experimentally measure the trapping force, which is controlled via the oscillation amplitude. Trapping forces up to 30 pN are generated while exerting moderate shear stresses (shear stresses e 1.5 N/m2) on the trapped cell. The magnitude of this trapping force is comparable to that of optical tweezers or dielectrophoretic traps, without requiring an external field outside the physiological range for cells (the shear stresses are comparable to those found in arterial blood flow). The unique combination of predictable 3-D positioning, insensitivity to cell and medium properties, strong adjustable trapping forces, and a gentle fluid environment makes hydrodynamic tweezers a promising new option for noncontact trapping of single cells in suspension. Traditional measurements of cell processes provide only the average behavior of the population, and any variation between individual cells is lost in the measurement. Recently, it has become clear that individual cells, even those with the same genes, can express a distribution of phenotypes that change over time.1 Neither population-averaged bulk measurements nor single-cell “snapshots” provided by flow cytometry offer the ability to dynamically monitor the history and fate of a single cell, and this limits their ability to provide insight into the origin and consequences of variation in cell expression. Microfluidic devices offer * Corresponding author. Phone: (206) 685-4815. Fax: (206) 543-3778. Email: [email protected]. (1) Lidstrom, M. E.; Meldrum, D. R. Nat. Rev. Microbiol. 2003, 1, 158-164. 10.1021/ac060555y CCC: $33.50 Published on Web 07/07/2006

© 2006 American Chemical Society

opportunities to study dynamic behavior of individual cells under controlled chemical conditions, provided that cells can be appropriately manipulated.1-3 Dynamic single-cell measurements require methods capable of holding an individual cell in place for repeated measurements, and it is important that the cell behavior is not perturbed by cell handling methods. Some cells function naturally when allowed to adhere and grow on a surface; other cells normally live suspended in a fluid and require suspension to function naturally (e.g., motile cells, circulating blood cells). One class of microfluidic devices allows cells to settle and adhere onto plain or treated surfaces, where they can be chemically treated by fluid flow and monitored over time. Cells can be held at fixed trapping locations by aspirating the cell against small ports, providing a microfabricated parallel version of the conventional micropipet approach.4-7 Similarly, cells can be pressed against a solid obstacle, such as a dam, weir, or wall, using drag forces created by fluid flow past the cell.8-11 These methods employ direct physical contact with the cell, which can trigger an undesirable response in suspension cells. Trapping cells in suspension requires the ability to generate a force that meets or exceeds forces that would otherwise lead to cell movement (e.g., motility, drag due to fluid flow, gravity). However, forces available for noncontact cell trapping are limited. Optical tweezers (OT), introduced by Ashkin over three decades ago, offer the best-known and most widely used means of manipulating single cells in suspension.12-18 Conventional OT use (2) Andersson, H.; van den Berg, A. Sens. Actuators, B 2003, 92, 315-325. (3) Andersson, H.; van den Berg, A. Curr. Opin. Biotechnol. 2004, 15, 44-49. (4) Pantoja, R.; Nagarah, J. M.; Starace, D. M.; Melosh, N. A.; Blunck, R.; Bezanilla, F.; Heath, J. R. Biosens. Bioelectron. 2004, 20, 509-517. (5) Prokop, A.; Prokop, Z.; Schaffer, D.; Kozlov, E.; Wikswo, J.; Cliffel, D.; Baudenbacher, F. Biomed. Microdevices 2004, 6, 325-339. (6) Seo, J.; Ionescu-Zanetti, C.; Diamond, J.; Lal, R.; Lee, L. P. Appl. Phys. Lett. 2004, 84, 1973-1975. (7) Park, J.; Jung, S. H.; Kim, Y. H.; Kim, B.; Lee, S. K.; Park, J. O. Lab Chip 2005, 5, 91-96. (8) Yang, M. S.; Li, C. W.; Yang, J. Anal. Chem. 2002, 74, 3991-4001. (9) Wheeler, A. R.; Throndset, W. R.; Whelan, R. J.; Leach, A. M.; Zare, R. N.; Liao, Y. H.; Farrell, K.; Manger, I. D.; Daridon, A. Anal. Chem. 2003, 75, 3581-3586. (10) Peng, X. Y.; Li, P. C. H. Anal. Chem. 2004, 76, 5273-5281. (11) Li, P. C. H.; de Camprieu, L.; Cai, J.; Sangar, M. Lab Chip 2004, 4, 174180. (12) Ashkin, A. Phys. Rev. Lett. 1970, 24, 156. (13) Ashkin, A. Science 1980, 210, 1081-1088. (14) Ashkin, A.; Dziedzic, J. M. Science 1987, 235, 1517-1520. (15) Ashkin, A.; Dziedzic, J. M.; Yamane, T. Nature 1987, 330, 769-771. (16) Ashkin, A. Biophys. J. 1992, 61, 569-582.

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a tightly focused laser beam to generate forces on a cell based on the difference in refractive index between the cell and the medium, and recently developed holographic methods allow spatial control over laser illumination to create trapping arrays and to reduce the impact on cell health by tailoring trap geometry. Dielectrophoretic (DEP) traps create a trapping force by acting on cell polarization induced by an oscillating electrical field.19-21 Acoustical tweezers (AT) generate trapping forces based on the difference in compressibility between a cell and its medium.22-26 The absorption of high-frequency acoustic energy (ultrasound) within the cell and fluid generates pressure forces that cause aggregation of cells at pressure nodes or antinodes. OT, DEP, and AT can be designed to allow three-dimensional (3-D) suspension trapping, and they generate strong trapping forces capable of holding motile cells. These trapping methods inherently rely on conditions far outside the physiological range for typical cells, and their effects on cell behavior and viability are still debated in the literature.14,15,27-31 Moreover, the experimental systems required for OT, DEP, and AT are typically sophisticated, and trap control can be complicated by variations in the physical properties of the specific cell and medium. Nevertheless, these methods are appealing for cell studies due to their unique ability to trap cells in suspension. There is a continuing need to develop single-cell suspension trapping methods that are easy to implement, insensitive to cell and medium properties, and capable of trapping under conditions that do not perturb cell behavior. We describe a simple microfluidic design that functions as “hydrodynamic tweezers” to suspend single cells using only gentle secondary hydrodynamic forces. The suspended cells can be less or more dense than the surrounding medium. Traps are created by low audible frequency (e1000 Hz) oscillations of the fluid medium in a microchannel containing a single fixed cylinder, as illustrated schematically in Figure 1. It is well-known that the interaction of an oscillating fluid with solid boundaries can create a time-averaged secondary flow known as steady streaming,32-38 (17) Svoboda, K.; Block, S. M. Annu. Rev. Biophys. Biomol. Struct. 1994, 23, 247-285. (18) Wright, W. H.; Sonek, G. J.; Berns, M. W. Appl. Opt. 1994, 33, 17351748. (19) Fuhr, G.; Arnold, W. M.; Hagedorn, R.; Muller, T.; Benecke, W.; Wagner, B.; Zimmermann, U. Biochim. Biophys. Acta 1992, 1108, 215-223. (20) Schnelle, T.; Hagedorn, R.; Fuhr, G.; Fiedler, S.; Muller, T. Biochim. Biophys. Acta 1993, 1157, 127-140. (21) Voldman, J.; Gray, M. L.; Toner, M.; Schmidt, M. A. Anal. Chem. 2002, 74, 3984-3990. (22) Wu, J. R. J. Acoust. Soc. Am. 1991, 89, 2140-2143. (23) Takeuchi, M.; Yamanouchi, K. Jpn. J. Appl. Phys. Part 1 1994, 33, 30453047. (24) Hertz, H. M. J. Appl. Phys. 1995, 78, 4845-4849. (25) Saito, M.; Izumida, S.; Hirota, J. Appl. Phys. Lett. 1997, 71, 1909-1911. (26) Yamakoshi, Y.; Noguchi, Y. Ultrasonics 1998, 36, 873-878. (27) Archer, S.; Li, T. T.; Evans, A. T.; Britland, S. T.; Morgan, H. Biochem. Biophys. Res. Commun. 1999, 257, 687-698. (28) Neuman, K. C.; Chadd, E. H.; Liou, G. F.; Bergman, K.; Block, S. M. Biophys. J. 1999, 77, 2856-2863. (29) Peterman, E. J. G.; Gittes, F.; Schmidt, C. F. Biophys. J. 2003, 84, 13081316. (30) Bohm, H.; Anthony, P.; Davey, M. R.; Briarty, L. G.; Power, J. B.; Lowe, K. C.; Benes, E.; Groschl, M. Ultrasonics 2000, 38, 629-632. (31) Bazou, D.; Foster, G. A.; Ralphs, J. R.; Coakley, W. T. Mol. Membr. Biol. 2005, 22, 229-240. (32) Nyborg, W. L. M. In Physical Acoustics: Principles and Method; Mason, W. P., Ed.; Academic Press: New York, 1965; Vol. 2, Part B, pp 265-331. (33) Nyborg, W. L. In Nonlinear Acoustics; Hamilton, M. F., Blackstock, D. T., Eds.; Academic Press: San Diego, CA, 1998; pp 207-231.

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Figure 1. Hydrodynamic traps for single cells are created by lowfrequency oscillations (frequency ω, amplitude s) around a cylinder (radius a) in a microchannel (height h, width w). The oscillation drives four distinct steady streaming eddies, and a single cell is strapped in suspension near the center of each eddy without contacting any solid surface. The eddy flow at the cylinder midsection (channel midplane) resembles the two-dimensional (2-D) steady streaming flow around an infinitely long cylinder. A more complex three-dimensional (3-D) steady streaming created near the cylinder ends (not shown) limits the depth of the eddy traps so that one cell is trapped at the channel midplane.

and this flow usually involves fluid recirculation that is governed by the geometry and oscillation conditions. Steady streaming has found limited application for microscale mixing,39-47 and it has recently been exploited for controlled cell lysis48 and transporting cells within a device.49 Here, we show that steady streaming eddies created by audible-frequency oscillations have the remarkable ability to capture single cells and suspend them at predictable locations in 3-D. For the geometry of Figure 1, the oscillation creates four symmetric eddies that circulate within the midplane of the channel (Figure 1).50 We find that each eddy traps a cell near the eddy center, precisely at the channel midplane (i.e., cylinder midsection), and the trapped cell is completely suspended by the fluid without touching any solid surface. We use microspheres and motile phytoplankton cells to measure the trapping location and trapping force, which are directly controlled via the oscillation frequency and amplitude. Trapping forces are comparable to DEP traps and OT, whereas the trap environment is within physiological limits for shear in arterial blood flow. Traps are insensitive to variations in cell shape and density as well as (34) Riley, N. J. Inst. Math. Appl. 1967, 3, 419-434. (35) Riley, N. Theor. Comput. Fluid Dyn. 1998, 10, 349-356. (36) Riley, N. Annu. Rev. Fluid Mech. 2001, 33, 43-65. (37) Lighthill, J. J. Sound Vibr. 1978, 61, 391-418. (38) Rooney, J. A. In Ultrasonics; Edmonds, P. D., Ed.; Academic Press: New York, 1981; Vol. 19, pp 299-345. (39) Boraker, D. K.; Bugbee, S. J.; Reed, B. A. J. Immunol. Methods 1992, 155, 91-94. (40) Nishimura, T.; Murakami, S.; Kawamura, Y. Chem. Eng. Sci. 1993, 48, 1793-1800. (41) Rife, J. C.; Bell, M. I.; Horwitz, J. S.; Kabler, M. N.; Auyeung, R. C. Y.; Kim, W. J. Sens. Actuators, A 2000, 86, 135-140. (42) Suri, C.; Takenaka, K.; Yanagida, H.; Kojima, Y.; Koyama, K. Ultrasonics 2002, 40, 393-396. (43) Liu, R. H.; Yang, J. N.; Pindera, M. Z.; Athavale, M.; Grodzinski, P. Lab Chip 2002, 2, 151-157. (44) Liu, R. H.; Lenigk, R.; Druyor-Sanchez, R. L.; Yang, J. N.; Grodzinski, P. Anal. Chem. 2003, 75, 1911-1917. (45) Carlsson, F.; Sen, M.; Lofdahl, L. Eur. J. Mech. B 2005, 24, 366-378. (46) Lutz, B. R.; Chen, J.; Schwartz, D. T. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 4395-4398. (47) Lutz, B. R.; Chen, J.; Schwartz, D. T. Anal. Chem. 2006, 78, 1606-1612. (48) Marmottant, P.; Hilgenfeldt, S. Nature 2003, 423, 153-156. (49) Marmottant, P.; Hilgenfeldt, S. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 9523-9527. (50) Lutz, B. R.; Chen, J.; Schwartz, D. T. Phys. Fluids 2005, 17, 023601.

composition of the fluid medium. These traps provide strong, gentle, noncontact trapping that is well-suited for a variety of cell types, including motile cells and sensitive suspension cells. This approach could be used to hold single cells in suspension for dynamic observation, such as whole-cell fluorescence detection commonly used in cell microscopy and flow cytometry. METHODS The experimental setup consisted of a channel flow cell containing a small fixed cylinder (Figure 1), a driver for oscillation of the channel fluid, and a flow visualization system.50 The channel was formed by an adhesive Mylar spacer layer (h ) 425 µm) cut lengthwise to form a long channel (w ) 1500 µm) and enclosed by two acrylic sheets. A small cylinder (radius a ) 125 µm) was inserted perpendicular to the channel axis through a drilled hole in one acrylic cap, and the cylinder ends were sealed to the cap using small amounts of epoxy. The cylinder extended from wall to wall across the narrow channel dimension (425 µm). Holes at one end of the channel allowed fluid input and coupling of the fluid channel to an oscillation unit. A piezoelectric diaphragm (Radio Shack 273-073A) driven by a sine wave generator (Wavetek 111B) and an audio amplifier oscillated the fluid along the channel at low audible frequencies (250 e ω e 1000 Hz) and moderate displacement amplitudes (5 e s e 30 µm). The oscillation frequency and amplitude were the only controls used in experiments (no net flow), and traps were turned on and off by starting and stopping the oscillation. The flow cell was illuminated by an expanded laser beam (SDL8630, 668 nm) and viewed using a video microscope. For trapping visualization, the laser was pulsed (∼10% of an oscillation period) using a built-in trigger driven by the oscillation source to remove small oscillations. Video sequences were analyzed by manually tracking objects frame-by-frame in ImageJ. The oscillation amplitude (s) was measured directly from streaklines of small tracer particles under continuous illumination. Trapping experiments used polystyrene spheres and the motile phytoplankton Prorocentrum micans. Polystyrene spheres (density Ff ) 1.05 g/cm3; radii b ≈ 22 µm, polydisperse) were suspended either in water (Ff ) 1.00 g/cm3, kinematic viscosity ν ) 0.0095 cm2/s) or deuterated water (Ff ) 1.10 g/cm3). Axemic P. micans samples (Fp > 1.03 g/cm3; size ∼45 µm × 25 µm × 10 µm) were used in their seawater growth medium (Ff ) 1.03 g/cm3, ν ) 0.0098 cm2/s) without treatment. Orientation of the device with respect to gravity had no significant effect on the trapping behavior for these spheres and cells. All experiments were conducted at room temperature. Flow in the midchannel plane where particles trap has quantitative traits that accurately match 2-D steady streaming with an infinitely long cylinder.41 Thus, simplified computations of 2-D steady streaming were used to connect trapping locations to the eddy structure. Computations were based on an efficient analytic/ numeric formulation using regular perturbation and finite Fourier transforms of the Navier-Stokes equations and boundary conditions, followed by finite element analysis of the resulting coupled stationary equations.51 The flow fields were solved using FEMLab 3.0a running on a desktop computer (Pentium 4, 3.2 GHz). The (51) Bowman, J. A.; Schwartz, D. T. Int. J. Heat Mass Transf. 1998, 41, 10651074.

Figure 2. Steady streaming eddies created by audible frequency oscillations collect objects from a channel and trap them at specific locations in three dimensions. (A) Time-exposed image of flow tracer particles showing the formation of four symmetric steady streaming eddies adjacent to the cylinder (ω ) 300 Hz, ν ) 0.0095 cm2/s). (B) Capture trajectories of four polystyrene microspheres for conditions of 2A (Fp/Ff ) 1.05, sphere radii b ≈ 22 µm). The initial location of each sphere is shown by arrows and number labels, and circles represent their positions at 100 ms intervals. The sphere labeled iv crosses a symmetry plane due to the influence of gravity (downward) during collection. (C) Time-exposed image showing the final trapping location of the four spheres from part B. In all images, the camera is focused to the channel midplane, and pulsed illumination (∼10% of oscillation period) is used to remove small oscillations.50 Doubleheaded arrows indicate oscillation direction. Scale bars, 250 µm.

location of the dividing streamline and eddy center were computed from existing analytical formulas.52 The effective Stokes radius for P. micans was determined by direct computation of the drag force due to Stokes flow over a numerical model of the cell. RESULTS AND DISCUSSION Low-frequency fluid oscillation in a channel containing a fixed cylinder results in a 3-D steady streaming flow, which we have described in detail.50 The eddies represented in Figure 1 are limited to a narrow region at the cylinder midsection, where the flow is indistinguishable from the well-known 2-D eddy flow around an infinitely long cylinder.51-55 Figure 2A shows the closed streamlines of the four symmetric eddies in this 2-D region imaged when the camera is focused to the channel midplane (ω ) 300 Hz). Small particles shown in the image faithfully trace the fluid motion, and we find that larger objects experience a force that pushes them across streamlines toward the eddy center, where they become trapped. Figure 2B shows the initial location of four spheres indicated by arrows and the collection paths followed by the spheres when the channel fluid is oscillated at low frequency (ω ) 300 Hz; sphere radii b ≈ 22 µm). The camera focal plane is set at the midplane of the 425-µm channel depth, and the two channel walls parallel to the image plane are out of focus. The (52) Bertelsen, A.; Svardal, A.; Tjotta, S. J. Fluid Mech. 1973, 59, 493-511. (53) Holtsmark, J.; Johnsen, I.; Sikkeland, T.; Skavlem, S. J. Acoust. Soc. Am. 1954, 26, 26-39. (54) Raney, W. P.; Corelli, J. C.; Westervelt, P. J. J. Acoust. Soc. Am. 1954, 26, 1006-1014. (55) Skavlem, S.; Tjotta, S. J. Acoust. Soc. Am. 1955, 27, 26-33.

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three spheres labeled i, ii, and iii start near the channel midplane when oscillation of the fluid begins, and they move exclusively within that plane (open circles, imaged at 100-ms intervals). Initially, the spheres seem to follow the closed streamlines of the recirculating eddy flow, but as they approach the cylinder, their speed increases, and they spiral across streamlines into a final distinct trapping position (see video 1 of the Supporting Information). The conditions of Figure 2 allow trapping of objects within a certain approximate size range, as discussed further below, and smaller objects fall into fixed orbits around the traps (video 1). The sphere labeled iv initially lies below the midplane where the 2-D eddies of Figure 2A are created, but it is fed into the trapping eddies by the 3-D streaming formed near the cylinder ends. Simple hydrodynamic scaling theory given elsewhere50 connects the device geometry, oscillation frequency, and fluid kinematic viscosity so that the depth of the trapping eddies can be set to roughly match the sphere diameter, allowing a single sphere to fit in the vertical dimension of each trap site. Despite different initial locations within the channel depth, Figure 2C shows that each sphere is ultimately positioned at specific locations within the channel midplane (i.e., focal plane of Figure 2). The spheres remain trapped at this location so long as the oscillation is applied, and the fluid continues to circulate around them. Their positions are quickly restored after transient disruptions, such as the passage of bubbles through the device, and the traps also tolerate moderate flows imposed by the loading syringe. Trapped objects are completely suspended within the fluid without touching any solid surface. In these experiments, the only flow controls used are the oscillation frequency and amplitude. For different oscillation conditions, traps are always located at the channel midplane near the center of the eddies. Increasing the oscillation amplitude results in more rapid capture (i.e., fewer orbits before settling), suggesting that amplitude controls the trap strength. Although we do not present a theory to describe the observed particle motion in this flow, we can use well-known scaling for steady streaming fluid motion to relate the trapping behavior to the oscillation controls. The Stokes layer thickness, δAC ) (ν/ω)1/2, is a natural scaling parameter for oscillating flows that describes how far viscous damping of an oscillating velocity gradient persists from a surface, where ω is the oscillation frequency, and ν is the fluid kinematic viscosity. Steady streaming is driven by Reynolds stresses that are created within the Stokes layer near any solid boundary (a cylinder here) that bends the oscillating fluid streamlines. We have shown that streaming flow at the channel midplane where traps are created is quantitatively described by theory for 2-D steady streaming around an infinitely long cylinder.50 This 2-D steady streaming is controlled via a dimensionless frequency, M2 ) (a/δAC),2 and a dimensionless amplitude,  ) s/a, where s is the displacement amplitude of the oscillating fluid and a is the cylinder radius. It is important to emphasize that the oscillation creating this flow is both low-frequency (ωa/c , 1, where c ) 1540 m/s is the speed of sound in water) and lowintensity (ωs/c , 1). In other words, acoustic effects associated with particle radiation forces (e.g., acoustical tweezers) and bulk energy absorption (e.g., quartz wind) are not important under our experimental conditions. Rather, the oscillation that creates these traps is a simple back-and-forth motion of fluid in the channel (i.e., 5432 Analytical Chemistry, Vol. 78, No. 15, August 1, 2006

Figure 3. Oscillation frequency controls the trapping location. (A) Representative experimental image and measured trapping location (rt) of a sphere trapped in water (ω ) 1000 Hz, ν ) 0.0095 cm2/s, Fp/Ff ) 1.05). The offset from the 45° line (dashes) was typical in experiments. Scale bar, 125 µm. (B) Representative streamline computation (contours, uniform streamline spacing) for steady streaming flow around the cylinder (M2 ) 100). The dividing streamline defines the eddy size (rds), and the point of zero velocity defines the eddy center (rc). (C) Comparison of the computed eddy size (dashed curve, rds), computed eddy center location (solid curve, rc), and measured trap location (solid circles, rt). The radial dimension is the distance from the cylinder center normalized by the cylinder radius (a); the scale is linear. Error bars represent one standard deviation from at least three replicates. Double-headed arrows indicate oscillation direction in parts A and B.

viscous flow of an incompressible fluid). For a small oscillation amplitude (i.e.,  , 1), M2 alone controls the size of 2-D eddies, and at a given frequency,  controls the magnitude of the steady flow velocity inside the eddies.51-55 We take advantage of this simple scaling for oscillating flow and 2-D steady streaming to describe the basic features of this trap, including control over the trap location via oscillation frequency and control over the trapping force via the oscillation amplitude. Figure 3A and B shows the measured trap location and computed 2-D flow structure for a small eddy (M2 ) 100) in one quadrant around the cylinder. Figure 3A shows the measured trap location (rt); the offset from the 45° diagonal (dashed line) was typical of the experiments. Computations in Figure3B show the streamlines for the 2-D steady streaming (smooth contours) and the location of the eddy center (rc). The dividing streamline location (rds) defines the boundary of confined recirculating fluid within the closed streamlines of the eddy. For the small amplitude used in these experiments, the flow structure (i.e., eddy size and eddy center) is controlled only by the oscillation frequency.51-55 Figure 3C compares the measured trapping location to key structural features of the 2-D eddy. The abscissa scale, 1/M ) δAC/a, is chosen as the frequency parameter to show the near proportionality between the eddy center location (solid curve) and the Stokes layer thickness. The measured trapping location (solid circles) is consistent with the eddy center over a large range of frequencies. It is interesting to note that the trapping location in Figure 3C changes moderately over the frequency range, whereas the eddy size (dashed curve, rds) changes much more dramatically. Since rds indicates the eddy size that will sweep objects into the trap (shaded region in Figure 3C), it is quite easy to select a

Figure 4. Oscillation amplitude controls the trapping force. (A) Path for a free-swimming P. micans cell (white circles) in seawater (ν ) 0.0098 cm2/s) and the capture trajectory (black circles) once a strong trap is initiated (ω ) 250 Hz,  ≈ 0.25). (B) Finite element model of P. micans used to compute its effective Stokes radius (beff ) 11 µm) used in the calculation of the Stokes drag force. The cell swims with velocity, V, in the direction of its sharp taper. (C) Escape of a cell from a trap when the trap strength is decreased in small steps via the oscillation amplitude. The cell escapes when its motility force just overcomes the trapping force generated at a specific oscillation amplitude. Black circles represent the cell position while the trap is on. The free-swimming velocity (V) is measured after the oscillation is stopped (white circles). (D) Relationship between the measured cell motility force (F) and the minimum oscillation amplitude () able to hold individual P. micans with different swimming strengths. Black dots are measurements for individual cells, and the dashed curve illustrates an apparent quadratic dependence on the oscillation amplitude (2). Oscillation amplitude is measured from streaklines of oscillating tracer particles imaged under continuous illumination. Circles in parts A and C are spaced at 100-ms intervals, and white-headed arrows show the location of a P. micans cell. Pulsed illumination is used for all images. Double-headed arrows indicate oscillation direction. Scale bars, 250 µm.

frequency that reaches a great distance into the fluid (e.g., Figure 2A, M2 ) 30). Dynamic control of the fluid oscillation frequency thus allows us to identify a fairly distant object and grab it, pulling it into a specific trap location near the cylinder. The microspheres trapped in Figures 2 and 3 are idealized models of spherical cells, but this flow is also able to trap nonspherical motile cells. P. micans is a motile single-celled plant with a strongly flattened tear-drop shape (∼45 µm × 25 µm × 10 µm) that swims in a corkscrew motion using spinning flagella. Figure 4A shows the trapping of a single P. micans cell from its seawater medium. The characteristic wavy motion shows the path of P. micans while swimming freely in stagnant fluid (white circles, no oscillations). After the fluid oscillation begins (black circles, M2 ) 25), the cell is quickly drawn toward the cylinder and trapped (see video 2 of the Supporting Information). Unlike microspheres shown in Figure 2, the somewhat scrambled path within the trap indicates continued swimming efforts that lead to partial escape and retrapping. This movement is expected for any trapping method that applies a finite force to counteract motility forces. Nonmotile (i.e., dead) P. micans are trapped with the expected rotation about a fixed axis, and they tend to orient with their flat dimension lying in the 2-D flow plane. The motility of this cell and its unusual shape posed no problem for trapping, and the most strongly swimming cells were not able to escape traps formed at sufficiently large oscillation amplitude. We exploit the motility of P. micans to experimentally measure the trapping force. When a cell swims at constant velocity, it generates a motility force that equals the fluid drag force over its body. Cell swimming occurs at low Reynolds number (Re ∼ 0.001 here), and it is common to calculate cell motility force from the Stokes drag force, F ) 6πµbeffV, where µ is the fluid viscosity (µ ) 1.0 cP), beff is the effective Stokes radius for the cell, and V is the free-swimming velocity. We account for the highly nonspherical shape of P. micans by computing its effective Stokes

radius from Stokes flow around a numerical model of the cell (see Figure 4B, beff ) 11 µm). The long straight swimming trajectories of these cells (e.g., Figure 4A, white circles) result from a sustained motility force, and a cell can be held by the trap only when the trapping force generated by the flow is greater than the motility force generated by the cell. The trapping force measurement involves capturing a single P. micans cell in a strong trap created at large oscillation amplitude, as shown in Figure 4A for one specimen (video 2). As the oscillation amplitude is decreased in small steps, excursions from the trap center become larger and more frequent, until, at a specific oscillation amplitude, the cell is able to break free of the trap and swim away (Figure 4C, black circles). At the condition of escape for each individual cell, the trapping force generated at the measured amplitude is approximately equal to the cell’s motility force, which is calculated from the free-swimming velocity measured after the oscillation is stopped (Figure 4C, white circles). Swimmers of different strength were available from the natural population variation, as well as the changing cell activity as the cold cell sample (culture temperature, 18 °C) approached ambient temperature. Figure 4D plots the measured force (F) versus the oscillation amplitude () at which each P. micans escaped the trap. Weak swimmers can be trapped at low oscillation amplitude; strong swimmers require traps created at large oscillation amplitude. The dashed curve is added to illustrate an apparent quadratic dependence of the trapping force on oscillation amplitude (2), which is proportional to the magnitude of the steady flow velocity inside the eddies.51-55 Figure 4D shows that the oscillation amplitude directly controls the trapping force for fixed oscillation frequency. At the highest oscillation amplitudes used, the trapping force exceeds 30 pN, making it comparable to forces generated by DEP traps20 and optical tweezers.16-18 Despite the ability to create large trapping forces, the trap environment is quite gentle. Both the oscillating flow and steady Analytical Chemistry, Vol. 78, No. 15, August 1, 2006

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streaming are laminar flows characterized by moderate Reynolds number (i.e., Re ) M2 ∼ 10 for oscillating flow, Res ) 2M2 ∼ 1 for steady streaming).51-55 A trapped cell experiences shear stress (G) due primarily to the oscillating flow near the cylinder, where the peak shear stress is G ∼ O(s{µFfω3}1/2). For the strongest flows used in Figure 4C, G ∼ 1.5 N/m2, which is comparable to arterial shear stresses in the circulatory system. Of course, weaker swimmers and nonmotile cells can be trapped under milder conditions. In short, the hydrodynamic approach described here creates trapping forces comparable to OT and DEP under shear conditions that are normal, and relatively well understood, for many cells. No potentially perturbative external fields are needed. This hydrodynamic approach is also quite tolerant to changes in cell and medium properties. We are able to trap polystyrene microspheres in water and nonspherical motile cells in seawater without any special effort or adjustments. The spheres and cells trapped in Figures 2-4 are more dense than the surrounding fluid (Fp/Ff ≈ 1.05), but we observe the same trapping behavior for light objects, as well (Fp/Ff ) 0.95, not shown). Most cell systems will naturally fall within a similar range of density ratios (i.e., it is a strange cell that sinks or rises quickly in its medium). In addition, the only medium property that affects the flow is the kinematic viscosity, which falls in a fairly narrow range for most cell growth media (e.g., water ν ) 0.0095 cm2/s, seawater ν ) 0.0098 cm2/s), and we expect similar trapping in biological fluids, such as blood, that show deviations from ideal Newtonian behavior. Thus, application to different cell systems (e.g., shape, density, motility) and dynamic control over the medium composition (e.g., for chemical dosing, indicator delivery, washing steps, etc.) will have little impact on these hydrodynamic traps. The unique flow patterns offered by steady streaming have made it valuable for microscale chemical mixing applications,39-47,56,57 but applications of steady streaming for cell manipulation have been largely unexplored. Steady streaming around bubbles was recently used for cell transport effected by drag forces acting parallel to streamlines49 and cell lysis effected by large shear stresses in a viscous medium.48 In contrast, we use steady streaming to generate a force that causes cells to move across streamlines and creates distinct single-cell traps at low shear. The complementary nature of these very different results shows that steady streaming can be tuned via operating conditions to provide a versatile strategy for cell manipulation. The trapping observed here is distinguished by operation at frequencies at which the cell size is comparable to the Stokes layer thickness (i.e., b/δAC ≈ 1). The conditions of Figure 2 allow robust trapping of spheres with radii of approximately 10 e b e 36 µm (0.4 e b/δAC e 1.5). Spheres at the low end of this range require more orbits before settling, and even smaller spheres tend to orbit around the traps. In fact, we use very small particles (b ) 1.5 µm, b/δAC ) 0.06) as passive tracers to visualize the fluid motion (e.g., Figure 2A). Larger objects simply cannot fit within the eddies where strong trapping forces are generated. Previous work using higher frequencies led to very thin boundary layer eddies too small to fit large cell vesicles used in experiments (b/δAC g 2.5); vesicles followed the streamlines of the far-field flow formed outside the thin eddies.48,49 This work noted that an object could be held in a stationary position near an oscillating bubble, but the behavior was not discussed. By operating at lower 5434

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frequencies (i.e., b/δAC ≈ 1), we create eddies large enough to hold the targeted cell; the eddy flow draws cells toward the cylinder, where they spiral across streamlines to a specific trap location. We have since designed traps for cells of different sizes (b g 2.5 µm) by changing the cylinder radius while holding the dimensionless groups b/a and b/δAC constant.58 We also routinely observe trapping around wall defects, bubbles, and debris of various sizes when b/δAC ≈ 1, which suggests that the size and geometry of the obstacle are not critical for trapping. The cylindrical obstacle used here results in a simple example of 3-D trapping, but we expect eddies generated in many different geometries to allow trapping when operated at b/δAC ≈ 1. We describe the main features of these traps through simple scaling for the oscillating and steady streaming flows, but we do not identify the force responsible for trapping. Theory for steady streaming fluid motion has been extensively developed,32-38 but there is no available theory for particle motion in steady streaming to account for the trapping observed here. Any theoretical approach must consider particle forces generated by the steady streaming flow as well as time-dependent particle forces generated by the oscillating flow, and it must identify a force that acts to move objects, both heavy and light, across streamlines in this flow. Although this is a complex problem in particle-fluid dynamics, the approach is simplified by our observation that traps are located within a region of the flow that quantitatively follows well-known theory for 2-D steady streaming.50 The scaling of trap location (Figure 3C) and trapping force (Figure 4D) reported here can be used to directly test particle motion theory applied to readily computed 2-D steady streaming flow fields. CONCLUSIONS For bulk measurements and single-cell studies alike, it is important that cell handling methods do not introduce artifacts that affect the natural cell behavior. Beyond providing the appropriate growth medium and temperature, the choice between cell handling methods that require physical contact with the cell and those that do not may be the most important consideration to preserve natural cell function. There are many options for holding cells in place when physical contact is desired, but it is a considerable challenge to develop methods that create forces to suspend cells without touching them. Successful application of suspension trapping methods to cell studies, primarily using optical tweezers, has resulted from a long history of refinement to establish operating conditions that reduce impact on cell behavior and viability. The hydrodynamic approach described here uses only a gentle fluid flow to generate strong trapping forces that allow predictable single-cell positioning. This approach has the unique advantage that the potentially perturbing condition introduced by the traps, namely, shear stress, falls within the physiological range for many cells. Adjustable trapping forces make these traps useful for motile cells requiring strong traps as well as sensitive cells, such as mammalian suspension cells, that require exceedingly gentle traps. Traps can be created and (56) Matta, L. M.; Zhu, C.; Jagoda, J. I.; Zinn, B. T. J. Propul. Power 1996, 12, 366-370. (57) Liu, R. H.; Lenigk, R.; Grodzinski, P. J. Microlithogr. Microfabr. Microsyst. 2003, 2, 178-184. (58) Lutz, B. R.; Meldrum, D. R. Proceedings of MicroTAS 2005 Conference, Boston, MA 2005; 512-514.

controlled in a simple microfluidic device, and they can easily accommodate common variations in cell properties and medium properties. Because trapped cells rotate and oscillate within the traps, this approach may not be appropriate for dynamic imaging of detailed cell structure; however, cell oscillation can be perfectly removed by pulsed illumination, and optical measurements requiring short exposure times (e.g., bright-field microscopy) may be possible. This approach is well-suited for whole-cell measurements, such as detection of overall cell fluorescence using commonly available fluorescence indicators or recombinant expression of fluorescent proteins (e.g., GFP), which are routinely used in cell microscopy and flow cytometry. As with other trapping methods, concentrated cell suspensions can lead to multiple cells being caught in a trap. We have since shown that cells from concentrated suspensions can be distributed into single-occupancy traps using net flow through the channel,58 and the recirculating flow surrounding the traps provides mixing46,47,51 that could aid delivery of nutrients, indicators, reagents, etc., to trapped cells. Traps can be numbered-up to create trapping arrays that capture cells from a flowing medium;58 however, individual trap control possible with DEP traps and OT are not possible with hydrodynamic traps created around fixed obstacles. Like traps based on DEP, the location of these hydrodynamic traps is largely predetermined by the fabrication, and cells cannot be

arbitrarily moved about under a controlled trapping force, as with OT. Nevertheless, this hydrodynamic approach provides the essential function of gently holding single cells at predictable locations for repeated measurements. The unique combination of predictable 3-D positioning, insensitivity to cell and medium properties, strong adjustable trapping forces, and a gentle fluid environment makes hydrodynamic tweezers an appealing new option for noncontact trapping of single suspension cells. ACKNOWLEDGMENT This work was supported by the Microscale Life Sciences Center (MLSC), an NIH Center of Excellence in Genomic Science at the University of Washington, and the Boeing-Sutter Endowment for Excellence in Engineering. We thank Adam Lausche, Rhonda Marohl, and Professor Ginger Armbrust of the University of Washington School of Oceanography for supplying P. micans cultures. SUPPORTING INFORMATION AVAILABLE Two movies as mentioned in text. This material is available free of charge via the Internet at http://pubs.acs.org. Received for review March 28, 2006. Accepted June 2, 2006. AC060555Y

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