WO2019006188A1 - Quantitative deformability cytometry: rapid, calibrated measurements of cell mechanical properties - Google Patents

Abstract

Here we demonstrate rapid, calibrated, mechanical measurements of single cells using quantitative deformability cytometry (q-DC). Cells are driven to deform through micron-scale constrictions at rates of thousands of cells per minute by applying a pressure gradient across the microfluidic device. To obtain quantitative measurements of cell mechanotype, the time-dependent strain of individual cells is tracked and the applied stresses are calibrated using gel particles with well-defined elastic moduli. The q-DC platform enables rapid, calibrated mechanotyping, which should deepen our understanding of cells as materials. In various embodiments the mechanical measurements can be used to predict clinically or functionally relevant phenotypes such as invasion.

Description

QUANTITATIVE DEFORMABILITY CYTOMETRY: RAPID,

CALIBRATED MEASUREMENTS OF CELL MECHANICAL

PROPERTIES

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and benefit of USSN 62/527,411, filed

June 30, 2017, and to USSN 62/539,977, filed on August 1, 2017, both of which are incorporated herein by reference in their entirety for all purposes.

STATEMENT OF GOVERNMENTAL SUPPORT

[0002] This invention was made with Government support under DBI-1254185, awarded by the National Science Foundation. The Government has certain rights in the invention.

BACKGROUND

[0003] Eukaryotic cells are complex, viscoelastic materials that undergo chang their mechanical phenotype, or mechanotype, during many physiological and disease processes. For example, pluripotent stem cells become more resistant to deformation as they differentiate (Pajerowski et al. (2007) Proc. Natl. Acad. Sci. USA, 104: 15619-15624;

Maloney et al. (2010) Biophys. J. 99: 2479-2487; Engler et al. (2006) Cell, 126: 677-689; Chowdhury et al. (2010) Nat. Mater. 9: 82-88), and the deformability of cancer cells is associated with their invasive potential (Xu et al. (2012) PLoS One, 7: e46609; Qi et al. (2015) Sci. Rep. 5: 17595; Nguyen et al. (2016) Integr. Biol. 8: 1232-1245). Thus, cell mechanotype is emerging as a label-free biomarker for altered cell and pathological states. In addition, mechanotyping methods have demonstrated the potential for enhancing cancer diagnoses (Henry et al. (2013) Sci. Transl. Med. 5: 212ral63-212ral63) and enriching stem cell populations (Lee et al. (2014) Proc. Natl. Acad. Sci. USA, 111 : E4409-E4418). Rapid, calibrated measurements of cell viscoelastic properties could enable robust longitudinal and cross-study comparisons, and thus further advance the utility of cell mechanotyping.

[0004] Standardized measurements of cell mechanical properties, such as elastic modulus, E, compliance, J, or viscosity, η, are acquired by probing cells with well-defined stresses and measuring the resultant deformations. Such measurements can be achieved using atomic force microscopy (AFM) (Xu et al. (2012) PLoS One, 7: e46609; Rotsch & Radmacher (2000) Biophys. 7. 78: 520-535; Agus et al. (2013) Sci. Rep. 3 : 1449),

micropipette aspiration (Evans & Yeung (1989) Biophys. 7. 56: 151-160; Needham &

Hochmuth (1990) J. Biomech. Eng. 112: 269-276; Tsai et al. (1993) Biophys. 7 65: 2078- 2088), optical stretching (Maloney et al. (2010) Biophys. 7. 99: 2479-2487; Zhang & Liu (2008) J. R. Soc. Interface. 5: 671-690; Ekpenyong et al. (2012) PLoS One, 7(9): e45237; Guck et al. (2005) Biophys. 7. 88: 3689-3698), and microplate compression (Thoumine & Ott (1997) 7. Cell Sci. 110( Pt 1): 2109-2116; Caille et al. (2002) 7 Biomech. 35: 177-187), and can reveal physical principles that underlie cell mechanical properties, including viscoelastic and stress stiffening behaviors (Fabr et al. (2001) Phys. Rev. Lett. 87: 148102; Despra et al. (2005) Biophys. 7. 88: 2224-2233; Deng et al. (2006) Nat. Mater. 5: 636-640). Identifying such universal characteristics of cells can deepen our understanding of the role of

mechanotype in physiology and disease. Moreover, standardized measurements enable accurate longitudinal and cross-study comparisons (Agus et al. (2013) Sci. Rep. 3: 1449). However, measurements of mechanical moduli, for example, those obtained using AFM or micropipette aspiration, are typically acquired at rates of <1 cell/min. Higher throughputs are critical for measuring large numbers of single cells in clinical samples (23, 24) and elucidating the origins of phenotypic variability within a population.

[0005] Fluid-based deformability cytometry (DC) enables rapid single cell mechanotyping at faster rates of 10² - 10⁶ cells per minute. Such DC methods demonstrate the potential of mechanotype for varying applications such as classifying cells at different stages of the cell cycle by their distinct mechanical properties (Otto et al. (2015) Nat. Meth. 12: 199-202) and enhancing the accuracy of clinical diagnoses by mechanotyping pleural effusions (Henry et al. (2013) Sci. Transl. Med. 5: 212ral63-212ral63). In one DC method, the hydrodynamic forces of inertial flow deform cells on the microsecond timescale (Gossett et al. (2012) Proc. Natl. Acad. Sci. USA, 109: 7630-7635). While this method facilitates the analysis of large populations, the external stresses on single cells are challenging to model and calculate. In the real-time DC (rt-DC) method, the shear stresses of fluid flow induce cell deformations; as these shape changes are well described by a continuum elastic model (Mietke et al. (2015) Biophys. 7. 109: 2023-2036), E can be measured for single cells on millisecond to microsecond timescales (Otto et al. (2015) Nat. Meth. 12: 199-202). With the transit DC method, cells are driven to deform and transit through microfluidic constrictions on millisecond timescales (Ekpenyong et al. (2012) PLoS One, 7(9): e45237; Rosenblut et al. (2008) Lab Chip. 8: 1062-1070; Rowat et a/. (2013) 7 Biol. Chem. 288: 8610-8618; Hoelzle et al. (2014) J. Vis. Exp. 91 : e51474-e51474; Hou et al. (2009) Biomed. Microdevices. 11 : 557-564; Lange et al. (2015) Biophys. J. 109: 26-34; Byun et al. (2013) Proc. Natl. Acad. Sci. USA, 110: 7580-7585; Shaw Bagnall et al. (2015) Sci. Rep. 5: 18542; Lange et al. (2017) Biophys. J. 1 12: 1472-1480). The time required for cells to transit through microfluidic constrictions can depend on cell size, mechanical properties, and surface properties, but the initial deformation into microfluidic constrictions is dominated by cell deformability (Byun et al. (2013) Proc. Natl. Acad. Sci. USA, 110: 7580-7585; Shaw Bagnall et al. (2015) Sci. Rep. 5: 18542; Nyberg et al. (2016) Lab Chip, 16: 3330-3339); cells and particles that have a higher E exhibit longer deformation timescales (Ekpenyong et al. (2012) PLoS One, 7(9): e45237; Nyberg et al. (2016) Lab Chip, 16: 3330-3339; Chan et al. (2015) Biophys. J. 108: 1856-1869). Such transit experiments are widely used to mechanotype various cell types from breast cancer cells to neutrophils based on relative deformation timescales (Rosenblut et al. (2008) Lab Chip. 8: 1062-1070; Hou et al. (2009) Biomed. Microdevices. 11 : 557-564). The average E of a population can be determined by driving cells through microfluidic constrictions with a range of pressures and fitting a viscoelastic model to the resultant strain and transit time data for thousands of cells (Lange et al. (2015) Biophys. J. 109: 26-34; Lange et al. (2017) Biophys. J. 112: 1472-1480). However, single cell analysis is critical for characterizing population heterogeneity (Ca et al. (2013) Biophys. J. 105: 1093-1102).

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Figures 1 A and IB, illustrate an embodiment of a device suitable for quantitative deformability cytometry (q-DC), e.g., as described by Hoelzle et al. (2014) J. Vis. Exp., 91 : 51474. Fig. 1A shows a schematic illustration of one embodiment of an experimental setup showing illustrative peripheral connections. Fig. IB shows that in the illustrated embodiment the device design has 4 functional regions: entry port, cell filter, constriction array, and exit port. Architecture of the microfluidic device showing its main features; inset shows a transmitted light image of the constricted channels. Scale, 10 μπι.

[0007] Figure 2, panels A-E, illustrates cell shape changes during transit through microfluidic constrictions. Panel A: Schematic of a single cell transiting through a micron- scale constriction by pressure-driven flow where AP is the pressure drop across the cell. Cell shape is evaluated by measuring circularity, C(f) = 4nA(t)IP(tf, during transit, and the time- dependent strain, c(t), is defined as 1 - C(t). Panel B: Time sequence of a representative HL- 60 cell transiting through a microfluidic constriction that exhibits the median transit time and cell size of the cell population. The white border illustrates the cell boundary, as detected by our imaging algorithm. Color overlay illustrates the change in circularity, C, during deformation. Scale, 15 μιη. Panels C-D: Timescale and shape change during transit through a microfluidic constriction. The x-axis represents the position of the centroid of the cell. We extract (panel C) transit time, which is the time required for the leading edge of the cell to enter and exit the constriction region; and (panel D) time-dependent strain or creep, which is determined by the changes in shape (circularity) of the cell as it deforms into the pore. The creep time begins when the leading edge of the cell enters the constriction; it ends when the centroid exits the constriction, as illustrated by the dashed lines. Panel E: Creep trajectories for the population of HL-60 cells (N = 550). The gray dotted lines represent data from individual cells. The solid gray line represents the creep trajectory of the representative HL- 60 cell.

[0008] Figure 3, panels A-B, illustrates stress calibration using agarose gel particles.

Panel A: Elastic moduli of gel particles made with varying concentrations of agarose from 1.0 - 3.0% (w/w) as measured by AFM. Data represent average ± standard deviation for N = 12 - 53 particles over two independent experiments. Panel B: Agarose calibration particles are used to determine the applied stresses in the q-DC device by measuring the minimum threshold pressure Pthreshoid required to induce a critical strain ecritical for a particle to deform through a constricted channel. Shown here is representative data for N > 140 particles transiting through a 5 μπι x 5 μπι channel. X-error bars represent the standard deviation of the elastic modulus as in Fig. 3 A. Y-error bars represent the standard deviation of the threshold pressure-to-particle strain ratio. The red line is the linear fit determined by the Deming method. The shaded region illustrates the 95% confidence interval of the fit. The inverse of the slope characterizes the calibration factor, A.

[0009] Figure 4, panels A-D, illustrates power law rheology for cell mechanotyping by q-DC. Panel A: Creep trajectory for a single, representative HL-60 cell (gray dots). Lines represent the least-squares fits of viscoelastic models to the creep data: Maxwell (red dotted line); Kelvin- Voigt (KV, purple long-dashed line); standard linear solid (SLS, blue dot- dashed line); and power law rheology (PLR, green short-dashed line). Panel B: Residuals for the least-squares fits of the viscoelastic models to the creep trajectories of a population of HL-60 cells (N = 550), as shown in Fig. 2, panel E. Shown here are the bootstrapped median residuals; error bars represent the bootstrapped confidence interval. *p < 0.05, ***p « 0.001. Panels C-D: Heat maps show the (panel C) apparent elastic modulus, E_a, and (panel D) fluidity, β, of HL-60 cells as a function of transit time, T_T, and cell diameter, D_cell, which is measured in the microfluidic channel before the cell enters the constriction. Each bin represents the median E_a or β of N = 3 - 47 single cells.

[0010] Figure 5, panels A-C, shows that the mechanotype of HL-60 cells depends on applied pressure and cell-to-pore size ratio. Panel A: Density scatter plots show apparent elastic modulus E_a as a function of cell size. The cell diameter D_cell is measured in the microfluidic channel before the cell enters the constriction. Data represents the deformation response for HL-60 cells that are driven to deform through 5 μιη x 10 μιη constrictions with increasing applied pressure. The calibrated applied stress is marked on the bottom right corner of each panel. Dots represent single cell data. Color represents the density of data points. Cell size measured by q-DC increases with applied pressure, as there is a higher probability that larger cells will transit at higher pressures; at lower pressures, larger cells have a higher probability of occluding constrictions. To compare data sets, we bin cells by the median cell diameter, as indicated by the gray dashed line; the resultant size-binned data is shown in the boxplots. Panel B: Density scatter plot illustrates elastic modulus E_a as a function of cell size for HL-60 cells deforming through 9 μιη x 10 μιη constrictions. Panel C: Boxplots show the size-gated distributions of Ea for HL-60 cells with D_cell = 16 ± 1 μιη. Cells are subject to varying applied stresses, σ , and constriction geometries: white lines represent the median, boxes represent the interquartile ranges, whiskers represent the 10th and 90th percentiles, and white squares represent the bootstrapped median. N > 200 for each cell type. Statistical significance is determined using the Mann-Whitney U test: *p < 0.05, **p < 0.01, ***p < 0.001.

[0011] Figure 6, panels A-B, illustrates mechanotyping of HL-60 cells treated with cytoskeletal-perturbing drugs using q-DC. HL-60 cells are treated with blebbistatin (Bleb), cytochalasin D (CytoD), and jasplakinolide (Jasp). Panel A: Density scatter plots show apparent elastic modulus Ea and fluidity β as functions of cell size, which is measured in the microfluidic channel before the cell enters the constriction. The cell diameter shown here is larger than the actual cell diameter (Fig. 15, panel A) as cells are confined when flowing through the microfluidic device with 5 μπι height. Each dot represents a single cell. Color represents the density of data points. To compare data sets, we bin cells by size, as depicted by the gray dotted lines. Cell size distributions are shown in Fig. 15. Cell size measured by q-DC in these 5 μm-height devices is larger than cell size in the 10 μm-height devices (Fig 5), due to the axial compression that occurs when the device height is smaller than the cell diameter. Panel B: Boxplots represent the size-binned distributions of E_a and β for cells with D_ceii = 21 ± 1 μιη, white lines represent the median, boxes represent the interquartile ranges, whiskers represent the 10th and 90th percentiles, and white squares represent the

bootstrapped median. N > 500 for each cell type. Statistical significance is determined using the Mann-Whitney U test: *p < 0.05, **p < 0.01, ***p < 0.001. [0012] Figure 7, panels A-B illustrates mechanotyping of human breast cancer cell lines using q-DC. Panel A: Density scatter plots show E_a ^-1 and β as functions of cell size for MCF-7 and MDA-231 cell lines. Color represents the density of data points. To compare cell populations, we bin data by cell size, as depicted by the grey dotted lines. Cell diameter is measured in the microfluidic channel before the cell enters the constriction. Panel B: Boxplots represent the size-binned distributions of E_a and β for cells with D_ceii = 21 ± 1 μπι. White lines represent the median. Boxes denote the interquartile ranges and whiskers denote the 10th - 90th percentiles. White squares represent the bootstrapped medians. N > 100 for each cell type. The Mann-Whitney U test is used to determine statistical significance: *p < 0.05, **p < 0.01, ***p < 0.001. [0013] Figure 8, panels A-B, shows agarose calibration particles exhibit size- independent elastic moduli. Panel A: Elastic modulus of particles composed of 1.5% (w/w) agarose as a function of particle diameter as measured by AFM. Data represents the mean ± standard deviation for each particle probed 2-5 times. The red dotted line illustrates the average elastic modulus. Data collected over two independent experiments (N = 15). Panel B: Distribution of diameters for particles composed of 1.5% (w/w) agarose as they transit through 5 μπι x 5 μπι constrictions. The 50th - 100th percentile of sizes are considered to determine the median maximum strain at the threshold pressure conditions as depicted by the red bars (N = 220).

[0014] Figure 9, panels A-B, shows the effects of surfactant on cell mechanotyping. Apparent elastic modulus E_a (panel A) and fluidity (panel B) β values of HL-60 cells treated with pluronic F-127 during transit through microfluidic constrictions. White lines represent the median E_a and β. Boxes represent the interquartile ranges and whiskers represent the 10th - 90th percentiles (N > 500). The Mann-Whitney U test is used to evaluate statistical significance, n.s. denotes p > 0.05. [0015] Figure 10 shows the residuals of PLR creep fit depends on frame number.

Scatter plot of the residuals per frame for HL-60 cells. The gray dots represent the residuals for individual cells. The triangles illustrate the median residual for each number of frames. The error bars represent the interquartile range. N = 550. There exists a trade-off between the quality of PLR fitting and the dynamic range of q-DC. By minimizing the required number of frames for creep trajectories, the dynamic range extends to sample longer deformation timescales within a population of cells. [0016] Figure 11, panels A-B, shows the threshold transit conditions for

characterizing applied stress in microfluidic constrictions. Threshold applied pressures in the (panel A) 5 μπι x 10 μπι and (panel B) 9 μπι x 10 μπι microfluidic device geometries for calibration particles with a range of elastic moduli, 0.6 - 2.4 kPa. X-error bars represent the standard deviation of the elastic modulus as determined by AFM. Y-error bars represent the standard deviation of the pressure-to-particle strain ratio. The red line is the linear fit; the red shaded region illustrates the 95% confidence interval of the linear fit. The inverse of the slope characterizes the applied pressure-to-stress scaling factor. N > 650 for strain measurements at each threshold condition.

[0017] Figure 12, panels A-B, illustrates a power law exponent for oil particles. Panel A: Validation of power law rheology using oil-in-water emulsion droplets made with silicone oils of varying viscosities. Power law exponents, β, for oil droplets calculated by the least-squares fit of deformation trajectories with power law rheology model. Density scatter plots represent β as a function of droplet size. Each dot represents a single cell. Color represents the density of points. White diamonds show the highest density of points. N > 500 oil droplets. Panel B: Bootstrapped median values of β for droplets of silicone oils. Error bars denote the bootstrapped confidence intervals.

[0018] Figure 13, panels A-C, illustrates numerical simulations of single cells deforming through a constriction. Panel A: Simulation of a cell deforming through a micron- scale constriction. Shown here is a representative cell with a diameter of 16.3 μπι transiting through a constriction with a width of 8.1 μπι; the cell-to-pore size ratio is 2. The red arrows represent the flow vector field. Panels B-C: The total hydrodynamic stress (panel B) and normal stress (panel C) acting on a cell as it transits through a constriction; cell-to-pore size ratio is 1. When the cell is transiently occluding the pore, there are positive normal forces that deform the cell. As the transiting cell continually deforms through the constriction, there is also a drop in hydrodynamic force: according to Stokes' law, the hydrodynamic force is proportional to the cell velocity and thus a decrease in the cell velocity leads to a decrease in the hydrodynamic force. The black dotted line represents the baseline hydrodynamic stress acting on the cell before it reaches the constriction. [0019] Figure 14 provides a graphic representation of shape changes in cells with a range of sizes during transit through a microfluidic constriction. Cell-to-pore size ratio is determined by the ratio between the unconstrained cell diameter and the width of the constriction, where the unconstrained cell diameter is calculated as the diameter of a perfect circle with an area of the cell's projected area.

[0020] Figure 15, panels A-B, shows the size distributions of HL-60 cells treated with cytoskeletal-perturbing drugs and breast cancer cell lines. Box plots represent the cell diameters as determined by bright field imaging during q-DC measurements. White lines represent the median, boxes represent the interquartile ranges, whiskers represent the 10th and 90th percentiles, and white squares represent the bootstrapped median.

[0021] Figure 16, panels A-B, illustrates cell and nuclear size in HL-60 cells. Scatter plots of (panel A) nuclear diameter versus cell diameter and (panel B) nuclear-to-cell area ratio versus cell diameter for HL-60 cells. Cells are stained with Hoechst and Calcein AM; thereafter, samples are imaged via confocal microscopy. Each point represents data for a single cell. Black dotted line shows linear fit to the data.

[0022] Figure 17, panels A-E, illustrates an overview of cell physical phenotyping by quantitative deformability cytometry (q-DC). Panel A: Image of q-DC microfluidic device mounted on a glass coverslip next to an American penny for scale. Scale, 19 mm. Panel B: Schematic overview of physical phenotyping by q-DC. By deforming cells through microfluidic constrictions, we obtain measurements of elastic modulus E, cell fluidity β, transit time T_T, entry time T_E, cell size D_ceu, and maximum strain £_maxior individual cells. Panel C: A representative cell deforming through a microfluidic channel of the q-DC device. Entry time T_E is the time required for a cell to reach maximum strain e_max; transit time T_T is the time required for the cell to transit through the constriction. Scale bar, 20 μηι. Panel D: Black dots represent the strain of the single cell shown in panel C as a function of time. Red solid line represents power law fit to single-cell strain trajectory over the entry timescale, T_E. Using power law rheology, we extract elastic modulus, E, and fluidity exponent, β. Panel E: Representative scatter plot of E and D_ceii for human pancreatic ductal epithelial (FIPDE) cells. Each dot represents a single cell and color denotes number density. Shown here are a total of N = 3231 cells.

[0023] Figure 18, panels A-D, illustrates the predictive power of q-DC outputs for cell classification. Panel A: Accuracy of k-nearest neighbor machine learning algorithm for classifying human pancreatic cell lines. Each bar represents the accuracy of models built with varying combinations of q-DC predictors as indicated by the colored dots; grey dots represent excluded predictors. Orange bars and dots represent the highest accuracy that can be achieved with a set of one, two, three, and four physical phenotypes. Turquoise bars and dots show accuracy obtained by all other combinations of physical phenotypes. Asterisk shows the reduced set of predictors that provides the greatest accuracy with the least number of parameters. White numbers show the accuracy, which is calculated as the percentage of data subsets that are correctly identified as one of the five pancreatic cell lines. Panel B: Scatter plot of training and test sets for a single, representative cross-validation step. Data is shown in a visual interactive stochastic neighbor embedding (viS E) scatter plot (Kim et al. (2016) J. Cell Sci. 129(24): 4563-4575; Krijthe & van der Maaten (2017) T-Distributed Stochastic Neighbor Embedding using a Barnes-Hut Implementation [Internet]. Vienna, Austria: R Foundation for Statistical Computing; Available from:

//github.com/jkrijthe/Rtsne), which projects the reduced set {E, T_T, D_ceii, £max) data onto a 2D vector space. Transparent markers illustrate the data used in the training set. Opaque markers represent the test set. Circles show samples that are correctly identified (true). Triangles represent samples that are incorrectly classified (false). See Fig. 25 for more detailed representation of the incorrectly classified samples, where the internal color of the triangle represents the true identity and the external color represents the false identity. Panels C-D: Confusion matrices show the performance of the k-NN algorithm for (panel C) transit time T_T, and (panel D) reduced set of q-DC predictors: elastic modulus E, transit time T_T, cell size D_ceii, and maximum strain e_max. Rows represent the true cell line; columns represent the predicted cell line. Color scale denotes the proportion of cells predicted as each cell type.

[0024] Figure 19, panels A-D, shows q-DC parameters as predictors of invasion across cancer cell types. Panel A: Schematic illustration the reduced set of physical phenotypes, which we use to predict cell invasion, elastic modulus E, transit time T_T, cell size D_ceii, and maximum strain e_max, as measured using 3D invasion assay. Panel B : Plots showing invasion versus single physical phenotypes for pancreatic adenocarcinoma (PDAC) cell lines (blue circles) and ovarian cancer (HEYA8) cells that overexpress a panel of tumor suppressor microRNAs (red triangles). Each data point represents the median value for a cell sample. Error bars represent standard deviation. Dashed lines show best linear fits. Panel C:

Correlation between measured and predicted invasion using the physical phenotype model for invasion. Dashed lines show best linear fit for the microRNA-overexpressing cells. Data points represent the average value for a cell sample. Error bars represent standard deviation. Panel D: The strength of correlations between measured and predicted invasion from linear regression models built with combinations of physical phenotypes for microRNA- overexpressing ovarian cancer cells. Colored circles illustrate the set of predictors used in the model. Bars represent adjusted-R² (R_adj ²) values, which reflect the average strength of the correlation, while accounting for the number of fitting parameters to data points. Error bars represent standard deviation.

[0025] Figure 20, panels A-F, illustrates the prediction of invasion by multiparameter physical phenotyping. Panels A-C) The four key physical phenotypes that comprise the reduced set for: (panel A) breast cancer cells, MCF-7, MDA-MB-468, and MDA-MB-231; (panel B) ovarian cancer cells, OVCA433-GFP control, and OVCA433 that overexpresses Snail (OVCA433-Snail), a key transcription factor in epithelial-to-mesenchymal transition (EMT); (panel C) Highly metastatic human breast cancer (MDA-MB-231-HM) cells with activation of β-adrenergic signaling by treatment with 100 nM isoproterenol (+ISO) or vehicle (Control) for 24 h. N > 400. Panels D-F: Average predicted invasion as determined by the physical phenotyping model for invasion. Error bars represent the standard deviation. Colors represent previously determined invasive potentials, as described in literature (see, e.g., Kim et al. (2016) J. Cell Sci. 129(24): 4563-4575; Gordon et al. (2003) Int. J. Cancer. 106(1): 8-16; Albini et al. (1987) Cancer Res. 47(12): 3239-3245; Sheridan et al. (2006) Breast Cancer Res. 8(5): R59; Chekhun et al. (2013) Exp. Oncol. Ukraine 35(3): 174-179).

[0026] Figure 21, panels A-B, illustrates a cell classification training flowchart. Panel

A: Training of the cell classification algorithm from data input to model output. Panel B: Flow chart of k-nearest neighbors machine learning algorithm where k=10.

[0027] Figure 22 illustrates a cross-correlation analysis. Spearman's rank correlation coefficients for pairs of q-DC outputs: elastic modulus E, cell fluidity β, transit time T_T, entry time T_E, cell size D_ceii, and maximum strain c_max. Color represents the magnitude of the correlation coefficient, r, as detailed in Table 7. Gray 'X' denotes not statistically significant (n.s.).

[0028] Figure 23 shows that sets of q-DC predictors alter the accuracy of cell classification algorithms. Bars show the accuracy of classification algorithms that are built using varying sets of q-DC predictors; white text denotes the numeric values of accuracy. [0029] Figure 24 shows the correlation between experimental and predicted invasion of PDAC cells using physical phenotyping. R² and adjusted R² (R_adj ²) values of physical phenotyping models of invasion, which use varying sets of parameters. Blue bars represent R² values; navy blue bars represent R_adj ² values, which reflect goodness of fit, while accounting for the number of parameters to data points. Colored circles illustrate the set of predictors.

[0030] Figure 25. False positives in q-DC classification test set. As shown in Fig.

18, panel B, scatter plot illustrates the training and test sets for a single, representative cross- validation step. Data is shown in a visual interactive stochastic neighbor embedding (viS E) scatter plot ( Otto et al. (2015) Nat. Meth. 12(3): 199-202; Darling & Guilak (2008) Tissue Eng. Part A. 14(9): 1507-1515), which projects the reduced set {E, T_T, D_ceu, c_max} data onto a 2D vector space. Transparent markers illustrate the data used in the training set. Opaque markers represent the test set. Circles show samples that are correctly identified. Triangles represent samples that are incorrectly classified where the internal color represents the true identity and the external color represents the false identity. Regions with incorrectly classified cell samples are magnified for better visualization of the marker colors.

DETAILED DESCRIPTION

[0031] Advances in methods that determine cell mechanical phenotype, or mechanotype, have demonstrated the utility of biophysical markers in clinical and research applications, ranging from cancer diagnosis to stem cell enrichment. Here, we introduce quantitative deformability cytometry (q-DC), a method for rapid, calibrated, single cell mechanotyping. We track changes in cell shape as cells deform into microfluidic

constrictions, and calibrate the mechanical stresses using gel beads. We observe the time- dependent strain follows power law rheology, enabling single cell measurements of apparent elastic modulus, E_a, and power law exponent, β. To validate our method, we mechanotype human promyelocytic leukemia (HL-60) cells, and thereby confirm q-DC measurements of E_a = 0.53 ± 0.04 kPa. We also demonstrate q-DC is sensitive to pharmacological

perturbations of the cytoskeleton, as well as differences in the mechanotype of human breast cancer cell lines (E_a = 2.1 ± 0.1 and 0.80 ± 0.19 kPa for MCF-7 and MDA-MB-231 cells). To establish an operational framework for q-DC, we investigate the effects of applied stress and cell-to-pore-size ratio on mechanotype measurements. We show that E_a increases with applied stress, which is consistent with stress stiffening behavior of cells. We also find that E_a increases for larger cell-to-pore size ratios, even when the same applied stress is maintained; these results indicate strain stiffening and/or the dependence of mechanotype on deformation depth. Taken together, the calibrated measurements enabled by q-DC should advance applications of cell mechanotype in basic research and clinical settings.

[0032] The physical properties of cells, such as cell deformability, are promising label-free biomarkers for cancer diagnosis and prognosis. As described in Example 2, we have investigated the physical phenotypes that best distinguish human cancer cell lines, and the relationship of these parameters to cell invasion. We use the microfluidic-based method, quantitative deformability cytometry (q-DC) (see, e.g., Figures 1A and IB), to rapidly measure 6 different physical phenotypes of populations of single cells including elastic modulus E, cell fluidity β, transit time T_T, creep time 7c, cell size D_ceii, and maximum strain emax at rates of 10² cells/s. By training a simple k-nearest neighbor machine learning algorithm, we demonstrate that elastic modulus E, transit time T_T, cell size 7J_ce¾ and e_max enable classification of pancreatic cancer cell lines (MIA PaCa-2, PANC1, AsPC-1, and Hs766) as well as a pancreatic epithelial cell line (HPDE) with 96% accuracy, which is 31% higher than the highest accuracy achieved by a single parameter alone. We also identify the physical phenotypes that are the strongest indicators of cell invasion. E is the single parameter that is most highly correlated with invasion of pancreatic cell lines as measured by a 3D scratch wound invasion assay. We also investigate human ovarian cancer (HEYA8) cells, which overexpress a panel of tumor suppressor microRNAs; both E and D_ceii are moderately correlated with invasion of these microRNA-overexpressing cells, but alone are not sufficient to predict invasion. However, multiple linear regression using the set of 4 physical phenotypes, E, T_T, D_ceii, and c_max yields invasion values that are highly correlated to our experimental results. We then physically phenotype seven additional breast and ovarian cancer cell samples, and determine that our multiparameter approach successfully ranks the invasive potential of five out of seven cancer cell lines. Our results highlight how physical phenotyping of single cells coupled with machine learning algorithms can provide a complementary method to predict the invasive behavior of cancer cells.

EXAMPLES

[0033] The following examples are offered to illustrate, but not to limit the claimed invention. Example 1

Quantitative Deformability Cytometry (q-DC): rapid measurements of single cell viscoelastic properties

[0034] Here we demonstrate rapid, calibrated, mechanical measurements of single cells using quantitative deformability cytometry (q-DC). We drive cells to deform through micron-scale constrictions at rates of thousands of cells per minute by applying a pressure gradient across the microfluidic device (Hoelzle et al. (2014) J. Vis. Exp. 91 : e51474- e51474). To obtain quantitative measurements of cell mechanotype, we track the time- dependent strain of individual cells and calibrate the applied stresses using gel particles with well-defined elastic moduli. Our results show that the deformation response of single cells follows power law rheology (PLR), which enables us to determine an apparent elastic modulus, E_a, and power law exponent, β or fluidity, for single cells. We validate our q-DC method by measuring E_a and β for human promyelocytic leukemia (HL-60) cells. We find that E_a increases with cell strain and applied stress on these time and length scales. We also demonstrate that q-DC is sensitive to changes in HL-60 mechanotype following treatment with cytoskeletal-perturbing drugs. Differences in the mechanotype between human breast cancer cell lines, MCF-7 and MDA-MB-231 cells, can also be detected. Taken together, the q-DC platform enables rapid, calibrated mechanotyping, which should deepen our understanding of cells as materials. Materials and Methods.

Cell culture.

[0035] Cells are cultured at 37°C with 5% C0₂. Cell media and L-Glutamine are from Life Technologies, Carlsbad, CA, USA; fetal bovine serum (FBS) and penicillin- streptomycin are from Gemini BioProducts, West Sacramento, CA, USA. Human promyelocytic leukemia (HL-60) cells are cultured in RPMI-1640 medium with L-

Glutamine, 10% FBS, and 1% penicillin-streptomycin. To perturb the cytoskeleton, cells are treated for 1 hr with: 2 μΜ cytochalasin D (Santa Cruz Biotechnology, Santa Cruz, CA, USA), 100 μΜ blebbistatin (Santa Cruz Biotechnology, Santa Cruz, CA, USA), and 100 nM jasplakinolide (Life Technologies, Carlsbad, CA, USA). Cell viability is determined using trypan blue staining {see, Table 1). Human breast cancer cell lines, MCF-7 and MDA-MB- 231, are cultured in high glucose, L-glutamine, sodium pyruvate Dulbecco's Modified Eagle Medium (DMEM) medium with 10% fetal bovine serum and 1% penicillin-streptomycin. The human promyelocytic leukemia (HL-60) cells and human breast cancer cell lines (MCF- 7 and MDA-MB-231) are from the American Type Culture Collection (ATCC). The identity of each cell line is confirmed using multiplex short tandem repeat (STR) profiling (Laragen Inc., Culver City, CA, USA). Table 1. Viability of HL-60 cells after pharmacological perturbations. Cell viability is determined using a Trypan blue assay

Fabrication of calibration particles.

[0036] Silicone oil droplets and gel particles are fabricated using methods previously described (Nyberg et al. (2016) Lab Chip, 16: 3330-3339). In brief, silicone oil droplets are formed by generating oil-in-water emulsions where the dynamic viscosity of the silicone oil varies from 10^"2 to 10¹ Pas (Sigma- Aldrich, St. Louis, MO, USA). Deionized (DI) water with silicone oil (1 :5 v/v) and 4% (w/v) Tween 20 surfactant (Sigma-Aldrich, St. Louis, MO, USA) are vortexed for 1 minute. The concentration of Tween 20 is significantly larger than the critical micelle concentration of 0.01% (w/v), such that the droplet surface is saturated with surfactant and the droplets are effectively stabilized while transiting through the microfluidic device. Prior to transit experiments, the emulsion is centrifuged at 157 x g for 3 minutes to remove air bubbles and filtered through a 35 μπι mesh filter (BD Biosciences, Franklin Lakes, NJ, USA) to create a size distribution of droplets that is similar to cells (Id.). To further ensure droplet stability during transit through the microfluidic devices,

experiments are conducted within one hour after plasma treatment to maintain hydrophilic surface properties. Channels are also filled with DI water 5 min after plasma treatment to reduce hydrophobic recovery.

[0037] To fabricate agarose microgels, water-in-oil emulsions are generated, such that the aqueous phase contains the desired w/w percentage of low gelling temperature agarose (#A4018-5G, Sigma-Aldrich, St. Louis, MO, USA). The agarose/DI water mixture is heated to 90°C on a heating block for 10 minutes until the agarose is fully dissolved. The liquid agarose solution is then vortexed with mineral oil (1 :5 v/v) together with 1% w/w Span 80 for 30 seconds. After filtering the resultant emulsion through a 35 μπι mesh filter (BD

Biosciences, Franklin Lakes, NT, USA), the sample is immediately placed on ice for 1 hour to promote gelation and then stored in 4°C overnight. Thereafter, the microgels are removed from the oil phase by adding 5 mL of DI water and centrifuging at 157 x g for 10 minutes. To increase the yield, the samples are shaken vigorously after being removed from the centrifuge and spun down three more times removing the oil from the top of the solution by pipetting. Washing steps are repeated three times to ensure sufficient separation of the water and oil phases. The suspension is filtered one last time through a 35 μπι mesh filter.

Young's modulus characterization of agarose calibration particles.

[0038] To determine the elastic modulus of microgels with varying compositions of agarose from 1 to 3% (w/w), particles are indented using an AFM (MFP 3D-BIO system, Asylum Research, Goleta, CA, USA) that is mounted on an inverted microscope (Nikon Ti- E, Tokyo, Japan). To anchor the particles during AFM measurements, we incubate agarose microgels for 30 minutes on a glass substrate pretreated with 0.01% (w/v) poly-L-lysine overnight prior to AFM (Sigma- Aldrich, St. Louis, MO, USA). AFM is performed using a silicon nitride cantilever with an attached 12 μm-diameter borosilicate glass sphere as an indenter (Product #HYDRA6R-200NG-BSG-B-5, AppNano, Mountain View, CA, US). The particles are probed using a 1 μιη/s approach velocity. Thereafter, the AFM force curves are fit to the Hertz model with a spherical indenter to determine the Young's moduli of the agarose microgels (Fig. 3, panel A). We use a Poisson ratio of 0.5. By brightfield imaging of each particle prior to AFM indentation, we measure particle size and confirm that there is no observable dependence of elastic modulus on particle size (Fig. 8, panel A).

Microfluidic device fabrication.

[0039] Microfluidic devices are fabricated using standard soft lithography methods (Duffy, et al. (1998) Anal. Chem. 70: 4974-4984). To fabricate the master wafer, SU-8 3005 or 3010 (MicroChem, Westborough, MA, USA) is spin-coated on a silicon wafer to a final thickness of 5 μπι or 10 μπι. A negative photomask is placed on the SU-8-coated wafer and the photoresist is crosslinked upon exposure to UV light with 100 mJ/cm² of exposure energy (Nyberg et al. (2016) Lab Chip, 16: 3330-3339). The height of the resulting relief of the microfluidic channels is measured using a Dektak 150 Surface Profilometer (Veeco,

Fullerton, CA). A 10: 1 w/w mixture of base and curing agent for polydimethylsiloxane (PDMS) (Sylgard Dow Corning, Midland, MI, USA) is poured onto the master wafer. The mixture is degassed for 1 hour under vacuum and cured in a 65°C oven for 2 hours. Prior to bonding, inlets and outlets are excised using a biopsy punch with a 0.75 mm bore size. To bond the PDMS to a coverglass (#1.5 thickness), the complementary surfaces are exposed to plasma for 30 seconds and press together with light pressure. After bonding, the microfluidic devices are baked at 80°C for 20 minutes to further promote covalent attachment between PDMS and glass. To reduce possible measurement artifacts due to temporal changes in surface properties, devices are consistently used 24 hours after plasma bonding {Id.). q-DC device design.

[0040] The q-DC microfluidic device consists of a bifurcating network of channels that extends into a parallel array of 16 channels that contain micron-scale constrictions (Rosenblut et al. (2008) Lab Chip. 8: 1062-1070; Rowat et a/. (2013) J. Biol. Chem. 288: 8610-8618). To reduce the effect of transient channel occlusions as multiple cells transit simultaneously through the constriction region, a bypass channel is included in the device design and post-acquisition filtering is performed to exclude data when more than 10 channels, or 65% of the channels, are occupied (Nyberg et al. (2016) Lab Chip, 16: 3330- 3339). Below this cutoff, there are fluctuations in flow rate below 7% variability {Id.). q-DC microfluidic experiment.

[0041] To perform q-DC experiments, microfluidic devices are mounted onto an inverted microscope (Zeiss Observer, Zeiss, Oberkochen, Germany) that is equipped with a 20x/0.40 NA objective. To drive the suspension of cells through the channels, constant air pressure is applied to the device inlet, which is regulated using a pneumatic valve (OMEGA Engineering, Inc., Norwalk, CT, USA). As cells flow into the device, a downstream filter traps foreign particles and cell aggregates that are larger than 20 μπι. As cells deform through the constrictions (Hoelzle et al. (2014) J. Vis. Exp. 91 : e51474-e51474), brightfield images are acquired at rates of 200 to 2000 frames per second using a CMOS camera

(MircoEx4, Vision Research, Wayne, NJ, USA) in order to track cell shape and displacement (Fig. 2, panels A, B). This enables measurements of cell size D_ceii, time-dependent strain eft), critical strain 8_criticab creep time T_c, and transit time T_T. When a driving pressure of 28 kPa (4 psi) is applied to a cell suspension with a density of 2 x 10⁶ cells/mL, single-cell

measurements can be acquired at rates of ~10³ cells/min. For applied pressures of 69 kPa (10 psi), measurements can be acquired at ~10⁴ cells/min. [0042] To minimize cell-surface interactions, measurements are conducted in the presence of 0.01% (w/v) Pluronic F-127 surfactant (Sigma-Aldrich, St. Louis, MO, USA). For some cell types such as human pancreatic ductal epithelial (HPDE) cells, we qualitatively observe a decrease in cell-PDMS adhesion when Pluronic F-127 surfactant is added to the cell suspension (Nyberg et al. (2016) Lab Chip, 16: 3330-3339); therefore we consistently use this treatment across all cell types. There is no significant quantitative or qualitative effect of F-127 treatment on the E_a values of HL-60 cells (Fig. 9). While cell-surface interactions can contribute to cell transit through long, narrow microfluidic channels, the timescale required by cells to enter microfluidic constrictions is largely determined by cell deformability (Byun et al. (2013) Proc. Natl. Acad. Sci. USA, 110: 7580-7585; Shaw Bagnall et al. (2015) Sci. Rep. 5: 18542; Nyberg et al. (2016) Lab Chip, 16: 3330-3339).

Tracking of cell strain during deformation through microfluidic constrictions.

[0043] To extract cell mechanical properties from transit experiments, cell position and shape are tracked by applying thresholding and morphological filters to the high frame rate images in a MATLAB code (Mathworks, Natick, MA; code available online on GitHub). The creep function, J(t), is determined as the ratio between the observed strain and applied stress:

where e(f) is the strain and σ is the time-averaged stress. Here, the strain is measured as the change in circularity, C:

= Eq. 2 where C(f) = 4nA(t)/P(t)². We find that circularity compared to length extension and width compression more robustly captures the deformation of cells through the curved microfluidic constrictions. Prior to entering the constriction, circularity values are close to 1, the value of a perfect circle. Therefore, the initial circularity is set to C₀ = 1. As a cell deforms through a constriction, the strain reaches a maximum as the cell extends and deforms through the narrow gap (Fig. 2, panels B-D). The quantification of creep begins one frame after the leading edge of the particle reaches the constriction, which corresponds to the initial projection of the cell into the constriction, and ends when the centroid of the cell leaves the constriction (Fig. 2). We use a minimum of four frames to achieve sufficient fits for the creep trajectories of individual cells. While fitting to a larger number of >15 frames can improve fitting accuracy, as indicated by the residuals (Fig. 10), this would exclude all cells that transit within less than 15 frames, or 7.5 ms. Increasing the frame rate captures cell deformations with higher temporal resolution, but the duration of the video is reduced to 3.7 seconds due to hardware limitations at the maximum frame rate of 3500 frames/sec.

Therefore, using a 4 frame cutoff for acquiring q-DC measurements enables us to resolve the power law behavior of individual cells that are representative of the population by acquiring data across a range of cell deformation timescales from milliseconds to seconds.

Calibration of time-averaged stress using gel particles.

[0044] Since the device has a finite fluidic resistance, the stress applied to a cell as it deforms in the microfluidic constriction does not equate to the applied driving pressure, or P applied, but rather scales with P_apPiied as:

Q = AP_applied, Eq. 3 where σ is the time-averaged stress at the constriction region and A is the calibration factor. To determine A, we calibrate the system using agarose particles with elastic moduli (E) ranging from 660 ± 86 Pa to 2.4 ± 0.44 kPa (average ± standard error), as confirmed by AFM (Fig 3, panel A); similar values are observed for agarose particles generated using droplet microfluidics (Kumachev et al. (2013) Soft Matter. 9: 2959).

[0045] To achieve particle transit through a fixed pore size, the applied stress must induce a minimum, critical strain, e_criticai, Assuming linear elastic behavior, the scaling factor, A, can be determined by the stress-strain relation at the threshold conditions where

P applied P threshold-

. Ecritical _

A = . Eq. 4

^threshold

We define the threshold pressure as the minimum applied pressure needed to drive the transit of over -80% of the particles through the constrictions. For example, when calibration particles with E = 1.5 ± 0.1 kPa are driven through a 5 μπι x 5 μπι device using an applied pressure below P threshold = 41 kPA, the majority of particles occlude the microfluidic constrictions on the experimental timescale of 1 minute. By contrast, with applied pressures above P threshold, over 80% of particles transit within this timescale. As we use a

heterogeneous size distribution of particles, we determine P threshold and 8_criticai for the largest (top 50^th to 100^th size percentile) gels that transit through the constriction for a given bead stiffness at P threshold (Fig. 8, panel B). Here, we calculate the critical strain as Scritical (Dagarose - w_COnstriction)/Dagarose- Across the range of particle stiffnesses (0.6 - 2.4 kPa) and strains (40 - 60%) that we investigated, we find a linear relation between stress and strain (Fig 2, panel B), which validates our assumption of linear elasticity.

[0046] By performing linear regression using the Deming method on I 'threshold/ 'e ^'critical versus E for our panel of calibration particles, we determine A for each device geometry (Fig. 3, panel B, Fig. 11) (Deming (1966) Some theory of sampling, Dover Pub. Inc. N.Y.). We find that .4 is 0.021 ± 0.002, which yields σ « 568 ± 53 Pa for P_appn_ed = 28 kPa in the 5 μηι χ 5 μπι device geometry. Combining Eqs. 3 and 4, the resultant creep J(t) for the 5 μπι x 5 μπι device is defined as J{t) = ^ Eq. 5

0.021 Papplied

The Deming method also enables us to determine the error in _^4 as it considers the error in both P threshold! £ critical ^and E. In addition to the variability in elastic moduli of the calibration particles, error in A may arise due to fluctuations in applied stress as particles transit and occlude neighboring channels. In our previous analysis of cell transit times, we found transit times significantly decrease when more than 10 neighboring lanes are occupied (Nyberg et al. (2016) Lab Chip, 16: 3330-3339); therefore we analyze data from particles and cells that transit when 10 or less neighboring lanes are occupied. Kirchoff s Law reveals that the flow rate can change by 7% within our experimental range of occluded neighboring lanes of 0 - 10 lanes; this is reflected in the error of applied stress of 10% {Id). Viscoelastic Cell Adhesion Model (VECAM) simulations.

[0047] To provide insight into the stresses on cells as they deform through

microfluidic pores, we use VECAM, a three-dimensional multiphase flow algorithm in which each of the phases is modeled as a viscoelastic or Newtonian fluid. The viscoelasticity of the cells and walls of the microchannel are described by the Oldroyd-B constitutive model (Khismatullin & Truskey (2012) Biophys. J. 102: 1757-1766; Khismatullin & Truskey(2005) Phys. Fluids. 17: 31505). Similar to our experiments, cells flow through the microchannel of a PDMS device in response to an applied pressure (Fig. 13, panel A). The simulations determine the total stresses acting on cells, including fluid shear stresses and normal stresses that result from the pressure drop across the cell as it transiently occludes the pore. To reduce the computational expense of the simulations, cells are modeled to have E = 10 Pa and an apparent viscosity of 1.0 Pa- s. To maintain the same ratio between cell and PDMS stiffness as in our experiments

~ 10 ), the stiffness of the microchannel is modeled as E ~ 10⁴ Pa. The carrier fluid of the cells during transit in the device is modeled as a Newtonian fluid.

Results and Discussion Time-dependent cell strain follows power law rheology.

[0048] Determining the material properties of cells from transit experiments requires a physical model to describe the relationship between stress and strain. To simplify analysis, we consider the cell as a homogeneous, isotropic, and incompressible material. This enables us to fit mechanical models to the creep trajectories for individual cells, such as the liquid drop and Kelvin- Voigt models. The deformation of cells entering microfluidic constrictions can be assessed using models that describe cells as liquid droplets (Byun et al. (2013) Proc. Natl. Acad. Sci. USA, 110: 7580-7585), elastic solids (Mietke et al. (2015) Biophys. J. 109: 2023-2036), as well as viscoelastic (Bathe et al. (2002) Biophys. J. 83 : 1917-1933) and soft glassy (Lange et al. (2015) Biophys. J. 109: 26-34) materials. However, it is not a priori known which model best describes the deformations of cells into the microfluidic constriction and provides the most accurate measurement of cell mechanical properties. Here, we evaluate how effectively four viscoelastic models - the Maxwell solid, Kelvin- Voigt, standard linear solid (SLS), and power law rheology (PLR) - describe cell creep through microfluidic constrictions. These models are described in greater detail in the supplemental materials (SI Material).

[0049] Our analysis reveals that PLR provides the best fit to our data: the least squares residuals are the lowest for PLR (3.9 ± 0.2 x 10^"9 Pa^"2) compared to other standard viscoelastic models (4.8 ± 0.3 x 10^"9 Pa^"2 to 8.0 ± 0.2 x 10^"9 Pa^"2) (Fig. 4, panels A,B). While an increasing number of fitting parameters can naturally result in reduced residuals, PLR has only two fitting parameters. By contrast, the SLS model has three fitting parameters, but the least squares residuals are higher than for PLR (6.0 ± 0.1 x 10^"9 Pa^"2, p « 0.001). Our results are consistent with observations of PLR behavior in cells that are subjected to stresses by micropipette aspiration (Zhou et al. (2010) Biomech. Model. Mechanobiol. 9: 563-572), optical stretching (Maloney et al. (2010) Biophys. J. 99: 2479-2487), transit DC (Lange et al. (2015) Biophys. J. 109: 26-34; Lange et al. (2017) Biophys. J. 112: 1472-1480), AFM (Fabr et al. (2001) Phys. Rev. Lett. 87: 148102), and magnetic twisting cytometry (Puig-De- Morales et a/. (2001) J. Appl. Physiol. 91 : 1152-1159). [0050] Using PLR, we extract the mechanical properties of single cells as they deform through microfluidic constrictions by analysis of the time-dependent creep function,

where τ is the characteristic timescale, which is commonly set to 1 s; E is the elastic modulus when t = τ; and β is the power law exponent that reflects the rate of stress dissipation and thus provides a measure of cell fluidity. When β = 0, the creep function describes a purely elastic material and Eq. 6 reduces to Hooke's law; when β = 1, Eq. 6 reduces to the Newtonian liquid drop model, reflecting a purely viscous material. While our data is consistent with PLR, we refer to the elastic modulus that we measure using q-DC as the apparent elastic modulus E_a because of the potential nonlinear effects that may contribute to our

measurements with the large 30 to 60 % strains in q-DC.

[0051] We also recognize that these mechanical measurements assume constant stress during cell transit. As shown by Viscoelastic Cell Adhesion Model (VECAM) simulations, the total stress on a cell varies as it deforms through a pore (Fig. 13). As the cell transits through the pore, there is a drop in the hydrodynamic forces on the cell, which are proportional to the cell velocity according to Stokes' law (Fig. 13, panel B). In addition, there is a pressure drop across the cell, where the applied pressure P_app at the trailing edge is higher than the pressure at the cell's leading edge, which is approximated by atmospheric pressure, P_atm (Fig. 13, panel C). Thus, when the cell is transiently occluding the pore, there are positive normal forces that deform the cell, and which vary during cell translocation due to the curved geometry of the pore.

Validation of PLR using oil droplets.

[0052] To validate the use of PLR in q-DC, we first quantify β, or fluidity, for droplets of silicone oil. We predict β = 1 for droplets of silicone oils, which are Newtonian fluids. We generate oil droplets that have a range of molecular weights and thus dynamic viscosities, η, from 10^"2 to 10¹ Pa s, and flow them through the constrictions at a constant driving pressure of 28 kPa. From 1000 random samplings of the β distributions, we obtain median bootstrapped values and confidence intervals of β. We observe β = 0.78 ± 0.08 for the lowest viscosity silicone oil (η = 10^"2 Pa s) (Fig. 11), which is close to purely viscous behavior. With increasing viscosity, we observe decreasing β, where the highest viscosity oil droplets (η = 10¹ Pa s) exhibit β = 0.54 ± 0.02. This decrease in β with increasing viscosity suggests a progressively increasing elastic response, which occurs due to the fast millisecond timescales of our measurements compared to the timescale of molecular rearrangements in the silicone oils that have increased molecular weight.

Single cell measurements of elastic modulus and fluidity.

[0053] To demonstrate the utility of q-DC for cell mechanotyping, we measure HL-60 cells, whose mechanical properties are well characterized using methods such as micropipette aspiration (Tsai et al. (1996) Biophys. J. 70: 2023-2029), AFM (Rosenbluth et al. (2006) Biophys. J. 90: 2994-3003; Wang et al. (2015) Lab Chip. 15: 532-540), and optical stretching (Ekpenyong et al. (2012) PLoS One, 7(9): e45237) (Table 3). Our results show that HL-60 cells have a median E_a and confidence interval of 0.53 ± 0.04 kPa (β = 0.29 ± 0.02), as measured by 1000 iterations of bootstrapped resampling (Fig. 4, Table 2); this is on the same order of magnitude as values obtained using AFM, where E = 0.9 ± 0.7 kPa (Rosenbluth et al. (2006) Biophys. J. 90: 2994-3003) and E = 0.9 ± 0.2 kPa (Wang et al. (2015) Lab Chip. 15: 532-540) (Table 3).

Table 2. E_a and β values from q-DC measurements. The median E_a and β are determined by 1000 bootstrapped samples from the density-gated q-DC data. Error represents the corresponding confidence intervals.

Table 3. E and β values from literature.

[0054] Since q-DC quantifies the mechanotype of single cells, the variability in mechanical properties across a cell population can be determined. To describe cell-to-cell variability, we use the interquartile range (IQR) as a quantitative metric. For HL-60 cells, the IQR spans half an order of magnitude from 0.30 to 0.71 kPa, as measured by aiQ_R __Ea = logio(75^th/25^th percentile) = 0.35 ± 0.06. We also find significant variability in β wit _aIQR = 0.25 ± 0.03.

[0055] By plotting E_a and β vs. D_ceii, we observe that larger cells tend to have higher E_a (Fig. 3, panel C, Fig. 4, panel A) and reduced β (Fig. 3, panel D, Fig. 4, panel A). For example, we find that for cells with D_ceii = 18 ± 1 μπι, Ea = 0.37 ± 0.06 kPa and β = 0.37 ± 0.04, whereas larger cells with D_ceU = 22 ± 1 μηι have E_a = 0.59 ± 0.04 kPa and β = 0.26 ± 0.02 (Fig. 3, panels C,D). Size-dependence of cell mechanotype is also observed in other DC methods, where larger cells have longer transit times (Lange et al. (2015) Biophys. J. 109: 26-34; Byun et al. (2013) Proc. Natl. Acad. Sci. USA, 110: 7580-7585; Shaw Bagnall et al. (2015) Sci. Rep. 5: 18542; Nyberg et al. (2016) Lab Chip, 16: 3330-3339) and exhibit more significant changes in shape due to forces exerted by fluid flow (Otto et al. (2015) Nat. Meth. 12: 199-202; Gossett et a/. (2012) Proc. Natl. Acad. Sci. USA, 109: 7630-7635). While larger cells could be inherently stiffer than smaller cells, larger cells undergo larger strains as the constriction width is fixed (Fig. 14). Since cells are non-linear materials, the length and time scales of deformation may influence their E_a as observed in cells (Fabr et al. (2001) Phys. Rev. Lett. 87: 148102; Despra et al. (2005) Biophys. J. 88: 2224-2233; Deng et al. (2006) Nat. Mater. 5: 636-640; Fernandez et al. (2006) Biophys. J. 90: 3796-3805; Marcy et al. (2004) Proc. Natl. Acad. Sci. USA, 101 : 5992-5997; Bieling et al. (2016) Cell. 164: 115- 127; Icard-Arcizet et al. (20080 Biophys. J. 94: 2906-2913) and biopolymer networks (Fabr et al. (2001) Phys. Rev. Lett. 87: 148102; Fernandez et al. (2006) Biophys. J. 90: 3796-3805; Hoffman et al. (2006) Proc. Natl. Acad. Sci. USA, 103 : 10259-10264; Janmey et al. (1991) J. Cell Biol. 113 : 155-160; Gardel et al. (2006) Proc. Natl. Acad. Sci. USA, 103 : 1762-1767).

Cell-to-pore size ratio affects mechanotype.

[0056] To further investigate the cell-to-pore size dependence of E_a, we vary the constriction width from 5 μπι to 9 μπι, while maintaining a constant constriction height of 10 μηι; thus, we achieve median cell-to-pore size ratios of ~3 and 1.5. To ensure cells are subjected to the same applied stress while undergoing different critical strains, we utilize the agarose calibration beads to determine the required applied pressures for each constriction geometry: P applied = 14 kPa for 5 μιη x 10 μιη geometry and P applied = 34 kPa for the 9 μιη x 10 μπι device (Table. 4). For cells of D_ceii = 16 ± 1 μπι, we observe a significant 70% decrease in E_a when measured using a 9 μπι with constriction (E_a = 230 ± 90 Pa), as compared to the 5 μπι-wide geometry (E_a = 860 ± 230 Pa, p « 0.001). These results suggest that the magnitude of cell strain affects E_a and are consistent with observations of strain stiffening in mechanical measurements of cells and biopolymer networks (Rotsch &

Radmacher (2000) Biophys. 7. 78: 520-535; Janmey et al. (1991) 7. Cell Biol. 113 : 155-160). Our findings of how mechanotype depends on cell-to-pore size ratio also substantiates the comparison of cells of similar sizes across samples.

Table 4. Calibration for applied stress in varying device geometries. The calibration factors are determined by the threshold pressure method. Utilizing agarose calibration particles, we are able to determine the applied stress at the constriction region.

[0057] Cells are also spatially heterogeneous materials. Therefore, the magnitude of deformation depth, or strain, may impact the resultant mechanotype measurements. The nucleus is a major contributor to subcellular deformations: this organelle is typically 2- to 5- times stiffer than the surrounding cytoplasmic region (Agus et al. (2013) Sci. Rep. 3 : 1449), and rate-limits the deformation of cells through microfluidic channels that are smaller than the diameter of the nucleus (Rowat et al. (2013) 7. Biol. Chem. 288: 8610-8618). HL-60 cell nuclei range in diameter from 5 to 14 μπι and have an average size of 9.2 ± 2.0 μπι (Fig. 16); thus for most cells, the nucleus must deform when cells transit through a 5 μπι- or 9 μιη-wide constriction. By quantitative image analysis, we find that larger HL-60 cells tend to have larger nuclei, as indicated by the positive correlation (R = 0.8) between nuclear and cellular diameter (Fig. 16, panel A). Thus, the increased E_a observed for larger cells could also result from the increased deformation of the nucleus that is required for transit. A similar increase in Young's modulus is observed with increasing AFM indentation depth into the nucleus (Agus et al. (2013) Sci. Rep. 3 : 1449). The dependence of cell and nuclear size on the deformation response of cells as they deform through pores further underscores the importance of comparing q-DC data from cells that undergo a similar magnitude of strain (Fig. 14). These findings also provide a guide for establishing parameters in q-DC experiments: a cell-to-pore size ratio of ~2 ensures cell deformation is required for transit through the pore, and typically results in a strain of 35 - 40%, which is on the lower range of cell strains that can be achieved with q-DC, and therefore minimizes strain-stiffening effects. Stress-stiffening behavior of cells using q-DC.

[0058] To determine the effects of applied stress on cell deformation behavior in q-

DC, we drive HL-60 cells through 5 μπι x 10 μπι constrictions with increasing applied pressures from 14 - 69 kPa. From our calibration, we determine the corresponding range of applied stress to be σ = 1.0 to 4.8 kPa. With an increase in σ from 1.0 to 2.4 kPa, we find a small 10%, albeit not significant, increase in elastic modulus (p = 0.34). Further increasing σ to 4.8 kPa, we observe a statistically significant stiffening reflected by the 60% increase in E_a (p < 0.001). From σ = 1.0 to 4.8 kPa we observe a significant 70% increase in E_a from 860 ± 230 Pa to 1.5 ± 0.5 kPa (p = 0.003) (Fig. 5, panel A, Table. 4). Taken together, these results indicate stress stiffening response of HL-60 cells on these deformation timescales of milliseconds to seconds. The stress stiffening behavior of cells is observed across varying cell types from airway smooth muscle cells to fibroblasts (Maloney et al. (2010) Biophys. J. 99: 2479-2487; Fabr et a/. (2001) Phys. Rev. Lett. 87: 148102; Fernandez et al. (2006) Biophys. J. 90: 3796-3805; An et al. (200) Am. J. Physiol. Physiol. 283 : C792-C801).

Therefore, we consider cells of similar sizes when comparing between populations of single cells to minimize possible bias from strain and stress on q-DC measurements.

Validation of mechanical measurements using HL-60 cells.

[0059] To demonstrate the sensitivity of q-DC to changes in cytoskeletal structure, we treat HL-60 cells with cytoskeletal perturbing drugs, which are known to alter cell mechanical properties (Rotsch & Radmacher (2000) Biophys. J. 78: 520-535; Tsai et al. (1996) Biophys. J. 70: 2023-2029; Ting-Beall et al. (1995) Ann. Biomed. Eng. 23 : 666-671; Maniotis et al. (1997) Proc. Natl. Acad. Sci. USA, 94: 849-854). For example, treatment with cytochalasin D inhibits F-actin polymerization (Rosenblut et al. (2008) Lab Chip. 8: 1062- 1070), while treatment with jasplakinolide inhibits F-actin depolymerization, thus stabilizing actin filaments. To compare cells of similar size, we size bin our data to investigate cells of the median diameter, D_ceii = 21 ± 1 μηι of HL-60 cells across all drug treatments (Fig. 6, panel A). We find that treatment with cytochalasin D results in a small but significant decrease in E_a from 0.53 ± 0.04 to 0.39 ± 0.05 kPa with an increase in cell-to-cell variability, from iQR E_fl = 0.35 ± 0.06 to 0.46 ± 0.08 (p « 0.001) (Fig. 6). In addition, we observe cytochalasin D treatment results in a marginal increase in cell fluidity from β = 0.29 ± 0.02, to β = 0.34 ± 0.03 (p = 0.006), as well as an increased variability in fluidity from alQK _β = 0.25 ± 0.03 to lQR J = 0.33 ± 0.04 (Fig. 6, panel B). By contrast, stabilizing F-actin with jasplakinolide treatment insignificantly increases E_a to 0.54 ± 0.06 kPa and OIQR ¾ = 0.30 ± 0.06; we also observe a concomitant, significant decrease in β to 0.27 ± 0.03 with OIQR_J= 0.27 ± 0.06 v (Fig. 6, panel B). Our observations of the effects of cytochalasin D and jasplakinolide are consistent with previous studies investigating the contributions of F-actin to cell transit through micron-scale channels (Rosenblut et al. (2008) Lab Chip. 8: 1062- 1070; Byun et al. (2013) Proc. Natl. Acad. Sci. USA, 110: 7580-7585; Gabriele et al. (2009) Biophys. J. 96: 4308-4318; Mak et al. (2013) Integr. Biol. 5: 1374-1384). These results demonstrate the proof-of-concept and utility of q-DC to achieve mechanical measurements of single cells with increased throughput.

[0060] We also investigate the effects of blebbistatin, which inhibits myosin II activity, and thus reduces crosslinking and actomyosin contractions. We observe no significant change in E_a following blebbistatin treatment as E_a = 0.52 ± 0.06 kPa and ^QR __EA = 0.40 ± 0.09. We observe a slight increase in cell fluidity to β = 0.29 ± 0.02 and σ_¾κ j = 0.28 ± 0.05; however this difference is not significant (Fig. 6, panela A,B). Previous observations show that blebbistatin treatment decreases the stiffness in adhered cells, as indicated by their reduced E (Martens & Radmacher (2008) Pflugers Arch. Eur. J. Physiol. 456: 95-100), and suspended cells, as indicated by their reduced transit time {et al. (2009) Biophys. J. 96: 4308-4318). However, other measurements of suspended cells show increased stiffness with inhibition of myosin II (Chan et al. (2015) Biophys. J. 108: 1856- 1869). As minor differences in blebbistatin concentrations and treatment times across studies do not seem to explain the observed differences in the mechanotype of cells in suspension, we speculate that the varied results may be explained by considering deformation depth. In methods that deform cells by ~5 to 6 μιη (Gabriele et al. (2009) Biophys. J. 96: 4308-4318), the nucleus may contribute more prominently to the deformation response; myosin II inhibition could cause softening of the 'prestressed' nucleus as intracellular tension diminishes. By contrast, when cells are subjected to smaller, 1 to 3 μιη deformations (Chan et al. (2015) Biophys. J. 108: 1856-1869), the cortical region may dominate the response; a less deformable cortex may result from decreased turnover of actin due to blebbistatin treatment. We also acknowledge that differences in cell genotype, culture conditions, and passage number of cell lines may also contribute to the varied results observed between studies.

Mechanotyping cancer cell lines.

[0061] To further benchmark our q-DC method, we next investigate the human breast cancer cell lines, MCF-7 and MDA-MB-231, whose mechanical properties are well characterized using methods including AFM and transit DC (Table 3). Since these breast cancer cells tend to be larger and stiffer than HL-60 cells(l 1), we use a 9 μιη x 10 μιη pore size with an applied stress of 2.2 ± 0.1 kPa, which ensures >95% of cells transit through the pores on the experimental timescale (Fig. 10, panel B); this enables us to acquire single cell measurements with a throughput of 10³ cells/min. For MCF-7 cells with D_ceii = 12 ± 1 μπι, we observe E_a = 2.4 ± 0.2 kPa (Fig. 7). We also measure MDA-MB-231 cells within the same size range, and find that E_a = 0.97 ± 0.50 kPa, which is 40% lower than MCF-7 cells (p « 0.001). Our findings that MDA-MB-231 cells are more compliant than MCF-7 cells are in agreement with previous reports (Calzado-Martin et al. (2016) ACS Nano. 10: 3365-3374; Coceano et al. (2016) Nanotechnology . 27: 65102) (Table 2). Using AFM and magnetic twisting cytometry, E for MCF-7 cells typically range from 0.2 to 1 kPa (Calzado-Martin et al. (2016) ACS Nano. 10: 3365-3374; Corbin et al. (20\ 5) Lab Chip. 15: 839-847; Omidvar et al. (2014) J. Biomech. 47: 3373-3379; Li et al. (2008) Biochem. Biophys. Res. Commun. 374: 609-613; Rother et al. (2014) Open Biol. 4: 140046), while for MDA-MB-231 cells E varies from 0.2 to 0.69 kPa (Agus et al. (2013) Sci. Rep. 3 : 1449; Lange et al. (2015)

Biophys. J. 109: 26-34; Calzado-Martin et al. (2016) ACS Nano. 10: 3365-3374; Corbin et al. (2015) Lab Chip. 15: 839-847; Omidvar et al. (2014) J. Biomech. 47: 3373-3379; Rother et al. (2014) Open Biol. 4: 140046). Considering the relatively higher 30 to 60% strains that are applied in q-DC compared to the local, < μπι indentations of AFM, the higher E_a values for MCF-7 cells that we observe are consistent with the dependence of E on deformation depth: MDA-MB-231 that are indented with 0.1 μπι deformation depths that penetrate into the nuclear region exhibit a 5-fold increase in Young's moduli compared to 0.8-μπι deformation depths (Agus et al. (2013) Sci. Rep. 3 : 1449; Calzado-Martin et al. (2016) ACS Nano. 10: 3365-3374). Our measurements also reveal that E_a and β are inversely correlated for the breast cancer cells, where β = 0.28 ± 0.01 for MCF-7 cells and β = 0.40 ± 0.03 for MDA-MB- 231 cells (p « 0.001) ((Fig. 5, Fig. 13, panel B); the inverse correlation is consistent soft glassy rheology (Maloney et al. (2010) Biophys. J. 99: 2479-2487; Fabr et al. (2001) Phys. Rev. Lett. 87: 148102; Lange et al. (2015) Biophys. J. 109: 26-34).

[0062] The differences in the mechanotype of MCF-7 and MDA-MB-231 cells that we observe may reflect underlying molecular differences between these cell lines. These cell types also exhibit distinct invasive behaviors: MDA-MB-231 cells are more invasive than the MCF-7 cells (Gordon et al. (2003) Int. J. cancer. 106: 8-16). While correlations between cancer cell invasive potential and mechanical properties are observed in other contexts (Xu et al. (2012) PLoS One, 7: e46609; Nguyen et al. (2016) Integr. Biol. 8: 1232-1245; Agus et al. (2013) Sci. Rep. 3 : 1449; Gordon et al. (2003) Int. J. cancer. 106: 8-16), the causal role of cell mechanotype in behaviors such as invasion is still unclear. The mechanotype of cancer cells could also have implications in how disseminated tumor cells resist shear forces during circulation and occlude narrow gaps, which is required for seeding metastatic sites. The ability of cells to transit versus occlude narrow capillaries is also critical for the deformability of blood cells, ranging from sickle cells (Evans et al. (1984) J. Clin. Invest. 73 : 477; Higgins et al. (2007) Proc. Natl. Acad. Sci. USA, 104: 20496-20500) to immunology (Ekpenyong et al. (2012) PLoS One, 7(9): e45237; Rowat et a/. (2013) J. Biol. Chem. 288: 8610-8618); in these contexts, changes in cell mechanotype have distinct biological implications.

Furthermore, the evidence of stress and strain stiffening that we observe as cells undergo large 40-60% strains through micron-scale gaps may be advantageous for cells to resist significant deformations in vivo.

[0063] While the biological relevance of mechanotype - which is most often measured in vitro - still remains an open question, it is notable that biological relevance is not a requisite to establish a valuable biomarker. For example, nuclear shape has been a diagnostic biomarker in breast and cervical cancers for decades (Elston & Ellis (1991) Histopathology, 19: 403-410), while the biological significance of the aberrant nuclear morphology of cancer cells remains unclear. Thus, robust differences in mechanotypes across cell types, which can be achieved using calibrated measurements, should have clinical value. Conclusions

[0064] Here we present a framework that uses calibration particles to quantify the external stresses in q-DC, a fluidic-based method that enables rapid measurements of cell mechanical properties. The use of calibration particles should ultimately enable standardized mechanotyping and longitudinal studies in clinical and research settings. To extract quantitative measurements of cell elasticity and fluidity, we use power law rheology (PLR), which is an effective analytical model for describing cell creep through microfluidic constrictions on timescales of milliseconds to seconds. Future studies will clarify the extent to which q-DC mechanotyping results add value as a biomarker, as well as the extent to which cell mechanotype impacts biological processes in physiology and disease.

Supplemental Information.

Viscoelastic Models.

[0065] To measure the mechanical properties of cells from individual creep trajectories, we evaluate the quality of fit of standard viscoelastic models. The Maxwell, Kelvin- Voigt, and Standard Linear Solid models are represented by combinations of springs and dashpots. Similar to the springs and dashpot models, Power Law Rheology (PLR) provides a measure of elastic and viscous components of cells, whereby the power law exponent, or fluidity, reflects the viscous behavior (Pajerowski et al. (2007) Proc. Natl. Acad. Sci. USA, 104: 15619-15624). While we show in this study that PLR minimizes the residuals for HL-60 cells, certain cell types may be better described using other viscoelastic models (see, e.g., Table 5; Maloney et al. (2010) Biophys. J. 99: 2479-2487).

Table 5. Viscoelastic models.

_SLS{ ) - ***** +

Standard

Linear Solid

Power Law

Rheology

Data analysis.

[0066] Analysis of q-DC data is performed using MATLAB (MathWorks, Natick,

MA, USA). The video processing code is available on Github. Median residuals and corresponding confidence intervals are determined by bootstrapping 5000 iterations of theoretical fits to single cell data. Residual fits are determined using the least squares method. A value reported in the text as 'X ± Y' is the bootstrapped median, 'X', using bootstrapped resampling with the confidence interval, '2*Υ'. This bootstrapping method is also employed for determining β values, as well as the interquartile ranges. To compare the distributions of q-DC outputs between cell lines and drug treatments, we apply the pairwise, nonparametric Mann-Whitney U statistical test as most q-DC parameters are not normally distributed. Density scatter plots are created using the dscatter function (R. Henson,

Mathworks File Exchange). We assess the strength of correlations between q-DC outputs by determining Pearson's correlation coefficients for pairs of parameters

Example 2

Label-Free Prediction of Cancer Invasion by Single-Cell Physical Phenotyping

[0067] The physical properties of cells are promising biomarkers for cancer diagnosis and prognosis. Here we determine the physical phenotypes that best distinguish human cancer cell lines, and their relationship to cell invasion. We use the high throughput, single- cell microfluidic method, quantitative deformability cytometry (q-DC), to measure six physical phenotypes including elastic modulus, cell fluidity, transit time, entry time, cell size, and maximum strain at rates of 10² cells/s. By training a k-nearest neighbor machine learning algorithm, we demonstrate that multiparameter analysis of physical phenotypes enhances the accuracy of classifying cancer cell lines compared to single parameters alone. We also discover a set of four physical phenotypes that predict invasion; using these four parameters, we generate the physical phenotype model of invasion by training a multiple linear regression model with experimental data from a set of human ovarian cancer cells that overexpress a panel of tumor suppressor microRNAs. We validate the model by predicting invasion based on measured physical phenotypes of breast and ovarian human cancer cell lines that are subject to genetic or pharmacologic perturbations. Taken together, our results highlight how physical phenotypes of single cells provide a biomarker to predict the invasion of cancer cells.

Introduction.

[0068] Predicting disease and treatment outcomes based on single-cell phenotypes is critical in medicine from cancer diagnosis to stem cell therapies. In clinical oncology and immunology, single-cell analysis of protein markers and DNA content using flow cytometry is valuable in diagnosis, prognosis, and monitoring patient response to therapy (1). Yet pathological and physiological changes can also manifest as altered cell physical phenotypes, including cell and nuclear size, stiffness, and viscosity. For example, grading of tumor biopsies based on nuclear morphology is widely used for cancer prognosis (2-4). The deformability of cancer cells is also emerging as a convenient biomarker as more invasive cancer cells have altered deformability compared to less invasive cells (5-17). Since cellular physical phenotypes, such as deformability, are inherent properties of cells, they can be rapidly measured without the use of fluorescent markers or labeling agents (18). However, the utility of cell deformability in predicting the invasion of cancer cells remains unclear: many studies show that more invasive cancer cells tend to be more compliant than less invasive or benign cells (5-12); but there are also contexts where more invasive cells are found to be stiffer (13-17). These contrasting findings suggest that the invasion of cancer cells cannot be universally predicted based on cell deformability, and incite studies into which additional physical phenotypes may collectively predict invasion. [0069] Microfluidic methods are especially valuable for physical phenotyping, as they enable rapid measurements of single cells. One such method is transit-based deformability cytometry, which probes physiologically-relevant deformations of cells through narrow gaps across varying deformation time and length scales (10, 19-22). While transit time T_T is a relative measurement, this parameter can distinguish cancer cell lines from benign cells (10,21). However, it is challenging to compare common metrics of cell physical phenotypes, such as deformability and transit time, across experiments because such measurements are not typically calibrated (23). We recently developed the quantitative deformability cytometry (q-DC) method, which uses calibration particles and power law rheology to obtain calibrated single-cell measurements of elastic modulus E and fluidity β, as well as four additional physical phenotypes (24). Performing such calibrated measurements across studies enables comparisons across cell types that can address how multiple cell physical phenotypes can be leveraged to predict cell invasion. [0070] Using multiple features of clinical samples to train machine learning algorithms is showing value in diagnosis and predicting disease outcomes (25-33). Since physical phenotypes are inherent properties of cells, such measurements can provide a low- cost way to increase the feature space for machine learning algorithms and to generate more robust models. For example, biophysical signatures of mesenchymal stromal cells can predict their regenerative capability in vivo as indicated by ectopic bone formation in mouse models (34). Analysis of sets of physical phenotypes also improves the classification of stem cells and their progenitors as demonstrated by studies using atomic force microscopy (AFM) (34-40), cross-slot deformability cytometry (41), and optofluidic time-stretch microscopy (42). Thus, we hypothesized that multiparameter physical phenotyping could be used to train a machine learning algorithm to predict the invasion of cancer cells.

[0071] Here we use calibrated, physical phenotype measurements obtained by q-DC to predict the invasion of human cancer cell lines. We perform multiparameter analysis of six physical phenotypes for eleven different cancer cell lines with eight genetic or pharmacologic perturbations, resulting in nineteen distinct cell samples. To measure the physical phenotypes of single cells, we use quantitative deformability cytometry (q-DC) to obtain calibrated measurements of elastic modulus E and cell fluidity β, as well as transit time T_T, entry time T_E, cell size D_ceii, and maximum strain c_max, at rates of 10² cells/s (24). We show that multiparameter analysis of these physical phenotypes can enhance classification of cancer cell lines. From measurements across well-established pancreatic cancer cell lines as well as ovarian cancer cells that overexpress tumor-suppressor microRNAs, we build the predictive physical phenotyping model for invasion, which we validate using both genetic and pharmacologic perturbations of cancer cells. Our results demonstrate the value of rapid physical phenotyping for predicting invasion.

Materials and Methods

Cell culture.

[0072] Nontransformed human pancreatic ductal epithelial (HPDE) cells are obtained from Dr. Ming-Sound Tsao (University Health Network-Princess Margaret Hospital, Canada and University of Toronto, Canada). HPDE cells are cultured in Keratinocyte-SFM medium supplemented with prequalified human recombinant Epidermal Growth Factor 1-53, Bovine Pituitary Extract, and 1% penicillin-streptomycin. The human pancreatic ductal

adenocarcinoma (PDAC) cell lines (AsPC-1, Hs766T, MIA PaCa-2, and PANC-1) are from the American Type Culture Collection (ATCC). AsPC-1, Hs766T, MIA PaCa-2 and PANC- 1 cells are grown in high glucose, L-glutamine without sodium pyruvate DMEM medium with 10% heat-inactivated fetal bovine serum and 1% penicillin-streptomycin. Fetal bovine serum and penicillin-streptomycin are from Gemini BioProducts, West Sacramento, CA. All cell media and additional media supplements are from Thermo Fisher Scientific Inc., Canoga Park, CA. To test the effects of microRNAs that are associated with improved patient survival (43), we overexpress microRNA mimics (microRNA-508-3p, microRNA-508-5p, microRNA-509-3p, microRNA-509-5p and microRNA-130b-3p) in human ovarian cancer (HEYA8) cells; microRNA mimics, mock, and scrambled (SCR) negative controls are from Dr. Preethi Gunaratne (University of Houston, USA) (43,44). HEYA8 cells are cultured in RPMI 1640 medium supplemented with 10% fetal bovine serum and 1% of penicillin- streptomycin. Cells are transiently transfected at 24 nM using Lipofectamine 2000 in serum- free OptiMEM medium, followed by the addition of 10% fetal bovine serum after 4 hours in serum-free conditions. All assays are performed 72 hours post transfection. Human ovarian cancer (OVCA433-GFP, OVCA433-Snail) cells are from Dr. Ruprecht Wiedemeyer (Cedars- Sinai Medical Center, USA) (45). OVCA433 cells are cultured in DMEM medium with L- Glutamine, Glucose, and Sodium Pyruvate. Medium is supplemented with 10% fetal bovine serum, 1% Anti-anti, and 2.5 μg/ml Plasmocin Prophylactic with 5 μg/ml blasticidin S HC1.

[0073] A highly metastatic variant of MDA-MB-231 cells (MDA-MB-231 -HM, gift from Dr. Zhou Ou, Fudan University Shanghai Cancer Center, China)(46) is cultivated in DMEM medium with L-Glutamine, Glucose, and Sodium Pyruvate, supplemented with 10% fetal bovine serum and 1% penicillin-streptomycin. The agonist (isoproterenol) for the β- adrenergic receptor is from Sigma-Aldrich (St. Louis, MO). Cells are treated for 24 hours prior to measurements.

[0074] All cells are cultured at 37°C with 5% C0₂. Cell line authentication is performed using short tandem repeat (STR) profiling (Laragen Inc., Culver City, CA, USA and CellBank Australia, Westmead, NSW, Australia). Prior to deformability measurements, 0.01% (v/v) Pluronic F-127 surfactant (Sigma-Aldrich, St. Louis, MO, USA) is added to the cell suspension to reduce cell adhesion to the PDMS walls. While F-127 treatment does not significantly affect E values of suspended cells (24), we observe a significant decrease in cell-to-PDMS adhesion in some cell types such as HPDE cells (23).

Microfluidic chip fabrication.

[0075] Negative photomasks are designed in AutoCAD (Autodesk, Inc., San Rafael, CA) and printed on chrome by the Nanolab at UCLA. The design of the q-DC devices is described previously (23). Silicone masters are fabricated using soft photolithography techniques (47). Polydimethylsiloxane (PDMS) (Sylgard Dow Corning, Midland, MI, USA) with a 10: 1 w/w ratio of base and curing agent is poured onto the master wafer and placed under vacuum to degas for 1 hour. To cure the PDMS, the wafer and PDMS mixture is placed in a 65°C oven for 2 hours. Inlets and outlets are created using a biopsy punch with a 0.75 mm bore size (Sigma-Aldrich, St. Louis, MO, USA). The devices are then bonded to coverglass (#1.5 thickness) by plasma and baked at 80°C for 5 minutes to facilitate bonding. To ensure consistent device surface properties, q-DC experiments are performed 24 h after plasma treatment (23). Under these conditions, PDMS has an elastic modulus on the order of 1 MPa (48). As the typical mechanical stress associated with a cell deforming through the constricted channel is ~ 10 kPa (24), the deformation of the PDMS is minimal while the cell transits through the constriction. q-DC microfluidic experiment.

[0076] To measure the physical properties of single cells, we use the q-DC method as previously reported (24). In brief, q-DC microfluidic devices are mounted onto an inverted microscope (Zeiss Observer, Zeiss, Oberkochen, Germany) that is equipped with a 20^χ/0.40 NA objective. A constant air pressure (69 kPa) drives cell suspensions to flow through the channels. As cells deform through microfluidic constrictions with 10 μπι height and 9 μπι width, a CMOS camera (MicroRNAcoEx4, Vision Research, Wayne, NJ, USA) is used to capture brightfield images at rates of 600 to 2000 frames per second. For cell suspensions with a density of 2 x 10⁶ cells/mL that are driven by an applied pressure of 69 kPa (10 psi), single-cell measurements can be acquired at rates of 10² cells/s. While the timescale of the initial cell deformation into microfluidic constrictions is largely determined by cell deformability (49-51), 0.01% (w/v) pluronic F-127 surfactant (Sigma-Aldrich, St. Louis, MO, USA) is added to the cell media to minimize cell-surface interactions. Measurements of cell physical properties using q-DC,

[0077] To conduct multiparameter analysis of cell physical properties, the

displacement and shape of single cells are tracked using a MATLAB code (Mathworks, Natick, MA, USA; code available online on GitHub) (24). This enables us to acquire cell size D_ceii, the time required for a cell to deform into the constriction T_E, and the time required for a cell to transit completely through the constriction T_T (24). We also measure the time- dependent strain as e(t) = ^C° where C is the circularity, C(t) = ^j . We set the initial circularity value as C₀ = 1, since the cells exhibit a circularity close to a perfect circle prior to entering the constriction. At the end of the entry time, the cell reaches a minimum circularity and corresponding maximum strain c_max.

[0078] To extract elastic modulus E and cell fluidity β, we determine the applied stress, <7, during cell deformation using agarose calibration particles with well-characterized Young's moduli. Measuring the stress-strain relationship for the calibration particles enables us to determine the stress as a function of driving pressure in both 9 x 10 μιη² and 7 x 10 μιη² device geometries (24). By fitting a power law rheology model to the time-dependent strain data obtained for individual cells, we can extract elastic modulus E and cell fluidity β: m = ^)^p > Eq. 1 where E is the elastic modulus when t = τ; τ is the characteristic timescale, set to 1 s; and β is the power law exponent, which represents cell fluidity. For purely elastic materials, β = 0; for purely viscous materials, β = I . As elastic modulus E, cell fluidity β, entry time T_E, and transit time T_T depend on cell size, we analyze cells that have D_ceii that is the population median ± 1 μπι.

Classifying cell lines using q-DC.

[0079] To evaluate the power of q-DC parameters to classify cells, we perform supervised machine learning using the k-nearest neighbor (k-NN) algorithm (Fig. 21, panel A). K-NN is a non-parametric algorithm that does not assume the underlying data fits a particular model and is among the simplest machine learning algorithms to conceptualize and execute (25). To implement the k-NN classification algorithm, we first map each cell sample into a multidimensional feature space of physical phenotypes (Fig. 18, panel B). We train the algorithm by considering the k nearest neighbors of individual data points based on their

Euclidean distance; the resultant clusters of data have the highest overlap in feature space or the most similar physical signatures. The class assigned to new data points is determined by the most common class of the k number of nearest neighbors in the training set. When selecting the integer, k, there is a tradeoff between overfitting and underfitting (52-54): when k = 1, the class is assigned based on only one closest neighbor in the feature space, and the algorithm is thus subject to noise and overfitting. By contrast, if k is the same size as the sample size, then the class assigned is the most common class in the feature space, and multiple classes cannot be assigned. Here we use k = 10, as it yields similar accuracies compared to k > 3, but spans a greater distance in the feature space to reduce overfitting; k = 10 also ensures that we can identify multiple classes ask is still significantly smaller than the training set of 400 samples per cross validation step (Fig. 21, panel B, Table 6).

Table 6. Performance on k-NN algorithm based on the value of k.

[0080] To implement k-NN, we first log-transform the physical phenotype data as single-cell populations exhibit non-normal distributions. Since training a k-NN algorithm is computationally expensive for large data sets (52), we use the median values of physical phenotypes as a proof-of-concept demonstration. We supply a known set of input data using statistical bootstrapping: for each cell line, we generate a representative training set of median q-DC predictors from 500 subsets of experimental data, which each contain 100 randomly- sampled cells with replacement. To determine classification accuracy, we execute the training and testing with 5-fold cross validation: the data is evenly partitioned into 5 subsets. For each round of cross validation, we combine 4 subsets to generate a training set, and use the fifth subset as the testing set. Classification accuracy is defined as the percentage of correct classifications over total classifications across each of the training sets.

Physical phenotype model of invasion using q-DC.

[0081] To evaluate if rapid physical phenotyping can predict cancer cell invasion, we build the physical phenotype model of invasion. We perform multiple linear regression using physical phenotype data obtained by q-DC to predict invasion rates that we previously measured using a 3D scratch wound invasion assay (12-14) (MATLAB, Mathworks, Natick, MA, USA) and were previously reported in the literature (55-58). As q-DC measurements of cell physical phenotypes depend on cell size (Fig. 17, panel E)(24), we bin our data based on the median cell size for each panel ± 1 μπι. We perform a log-transform as our data is non- normally distributed. To evaluate linear regression error, we utilize the single-cell q-DC data to train linear regression models using 1000 bootstrapped samples of single-cell physical phenotypes. Each bootstrapped sample generates a linear combination of physical phenotypes to predict invasion and their associated coefficients that minimize residuals. The physical phenotype model is determined by the median coefficient for each parameter. The correlation coefficient between predicted invasion and measured invasion is determined as the average correlation coefficient. Similar to the training analysis, we predict invasion using the physical phenotype model with 1000 bootstrapped samples of the q-DC data of single- cells; this enables us to determine the average predicted invasion. To evaluate the predictive accuracy of the model, we compare the ranking of measured invasion determined from both previous experiments (13, 14) and literature (55-58) with the invasion values obtained from the physical phenotyping model for invasion.

Results

Multiparameter physical phenotyping by q-DC.

[0082] To rapidly measure the physical phenotypes of single cells, we use transit- based deformability cytometry; this method uses a microfluidic device that consists of an array of branching channels (20,22,23,59,60), which lead to micron-scale constrictions (Fig. 17, panels A, B). The timescale for cells to transit through these narrow channels provides a simple measure of cell deformability (Fig. 17, panels B, C): stiffer cells tend to have longer transit times (T_T) compared to more compliant cells (61). To extract additional parameters from transit-based microfluidic measurements, we recently developed quantitative deformability cytometry (q-DC), which enables calibrated single-cell measurements of physical phenotypes including elastic modulus E and fluidity β that are extracted using power law rheology.

[0083] We find that a population of single cells exhibits variability in physical phenotypes, as shown in Fig 17, panel B. For this example showing the stiffness E of HPDE cells, we find the interquartile range of E spans 1.2 to 4.2 kPa, and displays a median E of 2.7 kPa, which is consistent with previous measurements by AFM (62). The heterogeneity in physical phenotypes across a population of single cells that we observe may be attributed to cell-to-cell variability in protein expression (63), F-actin organization (64,65), cell cycle stage (66-68), and nuclear-to-cytoplasmic ratio (69).

[0084] In addition to E, T_T, and β, we also obtain cell size D_ceii, from the diameter of the unconstrained cell prior to deformation; maximum strain <r_max, based on the minimum circularity that occurs as the cell deforms through the constriction; and entry time T_E, which is the time required for a cell to reach maximum strain (Fig 17, panel B). While q-DC enables measurements of multiple physical phenotypes, it is not clear how this additional information improves the accuracy of cell classification and prediction of invasion over standard measurements of T_T alone.

Pairwise correlation analysis of q-DC parameters.

[0085] To assess the value of multiple biophysical parameters for classification of different cell types, we use q-DC to measure physical phenotypes of human pancreatic ductal adenocarcinoma (PDAC) cell lines that are derived from primary tumors (PANC-1 and MIA PaCa-2), and secondary sites (AsPC-1 and Hs766T), as well as a non-transformed human ductal pancreatic epithelial (HPDE) control cell line. These cell lines exhibit distinct differences in invasion (13), and therefore provide a model system for testing q-DC classification of cells.

[0086] To identify which physical phenotypes provide unique information for classifying populations of single cells and which ones are statistically redundant, we first evaluate the correlation strength between pairs of the six q-DC outputs {E, β, T_T, T_E, D_ceii, and c_mas} (Fig. 22, Table 7). Spearman's rank correlation coefficients of -1 and +1 reflect pairs of parameters that are highly correlated and statistically dependent on each other. By contrast, correlation coefficients with a low absolute value indicate pairs of parameters that are weakly correlated with each other; each parameter from a weakly correlated pair will more likely provide unique information, as they are more statistically independent from each other.

Table 7. Pair-wise Spearman's rank correlation coefficients. Matrix of correlation coefficients for pairs of q-DC variables: cell diameter D_ceu, maximum strain c_max, transit time TV, entry time 7c, apparent elastic modulus E, and fluidity β. Correlation analysis is performed on the log-transformed q-DC data for pancreatic cancer cell lines.

[0087] Analysis of the Spearman's correlation coefficients reveals that T and 7k are highly correlated (r = 0.95; p < 0.001) (Fig.17, panel C, Fig.22, Table 7); this is expected as transit time is defined as the time for a cell to enter and exit the constriction. We also find that β and E are strongly correlated (r = -0.77; p < 0.001); this scaling of E and β is consistent with the behavior of soft glassy materials (19,70). All other pairwise comparisons between parameters, such as D_ceu to e_max, T_T, E, are weakly correlated with -0.48 < r < 0.64 (Table 7), suggesting that combinations of these parameters could provide unique information for characterizing cell lines. Multiparameter analysis for classification of pancreatic cells.

[0088] To assess the value of q-DC data sets in classifying PDAC cell lines, we use the k-nearest neighbors (k-NN) algorithm to classify cell lines based on physical phenotypes. In the k-NN method, training data establishes a multidimensional feature space, where q-DC parameters define each dimension; cell lines are then classified based on the identity of their k nearest neighbors in the pre-established feature space. To evaluate how the number of predictors and combinations thereof affect classification accuracy, we first assess the ability of single physical phenotypes to classify cells. We find that single parameters alone offer low classification accuracy of cell lines: TV yields 65% accuracy in predicting the correct cell line from our panel of PDAC cell lines, 7i yields 59% accuracy, and D_ceii gives 52% (Fig.18, panel A). [0089] Including additional physical phenotypes significantly enhances classification accuracy: {E, T_T) provide a model accuracy of 87% and with { T_T, D_ceii}, the model accuracy increases to 91% (Fig. 18, panel A, Fig. 23). Other combinations of two parameters yield accuracies ranging from 69% to 89% (Fig. 23). Including an additional third parameter further improves accuracy, but with smaller gains: both {E, T_T, D_ceu}and {E, c_max, D_ceu}resu\t in 94% accuracy. The highest accuracy of 96% can be obtained using four parameters {E, T_T, Dceii, c_max}(Fig. 18, panels A, B). Surprisingly, we find that using additional q-DC parameters does not improve classification accuracy, which ranges from 92% to 96% when using five and six physical phenotypes; this highlights how certain pairs of parameters, such as T_T and T_E, are highly correlated. Therefore, we use {E, T_T, D_ceii, c_max} as a reduced set of

parameters, which minimizes cross-correlations and provides the highest classification accuracy with the least amount of parameters.

[0090] Since transit time T_T is a common metric for cell deformability that is obtained by transit-based deformability cytometry (22), we next evaluate the benefit of q-DC parameters by comparing the performance of the k-NN algorithm using the reduced set of parameters to T_T alone (Fig. 18, panels C, D). For the k-NN algorithm using T_Tas a single predictor, we find the algorithm performs poorly: the true positive rate for each cell line ranges from 0.33 to 0.86 (Fig. 18, panel C). For example, the true positive rate for PANC-1 cells is 0.33, indicating that only 33% of PANC-1 samples are correctly identified as PANC-1 cells, 41%) are incorrectly identified as HPDE cells, and 26% as AsPC-1 cells (Fig. 18, panel C). When {T_T} is used, the true positive rate averaged across all cell lines is 0.65 and the false positive rate is 0.35. By contrast, the reduced set of q-DC parameters {E, T_T, D_ceii, Cmax) significantly improves the average true positive rate to 0.96. For example, the true positive rate for PANC-1 cells is 1.0, where 100% of PANC-1 samples are correctly identified.

Additionally, the true positive rate for Hs766T is 0.94, where 94% of Hs766T samples are correctly identified, while 6% are identified as MIA PaCa-2 (Fig. 18, panel D). We also observe the reduced set {E, T_T, D_ceii, Cmax) decreases the false positive rate, which ranges from 0 to 0.06 (average = 0.04) (Fig. 18, panel D). Taken together, these findings indicate that q-DC predictors increase the accuracy for classifying PDAC cell lines compared to T_T alone.

Relationship of physical phenotypes to cancer cell invasion.

[0091] To identify which physical phenotypes are the strongest indicators of cancer cell invasion (Fig. 19, panel A), we first evaluate the correlation between invasion and single physical phenotypes of the reduced set, {E, T_T, ¾_¾ e_max}. Across the panel of PDAC cell lines, we find that individual parameters from the reduced set have poor to moderate correlations with invasion as measured using a 3D scratch wound invasion assay (13,44): Pearson's correlation yields R² that range from R_D-inv² = 0.05 ± 0.001 to R_E-inv² = 0.45 ± 0.006 (Fig. 19, panel B). We find the strongest correlation of a single parameter with invasion for £ (RE-inv² = 0.45 ± 0.006), whereby cells that are more invasive tend to have lower E (Fig. 19, panel B). This trend of more invasive cells being more compliant is consistent with previous reports in breast and ovarian cancer cells (5-11). However, the inverse relationship between invasion and E does not hold across all PDAC cell lines as MIA PaCa-2 cells exhibit the lowest elastic modulus yet reduced invasion compared to Hs766T and PANC-1 cells (Fig. 19, panel B).

[0092] We also measure the physical phenotype of seven ovarian cancer cell samples that overexpress distinct microRNAs (microRNA-508-3p, microRNA-508-5p, microRNA- 509-3p, microRNA-509-5p and microRNA-130b-3p); higher levels of expression of these microRNAs are associated with improved patient survival, as identified through Cancer

Genome Atlas (TCGA) data (43). We previously found that microRNA-509-3p, microRNA- 509-3p, microRNA-508-3p, and microRNA-130b-3p decrease cell invasion (43,44) and increase cell transit time (44). Physical phenotyping by q-DC reveals that individual phenotypes of microRNA-overexpressing cells also exhibit only moderate correlations to invasion (Fig. 19, panel B). While we find that higher E and T_T are associated with decreased invasion across both established pancreatic cancer cell lines and ovarian cancer cells with manipulated microRNA levels, we find opposite trends for D_ceii and c_max (Fig. 19, panel B); these discrepancies further substantiate the low predictive power of individual physical phenotypes. As single physical phenotypes are not sufficient to predict invasion, we next investigate if multiparameter analysis using the reduced set of four physical phenotypes can collectively predict cancer invasion.

[0093] To develop a model that can predict cell invasion on the basis of physical phenotypes, we train a multiple linear regression model using {E, T_T, D_ceii, £max) and invasion data. While we use data from numerous cell samples, linear regression can be susceptible to overfitting when the number of fitting parameters approaches the number of data points. Therefore, we utilize the data set with the largest number of samples, which is the ovarian cancer cells overexpressing microRNAs that tend to decrease cell invasion (43,44). We account for the number of predictors in the strength of correlation between the measured and predicted invasion using the adjusted-R² (R² _adj),

where n is the number of observations and m is the number of predictors. For the PDAC cell lines, an R² _adj value does not exist, as there are four fitting parameters in the reduced set and five cell lines. However, building the linear regression model using invasion and physical phenotype data {E, T_T, D_ceii, Cmax) from seven ovarian cancer cell lines that overexpress distinct microRNAs results in invasion values that are highly correlated with experimental observations, as indicated by the high R² _adj = 1.00 ± 0.002 (Fig. 19, panel D); we call this multiple linear regression model built with the reduced set of parameters the 'physical phenotype model for invasion' . We also train models with smaller sets of predictors;

however, we find that the reduced set of physical phenotypes (E, T_T, D_ceii, tmax) yields the highest R_adf value, and thus generates the strongest predictive model with the smallest number of parameters (Fig. 19, panel D). Predicting invasion using physical phenotypes.

[0094] To validate the physical phenotyping model for invasion, we measure physical phenotypes of seven additional cancer cell samples, and determine how accurately we can predict invasion for samples that are independent of the training set. We first use q-DC to physical phenotype three breast cancer cell lines, MDA-MB-231, MDA-MB-468, and MCF-7 (Fig. 20, panel A). These cell lines are well characterized to have varying invasive potentials, from highest to lowest: MDA-MB-231 > MDA-MB-468 > MCF-7 (72,55-58). Other key characteristics of progression are also described for these cell lines, including the propensity to form cell colonies (MDA-MB-231 > MDA-MB-468 > MCF-7) (58). By physical phenotyping using q-DC, we find that MDA-MB-231 cells have decreased E compared to both MDA-MB-468 and MCF-7 cells (£_MDA-_MB-₂3_I = 1.2 ± 0.3 kPa < E_MC_F-_I = 2.0 ± 0.2 kPa < ^_MDA-_MB-₄68 = 2.7 ± 0.3 kPa ). Compared to the ranking of invasion of these cells types, we find a weak correlation between E and invasion, which is further quantified by Spearman's correlation coefficient (r = 0.5); these findings support that E alone is not sufficient to predict invasion. We find that transit times follow the same ranking as E, whereby T_T. _MDA-_MB-₂3₁ = 15 ± 3 ms < Jr - _MC_F-7 = 25 ± 5 ms < Γ_Γ- _ΜΟΑ-_ΜΒ-₄68 = 51 ± 21 ms (Fig. 20, panel A). Thus, neither E nor T_T is sufficient to predict invasion. However, we discover that the physical phenotyping model for invasion correctly ranks the invasion of these breast cancer cell lines, MDA-MB-231 > MDA-MB-468 > MCF-7 (Fig. 20, panel D). These results further substantiate the power of multiparameter analysis to predict invasion based on physical phenotyping of single cancer cells.

[0095] To further validate the physical phenotyping model for invasion, we predict the invasion of ovarian cancer (OVCA433) cells that have been genetically manipulated to generate a pair of epithelial- and mesenchymal-like cell lines. Cancer cells with

overexpression of Snail (45) (OVCA433-Snail), a key transcription factor in epithelial -to- mesenchymal transition (EMT) (73) are mesenchymal-like and exhibit increased invasion (73). By contrast, the control cells (OVCA433-GFP) are epithelial-type. Using q-DC to physical phenotype this pair of cell lines, we find that OVCA433-Snail cells have a reduced E compared to the OVCA433-GFP control cells £OVCA-GFP = 1.8 ± 0.1 kPa; EovcA-snaii = 1.0 ± 0.7 kPa; p « 0.001) (Fig 20, panel B). We also observe that OVCA433-Snail cells exhibit shorter transit times than OVCA433-GFP (7V - OVCA-GEP ⁼ 22 ± 2.8 HIS; JT- OVCA-Snail^— 16 ±

1.2 ms, p « 0.001), consistent with the decreased stiffness of the mesenchymal-type

OVCA433-Snail cells (Fig. 20, panel B). Using q-DC outputs, we demonstrate that the physical phenotype model for invasion has the power to predict the increased invasion of the OVCA433-Snail cells compared to the control OVCA433-GFP cells (Fig. 20, panel B); these results also demonstrate that physical phenotypes measured by q-DC are consistent with other hallmark characteristics of EMT, such as the increased vimentin to E-cadherin ratio (74) and ability to form cell colonies (75), which are commonly used to define mesenchymal-type cells.

[0096] We next assess how increased cell invasion that is caused by pharmacologic manipulation can be predicted by the physical phenotype model of invasion. We previously showed that cancer cells treated with the β-adrenergic agonist, isoproterenol, have increased invasion in vitro (14). Activation of β-adrenergic signaling also promotes metastasis in clinically-relevant orthotopic mouse models of breast cancer (46,76). Following treatment of highly metastatic human breast cancer (MDA-MB-231-FDVI) cells with isoproterenol, we find that E increases from ^control = 0.9 ± 0.4 kPa to £iso = 4.0 ± 0.6 kPa (p = 0.001) (Fig. 20, panel C). Similarly, T_T increases from T_T. control ⁼ 18 ± 4.2 ms to T_T. iso ⁼ 81 ± 31 ms (p « 0.001) (14) (Fig. 20, panel C). While pharmacological perturbation results in altered cell physical phenotypes, the phenotyping model does not accurately predict the effects of isoproterenol on cancer cell invasion (Fig 20, panel F). The inability of the physical phenotyping model to predict the increased invasion caused by this pharmacologic manipulation suggests that there is a fundamentally different relationship between the effect of β-adrenergic signaling on physical phenotypes and β-adrenergic regulation of invasion compared with the other sets of cancer cells that we investigate here.

Discussion.

[0097] Here we develop the physical phenotyping model to predict invasion using four parameters— elastic modulus E, transit time T_T, maximum strain e_max, and cell size Dceii— which can be rapidly measured using q-DC. We demonstrate the model's predictive power across ovarian, breast, and pancreatic cell lines that have inherent differences in invasive potential, as well as for cells that have increased invasive potential caused by genetic modification. To generate the physical phenotyping model, we use machine learning methods, which provide a powerful tool to predict clinically relevant phenotypes (25-33). Here we assess invasion, which is used as a metric to determine molecular mediators of metastasis and to validate therapeutic targets in drug discovery (77,78). However, typical invasion assays require hours to days (77,79). The ability to predict cancer cell invasion based on physical phenotyping of single cells within minutes would thus achieve order of magnitude advances in the time required to assess cell invasion; this could enable rapid evaluation of how patient samples, such as cells from pleural effusions or dissociated tumors, respond to drugs.

Physical phenotypes as indicators of invasion.

[0098] The physical phenotyping model for invasion relies on the reduced set of physical phenotypes— elastic modulus E, transit time T_T, maximum strain c_max, and cell size Dceii— which can be rapidly measured using q-DC:

Elastic modulus.

[0099] E is an essential indicator of invasion in the physical phenotype model. Our investigation of physical phenotypes across nineteen cell samples, including established cell lines and a range of genetic and pharmacologic perturbations, provide the opportunity to examine how broadly the relationship between cell stiffness and invasion can be generalized. We find that E is the physical phenotype that is most highly correlated with invasion (Fig. 24), reflecting the general trend that more invasive cells tend to be more compliant.

Interestingly, we identify several contexts where more invasive cells are stiffer. For example, while overexpression of many of the microRNAs cause ovarian cancer (HEYA8) cells to become stiffer and less invasive, overexpression of microRNA 509-5p causes cells to be stiffer and more invasive. We also observe that PANC-1 and Hs766T cells are stiffer and more invasive than MIA PaCa-2 cells. There are additional examples of more invasive cells being stiffer in the breast cancer panel, where MDA-MB-468 cells are stiffer, yet more invasive than MCF-7 cells. Treatment of MDA-MB-231 cells with isoproterenol also causes cells to be stiffer and more invasive. While the overall trend of our data suggests that elastic modulus and invasion are inversely correlated, these and other cases of more invasive cells that are stiffer (13-17), suggest that this inverse correlation is context-dependent.

Transit time.

[0100] While transit time T_T is commonly used to distinguish cancer cell types (22), this parameter alone is not a strong indicator of invasion. We find moderate to poor association between T_T and invasion across well-characterized cell lines and microRNA- overexpressing cells. The emergence of T_T as an indicator of invasion in the physical phenotyping model suggests that the ability of cells to continuously deform may be important in invasion. While E reflects the ability of a cell to resist initial deformation, and thus dominates viscoelastic response on short millisecond timescales (23), transit time captures the ability of a cell to deform through the entire constriction. We showed previously that T_T depends on both elastic and viscous properties (23); indeed, invasion occurs over hours to days (61), where viscous contributions may be more relevant. Size.

[0101] We find that cell size D_cen strengthens the accuracy of the physical phenotype model to predict invasion. We and others previously determined that cell size is inversely correlated with invasion potential (9,44). The effects of cell size may also reflect

contributions of the cell nucleus to q-DC measurements: nuclear size scales with cell size (13), and the nucleus tends to be stiffer than the surrounding cytoplasm (11). Moreover, increased nuclear-to-cytoplasmic volume is a hallmark of malignant cells that has diagnostic and prognostic value (2,80,81). Morphological parameters, such as eccentricity and circularity, are also identified as strong predictors of cancer cell types (38); the role of nuclear shape stability in cancer cell physical phenotypes that we investigate here remains to be determined.

[0102] This set of physical features {E, T_T, D_ceii, £_max} that we have identified enhances the accuracy of the model to predict cell invasion, but the extent to which they are implicated in invasion is still not fully understood. It is important to emphasize that a biomarker is not required to have a well-established physiological role in order to be an accurate predictor of a disease state. For example, nuclear shape is widely used for cancer prognosis (2-4), but the physiological consequences of aberrant nuclear morphology in cancer cells is still undefined.

Tradeoffs of using multiple physical phenotypes to predict invasion.

[0103] Our findings demonstrate the enhanced predictive power that can be achieved using multiple physical phenotypes obtained by q-DC, such as elastic modulus E, cell fluidity β, entry time T_E, and maximum strain c_max (24). However, extra computation is required to extract these parameters. The tradeoff between model accuracy and computational expense will ultimately depend on the specific application. For example, certain cancer cell populations can be distinguished using measurements of T_Tand D_ceii, which rely on simpler image analysis (10,21-23,59,61). With greater computational investment, such as tracking the time-dependent changes in cell shape during deformation and fitting power law rheology models to the time-dependent strain of single cells, additional parameters such as c_max and E can be determined (24). More complex algorithms that exploit the variability of physical phenotypes within cell samples may further improve the accuracy of prediction. However, such enhanced resolution may not be essential for specific applications. For example, the invasion of the epithelial-type OVCA433-GFP cells versus the mesenchymal-type

OVCA433-Snail cells is accurately ranked by the median E alone (Fig 20, panel E).

Benefits of q-DC method for machine learning.

[0104] Since q-DC enables us to obtain calibrated measurements of cell physical phenotypes, this approach addresses the lack of measurement standardization that often challenges the use of machine learning models to predict cellular behaviors (25,26,82,83). Using gel particles as a calibration standard, q-DC enables us to compare data across distinct sets of cell types while avoiding batch-to-batch variation. In addition, the q-DC method enables us to rapidly train the algorithm using a set of cell samples and then evaluate the model performance using a set of seven independent cell samples; this reduces the risk of overfitting by increasing the number of samples compared to the number of measured biomarkers, which is a major challenge in machine learning methods. The ability to rapidly obtain calibrated physical phenotyping data containing multiple features of cells thus provides a powerful complementary biomarker to enrich the feature space available for machine learning approaches.

[0105] In contrast to calibrated, physical phenotypes obtained by q-DC,

measurements of cell invasion are inherently relative. As the model is evaluated using invasion data from both previous experiments (12-14) and literature (55-58), the predicted invasion cannot be quantitatively compared to the measured invasion. For this reason, we present the assessment of the model's predictive power as a ranking of invasion of cell types. Future studies that investigate a larger panel of cell types within a single invasion experiment, or compare the invasion of cell types using the same experimental setup, would allow for more detailed evaluation of the accuracy of the predictive model for invasion.

[0106] The use of more sophisticated machine learning approaches could further improve performance of the model for invasion. Using stack combinations of machine learning methods can overcome the limitations of individual algorithms and thereby generate a more robust model (84). More advanced algorithms could also minimize the image analysis required for the physical phenotyping model for invasion; for example, neural network algorithms can be trained using images with minimal processing, and thus do not require the additional computational steps to extract physical phenotypes.

Effects of measurement techniques on the physical phenotyping model for invasion.

[0107] Since different methods for physical phenotyping investigate cells in suspended versus adhered states, it is not clear how broadly the predictors of invasion identified by q-DC can be translated to other physical phenotyping measurements.

Microfluidic methods, such as q-DC, probe cells in suspension, where cells exhibit an altered distribution of F-actin compared to when they are adhered to a substrate (13,85). In addition, cells attached to a substrate generate intracellular tension; this 'prestress' (86) can contribute to cell stiffness measurements when using a technique such as AFM (85,87). Considering the increased contractility and/or stress fiber formation of adhered cells may explain the difference in the ranking of elastic modulus values for PDAC cells measured by q-DC and AFM (13). Differences in the time and length scales of mechanical measurements by AFM and q-DC may further contribute to differences in measured physical phenotypes.

[0108] Measuring the mechanical properties of cells using complementary methods could provide valuable insight into the role of cell physical phenotypes at varying steps in the metastatic cascade. The stiffness of adhered cells depends on myosin II activity (88-91), which is required for cells to generate forces during invasion, extravasation, and intravasation (92,93); mechanotyping of adhered cells could provide an additional, complementary physical indicator of cell invasion. Indeed, traction stresses scale with cell metastatic potential (94). The ability of suspended cells to deform during circulation through the blood and lymphatic vasculature (92,93) and resist fluid shear stresses (95) is critical for tumor cell dissemination.

[0109] The method for measuring cancer cell invasion could also impact the physical phenotyping model for invasion. Results from the 3D scratch wound invasion assay used here are similar to data obtained using a transwell migration assay (13,44). However, the ranking of invasion across cancer cell lines could be influenced by tuning matrix stiffness and/or composition; instead of Matrigel, as used here, collagen or fibronectin, could recapitulate different physiological conditions, where some cell types may be more effective at invading. Since the ability of cells to invade through different matrix materials can differ, the relationship between cell physical phenotypes and invasion should be defined for each context. Such an approach could extend the applicability of this methodology to predict the migration of immune cells or neurons, or wound healing response.

Navigating the physical fitness landscape of invasion.

[0110] Invasion is a complex and highly dynamic process requiring deformation through micron-scale pores (93,96), protrusion formation (97), generation of traction forces (94), and secretion of proteases (98-100). While we cannot directly conclude from the predictive model that the reduced set of parameters—elastic modulus E, transit time T_T, maximum strain e_max, and cell size D_ceu~ contribute to cancer invasion, evidence in the literature suggests that these parameters have functional implications. The stiffness of cells determines their ability to deform through narrow gaps; thus, changes in cell physical properties could have consequences for functional behaviors, such as invasion. Cell size may impact how readily cells can invade through a matrix. Indeed, cell size determines the probability of cells to occlude narrow capillaries or pores (101, 102), and thus may be implicated in lodging of cells in metastatic target sites, such as the narrow capillaries of the pulmonary beds of the lung (93). Consistent with these findings, we observe that more invasive cells tend to have lower elastic modulus and smaller cell size (Fig 19, panel B). [0111] While the physical phenotype model predicts the invasion of most contexts we investigate here, the model does not predict the increased invasion of cancer cells with β- adrenergic activation. Specifically, activation of β-adrenergic signaling alters single-cell physical phenotypes and invasion in a way that is not consistent with the other cell samples, including both cell lines and genetically-modified cells. Further studies of how β-adrenergic signaling alters cell physical phenotypes may explain why these cells are stiffer and more invasive, and could facilitate the discovery of additional biomarkers, such as contractility, to predict invasion. For example, the increased stiffness of cells with activation of β-adrenergic signaling requires myosin II activity (14); myosin II is also required for actomyosin contractility, which increases cell stiffness (88-91) and generates forces required for cells to invade through 3D matrices (103,104).

[0112] It is intriguing to speculate that different physical phenotype signatures may reflect different strategies for cancer cell invasion. Deeper investigation of contexts where invasion cannot be predicted by the physical phenotype model for invasion may reveal another physical regime that is described by a different set of phenotypes that can predict invasion. Identifying additional complementary biomarkers could generate a more inclusive— even universal— model to predict invasion across varied contexts. Future studies to better elucidate the interplay between physical phenotypes in the invasion 'fitness landscape' will deepen our understanding of potential selective advantages acquired by cancer cells with altered physical phenotypes. In addition, the data that we have generated (SI) should be valuable to for the development of future mechanistic models of cell invasion (105-107), which could provide further insight into the role of these physical phenotypes in regulating invasion.

Conclusion.

[0113] The q-DC method for single-cell physical phenotyping coupled with machine learning algorithms provides an important step towards enhanced classification of cancer cell types. More broadly, the physical phenotyping model provides a framework for

understanding and predicting clinically relevant phenotypes. While we define here the relationship between physical phenotypes and invasion, the approach could be extended to investigate other clinically relevant phenotypes, such as sensitivity to chemotherapy agents. References.

[0114] 1. Brown M, Wittwer C. Flow cytometry: principles and clinical applications in hematology. Clin Chem. United States; 2000 Aug;46(8 Pt 2): 1221-9.

[0115] 2. Elston CW, Ellis IO. Pathological prognostic factors in breast cancer. I. The value of histological grade in breast cancer: experience from a large study with long-term follow-up. Histopathology. England; 1991 Nov; 19(5):403-10.

[0116] 3. Webster M, Witkin KL, Cohen-Fix O. Sizing up the nucleus: nuclear shape, size and nuclear-envelope assembly. J Cell Sci. 2009 May; 122(Pt 10): 1477-86.

[0117] 4. Guilak F, Tedrow JR, Burgkart R. Viscoelastic properties of the cell nucleus. Biochem Biophys Res Commun. Elsevier; 2000;269(3):781-6.

[0118] 5. Guck J, Schinkinger S, Lincoln B, Wottawah F, Ebert S, Romeyke M, et al.

Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence. Biophys J. Elsevier; 2005 May;88(5):3689-98.

[0119] 6. Cross SE, Jin Y-S, Rao J, Gimzewski JK. Nanomechanical analysis of cells from cancer patients. Nat Nanotechnol. 2007 Dec;2(12):780-3.

[0120] 7. Hur SC, Henderson-MacLennan NK, McCabe ERB, Di Carlo D.

Deformability-based cell classification and enrichment using inertial microfluidics. Lab Chip. England; 2011 Mar; l l(5):912-20.

[0121] 8. Xu W, Mezencev R, Kim B, Wang L, McDonald J, Sulchek T. Cell stiffness is a biomarker of the metastatic potential of ovarian cancer cells. PLoS One. Public Library of Science; 2012;7(10):e46609.

[0122] 9. Swaminathan V, Mythreye K, O'Brien ET, Berchuck A, Blobe GC,

Superfine R. Mechanical stiffness grades metastatic potential in patient tumor cells and in cancer cell lines. Cancer Res. United States; 2011 Aug;71(15):5075-80. [0123] 10. Hou HW, Li QS, Lee GYH, Kumar a. P, Ong CN, Lim CT.

Deformability study of breast cancer cells using microfluidics. Biomed Microdevices. 2009 Jun; l l(3):557-64.

[0124] 11. Agus DB, Alexander JF, Arap W, Ashili S, Asian JE, Austin RH, et al. A physical sciences network characterization of non-tumorigenic and metastatic cells. Sci Rep. England; 2013;3 : 1449. [0125] 12. Chan CK, Pan Y, Nyberg K, Marra MA, Lim EL, Jones SJ, et al. Tumour- suppressor microRNAs regulate ovarian cancer cell physical properties and invasive behaviour. Open Biol. 2016;6(11).

[0126] 13. Nguyen A V, Nyberg KD, Scott MB, Welsh AM, Nguyen AH, Wu N, et al. Stiffness of pancreatic cancer cells is associated with increased invasive potential. Integr Biol. England; 2016 Oct;

[0127] 14. Kim T-H, Gill NK, Nyberg KD, Nguyen A V, Hohlbauch S V, Geisse

NA, et al. Cancer cells become less deformable and more invasive with activation of beta- adrenergic signaling. J Cell Sci. England; 2016 Dec; 129(24):4563-75. [0128] 15. Liu C-Y, Lin H-H, Tang M-J, Wang Y-K. Vimentin contributes to epithelial-mesenchymal transition cancer cell mechanics by mediating cytoskeletal organization and focal adhesion maturation. Oncotarget. United States; 2015

Jun;6(l 8): 15966-83.

[0129] 16. Rathje L-SZ, Nordgren N, Pettersson T, Ronnlund D, Widengren J, Aspenstrom P, et al. Oncogenes induce a vimentin filament collapse mediated by HDAC6 that is linked to cell stiffness. Proc Natl Acad Sci U S A. United States; 2014

Jan; l l l(4): 1515-20.

[0130] 17. Weder G, Hendriks-Balk MC, Smajda R, Rimoldi D, Liley M,

Heinzelmann H, et al. Increased plasticity of the stiffness of melanoma cells correlates with their acquisition of metastatic properties. Nanomedicine. United States; 2014 Jan; 10(1): 141- 8.

[0131] 18. Darling EM, Di Carlo D. High-Throughput Assessment of Cellular

Mechanical Properties. Annu Rev Biomed Eng. United States; 2015; 17:35-62.

[0132] 19. Lange JR, Steinwachs J, Kolb T, Lautscham LA, Harder I, Whyte G, et al. Microconstriction Arrays for High-Throughput Quantitative Measurements of Cell

Mechanical Properties. Biophys J. Biophysical Society; 2015; 109(l):26-34.

[0133] 20. Hoelzle DJ, Varghese BA, Chan CK, Rowat AC. A Microfluidic

Technique to Probe Cell Deformability. JoVE. 2014;91 :e51474-e51474.

[0134] 21. Byun S, Son S, Amodei D, Cermak N, Shaw J, Kang JH, et al.

Characterizing deformability and surface friction of cancer cells. Proc Natl Acad Sci.

2013; 110(19):7580-5. [0135] 22. Rosenbluth MJ, Lam WA, Fletcher DA. Analyzing cell mechanics in hematologic diseases with microfluidic biophysical flow cytometry. Lab Chip. Royal Society of Chemistry; 2008 Jul;8(7): 1062-70.

[0136] 23. Nyberg KD, Scott MB, Bruce SL, Gopinath AB, Bikos D, Mason TG, et al. The physical origins of transit time measurements for rapid, single cell mechanotyping. Lab Chip. Royal Society of Chemistry; 2016;16(17):3330-9.

[0137] 24. Nyberg KD, Hu KH, Kleinman SH, Khismatullin DB, Butte MJ, Rowat

AC. Quantitative Deformability Cytometry (q-DC): rapid, calibrated measurements of single cell viscoelastic properties. Biophys J. 2017; 16(17). [0138] 25. Ko J, Baldassano SN, Loh P-L, Kording K, Litt B, Issadore D. Machine learning to detect signatures of disease in liquid biopsies - a user's guide. Lab Chip. England; 2018 Jan; 18(3):395-405.

[0139] 26. Kording KP, Benjamin A, Farhoodi R, Glaser JI. The Roles of Machine

Learning in Biomedical Science. In: Frontiers of Engineering: Reports on Leading-Edge Engineering from the 2017 Symposium. 2018.

[0140] 27. Chen CL, Mahjoubfar A, Tai L-C, Blaby IK, Huang A, Niazi KR, et al.

Deep Learning in Label-free Cell Classification. Sci Rep. England; 2016 Mar;6:21471.

[0141] 28. Agranoff D, Fernandez-Reyes D, Papadopoulos MC, Rojas SA, Herbster

M, Loosemore A, et al. Identification of diagnostic markers for tuberculosis by proteomic fingerprinting of serum. Lancet (London, England). England; 2006 Sep;368(9540): 1012-21.

[0142] 29. Varma VR, Oommen AM, Varma S, Casanova R, An Y, Andrews RM, et al. Brain and blood metabolite signatures of pathology and progression in Alzheimer disease: A targeted metabolomics study. PLoS Med. United States; 2018 Jan; 15(l):el002482.

[0143] 30. Levy B, Hu ZI, Cordova KN, Close S, Lee K, Becker D. Clinical Utility of Liquid Diagnostic Platforms in Non-Small Cell Lung Cancer. Oncologist. United States; 2016 Sep;21(9): 1121-30.

[0144] 31. Burrell RA, McGranahan N, Bartek J, S wanton C. The causes and consequences of genetic heterogeneity in cancer evolution. Nature. England; 2013

Sep;501(7467):338-45. [0145] 32. Crowley E, Di Nicolantonio F, Loupakis F, Bardelli A. Liquid biopsy: monitoring cancer-genetics in the blood. Nat Rev Clin Oncol. England; 2013 Aug; 10(8) :472- 84.

[0146] 33. Fu Q, Schoenhoff FS, Savage WJ, Zhang P, Van Eyk JE. Multiplex assays for biomarker research and clinical application: translational science coming of age.

Proteomics Clin Appl. Germany; 2010 Mar;4(3):271-84.

[0147] 34. Lee WC, Shi H, Poon Z, Nyan LM, Kaushik T, Shivashankar G V, et al.

Multivariate biophysical markers predictive of mesenchymal stromal cell multipotency. Proc Natl Acad Sci. United States; 2014 Oct; l l l(42):E4409-18. [0148] 35. Bongiorno T, Chojnowski JL, Lauderdale JD, Sulchek T. Cellular

Stiffness as a Novel Sternness Marker in the Corneal Limbus. Biophys J. United States; 2016 Oct; 111(8): 1761-72.

[0149] 36. Bongiorno T, Kazlow J, Mezencev R, Griffiths S, Olivares-Navarrete R,

McDonald JF, et al. Mechanical stiffness as an improved single-cell indicator of osteoblastic human mesenchymal stem cell differentiation. J Biomech. Elsevier; 2014;47(9):2197-204.

[0150] 37. Gossett DR, Tse HTK, Lee S a., Ying Y, Lindgren AG, Yang OO, et al.

Hydrodynamic stretching of single cells for large population mechanical phenotyping. Proc Natl Acad Sci. National Acad Sciences; 2012 May; 109(20): 7630-5.

[0151] 38. Lin J, Kim D, Henry TT, Tseng P, Peng L, Dhar M, et al. High- throughput physical phenotyping of cell differentiation. Microsystems Nanoeng. Nature Publishing Group; 2017;3 : 17013.

[0152] 39. Darling EM, Topel M, Zauscher S, Vail TP, Guilak F. Viscoelastic properties of human mesenchymally-derived stem cells and primary osteoblasts,

chondrocytes, and adipocytes. J Biomech. United States; 2008;41(2):454-64. [0153] 40. Darling EM, Guilak F. A neural network model for cell classification based on single-cell biomechanical properties. Tissue Eng Part A. United States; 2008 Sep; 14(9): 1507-15.

[0154] 41. Tse HTK, Gossett DR, Moon YS, Masaeli M, Sohsman M, Ying Y, et al.

Quantitative diagnosis of malignant pleural effusions by single-cell mechanophenotyping. Sci Transl Med. United States; 2013 Nov;5(212):212ral63. [0155] 42. Jiang Y, Lei C, Yasumoto A, Kobayashi H, Aisaka Y, Ito T, et al. Label- free detection of aggregated platelets in blood by machine-learning-aided optofluidic time- stretch microscopy. Lab Chip. England; 2017 Jul; 17(14): 2426-34.

[0156] 43. Pan Y, Robertson G, Pedersen L, Lim E, Hernandez -Herrera A, Rowat AC, et al. miR-509-3p is clinically significant and strongly attenuates cellular migration and multi-cellular spheroids in ovarian cancer. Oncotarget. United States; 2016

May;7(18):25930-48.

[0157] 44. Chan CK, Pan Y, Nyberg K, Marra MA, Lim EL, Jones SJM, et al.

Tumour-suppressor microRNAs regulate ovarian cancer cell physical properties and invasive behaviour. Open Biol. England; 2016 Nov;6(l 1).

[0158] 45. Qi D, Gill NK, Santiskulvong C, Sifuentes J, Dorigo O, Rao J, et al.

Screening cell mechanotype by parallel microfiltration. Sci Rep. Nature Publishing Group; 2015;5.

[0159] 46. Le CP, Nowell CJ, Kim-Fuchs C, Botteri E, Hiller JG, Ismail H, et al. Chronic stress in mice remodels lymph vasculature to promote tumour cell dissemination. Nat Commun. England; 2016 Mar;7: 10634.

[0160] 47. Duffy DC, McDonald JC, Schueller OJA, Whitesides GM. Rapid prototyping of microfluidic systems in poly(dimethylsiloxane). Anal Chem. 1998

Dec;70(23):4974-84. [0161] 48. Eddington DT, Crone WC, Beebe DJ. Development of process protocols to fine tune polydimethylsiloxane material properties. In: 7th International Conference on Miniaturized Chemical and Biochemical Analysis Systems. 2003. p. 1089-92.

[0162] 49. Byun S, Son S, Amodei D, Cermak N, Shaw J, Ho J, et al. Characterizing deformability and surface friction of cancer cells. 2013. [0163] 50. Shaw Bagnall J, Byun S, Begum S, Miyamoto DT, Hecht VC,

Maheswaran S, et al. Deformability of Tumor Cells versus Blood Cells. Sci Rep. England; 2015;5: 18542.

[0164] 51. Nyberg KD, Scott MB, Bruce SL, Gopinath AB, Bikos D, Mason TG, et al. The physical origins of transit time measurements for rapid, single cell mechanotyping. Lab Chip. 2016; 16(17). [0165] 52. Beyer K, Goldstein J, Ramakrishnan R, Shaft U. When is "nearest neighbor" meaningful? In: International conference on database theory. Springer; 1999. p. 217-35.

[0166] 53. Hall P, Park BU, Samworth RJ. Choice of neighbor order in nearest- neighbor classification. Ann Stat. JSTOR; 2008;2135-52.

[0167] 54. Hassanat AB, Abbadi MA, Altarawneh GA, Alhasanat AA. Solving the problem of the K parameter in the KNN classifier using an ensemble learning approach. arXiv Prepr arXiv 14090919. 2014.

[0168] 55. Gordon LA, Mulligan KT, Maxwell-Jones H, Adams M, Walker RA, Jones JL. Breast cell invasive potential relates to the myoepithelial phenotype. Int J cancer. Wiley Online Library; 2003; 106(1):8-16.

[0169] 56. Albini A, Iwamoto Y, Kleinman HK, Martin GR, Aaronson SA,

Kozlowski JM, et al. A rapid in vitro assay for quantitating the invasive potential of tumor cells. Cancer Res. United States; 1987 Jun;47(12):3239-45. [0170] 57. Sheridan C, Kishimoto H, Fuchs RK, Mehrotra S, Bhat-Nakshatri P,

Turner CH, et al. CD44+/CD24- breast cancer cells exhibit enhanced invasive properties: an early step necessary for metastasis. Breast Cancer Res. England; 2006;8(5):R59.

[0171] 58. Chekhun S, Bezdenezhnykh N, Shvets J, Lukianova N. Expression of biomarkers related to cell adhesion, metastasis and invasion of breast cancer cell lines of different molecular subtype. Exp Oncol. Ukraine; 2013 Sep;35(3): 174-9.

[0172] 59. Rowat AC, Jaalouk DE, Zwerger M, Ung WL, Eydelnant IA, Olins DE, et al. Nuclear Envelope Composition Determines the Ability of Neutrophil-type Cells to Passage through Micron-scale Constrictions. J Biol Chem. 2013 Mar;288(12):8610-8.

[0173] 60. Lange JR, Metzner C, Richter S, Schneider W, Spermann M, Kolb T, et al. Unbiased High-Precision Cell Mechanical Measurements with Microconstrictions.

Biophys J. Elsevier; 2017; 112(7): 1472-80.

[0174] 61. Ekpenyong AE, Whyte G, Chalut K, Pagliara S, Lautenschlager F, Fiddler

C, et al. Viscoelastic Properties of Differentiating Blood Cells Are Fate- and Function- Dependent. PLoS One. 2012;7(9). [0175] 62. Nguyen AV, Nyberg KD, Scott MB, Welsh AM, Nguyen AH, Wu N, et al. Stiffness of pancreatic cancer cells is associated with increased invasive potential. Integr Biol (United Kingdom). 2016;8(12).

[0176] 63. Soltani M, Vargas-Garcia CA, Antunes D, Singh A. Intercellular

Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes. PLoS Comput Biol. United States; 2016 Aug; 12(8):el004972.

[0177] 64. Gabriele S, Benoliel AM, Bongrand P, Theodoly O. Microfluidic investigation reveals distinct roles for actin cytoskeleton and myosin II activity in capillary leukocyte trafficking. Biophys J. Biophysical Society; 2009;96(10):4308-18. [0178] 65. Rosenbluth MJ, Lam WA, Fletcher DA. Force microscopy of nonadherent cells: a comparison of leukemia cell deformability. Biophys J. 2006;90:2994-3003.

[0179] 66. Otto et al. (2015) Nat. Meth. 12(3): 199-202.

[0180] 67. Needham D, Hochmuth RM. Rapid flow of passive neutrophils into a 4 microns pipet and measurement of cytoplasmic viscosity. J Biomech Eng. 1990; 112:269-76. [0181] 68. Tsai MA, Waugh RE, Keng PC. Cell cycle-dependence of HL-60 cell deformability. Biophys J. Elsevier; 1996;70(4):2023-9.

[0182] 69. Pajerowski JD, Dahl KN, Zhong FL, Sammak PJ, Discher DE. Physical plasticity of the nucleus in stem cell differentiation. Proc Natl Acad Sci. 2007;104(40): 15619- 24. [0183] 70. Fabry B, Maksym GN, Butler JP, Glogauer M, Navajas D, Fredberg JJ.

Scaling the microrheology of living cells. Phys Rev Lett. APS; 2001;87(14): 148102.

[0184] 71. Krijthe J, van der Maaten L. T-Distributed Stochastic Neighbor

Embedding using a Barnes-Hut Implementation [Internet]. Vienna, Austria: R Foundation for Statistical Computing; 2017. Available from: //github.com/jkrijthe/Rtsne. [0185] 72. Adams M, Jones JL, Walker RA, Pringle JH, Bell SC. Changes in tenascin-C isoform expression in invasive and preinvasive breast disease. Cancer Res. United States; 2002 Jun;62(l l):3289-97.

[0186] 73. De Craene B, Gilbert B, Stove C, Bruyneel E, van Roy F, Berx G. The transcription factor snail induces tumor cell invasion through modulation of the epithelial cell differentiation program. Cancer Res. United States; 2005 Jul;65(14):6237-44. [0187] 74. Behrens J, Mareel MM, Van Roy FM, Birchmeier W. Dissecting tumor cell invasion: epithelial cells acquire invasive properties after the loss of uvomorulin- mediated cell-cell adhesion. J Cell Biol. United States; 1989 Jun; 108(6):2435-47.

[0188] 75. Guadamillas MC, Cerezo A, Del Pozo MA. Overcoming anoikis— pathways to anchorage-independent growth in cancer. J Cell Sci. England; 2011 Oct; 124(Pt 19):3189-97.

[0189] 76. Creed SJ, Le CP, Hassan M, Pon CK, Albold S, Chan KT, et al. beta2- adrenoceptor signaling regulates invadopodia formation to enhance tumor cell invasion. Breast Cancer Res. England; 2015 Nov; 17(l): 145. [0190] 77. Hulkower KI, Herber RL. Cell Migration and Invasion Assays as Tools for Drug Discovery. Pharmaceutics [Internet]. MDPI; 2011 Mar 11;3(1): 107-24. Available from: www.ncbi.nlm.nih.gov/pmc/articles/PMC3857040.

[0191] 78. Eccles SA, Box C, Court W. Cell migration/invasion assays and their application in cancer drug discovery. Biotechnol Annu Rev. Netherlands; 2005; 11 :391-421. [0192] 79. Kramer N, Walzl A, Unger C, Rosner M, Krupitza G, Hengstschlager M, et al. In vitro cell migration and invasion assays. Mutat Res. Netherlands; 2013;752(1): 10-24.

[0193] 80. Johnston DG. Cytoplasmic :nuclear ratios in the cytological diagnosis of cancer. Cancer. United States; 1952 Sep;5(5):945-9.

[0194] 81. Foraker AG, Reagan JW. Nuclear size and nuclear: cytoplasmic ratio in the delineation of atypical hyperplasia of the uterine cervix. Cancer. United States;

1956;9(3):470-9.

[0195] 82. Vidyasagar M. Identifying predictive features in drug response using machine learning: opportunities and challenges. Annu Rev Pharmacol Toxicol. United States; 2015;55: 15-34. [0196] 83. Abu-Mostafa YS, Magdon-Ismail M, Lin H-T. Learning from data. Vol.

4. AMLBook New York, NY, USA:; 2012.

[0197] 84. Ko J, Bhagwat N, Yee SS, Ortiz N, Sahmoud A, Black T, et al.

Combining Machine Learning and Nanofluidic Technology To Diagnose Pancreatic Cancer Using Exosomes. ACS Nano. United States; 2017 Nov; l l(l l): 11182-93. [0198] 85. Maloney JM, Nikova D, Lautenschlager F, Clarke E, Langer R, Guck J, et al. Mesenchymal stem cell mechanics from the attached to the suspended state. Biophys J. Elsevier; 2010;99(8):2479-87.

[0199] 86. Gardel ML, Nakamura F, Hartwig JH, Crocker JC, Stossel TP, Weitz DA. Prestressed F-actin networks cross-linked by hinged filamins replicate mechanical properties of cells. Proc Natl Acad Sci. United States; 2006 Feb; 103(6): 1762-7.

[0200] 87. Rotsch C, Radmacher M. Drug-induced changes of cytoskeletal structure and mechanics in fibroblasts: an atomic force microscopy study. Biophys J. Elsevier;

2000;78(l):520-35. [0201] 88. Martens JC, Radmacher M. Softening of the actin cytoskeleton by inhibition of myosin II. Pflugers Arch Eur J Physiol. Springer; 2008;456(1):95-100.

[0202] 89. Murrell M, Oakes PW, Lenz M, Gardel ML. Forcing cells into shape: the mechanics of actomyosin contractility. Nat Rev Mol Cell Biol. England; 2015

Aug; 16(8):486-98. [0203] 90. Wang N, Naruse K, Stamenovic D, Fredberg JJ, Mijailovich SM, Tolic-

Norrelykke IM, et al. Mechanical behavior in living cells consistent with the tensegrity model. Proc Natl Acad Sci U S A. United States; 2001 Jul;98(14):7765-70.

[0204] 91. Wang N, Tolic-Norrelykke FM, Chen J, Mijailovich SM, Butler JP,

Fredberg JJ, et al. Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells. Am J Physiol Cell Physiol. United States; 2002 Mar;282(3):C606-16.

[0205] 92. Chambers AF, Groom AC, MacDonald IC. Dissemination and growth of cancer cells in metastatic sites. Nat Rev Cancer. England; 2002 Aug;2(8):563-72.

[0206] 93. Wirtz D, Konstantopoulos K, Searson PC. The physics of cancer: the role of physical interactions and mechanical forces in metastasis. Nat Rev Cancer. England; 2011 Jun; l l(7):512-22.

[0207] 94. Kraning-Rush CM, Califano JP, Reinhart-King CA. Cellular traction stresses increase with increasing metastatic potential. PLoS One. United States;

2012;7(2):e32572.

[0208] 95. Barnes JM, Nauseef JT, Henry MD. Resistance to fluid shear stress is a conserved biophysical property of malignant cells. PLoS One. United States;

2012;7(12):e50973. [0209] 96. Denais CM, Gilbert RM, Isermann P, McGregor AL, te Lindert M,

Weigelin B, et al. Nuclear envelope rupture and repair during cancer cell migration. Science. United States; 2016 Apr;352(6283):353-8.

[0210] 97. Olson MF, Sahai E. The actin cytoskeleton in cancer cell motility. Clin Exp Metastasis. Netherlands; 2009;26(4):273-87.

[0211] 98. Ma C, Wu B, Huang X, Yuan Z, Nong K, Dong B, et al. SUMO-specific protease 1 regulates pancreatic cancer cell proliferation and invasion by targeting MMP-9. Tumour Biol. United States; 2014 Dec;35(12): 12729-35.

[0212] 99. Zhao X, Gao S, Ren H, Sun W, Zhang H, Sun J, et al. Hypoxia-inducible factor-1 promotes pancreatic ductal adenocarcinoma invasion and metastasis by activating transcription of the actin-bundling protein fascin. Cancer Res. United States; 2014

May;74(9):2455-64.

[0213] 100. Nabeshima K, Inoue T, Shimao Y, Sameshima T. Matrix

metalloproteinases in tumor invasion: role for cell migration. Pathol Int. Australia; 2002 Apr;52(4):255-64.

[0214] 101. Doerschuk CM, Beyers N, Coxson HO, Wiggs B, Hogg JC. Comparison of neutrophil and capillary diameters and their relation to neutrophil sequestration in the lung. J Appl Physiol. United States; 1993 Jun;74(6):3040-5.

[0215] 102. Bathe M, Shirai A, Doerschuk CM, Kamm RD. Neutrophil transit times through pulmonary capillaries: the effects of capillary geometry and fMLP-stimulation.

Biophys J. Elsevier; 2002;83(4): 1917-33.

[0216] 103. Poincloux R, Collin O, Lizarraga F, Romao M, Debray M, Piel M, et al.

Contractility of the cell rear drives invasion of breast tumor cells in 3D Matrigel. Proc Natl Acad Sci U S A. United States; 2011 Feb; 108(5): 1943-8. [0217] 104. Petrie RJ, Koo H, Yamada KM. Generation of compartmentalized pressure by a nuclear piston governs cell motility in a 3D matrix. Science. United States; 2014 Aug;345(6200): 1062-5.

[0218] 105. Katira P, Bonnecaze RT, Zaman MH. Modeling the mechanics of cancer: effect of changes in cellular and extra-cellular mechanical properties. Front Oncol. Switzerland; 2013;3 : 145. [0219] 106. Katira P, Zaman MH, Bonnecaze RT. How changes in cell mechanical properties induce cancerous behavior. Phys Rev Lett. United States; 2012 Jan; 108(2):28103.

[0220] 107. Danuser G, Allard J, Mogilner A. Mathematical modeling of eukaryotic cell migration: insights beyond experiments. Annu Rev Cell Dev Biol. United States;

2013;29:501-28.

[0221] It is understood that the examples and embodiments described herein are for illustrative purposes only and that various modifications or changes in light thereof will be suggested to persons skilled in the art and are to be included within the spirit and purview of this application and scope of the appended claims. All publications, patents, and patent applications cited herein are hereby incorporated by reference in their entirety for all purposes.

Claims

CLAIMS What is claimed is:

1. A method of performing quantitative deformability cytometry, said method comprising:

providing a microfluidic device comprising a plurality of micron-scale constrictions;

applying cells to said device and driving said cells through said constructions by application of a pressure gradient across said device;

and determining at least two parameters independently selected from the group consisting of elastic modulus (E), cell fluidity (β), cell transit time (T_T), cell creep time (7c), cell size (D_cen), and maximum strain (ε_Μ3χ)·

2. The method of claim 1, wherein the measurements of elastic modulus (E), and/or cell fluidity (β) are calibrated measurements.

3. The method of claim 2, wherein the time-dependent strain of individual cells is tracked and the applied stresses are calibrated using gel particles with well- defined elastic moduli.

4. The method according to any one of claims 1-3, wherein said device comprises an array of branching channels.

5. The method of claim 4, wherein said array of branching channels leads to constructions ranging from about 5 μπι up to about 20 μπι, or to constructions ranging from about 7 μπι up to about 1 1 μπι, or to constructions of about 9 μπι.

6. The method according to any one of claims 1-5, wherein said microfluidic device is mounted on a microscope.

7. The method of claim 6, wherein said microfluidic device is mounted on an inverted microscope.

8. The method according to any one of claims 1-7, wherein said microfluidic device comprises a device as illustrated in Figure 1 A, and or Figure IB.

9. The method according to any one of claims 1-5, wherein creep trajectory is measured by change in electrical resistance.

10. The method according to any one of claims 6-8, wherein images are acquired of cells in said microfluidic device.

11. The method of claim 10, wherein said images of said cells are acquired at a rate of at least about 100 frames per second.

12. The method of claim 10, wherein said images of said cells are acquired at a rate ranging from about 200 to about 2,000 frames per second.

13. The method according to any one of claims 6-12, wherein said images track cell shape and/or displacement.

14. The method according to any one of claims 6-13, wherein one or more of cell size Z⁾ _ce//, time-dependent strain e(t), critical strain 8_cri_ti_cai, creep time T_c, and transit time T_T are derived from said images.

15. The method according to any one of claims 1-14, wherein said pressure gradient ranges from about 5 kPa, or from about 10 kPa, or from about 15 kPa, or from about

20 kPa up to about 100 kPa, or up to about 90 kPa, or up to about 80 kPa, or up to about 70 kPa.

16. The method according to any one of claims 1-15, wherein said pressure gradient ranges from about 25 kPa or from about 28 kPa up to about 69 kPa.

17. The method according to any one of claims 1-16, wherein said measurements are conducted in the presence of a surfactant in a cell suspension applied to said microfluidic device.

18. The method of claim 17, wherein said surfactant comprises Pluronic F-

127 surfactant.

19. The method according to any one of claims 17-18, wherein said surfactant is present in an amount ranging up to about 0.1% (w/v), or in an amount ranging up to about 0.05% (w/v), or in an amount of about 0.01% (w/v).

20. The method according to any one of claims 1-19, wherein said cells pass through said device at a rate of at least about 100 cells/min.

21. The method according to any one of claims 1-20, wherein said cells pass through said device at a rate of at least about 1000 cells/min.

22. The method according to any one of claims 1-21, wherein said cells pass through said device at a rate of at least about 10⁴ cells/min.

23. The method according to any one of claims 1-22, wherein said microfluidic device is calibrated with particles with defined elastic moduli.

24. The method of claim 23, wherein said particles comprise gel particles.

25. A method of determining the invasiveness of a cancer cell, said method comprising:

using a method according to any one of claims 1-24 to determine two or more cellular properties selected from the group consisting of elastic modulus (E), cell fluidity (β), cell transit time (7V), cell creep time (7c), cell size (D_ceii), and maximum strain (smax); and

categorizing invasiveness (or other clinically or functionally relevant phenotype including invasion or chemoresi stance) of a cell using two or more of said parameters where the categorization is made using a regression analysis and/or a machine learning model.

26. The method of claim 25, wherein said method comprises a categorization using cell transit time (T_T), and cell creep time (7c).

27. The method of claim 25, wherein said method comprises a categorization using cell transit time (7V), or cell creep time (7c), but not both.

28. The method according to any one of claims 25-27, wherein said method comprises a categorization using elastic modulus (E), and cell fluidity (β).

29. The method according to any one of claims 25-28, wherein said method comprises a categorization using elastic modulus (E), or cell fluidity (β), but not both.

30. The method of claim 25, wherein said method comprises a categorization using cell transit time (T_T), and cell size (D_ceii).

31. The method of claim 29, wherein said method comprises a categorization using cell transit time (T_T), cell size (D_ceu), and elastic modulus (E) and/or maximum strain (8max)-

32. The method of claim 31, wherein said method comprises a categorization using cell transit time (T_T), cell size (D_ceii), and elastic modulus (E).

33. The method of claim 31, wherein said method comprises a categorization using cell transit time (T_T), cell size (D_ceii), and maximum strain (8max)-

34. The method according to any one of claims 31-33, wherein said method comprises a categorization using cell transit time (T_T), cell size (D_cen), elastic modulus (£), and maximum strain (Smax).

35. The method according to any one of claims 25-34, wherein the categorization is made using a regression analysis.

36. The method according to any one of claims 25-34, wherein the categorization is made using a machine learning model.

37. The method of claim 36, wherein said machine learning model comprise a k-nearest neighbors (k-NN) machine learning algorithm.