Monitoring the mass, eigenfrequency, and quality factor of mammalian cells

The regulation of mass is essential for the development and homeostasis of cells and multicellular organisms. However, cell mass is also tightly linked to cell mechanical properties, which depend on the time scales at which they are measured and change drastically at the cellular eigenfrequency. So far, it has not been possible to determine cell mass and eigenfrequency together. Here, we introduce microcantilevers oscillating in the Ångström range to monitor both fundamental physical properties of the cell. If the oscillation frequency is far below the cellular eigenfrequency, all cell compartments follow the cantilever motion, and the cell mass measurements are accurate. Yet, if the oscillating frequency approaches or lies above the cellular eigenfrequency, the mechanical response of the cell changes, and not all cellular components can follow the cantilever motions in phase. This energy loss caused by mechanical damping within the cell is described by the quality factor. We use these observations to examine living cells across externally applied mechanical frequency ranges and to measure their total mass, eigenfrequency, and quality factor. The three parameters open the door to better understand the mechanobiology of the cell and stimulate biotechnological and medical innovations.

For each HeLa cell, the percentage of estimated cell mass is given as derived by dividing the cell mass measured shortly after cell attachment (≤ 1 min) to the microcantilever ( _ ≈ 65 -90 kHz) through the volumetric cell mass (  * ) expected from the optically measured cell diameter.The diameter of individual HeLa cells were estimated from their optical images (using Image J, version 2.3.0/1.53q)taken within 1 min after their attachment to the cantilever.The cell density  taken was 1.06 g cm -3 [1] .The graph illustrates that the bigger or heavier the cell, the less accurate the microcantilever-based mass measurement

Supplementary Figure 3 .Supplementary Figure 6 .
Mass measurements of single cells adhering to rectangular microcantilevers functionalized with different substrates.Representative mass measurements of HeLa cells on a, b collagen I, c, d Matrigel, e, f laminin, or g, h concanavalin A. The cell mass was recorded over 120 min after attaching the cell to a rectangular microcantilever ( _ ≈ 70 -92 kHz; 120 x 45 x 2 (l x w x t) µm) in cell culture medium under cell culture conditions.DIC images of the HeLa cell adhering to the microcantilever are shown for each measurement at five different time points.The mass data was analyzed and corrected to account for the cell position and movement on the cantilever using the pyIMD software (Methods).Scale bars, 20 µm.Supplementary Figure 5. Correlation between focal adhesion area and mean total mass and between spreading area and mean total mass.a, The mean total mass of HeLa cells adhering to collagen (ncell = 11, yellow dots), matrigel (ncell = 11, red dots) and laminin (ncell = 12, green dots) -functionalized cantilevers after 30, 60 and 120 min of attachment was correlated with mean focal adhesion area determined from HeLa cells (ncell = 22 -30 for each substrate) seeded on substrate-functionalized Petri dishes after 30, 60 and 120 min.The correlation between the mean total mass and mean focal adhesion area shows a Pearson coefficient of r = 0.9376 (P-value = 0.0002), suggesting a rather strong correlation.b, The mean total mass of HeLa cells adhering to collagen (ncell = 11, yellow dots), matrigel (ncell = 11, red dots), laminin (ncell = 12, green dots) and ConA (ncell = 14, blue dots) -functionalized cantilevers after 30, 60 and 120 min of attachment were correlated with the mean spreading area of cells (ncell = 29 -30 for each substrate) seeded on substrate-functionalized Petri dishes after 30, 60 and 120 min.The correlation between the mean total mass and mean spreading area shows a Pearson coefficient of r = 0.3352 (P-value = 0.2868), suggesting a very weak correlation.Statistical analysis for determining P-values used a two-tailed unpaired t-test (Welch).Stiffness of living and chemically crosslinked HeLa cells.a, Stiffness of living and chemically crosslinked HeLa cells as probed by AFM cantilevers.14 cells were probed per condition and 15 force-distance curves were taken per cell.The experiments were performed with soft (kcant ≈ 0.04 -0.14 N m -1 ) tipless cantilevers.Individual cells were picked up with ConA-functionalized cantilevers and after an attachment period of  2 min pressed against Petri dishes with a force of 5 nN.After this first mechanical probing of the cellular stiffness, the cells on the cantilever were chemically crosslinked with 2 % (v/v) glutaraldehyde for 20 min under cell culture conditions.Then, the glutaraldehyde-containing cell culture medium was completely exchanged with fresh medium, and the crosslinked cells were mechanically probed again.All experiments were carried out in cell culture medium under cell culture conditions (Methods).Each dot represents the stiffness of one HeLa cell as derived from the force-distance curves.t-test (Mann-Whitney): two-tailed P-value < 0.0001.b, Average stiffness of HeLa cells before (living) and after crosslinking.Grey dots in represent single cells with the thin dashed lines connecting the living cell to the same cell after crosslinking (n cell = 14).c, Stiffness change of individual cells (dots) due to chemical crosslinking.Values represent the mean (horizontal black line) and standard deviation (error bars).Force-distance curves were analyzed using the AFM software (JPK data processing software, version spm-4.3.55) and the slope between 1 nN and 4 nN was used to measure the cell stiffness (i.e., force per distance).Supplementary Figure 7. Time-dependent shape changes of HeLa cells adhering to ConA-coated micro-slides (Ibidi).The cells were chemically crosslinked with 2 % (v/v) glutaraldehyde at four time points from 5 to 120 min and stained with SiR-actin.Imaging was done using confocal microscopy (Methods).a, Summed projections of the z-stacks of HeLa cells.b, Summed projections of the orthogonal view.Z-stacks were projected using Image J2 (version 2.3.0/1.53q).c, 3D reconstructed, rendered, and preprocessed images of HeLa cells used for finite element method (FEM) simulations, were performed using the Imaris software (Methods).All scale bars, 10 µm.Supplementary Figure 8. Cell size influences the cell mass measured by oscillating microcantilevers.
Fig. 5d) were estimated from light microscopy images and Image J software (version 2.3.0/1.53q)(Methods).Each dot represents one bead (nbead = 108), black squares the mean, and error bars the standard deviation.e, Total mass of glass beads over seven different cantilever eigenfrequencies  _ .Data taken from Fig. 5d.Each colored dot represents a single cell experiment, black squares the mean and error bars the standard deviation (nbead = 108).The dashed black line indicates the mean bead mass of all data points.f, Total mass of HeLa cells after attachment (at  1 min) to ConA-coated microcantilevers over seven different cantilever eigenfrequencies  _ .Data taken from Fig. 5b.Each colored dot represents one

Table 1 . Focal adhesion areas (mean  SD) of HeLa cells on different substrates and time points after attachment to the substrate
. ncell = 22 -30 for each substrate and time point.

Table 2 . Statistical comparison between focal adhesion areas in Suppl. Table 3 of HeLa cells on different substrates and time points after attachment to the substrate.
Statistical testswere performed using the unpaired t-test with Welch's correction.This two-tailed test was used to test the (null) hypothesis that two populations have equal means.Measurements are taken from Fig.2band Supplementary Table1.

Table 3 . Spreading areas (mean  SD) of HeLa cells on different substrates and time points after attachment to the substrate. ncell
= 29 -30 for each substrate and time point.Measurements are taken from Fig. 2c.