# Noninvasive monitoring of single-cell mechanics by acoustic scattering

### Subjects

A Publisher Correction to this article was published on 19 February 2019

## Abstract

The monitoring of mechanics in a single cell throughout the cell cycle has been hampered by the invasiveness of mechanical measurements. Here we quantify mechanical properties via acoustic scattering of waves from a cell inside a fluid-filled vibrating cantilever with a temporal resolution of < 1 min. Through simulations, experiments with hydrogels and the use of chemically perturbed cells, we show that our readout, the size-normalized acoustic scattering (SNACS), measures stiffness. To demonstrate the noninvasiveness of SNACS over successive cell cycles, we used measurements that resulted in deformations of < 15 nm. The cells maintained constant SNACS throughout interphase but showed dynamic changes during mitosis. Our work provides a basis for understanding how growing cells maintain mechanical integrity, and demonstrates that acoustic scattering can be used to noninvasively probe subtle and transient dynamics.

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## Code availability

Code used in this study can be obtained from the corresponding author on reasonable request.

## Data availability

The data that support the findings of this study are available from the corresponding author on reasonable request.

## Change history

• ### 19 February 2019

The version of this paper originally published online contained an error in the x-axis of Fig. 2c: the LatB concentrations should be 0.4 and 1 μM, but during typesetting, the 1 μM label was incorrectly changed to 0.1 μM. The label is now correct in the print, PDF, and HTML versions of the paper. In addition, in the article’s online Supplementary Information, Supplementary Video 2 was a duplicate of Supplementary Video 1. The correct versions of both videos are now available online.

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## Acknowledgements

We thank K. Elias (Brigham and Women’s Hospital) for S-HeLa cells, and E. Vasile and the Koch Institute microscopy core, which is partly funded by Koch Institute Support Grant P30-CA14051 from the National Cancer Institute, for technical support. This work was funded in part by the Ludwig Center for Molecular Oncology (S.R.M.), the Cancer Systems Biology Consortium U54 CA217377 from the NCI (S.R.M.), and the Institute for Collaborative Biotechnologies through grant W911NF-09-0001 from the US Army Research Office (S.R.M.). T.P.M. is supported by the Wellcome Trust (Sir Henry Postdoctoral Fellowship grant 110275/Z/15/Z). J.H.K. acknowledges support from a Samsung scholarship.

## Author information

Authors

### Contributions

J.H.K. and S.R.M. conceptualized the study. J.H.K., with assistance from S.O., G.K. and S.R.M., designed the modeling and experiments done with beads. J.H.K. and T.P.M. designed the experiments with cells. J.H.K. performed all node deviation experiments and analyzed the data. J.H.K., with assistance from G.K., carried out the modeling. T.P.M. carried out all imaging experiments. S.O., with assistance from J.H.K. and T.P.M., carried out the image analysis. L.C. and P.S.D. created the hydrogel particles. T.P.M. and S.R.M. supervised the study. J.H.K., T.P.M., G.K. and S.R.M. wrote the paper with input from all other authors.

### Corresponding author

Correspondence to Scott R. Manalis.

## Ethics declarations

### Competing interests

S.R.M. is a founder of Travera and Affinity Biosensors.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Integrated supplementary information

### Supplementary Figure 1 SMR geometry and acoustic parameters from simulation.

a, SMR geometry, dimensions (Supplementary Table 2) and coordinates. The fluid channel in the detection regime is covered with thin silicon layers (dark gray). Inset shows the buried channel. All dimensions are listed in Supplementary Table 2. bd, Simulated acoustic pressure (b), z-velocity (c) and y-velocity (d). Amplitude (black) and phase (gray) are plotted along the top edge of the channel. The maximal amplitude of z-velocity and y-velocity were ~0.5 m/s and ~0.075 m/s, respectively. The second mode shape from the Euler–Bernoulli beam equation (u2) is plotted as a red dashed line.

### Supplementary Figure 2 Node deviation is independent of the mass change.

a, Frequency signals from simulations with 12-μm polystyrene bead (ρb = 1.06 g/cm3) immersed in fluids of different densities (ρf = 1.1, 1.08, 1.06, 1.03 and 0.997 g/cm3 for blue, green, black, orange and red traces, respectively). Frequency signals were normalized relative to the result obtained for ρf = 1.1 g/cm3 (blue). b, Node deviation from experiments with 12-μm polystyrene bead immersed in fluids of the same densities as in a (1.1, 1.08, 1.03 and 0.997 g/cm3; n = 17, 97, 84 and 120 beads, respectively, with the same colors as in a). Boxes indicate the interquartile range, squares represent means, whiskers extend to the 5th and 95th percentiles; P = 0.32 (one-way ANOVA). n.s., not significant. Inset: overlay of the frequency signal obtained from the density-matched fluid (ρf = ρb = 1.06 g/cm3, black) and water (ρf = 0.997 g/cm3, red). Buoyant mass (Δm, blue arrow) and node deviation (black arrow) are highlighted. c, Conceptual illustration of the frequency response, which is a superposition of the frequency response caused by both mass change, and the acoustic term independent of mass.

### Supplementary Figure 3 Node deviation is not sensitive to SMR drive amplitude, particle flow velocity across the channel or particle shape.

a, Node deviation from experiments with 10-μm polystyrene beads measured by SMR vibrating in different amplitudes (0.15, 0.4 and 0.7; n = 33, 21 and 21 beads, respectively). P = 0.37 (one-way ANOVA). n.s., not significant. b, Node deviation from experiments with 10-μm polystyrene beads measured by SMR with different fluid velocities (n = 35 beads). Velocities were derived from the transit time of the beads through the cantilever calculated from the duration of the resonant frequency shift of the beads. c, Node deviation versus aspect ratio (AR) from experiments with synthetic hydrogels of different shapes but the same volume (AR 1, 1.5 and 2.5; n = 384, 423 and 474 hydrogels, respectively). P = 0.10 (one-way ANOVA). n.s., not significant. In a,c, boxes indicate the interquartile range, squares represent means, and whiskers extend to the 5th and 95th percentiles.

### Supplementary Figure 4 Illustration of the methodology used for obtaining the size-normalized acoustic scattering (SNACS) from the node deviation.

a,b, Steps for obtaining SNACS: The resonant frequency shifts (Δf/f) for each cell (1–4; colored curves) are used to measure the buoyant mass (BM) at the antinode and the node deviation at the node (a). Scatter plot of volume-normalized node deviation (NV) versus volume (V) (b). The volume of each cell (V1,2,3,4) is obtained from the corresponding buoyant mass (BM1,2,3,4) using the included equation. $$\overline {\Delta \rho }$$ is the median density of the population relative to the fluid. Data points of cells (1–4) are fit with isoelasticity lines (colored lines) with slope m (c). We obtained the slope (m) by performing a linear regression on the population data in the NV-versus-V scatter plot shown in Fig. 2b. The SNACS of each cell is obtained via the included equation (d). Graphically, the SNACS of each cell corresponds to an NV value at the intersection point between the isoelasticity line (colored lines) and the vertical line, V = Vref (black dotted line), where Vref is set as the median volume of the population. See Methods for additional details.

### Supplementary Figure 5 SNACS correlates with cortical thickness but is not sensitive to cytoplasmic viscosity, intracellular pressure or cortical tension based on FEM simulation using the cortical shell–liquid core model.

ad, FEM simulation results of SNACS obtained from the cortical shell–liquid core model upon changes in cortical thickness (a), cytoplasm (internal fluid) viscosity (blue) (b), internal pressure (green) (c) and cortical tension (red) (d). SNACS changes relative to $$t_a/2{\mathrm{r}}_{\mathrm{c}} = 1{\mathrm{\% }},{\mathrm{\nu }}/{\mathrm{\nu }}_{{\mathrm{water}}} = 1$$, P = 0, and T = 0 are plotted, respectively. We simulated tension by applying initial stress to the elastic shell region, in-plane direction. See Supplementary Note 2 for additional details. Insets: illustration of liquid-core elastic shell model with parameters being solved in FEM simulation. For all simulations, the total radius (rc) and shell elastic modulus (Emod) were fixed at 6 μm and 5 MPa, respectively.

### Supplementary Figure 6 SNACS noise characterization.

a, Continuous SNACS measurements of a single 12-μm polystyrene bead (n = 79 repeated measurements), implementing the same fluidic control strategy for continuous monitoring of single-cell SNACS (Fig. 3a). The mean (set to zero) is shown by the red line, and ± s.d. (σ) is shown by the gray dashed lines. The gray area marks the data region within ±σ. b,c, Illustration (top) and simulation results (bottom) of the cell model (Fig. 2a) with total radius (rc) and shell elastic modulus (Emod) of 6 μm and 5 MPa, respectively, with x-positional (b) and z-positional (c) offset from center of the channel. Vertical lines mark the offset distance from the center to positions where the outer surface of the cell touches channel walls.

### Supplementary Figure 7 Microtubule perturbation affects actin cortex and SNACS.

a, SNACS measured from L1210 cells treated with microtubule-affecting drugs: nocodazole (Noc, 1 μg/ml, n = 760 cells, P = 2.8 × 10–16) and Taxol (25 μM, n = 511 cells, P = 0.12). Statistical comparisons (two-sided Welch’s t-test) were made to DMSO control (0.1%, n = 718 cells). Boxes indicate the interquartile range, squares represent means, and whiskers extend to the 5th and 95th percentiles; ****P < 0.0001; n.s., not significant. b, Representative images of actin cortex from live L1210 cells expressing LifeAct–RFP F-actin probe before (top) and after (bottom) treatment with nocodazole 1 μg/ml (n = 7 fields of views). Scale bars, 10 μm.

### Supplementary Figure 8 Continuous SNACS measurements do not affect interdivision time.

Interdivision time (doubling time) of each daughter cell from the same lineage (left column, black dots), single cells from different lineages (middle column, gray dots) and from bulk cell culture (right column, gray dots). All single cells grown in SMR were exposed to the same conditions reported in the manuscript (SNACS measurement every 1 min). Higher temporal resolution can be achieved. However, repeating measurements more often than every 30 s may start to interfere with cell growth. For middle and right columns, data depict mean ± s.d. Each mean ± s.d. is listed on top. P = 0.95 (one-way ANOVA). n.s., not significant.

### Supplementary Figure 9 Illustration of mass distribution correction in late mitosis.

a, DIC images of the mitotic L1210 cell acquired on-chip, simultaneously with SNACS and buoyant mass measurement in late mitosis. For each time point, cells were fitted with overlapping spheres (yellow dotted lines) based on the measured elongation length (blue double arrows). Each number on the image marks the time progression. Scale bars, 10 μm. b, Cell length measured (blue dots) is plotted as a function of time after onset of anaphase. Numbers correspond to the images shown in a. The linear elongation derived from the first (1) and last image (12) is shown by the red line. c, SNACS before correction (gray), after correction for the mass elongation using length directly measured from DIC images (blue dots) and assuming linear elongation (red), plotted as a function of time after onset of anaphase. Numbers correspond to the images in a. See Supplementary Note 3 for additional details.

### Supplementary Figure 10 SNACS change occurs in early mitosis and is reduced by EIPA treatment.

a, Buoyant mass (black) and SNACS (red) of L1210 treated with 2 μM RO-3306, a CDK1 inhibitor. Arrowhead marks the start of drug exposure. The cell arrested in G2 continues to grow above the average size of L1210 cells at the mitotic entry (gray dashed line). b,c, Buoyant mass (black), SNACS (red) and FUCCI (green, mAG-hGem) of a control L1210 cell (b) and an L1210 cell treated with 10 µM ethylisopropylamiloride (EIPA, an inhibitor of Na+/H+ antiporters) (c). The fluorescence detection limit of our system is shown by a green band at the bottom. An abrupt decrease in FUCCI (degradation of Geminin) marks the metaphase–anaphase transition. Vertical lines separate the cell cycle positions marked by color bars as shown in Fig. 3c. P, prophase; M, metaphase; A, anaphase; T, telophase.

### Supplementary Figure 11 The rate of swelling does not affect SNACS change.

Results of two independent experiments showing SNACS change relative to controls (red; n = 637 and 566 cells for replicates 1 and 2, respectively) after hypotonic shocks that are slow (dark blue; –Δ50 mOsm over 20 min; n = 558 and 544 cells for replicates 1 and 2, respectively) or fast (light blue; –Δ50 mOsm instantaneous; n = 507 and 569 cells for replicates 1 and 2, respectively). Boxes indicate the interquartile range, squares represent means, and whiskers extend to the 5th and 95th percentiles; ****P < 0.0001; n.s., not significant. P (control versus hypotonic, slow) = 2.82 × 10–11 and 9.8 × 10–18, P (control versus hypotonic, fast) = 6.63 × 10–14 and 5.1 × 10–15, P (hypotonic, slow versus hypotonic, fast) = 0.32 and 0.36 for replicates 1 and 2, respectively. P values were obtained by one-way ANOVA, Fisher’s least significant difference.

### Supplementary Figure 12 Illustration of the image analysis.

ah, Successive steps of image analysis to obtain full width at half-maximum (FWHM) of F-actin cortex in early mitosis. Deconvolved image of the LifeAct signal from L1210 FUCCI cells expressing LifeAct–RFP F-actin probe (a). The image after application of the median filter (b). Binary converted image (c). Automatic detection of cell boundaries (red circle) (d). 100 radial paths (yellow lines) on which the LifeAct signal was quantified (e). Overlay of all radial path signals (yellow) as a function of distance from the cell center (f). The median of the radial paths (black line) was used to determine baseline within the cell, maximum signal at the actin cortex and, consequently, the FWHM. g,h, Nuclear envelope breakdown (NEBD) was used for aligning different cells to the same point in the cell cycle. NEBD was detected by the abrupt spread of the green Geminin fluorescence of the FUCCI from a restricted nuclear localization (g) to the whole cytoplasm (h). il, Successive steps of image analysis to detect equatorial and polar regions of the F-actin cortex in late mitosis. Steps in order (top to bottom) and from different time points (left to right): deconvolved image of an L1210 FUCCI cell expressing LifeAct–RFP F-actin probe (i). Detection of one or two cells in the image (red circles) (j). Assignment of the polar regions (white areas) (k). Assignment of the equatorial regions (white areas) (l). See Methods for additional details.

### Supplementary Figure 13 F-actin cortical thickness decreases in early mitosis.

Mean FWHM (proxy of cortical thickness; black dots) and ± s.d. (gray bars) of cortical LifeAct signal from L1210 FUCCI cells expressing LifeAct–RFP F-actin probe in early mitosis (n = 29 cells). All FWHM signal was normalized to the time point at t = –2 h. Time 0 marks nuclear envelope breakdown (NEBD).

### Supplementary Figure 14 Fluorescence images of F-actin and FUCCI in late mitosis.

Left column (Overlay), overlay of LifeAct (F-actin probe, red channel) and FUCCI (mAG-hGem, green channel) as a function of time after anaphase onset (n = 7 cells undergoing mitosis). Scale bars, 10 μm. Middle column (Geminin), fluorescence from the green channel only. Right column (LifeAct), fluorescence from the red channel only.

### Supplementary Figure 15 Orientation-dependent noise and mass distribution correction during late mitosis.

a, Top, schematic showing the two extreme orientations of a cell during late mitosis: cells flowing parallel to the channel (θ = 0) and maximally rotated (θ = θmax). Note that the dimension of the channel walls (black lines) and elongation length of a cell at a given time point determines the maximal rotation angle (θmax). Bottom, SNACS is corrected assuming three different orientations relative to the channel when cell is at the node: θ = 0 (blue dash), θ = θmax (red dash) and θ = θmax/2 (black solid). The gray area marks the orientation-dependent noise. See Supplementary Fig. 9 for raw SNACS. b, Effect of uncertainty in cell orientation on measured SNACS and corrected SNACS for two hypothetical cells both elongating as L1210 cells in mitosis (top panel, blue), but with different mechanical changes (top panel, red): zero change (left) and dynamic mechanical change similar to L1210 cells in mitosis (right). Two extreme orientations illustrated in a mark the boundary (blue and red dash) of orientation-dependent noise (gray area) in measured SNACS (middle panel). Corrected SNACS signals assuming an intermediate orientation (θ = θmax/2) during the entire time course are shown in the bottom panel. Representation of SNACS traces corresponding to each orientation are the same as in a. See Supplementary Note 4 for additional details.

## Supplementary information

### Supplementary Text and Figures

Supplementary Figs. 1–15, Supplementary Tables 1–5 and Supplementary Notes 1–5

### Supplementary Video 1

Simulation of acoustic pressures and velocities inside the cantilever. Time evolution of acoustic pressures (color contour) and velocities (arrows) during one full cycle of vibration. Acoustic velocities are drawn from the center of the channel.

### Supplementary Video 2

Simulation of acoustic velocities with or without a bead placed at the node. Time evolution of acoustic velocities (magnitude in color contour, direction in arrows) along the length of the cantilever (y-axis) during one full cycle of vibration.

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Kang, J.H., Miettinen, T.P., Chen, L. et al. Noninvasive monitoring of single-cell mechanics by acoustic scattering. Nat Methods 16, 263–269 (2019). https://doi.org/10.1038/s41592-019-0326-x

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