High-throughput cell and spheroid mechanics in virtual fluidic channels

Abstract

Microfluidics by soft lithography has proven to be of key importance for biophysics and life science research. While being based on replicating structures of a master mold using benchtop devices, design modifications are time consuming and require sophisticated cleanroom equipment. Here, we introduce virtual fluidic channels as a flexible and robust alternative to microfluidic devices made by soft lithography. Virtual channels are liquid-bound fluidic systems that can be created in glass cuvettes and tailored in three dimensions within seconds for rheological studies on a wide size range of biological samples. We demonstrate that the liquid-liquid interface imposes a hydrodynamic stress on confined samples, and the resulting strain can be used to calculate rheological parameters from simple linear models. In proof-of-principle experiments, we perform high-throughput rheology inside a flow cytometer cuvette and show the Young's modulus of isolated cells exceeds the one of the corresponding tissue by one order of magnitude.

Fig. 1. Virtual fluidic channel inside microfluidic chip.

a Microfluidic chip as stitched microscopy image (upper half) and as the concentration plot of a finite element method (FEM) simulation of the full geometry (lower half). Arrows indicate inflow of 57 µM methylcellulose in PBS (MC, flow rate Q_sa = 48 nl s⁻¹) and 50 mM polyethylene glycol 8000 in PBS (PEG8000, flow rate Q_sh = 8 nl s⁻¹) forming a stable virtual fluidic channel between two liquid–liquid interfaces represented in dark gray (upper half) and in white (lower half). Scale bar is 50 µm. Top inset shows a bright-field image of the central constriction and the projected squared intensity gradient (arb. units) across the full channel width. Virtual channel width corresponds to distance w (white dashed lines) between the center of both intensity maxima. Scale bar is 10 µm. Bottom inset shows a cross-sectional view of the calculated (FEM) polymer concentration inside the channel. b Velocity profile (black circles) inside the center of the constriction derived from FEM simulations with the corresponding MC concentration distribution (blue solid line) used to identify the virtual channel width w. The red and the blue dashed lines indicate the parabolic flow profiles of the outer and inner aqueous phases. c Dynamic viscosities of sample and sheath solutions as a function of shear rate. Virtual channel formation is performed using MC as sample buffer (blue) and PEG as sheath buffer (dark red, orange, bright red). Data points are measured and for shear rates greater than 3000 s⁻¹ the shear-rate dependency is modeled as a power-law fluid (solid blue line) and as Newtonian fluid (solid orange and red lines). d Relative virtual channel width $\tilde{w}$ as a function of flow rate and viscosity ratios. The plot summarizes n = 146 experiments using different concentrations of MC, PEG8000 (PEG8K), and PEG40000 (PEG40K) for sample and sheath solution. The black curve is a solution to Eq. (1).

Fig. 2. Cell deformation in PDMS chip and virtual fluidic channel.

a Real-time deformability cytometry (RT-DC) of HL60 cells in polydimethylsiloxane (PDMS) channel yielding scatter plots of deformation versus cell size for control cells (left), dimethyl sulfoxide (DMSO) vehicle control (0.25% (v/v), center) and 1 µM CytoD (right). Measurements have been done at a total flow rate of 40 nl s⁻¹ in a PDMS chip with a 300 µm long channel and 20 µm × 20 µm squared cross-section using 57 µM MC for sample and sheath buffer, respectively. b RT-DC of HL60 cells in a virtual channel of 21 µm width and 30 µm height for control cells (left), DMSO vehicle control (0.25% (v/v), center) and 1 µM CytoD (right). Virtual channel is formed inside a PDMS chip with a 300 µm long channel and 30 µm × 30 µm squared cross-section using 57 µM MC (sample) as well as 50 mM PEG8000 (sheath). Measurements are taken at indicated position (Fig. 1a, gray rectangle) and a total flow rate of 94 nl s⁻¹ (Q_sa = 90 nl s⁻¹, Q_sh = 4 nl s⁻¹). Insets show representative cell images. c Time series of single HL60 cell passing a virtual channel (sample 57 µM MC, Q_sa = 72 nl s⁻¹, sheath 50 mM PEG8000, Q_sh = 8 nl s⁻¹). Average cell velocity within the channel is ~20 cm s⁻¹. Scale bar is 10 µm. Recording of time series has been repeated five times. Color in scatter plots indicates a linear density scale from min (blue) to max (red).

Fig. 3. Analysis of cytoskeletal alterations using virtual fluidic channels.

Statistical analysis using linear mixed models of three independent biological replicates for cell deformation (left), cell size (center) and Young’s modulus (right) inside a 20 µm × 20 µm PDMS chip (red) and 21 µm virtual fluidic channel inside a 30 µm × 30 µm PDMS chip (blue). Data compares control cells (n = 8024; PDMS and n = 4040; virtual channel), vehicle control (n = 8948; PDMS and n = 2778; virtual channel) as well as cells after treatment with 1 µM CytoD (n = 4148; PDMS and n = 1237; virtual channel). Data are presented as mean ± standard error of the mean (*p < 0.05; **p < 0.01; and ***p < 0.001).

Fig. 4. Virtual channel formation inside a flow cytometer glass cuvette.

a Technical drawing of glass cuvette and PDMS chip to scale for comparison. Arrows indicate length of constrictions of 2 cm for the cuvette and 300 µm for the PDMS device. b FEM simulations of concentration distribution for the cross-section of the cuvette performed for sample 114 µM MC at Q_sa = 200 nl s⁻¹ and sheath 5 mM PEG40000 at Q_sh = 1000 nl s⁻¹ yielding a 80 µm virtual channel (left). Arrows indicate the stress ${\sigma }_i$ due to the viscosity mismatch at the interface. Adjusting the flow rates to Q_sh = 50 nl s⁻¹ while keeping Q_sa constant, enables increasing the diameter of the constriction to 260 µm (right). c Representative image of a HL60 cell in a virtual channel of 88 µm diameter (sample 114 µM MC at Q_sa = 200 nl s⁻¹, sheath 5 mM PEG40000 at Q_sh = 1000 nl s⁻¹, top) and inside a virtual channel of 14 µm diameter (sample 114 µM MC at Q_sa = 15 nl s⁻¹, sheath 5 mM PEG40000 at Q_sh = 1000 nl s⁻¹, bottom). Projected line plots at top and bottom indicate the squared intensity gradient (arb. units) perpendicular to the flow direction while center between the maxima identify virtual channel interfaces (white dashed lines). Recording of cells and spheroids inside virtual channels has been repeated six times where a fluctuation in virtual channel size of 10% has been observed.

Fig. 5. High-throughput cell mechanics inside a flow cytometer glass cuvette.

a Fourier amplitudes of cellular shape modes for n = 25 HL60 cells inside a w = 88 µm (yellow) and w = 14 µm (green) virtual channel of a glass cuvette as well as n = 25 HL60 cells inside the virtual channel of PDMS chip shown in Fig. 2 (blue). The inset represents the total harmonic distortion calculated for the cells inside the virtual channel of a cuvette (green), a PDMS chip (blue) and a reference measurement (yellow). Data are presented as mean ± standard deviation. b Area strain of HL60 cells inside a w  = 14 µm virtual channel of a glass cuvette (Q_sa = 15 nl s⁻¹ and Q_sh = 1000 nl s⁻¹, top). Inset shows Young’s modulus distribution of HL60 cells calculated from area strain with ${\sigma }_{\mathrm{i}}$ = 78 Pa, shaded area indicates fraction of cells not confined by the virtual channel. Bottom graph compares the Young’s modulus of three independent biological replicates of HL60 cells (n = 2689), a DMSO vehicle control (0.25% (v/v); n = 3829), and HL60 cells treated with 1 µM CytoD (n = 3497). c Deformation of HL60 cells inside a w = 20 µm virtual channel of a glass cuvette (Q_sa = 20 nl s⁻¹ and Q_sh = 1000 nl s⁻¹, top). Inset shows Young’s modulus distribution of HL60 cells calculated from a hydrodynamic model considering shear- and normal stress on cell surface in steady-state. Bottom graph compares Young’s modulus of three independent biological replicates of HL60 cells (n = 19,018), a DMSO vehicle control (0.25% (v/v); n = 23,612) and HL60 cells treated with 1 µM CytoD (n = 15,245). Scale bar is 20 µm. Color in scatter plots indicates a linear density scale from min (blue) to max (red). Statistical data analysis is performed using linear mixed models and data are presented as mean ± standard error of the mean (*p < 0.05; **p < 0.01; ***p < 0.001).

Fig. 6. High-throughput cell and tissue mechanics inside glass cuvette.

a Bright-field images of HEK293T spheroids obtained at four subsequent days inside agarose mold. Initial seeding density is ∼30 cells per micro well (left). Exponential fit (solid line) to the mean cell number (black circles) per spheroid yields a doubling time of ~32 h. Time series has been recorded twice. Distribution of cell number per spheroid indicated in (c, center panel) is represented in blue box plot showing median (center line), 25 and 75 percentiles (lower and upper box bound) as well as 10 and 90 percentiles (whiskers). b Representative image of a HEK293T cell in virtual channel of 16 µm diameter (sample 114 µM MC at Q_sa = 20 nl s⁻¹, sheath 5 mM PEG40000 at Q_sh = 1000 nl s⁻¹, left). Corresponding scatter plots of area strain (center) and Young’s modulus (right) versus HEK293T cell size. Young’s modulus is calculated from area strain assuming an interfacial stress of 66 Pa. Shaded area indicates cells not confined inside the virtual channel. c Representative image of HEK293T spheroid in virtual channel of 190 µm width (sample 114 µM MC at Q_sa = 330 nl s⁻¹, sheath 5 mM PEG40000 at Q_sh = 200 nl s⁻¹, left). Projected line plots in (b) and (c) indicate the squared intensity gradient (arb. units) perpendicular to the flow direction while centers of the intensity maxima identify the virtual channel interfaces (dashed white lines). Corresponding scatter plots of deformation (center) and Young’s modulus (right) versus HEK293T spheroid size. Inset in right graph compares Young’s modulus of single cells (E = 0.79 ± 0.06 kPa) and spheroids (E = 84 ± 78 Pa) from three independent biological replicates consisting of n = 2433 single-cell and n = 762 spheroid measurements (p = 0.0003). Scale bar is 20 µm. Color in scatter plots indicates a linear density scale from min (blue) to max (red). Statistical data analysis is performed using linear mixed models and data are represented as mean ± standard error of the mean (***p < 0.001).