Anal. Chem. 2005, 77, 5294-5301
Cell Sorting by One Gravity SPLITT Fractionation Maria-Anna Benincasa,*,† Lee R. Moore,‡ P. Stephen Williams,‡ Earl Poptic,§ Francesca Carpino,‡ and Maciej Zborowski‡
Department of Chemistry, University of Rome “La Sapienza”, Ple A. Moro, 5. 00185 Rome, Italy, and Department of Biomedical Engineering and Hybridoma Core Facility, The Cleveland Clinic Foundation, 9500 Euclid Avenue, Cleveland, Ohio 44195
The need for innovative separative techniques suitable for the fractionation of biomaterials prompted this investigation into the performance of the gravitational split-flow thin channel (G-SPLITT) system as a cell sorter. The rigorous mathematical description of the separation mechanism allows achievement of fast separation of several million myeloma cells from healthy splenocytes using flow conditions calculated from theory. Separation in G-SPLITT is based on differences in sedimentation rate. For accurate prediction of the optimal working conditions, this parameter was directly measured by cell tracking velocimetry rather than relying on a measure of diameter (by Multisizer) and an assumed density for each cell population. We also discuss the influence of different flow conditions on the effectiveness of separation. Separation techniques suitable for sorting biological cells have attracted renewed scientific interest with the increasing demands for pure cell lines for biomedical and biotechnological applications.1 In the in vitro regeneration of tissues or organ systems, for instance, practical regeneration is obtained only with almost homogeneous stem or progenitor cell lines that do not contain diseased species. Various cell sorting methods follow different strategies but have certain universal requirements. For example, as in the case of isolation of stem/progenitor cells, there is a need for sufficient selectivity to discriminate between very similar cell populations, with a yield sufficient for clinically effective and rapid regeneration. There is also a common requirement for mild conditions to maintain cell viability. This is a general requirement for cell separation but is particularly important for selection of hybridoma cells. The mild separation conditions ensure the selected cells maintain their capability for producing antibodies at the expected rate. A large number of cell separation devices have been marketed. Although they generally offer high selectivity and good yield, they require a very considerable start-up investment of the order of $105 and have a level of mechanical complexity that requires well-trained personnel for operation and maintenance. In addition, for most established cell sorting * To whom correspondence should be addressed. E-mail:
[email protected]. Fax: +39-06-490631. † University of Rome “La Sapienza”. ‡ Department of Biomedical Engineering, The Cleveland Clinic Foundation. § Hybridoma Core Facility, The Cleveland Clinic Foundation. (1) Cell Separation Methods and Application; Recktenwald, D., Radbruch, A., Eds.; Marcel Dekker: New York, 1998.
5294 Analytical Chemistry, Vol. 77, No. 16, August 15, 2005
techniques, the sample must be subjected to a preliminary manipulation, often involving time-consuming modification of the membrane surface properties as in the case of magnetic or fluorescence labeling. Therefore, separative methodologies that discriminate between cells on purely physical grounds 2-8 are particularly attractive since they better preserve cell integrity and viability by eliminating sample pretreatment. In this work, we describe gravity-driven split-flow fractionation (G-SPLITT)9 for the separation of biomaterials. SPLITT fractionation systems are related to the broad array of separation techniques termed field-flow fractionation (FFF).10 As in the FFF techniques, the separative mechanism is based on the combined influence of a laminar flow that transports the sample along a thin channel and a field orthogonal to the flow. Whereas in FFF the field induces the selective segregation of particles into fluid laminas of differing velocities, in SPLITT the field induces differential transport across the channel thickness so that particles are carried to (usually two) different outlets. SPLITT fractionation therefore usually yields only a binary separation. The advantage of a SPLITT system compared to the FFF techniques, however, is that it allows a continuous mode of operation and hence the separation of large quantities of sample. Beside the possibility of high throughput, other considerations have stimulated the application of the SPLITT technique to the fractionation of biological materials. The gravitational field acting in G-SPLITT does not require the sample to have any specific property other than a density differing from that of the suspending fluid. The technique is thus applicable without preliminary treatment, which in the case of biomaterials is always desirable because it reduces the possibility of sample contamination and poor recovery. The opera(2) Lucas, M.;Lepage, F.; Cardot, P. In Field-Flow Fractionation Handbook; Schimpf, M. E., Caldwell, K. D., Giddings J. C., Eds.; John Wiley & Sons: New York, 2000; pp 471-486. (3) Rouard, H.;Leon, A.; De Reys, S.; Taylor, L.; Logan, J.; Marquet J.; Jouault, H.; Loper, K.; Maison, P.; Delfau-Larue, M.-H.; Beaujean, F.; Farcet, J.-P.; Noga, S. J. Transfusion 2003, 43, 481-487. (4) Yang, J.;Huang, Y.; Wang, X.-B.; Becker, F. F.; Gascoyne, R. C. Anal. Chem. 1999, 71, 911-918. (5) Williams, P. S.;Zborowski, M.; Chalmers, J. J. Anal. Chem. 1999, 71, 37993807. (6) Rodriguez, M. A.;Armstrong, D. W. J. Chromatogr., B 2004, 800, 7-25. (7) Bigelow, J. C.;Giddings, J. C.; Nabeshima, Y.; Tsuruta, T.; Kataoka, K.; Okano, T.; Yui, N.; Sakurai, Y. J. Immunol. Methods 1989, 117, 289-293. (8) Barman, N. B.;Ashwood, E. R.; Giddings, J. C. Anal. Biochem. 1993, 212, 35-42. (9) Springston, S. R.; Myers, M. N.; Giddings, J. C. Anal. Chem. 1987, 59, 344-350. (10) Giddings, J. C. Chem. Eng. News 1988, 66, 34-45. 10.1021/ac058013o CCC: $30.25
© 2005 American Chemical Society Published on Web 07/12/2005
Figure 1. Schematic diagram of a SPLITT channel showing the binary separation of two monodisperse particle populations.
tional conditions of laminar flow at flow rates that, to some extent, may be independently chosen ensures low shear stress, which is necessary for the separation of fragile materials such as cells. However, even under these gentle conditions, several million cells may be separated in a period of minutes. The regular channel geometry and simple construction, combined with the possibility of using commercially available ancillary equipment, make the system cost-effective and easy to operate and maintain. The simplicity of the system also lends itself to easy sterilization and maintenance of sterile conditions during cell separation. Moreover, unlike most fractionators that are specific for particle/cell separation, the same SPLITT device, operating under a diffusion mechanism, may also be used to fractionate macromolecules.11 In a SPLITT fractionator, whose edge view is shown in Figure 1, the separation takes place in a very thin empty channel, typically 300-400 µm thick, 15-20 cm long, and 3-4 cm wide with glass or polymer walls clamped between two blocks of some nondeformable material (most often Plexiglas). The aspect ratio, not respected in the figure, is much more in favor of length in the real system, as suggested by the typical dimensions given above. The thickness is expanded in the figure to illustrate the mechanism of separation. The thin sheet of fluid carrying the sample into the channel is obtained by the smooth merging of two substreams entering from opposite sides of the channel through ports a′ and b′ (see Figure 1) that are physically separated by a thin rigid flow splitter. A similar configuration of split flows is realized at the outlet end of the channel to smoothly divide the fluid to exit at outlets a and b. Inside the channel, the flow velocity profile is parabolic, except in the vicinity of the splitters and close to the side walls. Three regions of fluid bounded by the channel walls and by two virtual stream planes of different contour and position are recognized within the channel thickness. Following standard nomenclature, the fluid laminas determining the boundary planes separating these regions are labeled in Figure 1 as ISP and OSP, respectively, the inlet and outlet splitting planes. The position of the ISP, which divides the incoming sample substream entering at a′ from pure carrier entering at b′, and of the OSP separating the two outlet flows, may be adjusted by controlling the ratios of the inlet and outlet flow rates. The central region between these planes, referred to as the transport zone, may be viewed as a virtual liquid membrane. Penetration of this virtual membrane occurs only when material is driven across streamlines by interaction with the applied field. In the case of (11) Williams, P. S.; Levin, S.; Lenczycki, T.; Giddings, J. C. Ind. Eng. Chem. Res. 1992, 31, 2172-2181.
gravity-driven G-SPLITT separations, material must be denser than the carrier fluid so that it sediments across the transport zone. As in permeation through a real membrane, only cells sedimenting fast enough to cross both boundaries (the ISP and OSP) to reach the bottom region are carried out of the bottom outlet b. All other cells exit the top outlet a. By this mechanism, the injected mixture is divided in two fractions just as in cross-flow membrane filtration. However, unlike in cross-flow filtration, separation is achieved without limitation to the amount of sample analyzed, without membrane fouling phenomena, and with no need to select a specific membrane pore size and material. An effective separation by G-SPLITT occurs when the speed of transport by the carrier fluid along the channel length allows for a residence time inside the channel equal to or longer than the time needed for the faster sedimenting particles/cells to migrate into the lower region before reaching the outlet splitter, but not long enough for the smaller or less dense particles to cross the two splitting planes. This situation is obtained when the residence time is correlated to the time that the highly mobile species need to traverse the transport region. Since, as in all flowassisted separation techniques, the time spent by the sample inside the channel is controlled by the flow velocity, the flow rates set the conditions for the fractionation. THEORY The mathematical treatment of the SPLITT separation mechanism is derived by recognizing that the incremental time dt for a cell to sediment a distance dx across the channel thickness at velocity U is equal to the time for the cell to migrate distance dz along the longitudinal coordinate z at local velocity v. This yields the relationship dz/v ) dx/U. Consideration of the dependence of local velocity v on the incremental volumetric flow rate dV˙ over interval dx as v ) dV˙ /b dx gives for the distance increment dz
dz ) dV˙ /bU
(1)
∆V˙ ) bUL
(2)
Integration of eq 1 yields
since the summation over all dz elements gives the distance L between the edges of the splitters. ∆V˙ in eq 2 is the volumetric flow rate of the stream lamina traversed by the cell during its migration along the length of the channel. For a cell introduced at the top inlet to reach outlet substream b, its ∆V˙ must at least exceed the volumetric flow rate V˙ (t) of the transport region, which is given by the flow rate difference at the inlets and outlets:
V˙ (t) ) V˙ (a) - V˙ (a’) ) V˙ (b’) - V˙ (b)
(3)
Hence, from eq 2 the sedimentation velocity Ub needed for a cell population to reach the lower region and exit outlet b is
Ub > V˙ (t)/bL
(4)
However, this condition applies only to those cells whose initial position is close to the ISP. It may be shown12 that the condition Analytical Chemistry, Vol. 77, No. 16, August 15, 2005
5295
for the complete collection at the bottom outlet of cells with sedimentation rate Ub is given by
Ub g
V˙ (a′) + V˙ (t) V˙ (a) ) bL bL
(5)
and that for the full recovery of cells with lower sedimentation rate Ua at the opposite outlet a the following inequality must hold
Ua e
V˙ (t) V˙ (a) - V˙ (a′) ) bL bL
(6)
The conditions given by eqs 5 and 6 would allow for the complete fractionation of a binary mixture of cells with a difference in sedimentation rate ∆U ) Ub - Ua corresponding to
∆U g V˙ (a′)/bL
(7)
All cells with a value of U intermediate between Ua and Ub would be distributed between the two outlets. The previous treatment is based on the assumption that all cells introduced into the sample region start their vertical migration from the same position. This is an approximation stemming from neglecting the thickness of the feed lamina where particles could spread over different starting positions. It is apparent that the higher the sample flow rate V˙ (a′) relative to the total flow rate V˙ , the thicker is the sample region at the inlet, and the larger the required difference in sedimentation rate ∆U for complete separation (see eq 7). This may be considered as contributing to a loss in resolution of the separation. By compressing the feed substream into a thin lamina, the randomizing effect of differences in the initial positions of particles starting their migration is reduced and resolution enhanced. This situation may be obtained by positioning the ISP closer to the top wall, which corresponds to decreasing distance wa′ in Figure 1. It has been shown11 that the ratio wa′ /w, where w is the channel total thickness, is controlled by the relative value of the inlet flow rate V˙ (a′) to the total flow rate V˙ as
( ) ( )
wa′ V˙ (a′) )3 V˙ w
2
-2
wa′ w
3
(8)
The position of the lower splitting plane OSP may be determined using the same equation since the ratio wa/w is related to V˙ (a)/V˙ in a similar fashion. Once both the ISP and the OSP positions are fixed, the thickness of the transport region is also determined. It appears from eq 8 that the same configuration of the virtual splitting planes may be obtained with an infinite number of combinations of the substream flow rates and total flow rate V˙ . However, the effect on fractionation of all the different flow rates yielding the same position for the ISP and OSP would not be the same. As has been shown by computer simulation applied to an annular SPLITT sorter driven by magnetic field,13 different absolute values of flow rates, yielding the same transport lamina thickness and position, lead to different results. This is because the time available for (12) Giddings, J. C. Sep. Sci. Technol. 1992, 27, 1489-1504. (13) Hoyos, M.; McCloskey, K. E.; Moore, L. R.; Nakamura, M.; Bolwell, B. J.; Chalmers, J. J.; Zborowski, M. Sep. Sci. Technol. 2002, 37, 745-767.
5296
Analytical Chemistry, Vol. 77, No. 16, August 15, 2005
Figure 2. Experimental setup of the system for the G-SPLITT separation used in this study.
cells to migrate across the transport zone is dependent on the total flow rate. If flow rates are too low, there may be accumulation of the faster migrating cells at the bottom wall, where the fluid velocity approaches zero and the residence time becomes conversely infinite. If the flow rates are too high, there may be insufficient time for transverse migration of cells under the influence of the field. On the other hand, at higher flow rates, there may be some nonselective transport of species through the central region due to hydrodynamic interaction between cells. Under ideal conditions, the ultimate fate of a cell depends on the longitudinal transport velocity relative to its sedimentation rate. Equation 5, which establishes the value of the top outlet flow rate for complete collection at the bottom outlet b of an analyte with given migration speed, and eq 7, which sets the migration velocity difference between the cell populations to be separated, are the key relationships for the choice of the flow conditions. Consequently, eq 8 may be used either to calculate the boundary plane positions for a chosen V˙ or to obtain a total V˙ for the desired ISP and OSP positions. The procedure described above cannot be followed if the cell migration rates are not accurately known. The cell tracking velocimetry (CTV) technique14,15 developed at the Cleveland Clinic Foundation in collaboration with Ohio State University, to measure the magnetophoretic mobility of magnetic labeled or intrinsically magnetic cells, was used in this study to measure cell sedimentation rates in the absence of a magnetic field.16 EXPERIMENTAL SECTION G-SPLITT System. The experimental set up is shown in Figure 2. It featured a gravitational SPLITT channel similar to the commercially available channels from Postnova Analytics (Salt Lake City, UT) with a total thickness of 317 µm defined by the total thickness of two Mylar spacers and a stainless steel sheet forming the splitter plane sandwiched between the spacers. The (14) Nakamura, M.; Zborowski, M.;Lasky, L. C.; Margel, S.; Chalmers, J. J. Exp. Fluids 2001, 30, 371-380. (15) McCloskey, K. E.; Zborowski, M.; Chalmers, J. J. Cytometry 2001, 44, 137147. (16) Chalmers, J. J.; Haam, S.; Zhao, Y.; McCloskey, K. E.; Moore, L. R.; Zborowski, M.; Williams, P. S.Biotechnol. Bioeng. 1999, 64, 509-518.
channel had a length L of 20.0 cm and breadth b of 4.0 cm. The Mylar spacers had the usual shape for FFF channels with tapered ends to allow for smooth transition of the carrier fluid from and to the connecting tubes. All the channel elements were enclosed by two glass plates, which formed the channel walls. Glass was chosen as the channel material for its high mechanical stability, chemical inertness, and ease of cleaning and sterilization. The capacity for working under sterile conditions allows collection of cell fractions that can be used for culture of pure cell lines. All the channel components were held together by two Plexiglas blocks evenly clamped by bolts. The clamping operation was performed in a methodical, stepwise fashion using a torque wrench to a maximum of 1.5-2 N m. All the Teflon tubing in contact with the cells had inner diameter of 0.79 mm to reduce shear stress on the potentially fragile species. Two dual-syringe pumps (Harvard Apparatus, Holliston, MA), one operating in injection mode, the other in aspiration, were used to control both the incoming and outgoing substreams. The syringes (Becton-Dickinson, Franklin Lakes, NJ) of the aspirating pump placed at the outlets of two UV detectors served also for collection of the sorted cells. The HyperQuan VUV-10 detectors (Colorado Springs, CO), used for on-line inspection of the eluted fractions profiles, were equipped with 32-µL optical cells having 1.0-cm path lengths. All other parts of the detector in contact with the analytes were made of the biocompatibile PEEK material, with tubing i.d. of 0.040 in. (1.0 mm). The UV signal, monitored at 254 nm, was fed into an analog-digital converter (DI-190) and recorded on computer by software package (Windaq Lite). Both the converter and the data acquisition program were from Dataq Instruments (Akron, OH). Although a G-SPLITT instrument may be operated in continuous feed, in this work, a pulse injection method was employed using a six-way valve (Rheodyne 7725i, Alltech Associates, Inc., Deerfield, IL) equipped with a 1.0-mL loop to allow injection of large cell numbers. The loop was not completely filled, but rather 500 µL was accurately introduced by microsyringe. This procedure was chosen for improved quantitative sample introduction. It eliminates the effect of the parabolic velocity profile inside the sample loop that, due to the sluggish movement of the liquid at the walls, does not allow complete filling of the volume close to the tube walls. The carrier liquid employed during the G-SPLITT analyses was a Ca- and Mg-free phosphate buffer (PBS) solution comprising 0.25% w/v bovine serum albumin and 2 mM ethylenediamine tetraacetate in distilled water. The solution was freshly prepared by dilution from 10× concentrate PBS Liquid Concentrate (EM Science, Merck, KGaA, Darmstadt, Germany). It was filtered and degassed and had pH 7.3-7.5. All experiments were carried out at 25 °C. After completing the cell fractionation, the G-SPLITT system was flushed with Hema-Clean detergent (Allegiance Healthcare Corp., IL) and left overnight under this solution. Cell Size Analysis. The size distribution was determined on the unfractionated suspensions as well as on the fractions separated by gravitational SPLITT. A 200-µL sample of the original cell suspension, diluted with 10 mL of isotonic solution (Isoton, Beckman Coulter, Miami, FL), was analyzed by a Coulter Multisizer from Beckman Coulter (Fulllerton, CA) with 256 channels and a 70-µm aperture size. The analyte volume acquired for the 60.0-s
Figure 3. Setup of the cell tracking velocimetry apparatus.
count was always 500 µL. Cells sorted in fractions a or b were subjected to size analysis after centrifugation at 1500 rpm for 2-3 min and resuspension in 10 mL of Isoton solution. Sample Preparation. Myeloma and spleen cells, the latter from a laboratory mouse, were provided by the Hybridoma Core Facility (Cleveland Clinic Foundation, Cleveland, OH). They were suspended in BD Cell Mab culture medium with added glutamine (BD Bioscience, Sparks, MD) and kept in an incubator with 5% carbon dioxide at 37 °C. Prior to analysis, the cell concentration in the culture suspension was measured by Coulter Z-1 particle counter (Beckman-Coulter, Fullerton, CA) after diluting 200 µL to 10.2 mL with the same Isoton solution used for size analysis. Cell count was performed on 0.5 mL of this suspension in a size range selected according to type of cells analyzed. The result was used to calculate the suspension volume containing the number of cells to be fractionated during a single analysis. This volume was centrifuged at 1500 rpm for 2-3 min and the resultant pellet resuspended in the PBS carrier liquid, after discarding the supernatant. The final cell number concentration used for analysis ranged from ∼300 000 to ∼106/mL. During analysis, the unused sample suspension was kept on ice until injected into the G-SPLITT fractionator. Cells to be used for further analysis were collected from three or four repeated G-SPLITT runs. Although this procedure was not particularly time-consuming since each run took ∼10 min, it could have been overcome by using either a continuous sample feed or a higher analyte concentration. These options, however, were not chosen because conservation of sample was considered important for checking the effectiveness of fractionation. Cell Tracking Velocimetry for Measuring Cell Sedimentation Rate. The cell suspension was pumped into a custom borosilicate glass channel 0.6 × 1.7 mm i.d. (depth × height) and 0.4-mm wall thickness (VitroCom, Mountain Lakes, NJ) of the CTV apparatus (shown in Figure 3) using a syringe pump (PhD 2000, Harvard Apparatus). The pump was stopped and valves, positioned on either side of the ∼10-cm-long channel, were closed. The suspension was permitted to “relax” for 1-2 min, to allow for the dampening of residual convection currents. The cell sedimentation images were acquired with a 5× microscope objective and 2.5× photo eyepiece (Olympus, Tokyo, Japan). The image area was 1.71 × 1.27 mm (width × height). A CCD camera (model 4915, Cohu, San Diego, CA) operating at a frame rate of Analytical Chemistry, Vol. 77, No. 16, August 15, 2005
5297
30 Hz and a µ-Tech Vision 1000 PCI Bus Frame Grabber board (MuTech Corp., Billerica, MA) were used to convert the image into a 640 × 480 pixel array, where each pixel contained eight bits of gray-level information ranging from 0 (black) to 255 (white). The computer code used five successive images to establish the most probable path for a specific particle. From this most probable path, the algorithm determined and reported the 2-D location for each tracked frame. A linear fit of the location-time data gave the sedimentation velocity of each particle. Macros (written within Microsoft Excel) were used to compute statistics for the particle population including mean, standard deviation, and confidence limits. The analytical procedure outlined in the introduction was followed throughout this work. After separately measuring sedimentation rates of the myeloma and mouse spleen cells by CTV, the flow rate V˙ (a) was calculated on the basis of the myeloma sedimentation velocity using eq 5. V˙ (a′) was then obtained from the mobility difference between myeloma and spleen cells using eq 7. Once the two top substream flow rates are set, either the total flow rate V˙ or the ISP position may be chosen, the value of the selected parameter determining that of the other. In this work, distance wa′ was generally independently set and eq 8 solved for V˙ . Subsequently, wa was obtained from the same eq 8 replacing V˙ (a′) by V˙ (a) and wa′ by wa. RESULTS AND DISCUSSION SPLITT fractionation using the gravitational field relies on the capability of cells of different size and density injected from the top inlet a′ to either cross the channel thickness beyond the OSP and exit at the bottom outlet b or remain in the region above the OSP and be released at the top port a. Whether cells in a mixture will exit one outlet or the other depends on their possibility of sedimenting through the transport region before being disgorged from the channel. Accurate knowledge of the cell sedimentation rates facilitates the selection of the experimental conditions. Sedimentation rates of the myeloma and spleen cells measured using the modified cell tracking velocimetry apparatus are shown in Figure 4. The different sedimentation behavior of the myeloma cells from that of the splenocytes is evident in the top plot of Figure 4, not only in the more than 6-fold difference in their mean sedimentation velocities (7.7 × 10-4 mm/s for the spleen cells and 4.8 × 10-3 mm/s for the myeloma cells) but also in the broader distribution of sedimentation rates for the myeloma cells. The sedimentation velocities of the spleen cells are found to be relatively narrowly distributed, with a standard deviation just 28% of that of the myeloma cells. This is probably an indication that major aging processes were not present. Differences in the sedimentation of dying cells compared to live ones have been revealed by the SPLITT technique applied to hybridoma cells.17 The different sedimentation behavior of the spleen cells from the cancer cells correlates to their different size distributions. The size distribution of each cell sample obtained by Multisizer is shown in Figure 5. Here the spleen cells are seen to have a much lower mean size and size distribution compared to the myeloma cells. (17) Communication at the 11th International Symposium on Field-Flow Fractionation, Cleveland OH, October 7-10, 2003.
5298 Analytical Chemistry, Vol. 77, No. 16, August 15, 2005
Figure 4. Distribution of sedimentation rate for myeloma cells (top) and spleen cells (bottom) obtained by cell tracking velocimetry. Y-Axis reports the number of cells with a given velocity relative to the total number of cells.
Figure 5. Size distribution of myeloma (left) and spleen cells (right) measured by Multisizer analysis. On the Y-axis, the number of cells with a given diameter relative to the total number of cells is reported.
To assess the fractionating capability of the G-SPLITT system, a test mixture of spleen and myeloma cells was prepared, and this was analyzed by Multisizer before and after fractionation. The solid line in Figure 6 shows the size distribution of the unfractionated mixture superimposed on the size distributions obtained for suspensions separately collected at the top and bottom outlets of the G-SPLITT. In Figure 6, as well as in all the figures illustrating size distributions obtained by Multisizer, data below 2 µm are not meaningful because they are below the lower detectable limit of the instrument. Figure 6 shows that the population of healthy spleen cells is almost completely separated from that of the large diseased cells in a G-SPLITT run. Analysis time was ∼10 min. It is noted here that the flow rates used for the G-SPLITT fractionation were calculated for particles differing
overlap of the distribution of a single parameter for two distinct species may be obtained from18
Rs )
Figure 6. Size distribution of a mixture of spleen and myeloma cells registered by Multisizer before separation overlaid on the distributions for fractions a and b obtained after separate collection by G-SPLITT. Flow conditions for fractionation were V˙ (a) ) 1.469, V˙ (a′) ) 0.5980, V˙ (b) ) 1.031, and V˙ (b′) ) 1.902 mL/min. These flow rates yielded values of wa′/w ) 0.3186 and wa/w ) 0.5583. The number of spleen cells injected into the SPLITT fractionator was ∼800 000 whereas that of the myeloma cells was ∼650 000. The carrier liquid was the PBS buffer solution specified in the Experimental Section. The medium for size analysis was Isoton solution. Y-axis units as in Figure 5.
in sedimentation rate by 1.2 × 10-3 mm s-1, i.e., for smaller particles with 71% of the mean mobility of the larger ones. The size distributions shown in Figure 6 were obtained after centrifugation and resuspension in a smaller volume of buffer to overcome the low response that would be expected for highly diluted fractions following G-SPLITT fractionation. The separation mechanism acting in gravitational SPLITT shows in Figure 1 that the thickness of the transport zone, and the position of the splitting planes, are the parameters discriminating the fate of two monodisperse particle populations of different mobility. From the discussion in the introduction, it is apparent that the distance of the inlet and outlet splitting planes from the channel top wall (wa′ and wa) are chosen on the basis of the relative mobilities of the sample components and that the overall velocity of the fluid inside the channel is determined by the absolute mobilities. It is also apparent that ideal experimental conditions are expected to yield the highest recovery of each fraction.9 The latter may be quantified as the number of cells of a given size recovered at each outlet relative to the total number injected. In the case that the total number injected is not known, a fractional recovery can be evaluated as the number of cells of given size recovered in each fraction relative to the sum of cells recovered at both outlets. Following the original definition of the absolute recovery as the retrieval factor,9 the latter could be viewed as a relative retrieval factor. The ideal fractionation of a binary mixture of monodisperse species can be expected to yield unit and zero retrieval factors of one component at the two respective outlets and zero and unit at the other. Most biological mixtures however comprise species that are broadly disperse in one or more of their characteristic parameters (multivariance). A measure of the
X 2 - X1 2(σ1 + σ2)
(9)
where X1 and X2 are the average values of the specific parameter for, respectively, species 1 and 2 and σ1 and σ2 are their standard deviations. Equation 9 is most commonly used to determine the resolving index of analytical separations. In this case, X1 and X2 are the locations of the centers of gravity of two zones. Based on the size distributions of Figure 5, which give mean diameters of 9.9 µm for the myeloma cells and 5.4 µm for the splenocytes and standard deviations of the fitted Gaussian functions, respectively, of 1.3 and 1.0 µm, an Rs of approximately unity is calculated. A similar value is obtained for the resolution between fractions a and b in Figure 6. A unit value of Rs indicates partial overlap of the distributions of the two distinct species; only for Rs > 1.5 are two peaks considered fully resolved.18 An analogous analysis on the velocity distribution in Figure 4 must take into account that, even though most myeloma cells have sedimentation velocities well above the splenocyte maximum velocity, ∼15% of the former cells fall in the distribution range of the splenocytes. Therefore, even if most of the larger cancer cells and the spleen cells are completely resolved (Rs ∼1.7), under any experimental conditions, the spleen cell fraction would contain a certain amount of the less mobile myeloma cells. By contrast, a pure fraction of myeloma cells may be obtained from outlet b by appropriately setting the OSP. These predictions are confirmed by the distributions in Figure 6, which show that while fraction b contains only myeloma cells as expected, the amount of the splenocytes in fraction a is only ∼80% of the total as computed from the relative area. The amount of the myeloma cells found in fraction a is accounted for not only by cells falling in the range of sedimentation rate of the splenocytes but also by those cells falling in the incompletely resolved region. Under the flow conditions used for this fractionation, only cells with a sedimentation rate equal to or higher than 3.06 × 10-3 mm/s were expected to exit outlet b. By contrast, the migration rate of cells not mobile enough to cross the OSP was equal to or lower than 1.81 × 10-3 mm/s. Cells with mobility falling in the range between these values were predicted to be distributed between the two outlets. It is evident that fractionation of a binary mixture is best achieved under experimental conditions predicted from theory and that departure from the ideal, such as partial overlap of distributions in selective property, is expected to yield fractions that are contaminated to some extent. Different experimental conditions for the G-SPLITT fractionation of the same spleen and myeloma cells have been used to confirm this anticipation. Figure 7 shows the size distribution profiles of fraction a (dotted line) and fraction b (solid line) when wa′/w ) 0.3186 and wa/w ) 0.5676. These conditions were calculated for a sedimentation mobility of the larger particles only 2.1% higher than that of the faster sedimenting species of Figure 6. It is seen in Figure 7 that a lowering of the OSP by only 3 µm, corresponding to an increase of the transport lamina thickness (TLT) of ∼2.6%, brings about (18) Giddings, J. C. Unified Separation Science; Wiley: New York, 1991.
Analytical Chemistry, Vol. 77, No. 16, August 15, 2005
5299
Figure 7. Dimensional distributions for fractions a and b obtained by Multisizer after G-SPLITT fractionation of the same mixture of spleen and myeloma cells. V˙ (a) ) 1.500; V˙ (a′) ) 0.5980; V˙ (b) ) 1.000 and V˙ (b′) ) 1.902 mL/min. Carrier solution as well as the medium for size analysis was the PBS buffer. Y-Axis units as in Figure 5.
Figure 9. Size distribution as in previous Figures 5-7 with V˙ (a) ) 1.500, V˙ (a′) ) 0.700, V˙ (b) ) 1.000, and V˙ (b′) ) 1.800 mL/min. Carrier and suspension medium as in Figure 7. Y-Axis units as in Figure 5.
starting position and thus the effect of this on the cell fate following vertical migration. The small, yet evident, contamination of the myeloma fraction with spleen cells found in Figure 8 is due to the effect of the thicker feed lamina. If the inlet splitting plane position is lowered further, one should expect a more extensive contamination of both fractions with cells of different size. The low purity of fraction a in Figure 9 is very evident in the relatively higher number of myeloma cells found in this fraction, which the narrower transport lamina is not able to limit.
Figure 8. Size distribution of myeloma and spleen cells sorted by the G-SPLITT in two fractions. V˙ (a) ) 1.500, V˙ (a′) ) 0.6500, V˙ (b) ) 1.000, and V˙ (b′) ) 1.8500 mL/min. Carrier and suspension media as in Figure 7. Y-Axis units as in Figure 5.
greater contamination of the top fraction by the myeloma cells. As a result, the spleen cells contribute only ∼59% of the fraction collected from outlet a. The TLT, however, is not the only parameter controlling the purity of a particle population fractionated by SPLITT.11,12 The two fractions shown in Figure 8 were collected from the G-SPLITT at flow rates yielding the same OSP as in Figure 7 and a smaller thickness of the transport lamina obtained by lowering the position of the inlet splitting plane. It is evident from this figure that this flow configuration also decreases the system selectivity. In this case, both fractions are contaminated to some extent by cells of the other fraction. The lower position of the inlet splitting plane does not allow some of the more mobile myeloma cells to cross the transport zone during the time of elution. These cells reach the end of the channel before crossing the outlet splitting plane and exit the top outlet. High selectivity in SPLITT channels is contingent on a thin feed stream lamina thickness wa′. A thinner feed lamina enhances resolution since compressing entering cells into a narrower distribution over the cross section reduces differences in their 5300 Analytical Chemistry, Vol. 77, No. 16, August 15, 2005
CONCLUSIONS The performance of the gravitational SPLITT system applied to the separation of a mixture of myeloma and mouse spleen cells has confirmed the expectation that specific separation needs may be satisfied by choosing operating parameters on rational grounds. The separation of several million myeloma cells, much larger and faster sedimenting than mouse spleen cells, is accomplished with the retrieval factor predicted from theory when working conditions are based on the accurately measured sedimentation velocities. GLOSSARY a
outlet at top wall
a′
feed inlet
b
outlet at bottom wall
b′
inlet at bottom wall
b
channel breadth
Fa
particle number fraction exiting port a
Fb
particle number fraction exiting port b
ISP
inlet splitting plane
L
channel length
OSP
outlet splitting plane
Rs
resolution
U
field-induced velocity
Ua
sedimentation rate of particles to be collected at outlet a
Ub
sedimentation rate of particles to be collected at outlet b
V˙
total volumetric channel flow rate
Greek Characters
V˙ (a)
volumetric flow rate at outlet a
V˙ (a′)
∆V˙
volumetric flow rate of feed at inlet a′
volumetric flow rate of the stream lamina traversed during migration
σ
standard deviation
V˙ (b)
volumetric flow rate at outlet b
V˙ (b′)
volumetric flow rate at inlet b′
V˙ (t)
volumetric flow rate in the transport zone
w
channel thickness
wa
distance of the outlet splitting plane from the channel top wall
wa′
distance of the inlet splitting plane from the channel top wall
Received for review February 17, 2005. Accepted May 30, 2005.
z
distance along the channel
AC058013O
ACKNOWLEDGMENT M.-A.B. gratefully acknowledges partial support from M. Zborowski during her work at the Cleveland Clinic Foundation.
Analytical Chemistry, Vol. 77, No. 16, August 15, 2005
5301
