Anal. Chem. 2003, 75, 6868-6874
Magnetic Cell Separation: Characterization of Magnetophoretic Mobility Kara E. McCloskey,†,‡,§ Jeffrey J. Chalmers,*,† and Maciej Zborowski‡
Department of Chemical Engineering, The Ohio State University, 140 W. 19th Avenue, Columbus, Ohio 43210, and Department of Biomedical Engineering/ND-20, The Cleveland Clinic Foundation, 9500 Euclid Avenue, Cleveland, Ohio 44195
Magnetic cell separation has become a popular technique to enrich or deplete cells of interest from a heterogeneous cell population. One important aspect of magnetic cell separation is the degree to which a cell binds paramagnetic material. It is this paramagnetic material that imparts a positive magnetophoretic mobility to the target cell, thus allowing effective cell separation. A mathematical relationship has been developed to correlate magnetic labeling to the magnetophoretic mobility of an immunomagnetically labeled cell. Four parameters have been identified that significantly affect magnetophoretic mobility of an immunomagnetically labeled cell: the antibody binding capacity (ABC) of a cell population, the secondary antibody amplification (ψ), the particle-magnetic field interaction parameter (∆χVm), and the cell diameter (Dc). The ranges of these parameters are calculated and presented along with how the parameters affect the minimum and maximum range of magnetophoretic mobility. A detailed understanding of these parameters allows predictions of cellular magnetophoretic mobilities and provides control of cell mobility through selection of antibodies and magnetic particle conjugates. Cell isolation is an important cell preparation technique in a variety of biological and biomedical applications including the diagnosis and treatment of disease. For example, the isolation of rare hematopoietic progenitor cells from human umbilical cord blood and mobilized peripheral blood can be used as a substitute for bone marrow transplantation in patients having undergone irradiation and high-dose chemotherapy.1-3 Also, endothelial precursor cells found in adult peripheral blood and umbilical cord blood are valuable for therapeutic neovascularization.4 * To whom correspondence should be addressed. Tel.: (614) 292-2727. Fax: (614) 292-3769. E-mail:
[email protected]. † The Ohio State University. ‡ The Cleveland Clinic Foundation. § Current address: Parker H. Petit Institute for Bioengineering and Bioscience, Georgia Institute of Technology, 315 Ferst Drive, Atlanta, GA 30332-0363. E-mail:
[email protected]. Tel.: (404) 894-5971. Fax: (404) 894-2291. (1) Weissman, I. L. Science 2000, 287, 1442-1446. (2) Pick, M.; Nagler, A.; Grisaru, D.; Eldor, A.; Deutsch, V. Brit. J. Haematol. 1998, 103, 639-650. (3) Powles, R.; Mehta, J.; Kulkarni, S.; Treleaven, J.; Millar, B.; Marsden, J.; Sheperd, V.; Rowland, A.; Sirohi, B.; Tait, D.; Horton, C.; Long, S.; Singhal, S. Lancet 2000, 355, 1231-1237.
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Figure 1. Diagram of an immunomagnetically labeled cell. Note that the monoclonal antibodies are binding only to the specifically targeted cell surface molecules.
Magnetic cell separation has become a popular tool for the isolation of cells, especially rare cells, from a heterogeneous mixture. Magnetic cell separation typically employs the use of antibodies against specific cell surface epitopes to tag cells of interest with magnetic particle conjugates (Figure 1). The magnitude of the magnetophoretic mobility of a magnetically tagged cell is a parameter that distinguishes these cells from unlabeled or untagged cells. Effectively, the magnetophoretic mobility is the velocity of an immunomagnetically labeled cell in a magnetic energy gradient divided by the magnitude of that magnetic energy gradient. This velocity is the result of a magnetic force created on the cell by the interaction of the magnetic-susceptible material with the imposed magnetic energy gradient. In most separation processes, the increased difference between the physical-chemical parameters of the target cells and the contaminating cells allows increased separation performance.5,6 Figure 2 presents an example of experimentally determined magnetophoretic mobilities of nonmagnetic and magnetic particles. Clearly, the difference between the modal magnetophoretic mobilities of the two populations is significant and therefore should theoretically allow a clean separation. With the exception of deoxygenated blood cells, which contain high concentrations of (4) Murohara, T.; Ikeda, H.; Duan, J.; Shintani, S.; Sasaki, K.; Eguchi, H.; Onitsuka, I.; Matsui, K.; Imaizumi, T. J. Clin. Invest. 2000, 105, 15271536. (5) Comella, K.; Nakamura, M.; Melnik, K.; Chosy, J.; Zborowski, M.; Cooper, M. A.; Fehniger, T. A.; Caligiuri, M. A.; Chalmers, J. J. Cytometry 2001, 45, 285-293. (6) Nakamura, M.; Decker, K.; Chosy, J.; Comella, K.; Melnik, K.; Moore, L.; Lasky, L. C.; Zborowski, M.; Chalmers, J. J. Biotechnol. Prog. 2001, 17, 1145-1155. 10.1021/ac034315j CCC: $25.00
© 2003 American Chemical Society Published on Web 11/15/2003
Figure 2. Semilog histogram of the magnetophoretic mobilities of magnetic (right peak) and nonmagnetic (left peak) polymeric microspheres. Magnetophoretic mobility units are in mm3/T‚A‚s. Note that the m (and velocity) is approximately zero for the nonmagnetic micorspheres on the left.
paramagnetic hemoglobin, and magnetotactic bacteria, all other cells are just slightly diamagnetic (their magnetic susceptibility is negative, resulting in a very small velocity in the opposite direction to the magnetic energy gradient). Consequently, the mobility difference between the nontagged cells and the magnetically labeled cells is usually dependent on the magnitude of the magnetophoretic mobility of the magnetically tagged cells alone. One widely used batchwise magnetic cell separation device is the MiniMACS magnetic isolation system (Miltenyi Biotech, Bergisch Gladbach, Germany). Although this device is intended to isolate a wide variety of antigen defined cells, it has been demonstrated that the performance of the separation system depends on the magnetophoretic mobility of the labeled cell population.5 In contrast, nonbatch, continuous and flow-through immunomagnetic cell sorting devices have been under development for isolation of large numbers of cells.7-13 In continuous immunomagnetic cell separation, the design, operation, and efficiency of a separation are much more strictly dependent on the magnetophoretic mobility of the cell population than batchwise separations.14-16 (7) Sun, L.; Zborowski, M.; Moore, L.; Chalmers, J. J. Cytometry 1998, 33, 469475. (8) Moore, L.; Zborowski, M.; Sun, L.; Chalmers, J. J. Biochem. Biophys. Methods 1998, 37, 11-33. (9) Moore, L. R.; Rodriguez, A. R.; Williams, P. S.; McCloskey, K.; Bolwell, B. J.; Nakamura, M.; Chalmers, J. J.; Zborowski, M. J. Magn. Magn. Mater. 2001, 225 (1-2), 277-284. (10) Safarik, I.; Safarikova, M. J. Chromatogr., B 1999, 722, 33-53. (11) Hausmann, M.; Hartig, R.; Liebich, H.-G.; Lu ¨ ers, G.; Saalmu ¨ ller, A.; Teichmann, R.; Cremer, C. In Cell Separation: Methods and Applications; Recktenwald, D., Radbruch, A., Eds.; Marcel Dekker: New York, 1997; Chapter 10. (12) Hartig, R.; Hausmann, M.; Cremer, C. Electrophoresis 1995, 16, 789-792. (13) Hartig, R.; Hausmann, M.; Weber, G.; Cremer, C. Rev. Sci. Instrum. 1995, 66, 3289-3295. (14) Williams, P. S.; Zborowski, M.; Chalmers, J. J. Anal. Chem. 1999, 71, 37993807. (15) Hoyos, M.; Moore, L.; McCloskey, K.; Margel, S.; Zuberi, M.; Chalmers, J.; Zborowski, M. J. Chromatogr., A 2000, 903, 99-116. (16) Hoyos, M.; McCloskey, K.; Moore, L.; Nakamura, M.; Bolwell, B.; Chalmers, J.; Zborowski, M. Sep. Sci. Technol. 2002, 37, 745-767.
To measure and study the magnetophoretic mobility of immunomagnetically labeled cells, a cell tracking velocimetry (CTV) apparatus has been developed, which measures the velocity and magnetophoretic mobility of an immunomagnetically labeled cell (or particle) in a well-defined magnetic energy gradient.17-19 Complementary to this instrumentation development, mathematical relationships defining the magnetophoretic mobility of immunomagnetically labeled cells have also been developed.20 With use of the CTV apparatus, these relationships have been verified through direct measurement of the magnetophoretic mobility of several immunomagnetically labeled cells and calibration microbeads.20-22 Through the above-mentioned investigations,20-22 we found predominately four parameters which influence the magnetophoretic mobility of an immunomagnetically labeled cell: the antibody binding capacity (ABC) of a cell population, the secondary antibody binding amplification factor (ψ), the particlemagnetic field interaction parameter (∆χVm) of the magnetic particles (Figure 3), and the cell diameter (Dc). This paper provides a detailed presentation and analysis of how each of these parameters affects the magnetophoretic mobility of immunomagnetically labeled cells. Raw data from previous studies20-22 are used in theoretical calculations to report the current rangessand theoretical maximumssof magnetophoretic mobilities that can be expected under different magnetic labeling conditions. Adequate knowledge of the parameters that affect the binding of paramagnetic material to a cell now allow not only an accurate estimate of the magnetophoretic mobility of a cell population, but also finer control over the magnetophoretic mobility of a cell population by manipulation of the antibody reagents and magnetic particle conjugates used for immunomagnetic labeling. Model of Magnetophoretic Mobility. Magnetophoretic mobility is analogous to the electrophoretic and sedimentation mobilities encountered in electrical and sedimentation separations, respectively. For magnetic separands, the magnetophoretic mobility depends solely on the intrinsic properties of the magnetic particle and the medium including the viscosity of the medium, the particle size, and magnetic susceptibilities of both the medium and the magnetic particle. For a paramagnetically labeled cell or microbead, the forces determining its movement through a liquid suspension are magnetic (Fm), buoyancy (Fbou), gravity (Fg), and drag (Fd) forces. The paramagnetic force acting on an immunomagnetically labeled cell or microbead, using a two-step labeling protocol, can be represented as
Fm ) (n1θ1λ1)(n2θ2λ2)n3Fb
(1)
Subscripts “1” and “2” refer to the primary and secondary labeling (17) Chalmers, J.; Haam, S.; Zhao, Y.; McCloskey, K.; Moore, L.; Zborowski, M.; Williams, P. S. Biotechnol. Bioeng. 1999, 64, 509-518. (18) Chalmers, J.; Haam, S.; Zhao, Y.; McCloskey, K.; Moore, L.; Zborowski, M.; Williams, P. S. Biotechnol. Bioeng. 1999, 64, 519-526. (19) Chalmers, J.; Zhao, Y.; Nakamura, M.; Melnik, K.; Lasky, L.; Moore, L.; Zborowski, M.; Williams, P. S. J. Magn. Magn. Mater. 1999, 194, 231241. (20) McCloskey, K.; Chalmers, J.; Zborowski, M. Cytometry 2000, 40, 307315. Erratum in Cytometry 2000, 41, 150. (21) McCloskey, K.; Chalmers, J.; Zborowski, M. Cytometry 2001, 44, 137147. (22) McCloskey, K.; Comella, K.; Chalmers, J.; Margel, S.; Zborowski, M. Biotechnol. Bioeng. 2001, 75, 642-655.
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Figure 3. Comparison of immunomagnetically labeled cells with different values of antibody binding capacities (ABC), secondary antibody amplification (ψ), or magnetic-particle field interaction parameter (∆χVm). Notice that an increase in any one of these parameters will increase the amount of magnetic material bound to the cell and therefore should increase the cell’s magnetophoretic mobility.
antibodies, respectively; n1 is the number of antigen binding sites per cell, including specific and nonspecific antigen sites (ns + nns), and θ1 is the fraction of antigen molecules on the particle surface bound by primary antibody. The parameter, λ1, represents the valence of the primary antibody binding. The combined term n1θ1λ1 is equivalent to the commonly used term “antibody binding capacity” (ABC) of a cell population.23 Antibody binding capacity is a measure of the number of primary antibodies binding to a cell or microbead. This value includes not only the number of antigen molecules per cell but also variables such as valence of antibody binding, steric hindrance, binding affinities, and nonspecific binding. The same sequence of parameters is then repeated for the binding of the secondary antibody to sites on the primary antibody. In this case, n2 is the number of binding sites on the primary antibody recognized by the secondary antibody. θ2 is the fraction of binding sites on the primary antibodies that are bound by secondary antibodies, and λ2 represents the valence of the secondary antibody binding. These terms n2θ2λ2 can then be combined into one overall term, ψ, representing the antibody amplification due to the secondary antibody binding to multiple sites on the primary antibody or the number of secondary antibodies binding per primary antibody. The parameter n3 represents the number of magnetic nanoparticles conjugated to the antibody, in this example, the secondary antibody. Combining parameters ABC, ψ, and n3 into one overall term, Nmp, gives a value that represents the number of magnetic nanoparticles bound to each cell or microbead and is therefore referred to as the “magnetic particle binding capacity” of a cell or microbead. (23) Zagursky, R.; Sharp, D.; Solomon, K.; Schwartz, A. Biotechniques 1995, 18, 504-509.
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Fb is the magnetic force acting on one paramagnetic nanoparticle in the direction of the magnetic energy gradient and is described by
Fb )
1 ∆χVm∇B2 2µ0
(2)
where µ0 is the magnetic permeability of free space, ∆χ is the difference in magnetic susceptibility between the magnetic material, χb, and the surrounding medium, χf. Vm is the volume of paramagnetic material per paramagnetic nanoparticle, and B is the magnetic flux density. Note that the particle-magnetic field interaction parameter, ∆χVm, is a constant representing the magnetic property of a single magnetic nanoparticle.14 The CTV instrument, used to experimentally measure magnetophoretic mobility, is oriented such that the magnetic energy gradient in the experimental system is perpendicular to gravity; thus, the governing forces are magnetic force, Fm, as described in eq 1, and drag force, Fd, which follows Stokes’ law for slowmoving particles. The motion of micrometer-size bodies in an aqueous medium, determined by viscous forces, attain terminal velocities in a very short time compared to the separation times. This results in a balance between the magnetic and viscous drag forces acting on the cell over the entire cell path in the magnetic field. Setting these two opposing forces equal to one another (that is, neglecting particle inertia), we obtain a relationship for the magnetic energy gradient-induced velocity, vc, of the magnetized cell or microbead
vc )
(n1θ1λ1)(n2θ2λ2)n3|Fb| ABCψn3|Fb| ) 3πDcη f
(3)
where Dc is the diameter of the cell or microbead, η is the viscosity of the fluid, and f ) 3πDcη is the friction coefficient of the moving cell or microbead. The magnetophoretic driving force, Sm, is proportional to the magnetic energy gradient and is defined as
Sm )
∇B2 2µ0
(4)
and magnetophoretic mobility, m, is defined as
m)
vc Sm
(5)
Dividing the velocity value by the magnetophoretic driving force, Sm, gives us the magnetophoretic mobility, m, a “normalized” parameter analogous to electrophoretic mobility, of the immunomagnetically labeled cell or microbead:
m)
(n1θ1λ1)(n2θ2λ2)n3∆χVm ABCψn3∆χVm ) 3πDcη 3πDcη
(6)
From eq 6, the magnetophoretic mobility, m, of an immunomagnetically labeled cell is a function of the parameters ABC, ψ, n3, ∆χVm, as well as Dc and η. The viscosity of the carrier solution (aqueous), η, varies in a highly predictable manner over the temperature range of interest (typically between room temperature and 0 °C). Also, the functional number of magnetic particles conjugated per secondary binding antibody is usually 1 (or possibly less than 1 in some cases).24 Therefore, for constant temperature and carrier fluid composition, the most influential parameters on magnetophoretic mobility are ABC, ψ, ∆χVm (Figure 3), and Dc. The remainder of this paper will carefully investigate the ranges (both theoretically and through reported experimental values) of these most influential parameters ABC, ψ, ∆χVm, and Dc as they relate to magnetophoretic mobility. RESULTS AND DISCUSSION Antibody Binding Capacity, ABC. The first parameter to examine is the antibody binding capacity, ABC, which provides quantitative information about the number of antibodies binding to the surface molecules on individual cells. This term describes the expression level of the targeted antigen molecules on the cell surface,23,25-26 as well as the antibody binding mechanism of the antibody used, including the binding valence, steric hindrance, and binding affinity of the specific antibody. The cellular antigen expression levels have been shown to have phenotypic significance and, in some examples, proven to be valuable in the prognosis and diagnosis of disease.27-31 (24) Kantor, A. B.; Gibbons, I.; Miltenyi, S.; Schmitz, J. In Cell Separation Methods and Applications; Recktenwald, D., Radbruch, A., Eds.; Marcel Dekker: New York, 1998; pp 153-173. (25) Schwartz, A.; Ferna´ndez-Repollet, E.; Vogt, R.; Gratama, J. Cytometry 1996, 26, 22-31. (26) Schwartz, A.; Marti, G.; Poon, R.; Gratama, J.; Ferna´ndez-Repollet, E. Cytometry 1998, 33, 106-114. (27) Poncelet, P.; George, F.; Pap, S.; Lanza, F. Eur. J. Histochem. 1996, 40, 15-32.
Figure 4. Logarithmic plot of the maximum number of magnetic particles which are available to bind to a cell (Nmp) versus the diameter of the magnetic particles for two different cell diameters (15-µm cell, dashed line, and 7-µm cell, solid line). Note that the approximate sizes of some commercially available magnetic particles have been placed on the diagram.
The ABC affects magnetophoretic mobility of an immunomagnetically labeled cell (eq 6) in that cells expressing greater numbers of the targeted surface antigen will exhibit larger ABC values and, therefore, will often exhibit greater magnetophoretic mobilities.20,21 The increase in the amount of magnetic material bound to a cell with increased ABC is visually depicted in Figure 3. When the top panel is compared with the bottom left panel, the cell with the greater ABC value (due to more surface antigens) has a greater number of magnetic particles binding to that cell. It then follows that a cell with a larger number of magnetic particles would exhibit greater magnetophoretic mobility. This theoretical relationship between ABC and magnetophoretic mobility has been experimentally verified, showing that ABC is linearly proportional to magnetophoretic mobility within a limited region.20 Although Figure 3 depicts only an ABC ) 3, a cell population’s mean antigen expression, and therefore ABC, can actually range from a few hundred per cell to greater than 1 million.27 The relationship between ABC and magnetophoretic mobility is linear only within a limited range due to steric hindrance of the bound magnetic particles.20 Although at high ABC values there are a large number of sites available for the magnetic particles to bind, the surface area available for the magnetic particles is limited by (1) the cell diameter and (2) the size of the magnetic particles.20 Because of this limitation, theoretical estimates of the maximum number of magnetic particles that can bind have been calculated given a specific cell and magnetic particle size. The diversity in immunomagnetic particle sizes can range from 12 nm (ferritin) to 5 µm (Dynabeads, Dynal Biotech, Inc., Lake Success, NY). These calculations assume a densely packed hexagonal lattice of rigid magnetic spheres packed on the surface of a rigid, spherical cell.21 Figure 4 is a plot of these calculations, with the number of magnetic carriers bound per cell (Nmp) on the y-axis and the (28) Lavabre-Betrand, T.; Janossy, G.; Ivory, K.; Peters, R.; Secker-Walker, L.; Porwit-MacDonald, A. Cytometry 1994, 18, 209-217. (29) Liu, Z.; Hultin, L.; Cumberland, W.; Hultin, P.; Schmid, I.; Matud, J.; Detels, R.; Giorgi, J. Cytometry 1996, 26, 1-7. (30) Bikoue, A.; George, F.; Poncelet, P.; Mutin, M.; Janossy, G.; Sampol, J. Cytometry 1996, 26, 137-147. (31) Bikoue, A.; D’Ercole, C.; George, F.; Dameche, L.; Mutin, M.; Sampol, J. Clin. Immunol. Immunopath. 1997, 84 (1), 56-64.
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diameter of the magnetic particles on the x-axis. Two cell sizes were assumed: 7 µm (solid line) and 15 µm (dotted line). The labeled gray areas represent the range in diameters, including size distributions, of several reported magnetic particles. Note that Dynabeads are monodisperse microspheres that come in four discrete sizes of 1.05, 2.8, 4.5, and 5.0 µm. Because of the large range, both axes are reported in a logarithmic scale. Note that the number of magnetic particles that can bind to a cell ranges by 106, depending on the size of magnetic particles and that 10 times more magnetic particles may be bound to a 15-µm cell than a 7-µm cell. Secondary Antibody Binding Amplification, ψ. In immunofluorescent or immunomagnetic labeling of a cell, a two-step antibody labeling protocol is often employed where the secondary antibodies may target a variety of antigens on the primary antibody. These include the following: epitopes on the primary antibody (human, mouse, rat, etc.), fluorochromes that are conjugated to the primary antibody (FITC, PE, etc.), or other molecules conjugated to the primary antibody, such as biotin. In addition to providing flexibility, a two-step antibody-labeling protocol may also amplify the number of secondary antibodies binding to a cell because the primary antibody potentially provides multiple sites for the secondary antibody to bind. If magnetic particles are conjugated to the secondary antibodies, the number of magnetic particles bound to the cell will also be amplified, thus increasing a cell’s magnetophoretic mobility. An increase in magnetophoretic mobility due to the secondary antibodies binding to multiple epitopes on the primary antibody is referred to as the “secondary antibody binding amplification,” ψ.22 This amplification is visually depicted in Figure 3 by comparing the top panel with the middle lower panel. Secondary antibody binding amplification has been previously investigated and quantitated by comparing the mobilities from lymphocytes directly labeled with anti-CD4 MACS magnetic nanoparticles with the mobilities of the same lymphocytes labeled with two different indirect antibody-labeling schemes. Results showed that an average of 3.4 anti-FITC MACS magnetic nanoparticle secondary antibodies bind to each primary CD4 FITC antibody, ψ ) 3.4 ( 0.33, and approximately one, ψ ) 0.98 ( 0.081, anti-mouse MACS magnetic nanoparticle secondary antibody binds to each primary mouse CD4 FITC antibody on a CD4 positive lymphocyte.22 To further investigate the significance of ψ on magnetophoretic mobility, the magnetophoretic mobilities versus ABC were calculated for three levels of secondary antibody amplification, or ψ values (Figure 5). For these calculations, ∆χVm ) 2.5 × 10-16 mm3 (previously calculated for MACS magnetic nanoparticles20) and n3 ) 1 was assumed.24 The value range for ψ was chosen between 1 (no amplification) and 4 (based on previous calculations). The maximum value of ψ ) 4 is most likely a steric hindrance phenomena that could potentially increase slightly for smaller magnetic particles. In Figure 5, notice that the initial slope of each line is a function of the secondary antibody amplification factor, ψ, and the cell diameter, Dc. The slope of the line increases with increasing ψ and, due to the larger drag force on larger cells, decreases with increasing Dc. Also note the horizontal saturation lines, corresponding to the maximum number of bound magnetic particles, and thus a maximum achievable magnetophoretic mobility for the given cell size and magnetic particle size (50 nm). 6872 Analytical Chemistry, Vol. 75, No. 24, December 15, 2003
Figure 5. Plot of magnetophoretic mobilities versus antibody binding capacities of immunomagnetically labeled cells. The initial slope of this relationship is proportional to the secondary antibody binding amplification, ψ, and the cell diameter, Dc. Note that for larger cells (dashed line), the slope of the line is less steep due to drag forces, but that more magnetic particles may bind, resulting in potentially much greater maximum magnetophoretic mobilities.
Here we see that the maximum mobility is 2 times greater for a cell with a diameter that is approximately 2 times larger. Particle-Magnetic Field Interaction Parameter, ∆χVm. The particle-magnetic field interaction parameter, ∆χVm, is a product of the magnetic susceptibility of the magnetic material in the magnetic particle relative to the carrier fluid, ∆χ, and the volume of magnetic material, Vm, per magnetic particle. The value of ∆χVm is dependent on the specific magnetic particles that are conjugated to the antibody including the magnetic particle size (related to the volume of magnetic material, Vm) because larger magnetic particles (and those with greater magnetic susceptibilities) create larger forces on the cell, resulting in larger magnetophoretic mobility values. Comparing the top panel with the lower right panel in Figure 3, we see that the ∆χVm value will be larger for larger magnetic particles (greater Vm). The particle-field interaction parameter also increases with ∆χ (not shown). Although many types of magnetic microbeads and nanobeads have been used to label and separate cells, the most common are monodisperse polystyrene spheres modified by addition of iron.10 The iron oxide compounds usually consist of a mixture of ferromagnetic maghemite γ-Fe2O3 and magnetite Fe3O4. The advantage of Fe3O4 is that it attains high saturation magnetization at a low applied magnetic field. The advantage of Fe2O3 is that its magnetization is a linear function of the applied field for a relatively wide range of fields and is therefore easier to characterize by its magnetic susceptibility, in the same manner as are the paramagnetic, superparamagnetic, and diamagnetic compounds. The data in Figure 6 provide information on the range of magnetophoretic mobilities estimated for three different commercially available iron oxide magnetic particles: MACS microbeads (Miltenyi Biotech, Auburn, CA), Immunicon ferrofluids (Immunicon ferrofluids, Huntingdon Valley, PA, are now available through Molecular Probes, Eugene, OR), and Dynabeads M-450 (Dynal Biotech, Inc. Lake Success, NY). The value for the particle-magnetic field interaction parameter of MACS magnetic nanoparticles, ∆χVm ) 2.5 × 10-16 mm3, has been experimentally derived.20 With use of this ∆χVm value for MACS magnetic
greater magnetophoretic mobilities. In addition, a larger cell will also have more surface area available for the magnetic particles to bind, thus increasing the maximum number of magnetic particles that can bind to the cell (Figure 4), also increasing the maximum magnetophoretic mobility (Figures 5).
Figure 6. Logarithmic plot of the magnetophoretic mobilities versus the number of magnetic particles bound to an immunomagnetically labeled cell or microbead. Three different commercially available magnetic particles are included: MACS, Immunicon, and Dynabeads.
nanoparticles, an estimated ∆χVm is calculated to be 8.0 × 10-15 mm3 for the slightly larger Immunicon nanoparticles and 5.0 × 10-11 mm3 for the much larger Dynabeads. These estimates were obtained using vendor information about the size and composition of the magnetic particles. The mean diameters used were 50 nm for MACS nanoparticles, 140 nm for Immunicon, and 4.5 µm for Dynabeads M-450 and the corresponding weight percentages of magnetic material are approximately 55% for MACS, 80% for Immunicon, and 15% for Dynabeads. These estimates of ∆χVm for Immunicon and Dynabeads assume that Immunicon, Dynabeads, and MACS paramagnetic nanoparticles are composed of comparable composition ratios of γ-Fe2O3 and Fe3O4 magnetic materials. Note that for equal numbers of magnetic nanoparticles binding to a cell, the mobilities imparted by the Immunicon magnetic nanoparticles are almost 2 orders of magnitude greater than the MACS nanoparticles and that Dynabeads produce 5 orders of magnitude greater cell mobilities than the smaller MACS nanoparticles. Cell Diameter, Dc. The last parameter is the cell diameter, Dc. Although Dc is not an adjustable parameter, it might affect the magnetophoretic mobility in three possible ways. These include the drag force acting on the moving cell, the cell’s ABC, and the steric hindrance of the binding magnetic particles. The first mechanism is the drag force, Fd ) fvc, that opposes the magnetic force for an immunomagnetically labeled cell moving through a viscous medium (Stokes’ law) at a velocity vc. A larger cell will exhibit a larger friction coefficient, f ) 3πηDc; thus, the drag force on a larger cell will be greater, lowering a cell’s magnetophoretic mobility (eq 6). The effect of the cell diameter on magnetophoretic mobility is clearly evident by comparing the slopes in Figure 5. For equal amplification values, the slope of the line for smaller cells is much steeper than larger cells that exhibit greater drag forces. The two other mechanisms in which the cell diameter may affect the magnetophoretic mobility are both related to the surface area of the cells. If the antigen expression levels on a cell is a function of the size of that cell, that is, constant antigen density, larger cells would exhibit larger ABC values and, therefore,
CONCLUSIONS The most influential parameters affecting the magnetophoretic mobility of an immunomagnetically labeled cell are the antigen expression level (related to ABC), the type of antibodies used in immunomagnetically labeling of the cell: primary antibody (related to ABC) and the secondary antibody (related to ψ), the type of magnetic particles chosen for antibody conjugation, ∆χVm, and the cell’s size, Dc. A comprehensive understanding of these parameters enables magnetic cell separation users to optimize their separation efficiencies through manipulation of immunomagnetic cell labeling procedures. Although ABC and Dc are inherent biological parameters for a specific cell population, their values can be measured. The ABC of a cell can be measured using calibration microbeads designed for quantitative flow cytometry.23 The other two parameters, ψ and ∆χVm, may be manipulated to optimize magnetic cell separation. For example, if one desires to increase the magnetophoretic mobility of the cell sample, this could be achieved by either using an indirect antibody labeling protocol, thus amplifying the number of magnetic particles bound per primary antibody, or by using a larger magnetic particle. An indirect antibody labeling protocol could increase magnetophoretic mobility by up to 4-5 times, as seen in Figure 5, and choosing larger magnetic particles could increase the magnetophoretic mobility by several orders of magnitude, as seen in Figure 6. By increasing magnetophoretic mobility significantly, magnetic immunolabeling capabilities should theoretically be able to identify and sort cells with much lower antigen expression levels compared with immunofluorescent labeling capabilities. In addition to knowing information about each parameter, it is important to also understand the limitations that one parameter sets on the range of the other parameters. For example, in Figure 4 we see that 10 times more magnetic particles can bind to a 15µm cell than a 7-µm cell, yet because of the drag force imposed on larger cells, the maximum magnetophoretic mobility will only be approximately 2 times larger for the 15-µm cell. We have also seen that although larger magnetic particles are more magnetic, due to steric hindrance issues, fewer of these large magnetic particles will bind to the surface of a cell. Magnetic cell separation provides a very specific, simple, and rapid technique for isolation of a desired cell population from a heterogeneous mixture of cells. However, a basic understanding of immunomagnetic labeling is necessary for optimizing a magnetic labeling protocol for individual cell populations. The data presented in the paper summarize studies on the dependence of magnetophoretic mobility on the cell properties and various immunomagnetic labeling parameters. This information provides magnetic separation users with alternatives for manipulating these variables to either increase (or decrease) magnetophoretic mobility, thus optimizing their separation efficiency. ACKNOWLEDGMENT This work has been supported by grants from the National Science Foundation (BES-9731059, BES-0124897 to J.J.C. and Analytical Chemistry, Vol. 75, No. 24, December 15, 2003
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M.Z.) and the National Cancer Institute (R33 CA81662 to J.J.C. and R01 CA62349 to M.Z.). GLOSSARY ABC
antibody binding capacity
B
magnetic flux density (T)
Dc
diameter of the cell or microbead (m)
Fb
magnetic force acting on one paramagnetic nanoparticle (N)
Fbou
buoyancy force (N)
Fd
drag force (N)
Fg
gravitational force (N)
Fm
magnetic force (N)
f
friction coefficient (kg/s)
m
magnetophoretic mobility (mm3/T‚A‚s)
Vm
volume of paramagnetic material per paramagnetic nanoparticle (m3)
vc
velocity of moving cell or microbead (m/s)
χb
magnetic susceptibility of the magnetic material (SI unit system)
χf
magnetic susceptibility of the fluid (SI unit system)
∆χ
difference between χb and χf (SI unit system)
η
viscosity of the suspension fluid (kg/m‚s)
λ1
valence of primary antibody binding
λ2
valence of secondary antibody binding
µ0
magnetic permeability of free space (T‚m/A)
θ1
fraction of antigen site on the particle surface bound by primary antibody
θ2
fraction of sites on the primary antibody bound by the secondary antibody
ψ
secondary antibody binding amplification due to secondary antibodies binding to multiple sites on the primary antibody
nns
number of nonspecific binding sites per cell
ns
number of specific antigen molecule binding sites per cell
n1
number of antigen binding sites per cell
n2
number of binding sites on the primary antibody recognized by the secondary antibody
n3
number of magnetic nanoparticles conjugated to the antibody
Received for review March 28, 2003. Accepted September 19, 2003.
Sm
magnetophoretic driving force (T‚A/mm2) ) ∇B2/2µ0
AC034315J
6874
Analytical Chemistry, Vol. 75, No. 24, December 15, 2003
