Magnetic levitation of single cells

Our cell densitometry platform, MagDense, is composed of (i) two permanent magnets (50-mm length, 2-mm width, and 5-mm height) with the same poles facing each other, (ii) a channel (1-mm × 1-mm cross-section, 50-mm length and 0.2-mm wall thickness) between these magnets, and (iii) tilted side mirrors to measure the levitation height of cells inside the channel using a microscope (Fig. 1A and SI Appendix, Fig. S1). Cells spiked in a nonionic paramagnetic medium (i.e., Gadavist, Gd) move away from the larger magnetic induction site (B) (i.e., close vicinity to the magnets) to the lower magnetic field induction site (i.e., away from the magnets) (SI Appendix, Fig. S2) owing to the difference between the magnetic susceptibilities of cells and their surrounding medium (Δχ = χ_c − χ_m) (Fig. 1B). When they reach equilibrium, cells are levitated inside the medium at a position where the magnetic force (F_mag) equals the buoyancy force (F_b) (Fig. 1B). The equilibrium height of a cell along the channel height is calculated based on magnetic induction values B (25–27) and can be derived by solving the following equation:The gravitational acceleration is represented by g, µ₀ defines the permeability of the free space, Δρ is the volumetric density difference between cell and paramagnetic medium (i.e., ρ_c − ρ_m), and x, y, and z are the coordinates of a cell. The magnetic susceptibilities of cells (28) are negligible compared with the magnetic susceptibility of the paramagnetic medium (29). Thus, cells are equilibrated at a unique levitation height mainly based on their density, independent of their volume. For instance, cells with the same density as the paramagnetic medium are equilibrated in the middle of the channel (i.e., z = 0) and cells with densities different from that of the medium are equilibrated above (if ρ_c < ρ_m) or below the middle of the channel (if ρ_c > ρ_m). In addition, cells are focused along the x axis toward the middle of the channel (Fig. 1C), where the magnetic induction strength is lowest (SI Appendix, Fig. S2). As the paramagnetic solution concentration and/or cell radius increases, cells come to an equilibrium position more rapidly (Fig. 1D and SI Appendix, Fig. S3). By inducing a high magnetic induction gradient (i.e., 600 T m⁻¹) (SI Appendix, Fig. S2) using permanent magnets along the channel height, cell densities can be measured at a nontoxic paramagnetic concentration (i.e., lower than 100 mM) (SI Appendix, Fig. S4). Furthermore, densities of cells along the 1-mm channel height can be measured with a tunable resolution and range simply by changing the concentration of the paramagnetic medium (Fig. 1E). Various cell types with different sizes down to submicrometer level can be analyzed without changing the design of the platform (SI Appendix, Fig. S5).

We validated this platform using polyethylene beads (Fig. 2 and SI Appendix, Fig. S6). Beads spiked in fetal bovine serum (FBS) with 30 mM Gd were introduced into the levitation channel. In less than 5 min, several thousand beads levitated in different heights based on their density (Fig. 2A). The levitation height of beads can be altered using different Gd concentrations (i.e., 10 mM, 30 mM, and 50 mM) (Fig. 2B). Fitting the resulting plot of density versus levitation height to a liner curve provides a standard function to measure densities of cells and particles. The resolution can be tuned from 1 × 10⁻⁴ g⋅mL⁻¹ to 5.5 ×10⁻⁴ g⋅mL⁻¹ within a density range of 0.74–1.30 g⋅mL⁻¹ by changing the Gd concentration from 10 mM to 50 mM (Fig. 2C and SI Appendix, Table S2). As expected, these experimental results matched with the theoretical simulations, allowing reference-free measurements. Further information on modeling and simulation results is provided in Materials and Methods.

To assess our ability to characterize cells, we levitated and measured the densities of various mammalian cells (Fig. 3). Breast adenocarcinoma (MDA-MB-231), esophageal adenocarcinoma (JHEsoAD1), colorectal adenocarcinoma (HT29), colorectal carcinoma (HCT116), and nonsmall cell lung adenocarcinoma (HCC827) cell lines as well as different blood cells (i.e., white and red blood cells) were levitated in FBS containing 30 mM paramagnetic Gd solution. Within a few minutes, different cancer cell types were equilibrated at unique levitation heights, forming distinct cell-specific density bands (Fig. 3A). In addition, densities of several hundred cells were rapidly measured individually, producing a dot plot of densities as a function of cell size (Fig. 3B and SI Appendix, Fig. S7). In the literature, density distributions of red and white blood cells are reported to be between 1.080–1.120 g⋅mL⁻¹ and 1.055–1.095 g⋅mL⁻¹, respectively (30, 31). As expected, the average density of red and white blood cells was measured as 1.109 and 1.088 g⋅mL⁻¹ using our platform (SI Appendix, Table S3). The ability to distinguish rare circulating tumor cells (CTCs) from whole blood can further the understanding of cancer metastasis and enhance the monitoring and treatment of cancer patients. Notably, cancer cell populations showed signatures clearly distinguishable from those of white and red blood cells within the MagDense platform. Even colorectal cancer cells from different origins showed distinct density profiles; HCT116 and HT29 cells had a density of 1.063 ± 0.007 g⋅mL⁻¹ and 1.084 ± 0.012 g⋅mL⁻¹, respectively. Furthermore, we observed heterogeneity within each seemingly homogenous cell population (SI Appendix, Table S3). Breast cancer is a heterogeneous disease with many biological features and clinical behaviors (32). In this respect, we observed that, among various cancer cell populations, the MDA-MB-231 cell line has the most heterogeneous cancer cell population with a density variance (σ²) of 0.0003 (g⋅mL⁻¹)². Thus, our levitation-based density profiling approach provides a simple method to investigate multiple cell types without using any labels or external energy sources.

We investigated dynamic changes in cellular levitation and density signatures under environmental stress conditions (Fig. 4). While cell death occurs, cells change in size, surface-to-volume ratio, and density (33). Under neutral pH conditions, we observed that levitation heights and density profiles of human breast cancer cells are stable during 1 h of exposure. We, however, observed significant changes when these cells were exposed to acidic conditions over 1-h exposure (Fig. 4A). Using fluorescent markers (i.e., calcein and propidium iodide) as a measure of cell viability, we observed that cells turned from green to red as they sank toward the bottom of the channel, indicating a dying cell (Fig. 4B and Movie S1). We observed that changes in density of 5% preceded the onset of changes in fluorescence. Moreover, we quantified cell heterogeneous responses to the microenvironment in real time (Fig. 4C and SI Appendix, Fig. S8). During acidic treatment in 30 mM Gd solution, we observed dynamic changes in levitation heights and cell densities, ranging from 1.05 g⋅mL⁻¹ to 1.15 g⋅mL⁻¹. Dead cells also yielded a more heterogeneous density profile than live cells with a variance of 0.0007 (g⋅mL⁻¹)² (SI Appendix, Fig. S9). Thus, characteristic cellular levitation and density profiles changed dynamically in response to variations in the environmental condition and each individual cell presented its response in a different manner and time scale.

Another interesting application enabled by our platform is the levitation profiling and density measurement of microorganisms subjected to different drug treatments. During antibiotic treatment, bacterial cells undergo many biological changes that alter cellular composition. For instance, channels or ion pumps are created to excrete antibiotics. In addition, bacteria change their protein expression profiles and create antimicrobial destroying enzymes, which lead to changes in cell mass and density (34). Here, we rapidly detected significant changes in levitation and density profiles of Escherichia coli after various antibiotic treatments (Fig. 5A). Untreated E. coli cells had an average density of 1.139 ± 0.016 g⋅mL⁻¹, which is consistent with the reported values for bacteria (SI Appendix, Table S3) (35). However, ciprofloxacin, a fluoroquinolone antibiotic that inhibits DNA gyrase and cell division (36), killed 60% of the bacterial population (SI Appendix, Fig. S10). This led to the formation of a subpopulation at the 1.2–1.3 g⋅mL⁻¹ density range, which is denser compared with the untreated controls. In addition, gentamicin, an aminoglycoside antibiotic that irreversibly binds to the 30S subunit of the ribosome and interrupts protein synthesis (37), killed 99% of the bacterial population (SI Appendix, Fig. S10) and increased the density of the population to 1.2–1.3 g⋅mL⁻¹. Thus, antibiotics with different mechanisms of action affect bacterial levitation and density profiles in a different manner.

We also applied our platform to yeast (Saccharomyces cerevisiae) (Fig. 5B). The density of the wild-type BY4743 strain from an asynchronous population was 1.119 ± 0.011 g⋅mL⁻¹, consistent with the values reported in the literature (SI Appendix, Table S3) (38, 39). We then treated wild-type yeast with 100 μM cantharidin or fluconazole. CRG1 gene expression provides resistance to cantharidin and, as expected, we did not observe significant changes in levitation and density profiles when comparing cantharidin-treated to untreated control cells (40). However, because the wild-type strain is sensitive to fluconazole (SI Appendix, Fig. S11), the levitation and density profiles significantly changed after overnight treatment. We also observed that upon drug treatment live and dead microorganisms have distinct density signatures (Fig. 5C). Hence, changes in cellular levitation height and density are correlated with the efficacy of a drug treatment. Drug resistance is a growing global healthcare problem and a significant challenge of our age (41, 42). There is significant need for point-of-care tools to distinguish resistant strains from nonresistant strains, especially for slow-growing species. Thus, this platform has the potential to rapidly test the efficacy of antimicrobial treatments and it can be used for antimicrobial susceptibility testing.

We have shown that our platform can characterize densities of both prokaryotic and eukaryotic cell types, including cancer and blood cells, as well as smaller cells, such as bacteria and yeast. Moreover, each cell has its own characteristic levitation and density profile that can be detected without using biomarkers, antibodies, or tags. The current platform enables single-cell density measurements of hundreds of cells within a few minutes using an automated, custom software. For various biological applications, analyses of higher numbers of cells in shorter time periods are required. For instance, flow cytometry methods can analyze 1,000–5,000 cells per second (43). Future generations of our technology can potentially continuously process cells in parallel channels, in which cells are flowed, levitated, and analyzed simultaneously. This would enable high-throughput analysis of thousands of cells and enable applications such as monitoring of CTCs. Moreover, cells at different levitation heights might be collected for downstream transcriptomic and proteomic analysis towards personalized and precision medicine. The simplicity, small size scale, and versatility of our platform design make the system compatible with mobile devices for telemedicine applications and offer an easy to setup and use system for biological or clinical laboratories. Future applications of this system, when implemented as an inexpensive, energy-free, label-free diagnostic device, might include utilizations in resource-constrained settings such as monitoring sickle cell disease (44).

MagDense consists of two N52-grade neodymium magnets (NdFeB) (50-mm length, 2-mm width, and 5-mm height), microcapillary channel (1-mm × 1-mm cross-section, 50-mm length, and 0.2-mm wall thickness) and mirrors (SI Appendix, Fig. S1). These parts were assembled using 1.5-mm-thick polymethyl methacrylate (PMMA) pieces that were cut with a laser system (VLS 2.30 Versa Laser) (45). Before each separate measurement, a microcapillary channel was plasma treated for 2 min at 100 W, 0.5 Torr (IoN 3 Tepla) and then placed between the magnets. Two mirrors were placed at 45° to image levitation heights using an inverted microscope (Zeiss Axio Observer Z1) under a 5× objective or 20× objective. The illumination of the microscope was aligned with respect to our platform mirror (i.e., left mirror shown in Fig. 1A, Inset).

MDA-MB-231, HCT116, HT29, HCC827, and JHEsoAD1 cells were cultured in DMEM supplemented with 10% FBS and 100 units⋅mL⁻¹ penicillin–streptomycin (Invitrogen Corp.). The cells were grown at 37 °C and 5% CO₂ in a humidified atmosphere. E. coli (DH5α strain) cells were hydrated and streaked for isolation on a Luria Bertani agar plate. Following growth, a single isolated colony was selected and inoculated in 3 mL of LB media. The bacteria culture was grown on an incubator shaker for 18 h at 37 °C, 250 rpm until it reached the stationary phase. The concentration of stock cultures was calculated as 10⁸ cfu⋅mL⁻¹. Wild-type BY4743 yeast cells were grown in yeast extract peptone dextrose medium at 30 °C.

Cells and particles were spiked in FBS with various Gd concentrations (10 mM, 30 mM, 50 mM, and 100 mM). Thirty microliters of sample was pipetted into the microcapillaries and the channel was sealed with Critoseal. The samples were levitated for 30 min until they reached their equilibrium heights within the system. For bacteria, the samples were levitated for 2 h. Then, levitation heights and radiuses of cells were imaged and analyzed with in-house developed MATLAB code.

During levitation, magnetic force (F_mag), buoyancy force (F_b), and drag forces (F_d) are induced on the cells:

Cells are levitated in the channel with F_mag (27):

where B is the magnetic induction, ∇ is the del operator, and m is the magnetic moment, which is calculated as

with V the volume of the cell, µ₀ the permeability of the free space (1.2566 × 10⁻⁶ kg⋅m⋅A⁻²⋅s⁻²) and Δχ the magnetic susceptibility difference between the cell and paramagnetic medium. B induced in the channel by opposing magnets is simulated using finite element method with COMSOL 4.0a (SI Appendix, Fig. S2). In these simulations, the residual magnetic induction (B_r) of magnets is assumed as 1.45 T according to the manufacturer data (K&J Magnetics).

During the levitation, cell gained velocity v and F_d is exerted on the cell. F_d is calculated for spherical object as follows (27):

where R is the radius of the cell, η is the dynamic viscosity of the paramagnetic medium, and f_D is the drag coefficient, which is equal to 1 when the cell is far away from the channel wall.

F_b is calculated as (25)

where g is the gravitational acceleration (9.8 ms⁻²), in z direction (Fig. 1) and ρ is the difference between the volumetric densities of the cell and the paramagnetic medium.

In the setup, cells are focused on the x = 0 plane where B_x = 0 with magnetic forces. However, the cell levitates in a certain height in z direction along x = 0 plane until magnetic and buoyancy forces come into balance:

where χ_m is the magnetic susceptibility of the paramagnetic medium, which is stronger than the cell’s magnetic susceptibility [e.g., χ_c of RBC is around 4 × 10⁻⁶ (28)], and molar magnetic susceptibility of gadolinium-based paramagnetic solutions is 3.2 × 10⁻⁴ M⁻¹ (29). As derived from Eq. 8, cell radius (or V) does not affect the levitation height.

Cell motions in the setup are simulated using above equations in a custom-coded MATLAB program integrated with the B values calculated in COMSOL (SI Appendix, Fig. S2). RBC parameters are chosen in these simulations, where R is 3.5 µm and density of cell (ρ_c) is 1.1 g⋅mL⁻¹ (46). For modeling, medium density (ρ_m) and viscosity (η) were chosen as 1.025 g⋅mL⁻¹ and 1.105 cP (47), respectively. As shown in Fig. 1C, cells starting in different positions ended at the same final point along x = 0.

The longest cell trajectory path, which is p_I to p_f in Fig. 1C, is chosen to calculate the necessary equilibrium time of cells with different radiuses (Fig. 1D). As the paramagnetic solution concentration and/or radius of the cell increases, cells come to the equilibrium position more rapidly. For instance, at 30 mM Gd concentration, cells with 3.5-µm radius (i.e., similar to RBC) are equilibrated in less than 30 min, whereas cells with 10-µm radius (i.e., similar to cancer cells) are equilibrated in less than 5 min. These simulation results also match with the experimental results presented in SI Appendix, Fig. S3.

Density profile along the channel is also simulated using different Gd concentrations (Fig. 1E). Using lower Gd concentrations increases the resolution of the density measurement. At the same time, it decreases the density range. All of the curves intersect at the middle of the channel (z = 0), where cells with the same density as the medium equilibrate. The density curves coming from simulation results show perfect correlation with the experimental results presented in SI Appendix, Fig. S5.

Thermal energy (E_T) can be effective on the cell, so Brownian motion can prevent the cell from levitating in the system. E_T is calculated as (48)

where k is the Boltzmann constant (1.3806488 × 10⁻²³ m2⋅kg^-2⋅K⁻¹) and T is the temperature of the medium. To levitate cells, E_T should be lower than the sum of the kinetic energy (E_k) induced by magnetism, and the potential energy (E_p) induced by buoyancy. As shown in SI Appendix, Fig. S5, a wide range of cellular radius sizes, down to the submicrometer level, can be levitated using a 30 mM Gd concentration. To increase this radius range further, E_k can be increased using higher Gd concentrations. Bacteria and yeast can also be levitated using our setup (Fig. 5), which enables analysis of different types of cells and organisms without changing the platform design.

Fluorescent polyethylene beads (Cospheric LLC) (10–100 μm in size) with different densities (1.025 ± 0.007 g⋅mL⁻¹, 1.030 ± 0.007 g⋅mL⁻¹, 1.044 ± 0.007 g⋅mL⁻¹, 1.064± 0.007 g⋅mL⁻¹, and 1.089 ± 0.007 g⋅mL⁻¹) were suspended in FBS with various magnetic susceptibilities (10 mM, 30 mM, and 50 mM paramagnetic Gd solution). Then, the beads were loaded into the microcapillaries and levitated (SI Appendix, Figs. S5 and S6). Fitting the resulting plot of density (grams per milliliter) versus levitation height (micrometers) to a linear curve provided a standard function to measure densities. Based on these curves, resolution and dynamic range of density measurements were calculated for different Gd concentrations (SI Appendix, Table S2).

Blood samples from healthy donors were obtained from Stanford University Blood Center. Whole blood samples were diluted at a 1:100,000 ratio in FBS in 30 mM Gd.

Whole blood was mixed with RBC lysis buffer at a 1:10 ratio. After 10 min of incubation, RBC were lysed and the blood sample was suspended at 200 × g for 3 min. The resulting WBC pellet was resuspended in FBS in 30 mM Gd.

MDA-MB-231, HCT116, HT29, JHEsoAD1, and HCC827 cells were centrifuged at 200 × g for 3 min at room temperature. Then, culture medium was removed and cells were resuspended in FBS with 30 mM Gd. With respect to the measurements, cellular density versus radius distribution profile of cancer cells and also blood cells are presented in Fig. 3B and SI Appendix, Fig. S7. During magnetic levitation, cells can come close to each other and start to form aggregates, where cell–cell interactions could change the cellular morphology under long culture conditions (>2 d) (49). However, we do not expect to see this effect during these experiments because diluted cell samples and shorter levitation times were used.

Overnight cultures of E. coli cells (DH5α strain) were diluted at a 1:10 ratio. Then, the resulting cell solutions were treated with different classes of antibiotics: 1 mg/mL of ciprofloxacin (fluoroquinolone antibiotic) and gentamicin (aminoglycoside antibiotic), respectively. After 2 h of antibiotic treatment, cells were levitated in 50 mM Gd, covering the E. coli density range [i.e., 1.06–1.19 g⋅mL⁻¹ (35)]. Corresponding OD graphs and levitation micrographs are presented in SI Appendix, Fig. S10.

Overnight cultures of the S. cerevisiae strain BY4743 were diluted at a 1:100 ratio. Then, the resulting cell solutions were treated with 100 μM cantharidin or fluconazole. Untreated cultures were used as controls. After overnight treatment, cells were suspended at 1,500 × g for 5 min at room temperature. Then, cell media was removed and cells were resuspended in PBS with 50 mM Gd. Levitation micrographs and OD graphs are presented in SI Appendix, Fig. S11.

MDA-MB-231 cells were suspended at 200 × g for 3 min. Then, the cell pellet was resuspended in 10 mM calcein in PBS. Cells were stained for 20 min at 37 °C. After staining, cells were suspended at 200 × g for 3 min and resuspended in FBS with 30 mM Gd, propidium iodide (PI), and 100 mM HCl solution. Then, cells were levitated for 90 min and imaged every 20 s (Movie S1). Cellular positions were analyzed using a MATLAB program developed in-house to monitor cellular trajectories (SI Appendix, Fig. S8). Cells that were resuspended in FBS with 30 mM Gd and PI were levitated as controls. To measure the final density of breast cancer cells treated with 100 mM HCl, the same experiment was repeated in 100 mM Gd spiked in FBS (SI Appendix, Fig. S9). The viability assay was also conducted for the control and 100 mM HCl-treated cells without using the densitometry platform and Gd (SI Appendix, Fig. S12).

JHEsoAD1 cells were used for viability experiments (SI Appendix, Fig. S4). They were cultivated in DMEM supplemented with 10% FBS and penicillin/streptomycin (0.1 mg/mL) in a humidified incubator at 37 °C and 5% CO₂. The cells were seeded at a starting concentration of 25 × 10³ cells/mL in a 48-well plate. The cells were exposed to different concentrations of Gd solution (0, 30, 50, and 100 mM). Culture medium was changed every 3 d. During each medium change, a fresh Gd solution was added. Live/dead assay was conducted using calcein/ethidium homodimer mixture to observe the viability of cells exposed to Gd during culturing. The cells were stained for 20 min, washed with PBS, and imaged under the fluorescence microscope. Cell viability was calculated from fluorescence images using ImageJ software. Proliferation profiles were observed using the cell counting method. Four different batches of cells were used on days 0, 1, 3, and 5 for the calculation of cell numbers.