Anisotropy vs isotropy in living cell indentation with AFM

The measurement of local mechanical properties of living cells by nano/micro indentation relies on the foundational assumption of locally isotropic cellular deformation. As a consequence of assumed isotropy, the cell membrane and underlying cytoskeleton are expected to locally deform axisymmetrically when indented by a spherical tip. Here, we directly observe the local geometry of deformation of membrane and cytoskeleton of different living adherent cells during nanoindentation with the integrated Atomic Force (AFM) and spinning disk confocal (SDC) microscope. We show that the presence of the perinuclear actin cap (apical stress fibers), such as those encountered in cells subject to physiological forces, causes a strongly non-axisymmetric membrane deformation during indentation reflecting local mechanical anisotropy. In contrast, axisymmetric membrane deformation reflecting mechanical isotropy was found in cells without actin cap: cancerous cells MDA-MB-231, which naturally lack the actin cap, and NIH 3T3 cells in which the actin cap is disrupted by latrunculin A. Careful studies were undertaken to quantify the effect of the live cell fluorescent stains on the measured mechanical properties. Using finite element computations and the numerical analysis, we explored the capability of one of the simplest anisotropic models – transverse isotropy model with three local mechanical parameters (longitudinal and transverse modulus and planar shear modulus) – to capture the observed non-axisymmetric deformation. These results help identifying which cell types are likely to exhibit non-isotropic properties, how to measure and quantify cellular deformation during AFM indentation using live cell stains and SDC, and suggest modelling guidelines to recover quantitative estimates of the mechanical properties of living cells.

they did not affect the performed measurements since optical sectioning was done when cantilever was retracted from the surface, or during the dwell phase of the force curve (see below, protocol 1, and Fig. S11B), and force curves for mechanical analysis were acquired before the optical sectioning. In a previous study 1 , the signal coupling was observed between the epifluorescence excitation light and the cantilever deflection. Here, such coupling was also seen at the high laser intensities, but at the low laser intensities selected for the living cell observation, it was very weak and close to the noise level (Fig.   S11C). Refractive index (RI) mismatch between the immersion fluid (RI=1.518, Olympus, Japan) and the sample (for aqueous medium, RI is close to 1.33) introduces a decrease in intensity and a shift of the objective focus, thus accurate calibration of the axial distances in confocal microscopy is generally required. We performed this calibration in a preliminary study by placing the AFM probe at a certain distance from the surface (1, 3, 5, 7 μm) using AFM piezo. Then confocal Z-stacks were acquired using SDC from which these distances were calculated as well. By comparison of the distances from the AFM and confocal data, the correction factor 0.88 was obtained for latter which agrees with the theoretical prediction from the previous work 2 . As an additional check, the height of the stained cells calculated using AFM (by the difference in contact points of F-Z curves over the surface and the top of a cell) and from the confocal images was very similar (within 5%).
Synchronization between microscopes was achieved with a TTL trigger signal from AFM to SDC at the beginning of the indentation experiment. The imaging parameters were adjusted in preliminary experiments to decrease the acquisition time and still preserve high signal-to-noise ratio and low phototoxicity. Phototoxicity was observed at high laser intensities as indicated by plasma membrane blebbing, cell detachment, and cytoskeleton disassembly.
3 To outline the cell membrane or F-actin layer profile in the vertical cross-sections we utilized a method from 3,4 . For each vertical line (x position), the fluorescence peak position was determined by fitting several points around the pixel with maximum intensity with a Gaussian function. The peak of the Gaussian was taken to be the membrane (or F-actin layer) position at x. The width of peaks was comparable to the resolution of the microscope, indicating that the thicknesses of the plasma membrane and F-actin layer are below the resolution limit. The surface displacement profile and indentation depth were found by subtracting the cell profile during indentation from the cell profile prior to indentation. Cell height was measured based on plasma membrane or F-actin staining, since they provided similar results, and both types of fluorescent data were in agreement with the AFM height data.
Classification of cells into three different groups based on the perinuclear actin cap structure was adapted from previous studies [5][6][7] . The cells with well-developed perinuclear actin cap stress fibers, less-developed fibers (low thickness and low density), and without detectable fibers were classified as the "cap", "sparse cap", and "no cap" group, respectively. b. Simultaneous SDC imaging and AFM indentation. We used three different experimental approaches to combine SDC imaging with AFM indentation to achieve a better visualization of the cell indentation process (Fig. S3). The standard approach used previously (referred to here as the "protocol 1") is to obtain full z-stack of optical slices for selected cell before and after engagement of the cantilever with prescribed force or indentation depth 3,8,9 (Fig. S3A and Fig. 4 in the main text). In that case, the Z-position of the cantilever is kept constant during the image acquisition (dwell phase of the force curve), but force and indentation depth could change due to cantilever deflection. This approach does not require high temporal resolution, but single z-stack does not provide data on the ongoing viscoelastic relaxation and other force-induced processes in the cell under the engaged cantilever. The relaxation is manifested as decay in the force during the dwell phase of the force curve. A second approach ("protocol 2"), providing the highest temporal resolution, involves the acquisition of a single optical section at selected height during the whole process of cantilever indentation. In this approach, one would expect to see fast rearrangements of cytoskeletal structures but only in the single plane of the view (Fig. S3B, Fig. 3 in the main text, Movies S1-S3). As a compromise, a third approach ("protocol 3") involves partial Z-stacks, while F-Z curves are acquired with the low indentation speed to capture the process (Fig. S3C). Reconstructed cross-sections could 4 be used to measure the indentation depth ( Fig. S4 and S10), which agreed with the AFM data (not shown). The F-Z curves were taken at 200 nm/s and 50 nm/s piezo displacement speed along the Z axis for the protocol 3 and 2, respectively. Before implementing any of the described protocols, the mechanical properties of the selected cell were characterized by a set of the force curves taken at 2 μm/s, as described in the All experiments showed that deformation is reversible at the used indentation parameters (speed, depth and force set-point) (Fig. S9). The force set-point used here was at the level of 1-2 nN, which is comparable with the force cell can generate through a single focal adhesion 10 . Cell viability was preserved and no significant rearrangements of both actin and microtubule cytoskeleton was recorded after the indentation. As shown in a previous study, such rearrangements could be observed when the probe is coated with ECM protein and at longer interaction times 11 . Also, significant remodeling of the microtubule network was found when large probe (50 um diameter) and high forces (20 nN) were applied to the cell 12 , but it was not the case here. Membrane patches attached to the probe in some cases, but this did not lead to the cell death or visible damage. c. Effect of live-cell stains on cell properties. We tested whether the used live-cell imaging stains (probes) affect the mechanical properties of the studied cells as measured by AFM ( Fig.1 and Fig S1). Among all stains used, only SiR-actin caused significant cell  Table S1) and decrease in power law exponent α (~20%, p<0.001), meaning solidification of the cell (α=0 for solid material and α=1 for liquid). SiRtubulin staining, on the other hand, did not lead to significant changes in cell mechanical properties, as well as overnight incubation with the 10 µM verapamil alone. Data for cell 5 viscoelastic properties are presented in Fig. 1B and Table S1. In agreement with a previous study 13 , no effects of SiR probes on cell viability and morphology were noticed.
SiR probes are well suitable for live-cell imaging, have excellent brightness and photostability, and more convenient than genetically encoded probes, which require transfection 13 . The SiR-actin probe is based on the jasplakinolide derivative 13 , which binds to polymerized actin filaments. Jasplakinolide binding stabilizes actin fibers making them more rigid 14 , and is known to promote actin polymerization in the short term 15 . SiRactin probe could preserve some of its action, which was observed here as increase in cell stiffness (Table 1). We did not notice any effect on viability, morphology, or motility of the cells, which is in agreement with a previous study 13  SiR-tubulin staining, on the other hand, did not lead to significant changes in cell mechanical properties. SiR-tubulin probe is based on the docetaxel derivative 13 , which binds to the microtubules and likely stabilizes them, although SiR-tubulin labeling did not manifest in increased cell stiffness. The dynamic behavior of the microtubules was seen occasionally, probably associated with sliding or disassembly, and was not significantly affected by the indentation process.
Other used fluorescent stains did not significantly affect cell mechanical properties in experimental conditions used here, although some effects from actin-GFP were seen in the previous study 16 . Verapamil, broad spectrum efflux pump inhibitor which was used to improve the SiR-probe labeling efficiency, was shown to affect actin cytoskeleton structure, but at higher concentration and longer incubation times than used here 17 .
where moduli and Poisson's ratios are expressed in terms of "a" for axial (longitudinal) and "t" for transverse ( Fig. 6A in the main text). From the seven material parameters  , only five are mutually independent, while other are related by: The number of independent parameters reduces further if we apply an assumption about the incompressibility of the material. This requires 18 : A several 3D models were designed. To conduct a general geometry-independent 7 analysis, the sample was modeled as 20x20x20 µm 3 block and the indenter was a sphere with radius 1 µm. The sphere indented the block up to a maximum penetration of 0.5 µm using a displacement-controlled simulation.
We used a structured mesh composed of 224000 three-dimensional solid elements These results indicate that even a small block can capture the anisotropy-induced displacement difference. For the ellipsoidal cap geometry, we observed small difference in indentation profiles for the isotropic material. The calculated D.A. was 1.05, which is only 5% deviation from the expected value 1.0 (Fig. S6E) (Table S4) Since mechanical properties of the stress fibers are not exactly known and will depend on the pre-stress, we can only make a numerical analysis with some relevant range of values. We also assumed that when the cell lacks the apical stress fibers as seen from the SDC images, the measured values corresponded to the matrix (including membrane, cytoplasm, actin cortex and other components, but not the stress fibers). The stress fibers were considered to be stiffer than the matrix 21