Anal. Chem. 2007, 79, 6542-6550
Density-Based Diamagnetic Separation: Devices for Detecting Binding Events and for Collecting Unlabeled Diamagnetic Particles in Paramagnetic Solutions Adam Winkleman,† Raquel Perez-Castillejos,† Katherine L. Gudiksen,† Scott T. Phillips,† Mara Prentiss,‡ and George M. Whitesides*,†
Department of Chemistry and Chemical Biology and Department of Physics, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138
This paper describes the fabrication of a fluidic device for detecting and separating diamagnetic materials that differ in density. The basis for the separation is the balance of the magnetic and gravitational forces on diamagnetic materials suspended in a paramagnetic medium. The paper demonstrates two applications of separations involving particles suspended in static fluids for detecting the following: (i) the binding of streptavidin to solidsupported biotin and (ii) the binding of citrate-capped gold nanoparticles to amine-modified polystyrene spheres. The paper also demonstrates a microfluidic device in which polystyrene particles that differ in their content of CH2Cl groups are continuously separated and collected in a flowing stream of an aqueous solution of GdCl3. The procedures for separation and detection described in this paper require only gadolinium salts, two NdFeB magnets, and simple microfluidic devices fabricated from poly(dimethylsiloxane). This device requires no power, has no moving parts, and may be suitable for use in resourcepoor environments. This paper describes the fabrication and utility of a microfluidic device for detecting and separating diamagnetic materials that differ in density. The basis for the separation is the balance of the magnetic and gravitational forces on diamagnetic materials suspended in a paramagnetic medium. We demonstrate the value of this device by (i) detecting the binding of streptavidin to polymer-supported biotin, (ii) detecting the binding of citratecapped gold nanoparticles to amine-modified polystyrene spheres, and (iii) separating polystyrene particles that differ in CH2Cl content within a flowing microfluidic system. The protocols for detection and separation require only gadolinium chloride (or diethylenetriaminepentaacetic acid gadolinium(III) dihydrogen salt (Gd3+‚DTPA)), two NdFeB magnets, and simple microfluidic devices fabricated from poly(dimethylsiloxane) (PDMS). The simplicity and versatility of these methods make them useful for general laboratory protocols; we believe they are also suitable for use in remote locations where electricity is not available and where * To whom correspondence should be addressed. E-mail: gwhitesides@ gmwgroup.harvard.edu. † Department of Chemistry and Chemical Biology. ‡ Department of Physics.
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portability and operational ease are essential.1,2 We believe that these density-based detection and separation methods have the potential to be widely useful as analytical tools for the physical and biological sciences. Magnetic labels facilitate the separation and purification of chemical and biological samples.3,4 These labels are often superparamagnetic nano- or microspheres (e.g., Invitrogen’s Dynabeads),5 which can be covalently attached to most chemical and biological samples. For example, immunomagnetic separation employs antibodiessoften monoclonalsbound to magnetic particles for the removal of prokaryotic and eukaryotic cells from suspension.4,6 Many techniquessincluding cell separation,7,8 free flow magnetophoresis,9 and immunoassays10shave been developed for use in microfluidic devices for lab-on-a-chip technology.11,12 These magnetic labeling techniques have several limitations: (i) the separations are binary; i.e., magnetic particles are separated from diamagnetic particles; (ii) the labeling of a diamagnetic material requires a chemical reaction; (iii) the presence of a magnetic particle attached to a diamagnetic materialsspecifically a cell, antibody, or proteinsalters the functionality and properties of the surface of the material; and (iv) the magnetic label must be removed after separation to obtain a pure diamagnetic sample. New label-free techniques for manipulating and separating diamagnetic materials in suspension that overcome these limitations would be useful. Magnetic separations are used extensively (1) Yager, P.; Edwards, T.; Fu, E.; Helton, K.; Nelson, K.; Tam, M. R.; Weigl, B. H. Nature 2006, 442, 412-418. (2) Sia, S. K.; Linder, V.; Parviz, B. A.; Siegel, A.; Whitesides, G. M. Angew. Chem., Int. Edit. 2004, 43, 498-502. (3) Ito, A.; Shinkai, M.; Honda, H.; Kobayashi, T. J. Biosci. Bioeng. 2005, 100, 1-11. (4) Safarik, I.; Safarikova, M. J. Chromatogr., B 1999, 722, 33-53. (5) Lund, V.; Schmid, R.; Rickwood, D.; Hornes, E. Nucleic Acids Res. 1988, 16, 10861-10880. (6) Islam, D.; Lindberg, A. A. J. Clin. Microbiol. 1992, 30, 2801-2806. (7) Inglis, D. W.; Riehn, R.; Sturm, J. C.; Austin, R. H. J. Appl. Phys. 2006, 99, No. 08K101. (8) Furdui, V. I.; Harrison, D. J. Lab Chip 2004, 4, 614-618. (9) Pamme, N.; Manz, A. Anal. Chem. 2004, 76, 7250-7256. (10) Choi, J. W.; Oh, K. W.; Thomas, J. H.; Heineman, W. R.; Halsall, H. B.; Nevin, J. H.; Helmicki, A. J.; Henderson, H. T.; Ahn, C. H. Lab Chip 2002, 2, 27-30. (11) Pamme, N. Magnetism and microfluidics. Lab Chip 2006, 6, 24-38. (12) Gijs, M. A. M. Magnetic bead handling on-chip: new opportunities for analytical applications. Microfluids Nanofluids 2004, 1, 22-40. 10.1021/ac070500b CCC: $37.00
© 2007 American Chemical Society Published on Web 08/04/2007
in biomedicine, and other areas, usually in systems that separate magnetic particles from diamagnetic media.5,13-15 Magnetic media have been used, however, to separate diamagnetic particles, with ferrofluids providing the largest magnetic response.16,17 Techniques for the levitation of diamagnetic particles in magnetic medium have developed as an alternative method to magnetic labeling techniques for separating diamagnetic materials.15,18-21 In the past decade, the magnetic levitation of diamagnetic materials has become more accessible to standard laboratory facilities as the early experimental setup consisting of superconducting magnets (>10 T) and a pressurized oxygen atmosphere22 has been replaced by small rare-earth magnets and aqueous paramagnetic salt solutions.23-27 As an extension of levitation, diamagnetic traps were developed to control, manipulate, and direct the positioning of cells and polymer microspheres suspended in solution.28,29 In microfluidic systems, diamagnetic particles suspended in ferrofluid30 or an aqueous paramagnetic solution19,31 have been trapped and their trajectory manipulated while traversing the inhomogeneous magnetic fields. In this paper, we expand upon these label-free approaches and describe the design of a new device that exploits the principle of diamagnetic levitation to observe changes in density due to biological or electrostatic binding events and to separate and collect diamagnetic materials with different densities using a microfluidic system. EXPERIMENTAL DESIGN We designed and built a system for detecting and separating diamagnetic particles (5-5000 µm in diameter) based on differences in density. We will discuss two modes and uses of this system: a static modesusing no flow of fluidsas a diagnostic for detecting molecular or colloidal binding to polymer microspheres, and a flowing mode (within a microfluidic device) as a tool for continuously collecting separated diamagnetic particles. The system (in either mode) requires only simple components that include solutions of Gd3+ salts sandwiched between a set of rare earth magnets, like those shown in Figure 1, where z indicates the vertical direction. (13) Haukanes, B. I.; Kvam, C. Biotechnology 1993, 11, 60-63. (14) Oberteuffer, J. A. IEEE Trans. Magn. 1974, MA10, 223-238. (15) Simon, M. D.; Geim, A. K. J. Appl. Phys. 2000, 87, 6200-6204. (16) Raj, K.; Moskowitz, R. J. Magn. Magn. Mater. 1990, 85, 233-245. (17) Raj, K.; Moskowitz, B.; Tsuda, S. Indian J. Eng. Mater. S. 2004, 11, 241252. (18) Brandt, E. H. Science 1989, 243, 349-355. (19) Watarai, H.; Namba, M. J. Chromatogr., A 2002, 961, 3-8. (20) Franzreb, M.; Siemann-Herzberg, M.; Hobley, T. J.; Thomas, O. R. T. Appl. Microbiol. Biotechnol. 2006, 70, 505-516. (21) Jayawant, B. V. Rep. Prog. Phys. 1981, 44, 411-477. (22) Hirota, N. K. M.; Iwasaka, M.; Ikehata, M.; Uetake, H.; Takayama, T.; Nakamura, H.; Ikezoe, Y.; Ueno, S.; Kitazawa, K. Physica B 2004, 346, 267271. (23) Catherall, A. T.; Eaves, L.; King, P. J.; Booth, S. R. Nature 2003, 422, 579579. (24) Ikezoe, Y.; Hirota, N.; Nakagawa, J.; Kitazawa, K. Nature 1998, 393, 749750. (25) Ikezoe, Y.; Kaihatsu, T.; Sakae, S.; Uetake, H.; Hirota, N.; Kitazawa, K. Energy Convers. Manage. 2002, 43, 417-425. (26) Kimura, T.; Mamada, S.; Yamato, M. Chem. Lett. 2000, 11, 1294-1295. (27) Lyuksyutov, I. F.; Lyuksyutova, A.; Naugle, D. G.; Rathnayaka, K. D. D. Mod. Phys. Lett. B 2003, 17, 935-940. (28) Kimura, T.; Sato, Y.; Kimura, F.; Iwasaka, M.; Ueno, S. Langmuir 2005, 21, 830-832. (29) Winkleman, A.; Gudiksen, K. L.; Ryan, D.; Whitesides, G. M.; Greenfield, D.; Prentiss, M. Appl. Phys. Lett. 2004, 85, 2411-2413. (30) Feinstein, E.; Prentiss, M. J. Appl. Phys. 2006, 99, No. 064901. (31) Watarai, H.; Namba, M. Anal. Sci. 2001, 17, 1233-1236.
Figure 1. Schematic representations of the magnetic field, the distribution of magnetic forces, and a graph of the calculated magnitude of magnetic field along the axis of the magnets used for separation. (A) The calculated value of the magnitude of the magnetic field, |B B|, of the system is shown for a set of magnets, 50 mm long (L), separated by (L/2)x3 ≈ 43 mm. The shading in the plot indicates the magnitude of the magnetic field; the darker regions correspond to higher field intensities (white is ∼0 T and black is ∼0.4 T). This field was calculated using a finite element modeling software under axisymmetric boundary conditions. (B) Distribution of magnetic forces (eq 1) on diamagnetic material within our apparatus. The calculation shows that a diamagnetic particle would be repelled from the surfaces of the magnets and would be trapped along the axis between the magnets. (C) A graph of the calculated magnitude of the magnetic field in the vertical direction, Bz, along the axis between the two magnets (the dotted line in Figure 1A); the direction of a positive z-vector was chosen to be toward the upper magnet. The other components of the magnetic field along the chosen path are zero. Note that the gradient of the magnetic field in the vertical direction is constantsi.e., a constant slope in the variation of the magnetic field along the axis.
Theory for Density-Based Separations of Diamagnetic Particles. Density-based separations of diamagnetic particles are determined by the balance between the magnetic force and the buoyant force on a diamagnetic particle in a paramagnetic solution. In a static system, the force per unit volume (F B/V) on a particle in a magnetic field is the sum of the gravitational and magnetic forces (eq 1),32
B F/V ) -(Fl - Fp)g b-
(χl - χp) (B B‚∇ B )B B µ0
(1)
where the density of the liquid is Fl, the density of the particle is (32) This equation is valid for systems in which mB , kT, the paramagnetic solution has no hysteresis, and the diamagnetic particle behaves as if it were in a continuous medium with a constant magnetic susceptibility. All three of these conditions are true in the system described here. Shevkoplyas, S. S.; Siegel, A. C.; Westervelt, R. M.; Prentiss, M. G.; Whitesides, G. M. Lab Chip 2007, in press.
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Fp, the acceleration due to gravity is b g, the magnetic susceptibilities of the liquid and the particle are χl and χp, respectively, the magnetic permeability of free space is µ0, and the local magnetic field is B B ) (Bx, By, Bz). Both the magnetic field and its gradient contribute to the magnetic force and need to be optimized according to the dimensions of the system in order to maximize the separation. Equation 1 can be simplified for the levitation of a point particlesi.e., an infinitesimally small particlesin a system at equilibrium in which the magnetic field only has a vertical component (Bz); that is, the two other normal components of the applied magnetic field (Bx and By) are zero (eq 2).
(Fl - Fp)g )
(χl - χp) ∂Bz Bz µ0 ∂z
(2)
The distribution of magnetic field is determined by the size, geometry, orientation, and nature or type of the magnets (Figure 1A). We used a set of solid-state NdFeB magnets (with length, width, and height of 5, 5, and 2.5 cm, respectively), having a magnetic field of ∼0.4 T at their surface, to generate the required magnetic field and magnetic field gradient. Two magnets oriented toward each other in the design of an anti-Helmholtz coil established the magnetic field distribution in our system. In this geometry, the Bx and By components of the magnetic field are exactly zero only along the axis of the magnets, that is, along the vertical dashed line in Figure 1A, as confirmed by the completely vertical orientation of the force along this axis (Figure 1B). The Bz component of the magnetic field also becomes zero over this axis, but only at the midpoint between the two magnets. The effect of the magnetic force in this geometry is to attract the paramagnetic solution toward one or the other of the two magnets and, as a consequence, to trap all diamagnetic particles at the central region between the magnets (Figure 1B)si.e., where B B is close to zero. Equation 2 can be used to calculate approximately the balance of forces occurring on particles located along the axis of the magnets. When the distance between the two magnets is (L/2)x3 times the radius of the magnets, the magnetic field profile is approximately linear and the gradient of the magnetic field is approximately constant in the z-direction (Figure 1C).33 From eq 2, a constant gradient (∂Bz/∂z) yields an equal separation distance between pairs of particles of materials with similar differences in density (Fl - Fp); that is, for two diamagnetic particles, A and B, zA - zB ∝ FA - FB. This configuration is the optimal arrangement for separating many particles that differ in density. In order to separate diamagnetic objects with solid-state magnets, the solution must have a positive magnetic susceptibility. We used a paramagnetic aqueous solution of Gd3+sas either GdCl3 or the Gd3+‚DTPA complex. There are four characteristics of Gd3+ cations that are attractive for our system: (i) they (along with some of the other lanthanide cations) possess the largest magnetic susceptibilities (χ ) +0.028 cm3/mol GdCl3) of any ionic species;34 (ii) they permit straightforward visualization of samples because their solutions are colorless; (iii) they are compatible with (33) Purcell, E. M. Electricity and magnetism; McGraw-Hill, Inc.: New York, 1985. (34) Berger, L. I., Ed. CRC Handbook of Chemistry and Physics, 85th ed.; CRC Press LLC: Boca Raton, FL, 2000.
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proteins and cells when chelated (e.g., Gd3+‚DTPA complex);29,35,36 and (iv) they have acceptable cost (salts of Gd3+ can cost
