Stiffness of MDCK II Cells Depends on Confluency and Cell Size

Abstract

Mechanical phenotyping of adherent cells has become a serious tool in cell biology to understand how cells respond to their environment and eventually to identify disease patterns such as the malignancy of cancer cells. In the steady state, homeostasis is of pivotal importance, and cells strive to maintain their internal stresses even in challenging environments and in response to external chemical and mechanical stimuli. However, a major problem exists in determining mechanical properties because many techniques, such as atomic force microscopy, that assess these properties of adherent cells locally can only address a limited number of cells and provide elastic moduli that vary substantially from cell to cell. The origin of this spread in stiffness values is largely unknown and might limit the significance of measurements. Possible reasons for the disparity are variations in cell shape and size, as well as biological reasons such as the cell cycle or polarization state of the cell. Here, we show that stiffness of adherent epithelial cells rises with increasing projected apical cell area in a nonlinear fashion. This size stiffening not only occurs as a consequence of varying cell-seeding densities, it can also be observed within a small area of a particular cell culture. Experiments with single adherent cells attached to defined areas via microcontact printing show that size stiffening is limited to cells of a confluent monolayer. This leads to the conclusion that cells possibly regulate their size distribution through cortical stress, which is enhanced in larger cells and reduced in smaller cells.

Introduction

Cellular biophysics with emphasis on the mechanical properties of adherent cells has received increasing attention over the past decades, as multiple techniques have shown that biomechanics is involved in a variety of processes such as cell spreading (1, 2), migration (3, 4), proliferation, and stem cell differentiation (5, 6, 7) and is altered depending on the malignancy of certain types of cancer (8, 9). One way to assess the mechanical properties of cells is to externally deform them with a defined force or pressure and measure the response function. Viscoelastic responses to external mechanical stimuli are found to originate mainly from the actin cortex attached to the plasma membrane (10). Deformation of cells either globally or locally with a sharp indenter is usually interpreted either in terms of a contact mechanics model, providing the Young’s modulus, or in terms of a tension model, in which cortical tension prevails at low strain, whereas area dilatation dominates at large strain (11, 12). Here, we focus on the apical mechanics of adherent epithelial cells in terms of contact mechanics, in which studies have already shown that the thin actomyosin cortex, together with the plasma membrane of such cells, dominates the repulsive forces that are experienced by nanoindenters (13, 14). In epithelial cells, mechanical homeostasis is of major importance and must continue even in challenging environments, e.g., high or low osmolarity, to ensure layer integrity (15). Disruption of this integrity by the creation of defects in the cell layer leads to altered mechanical properties of the remaining cells surrounding the defect. This change holds for multiple spheres of influence up to several tens of micrometers away from the defect (16, 17, 18, 19).

Based on these findings, information on mechanical changes within a layer may be naturally transmitted between cells and poses an ideal way of establishing and maintaining mechanical homeostasis within the layer. Homeostasis of cellular morphology within monolayers is a prerequisite for their functionality. Although epithelial cells like the MDCK II cell line show high proliferation rates under subconfluent conditions, their growth is restricted upon reaching confluency by contact inhibition (20, 21). Although this might seem like epithelial morphogenesis is finished in early confluent monolayers of these cells, further development persists even for days after reaching confluency, during which cell-cell contacts are strengthened and supercellular structures like domes or tubules are being formed (22, 23). Although downregulated, cell division still takes place and depends on the area occupied by the dividing cell, with larger cells exhibiting higher division rates (24).

In this study, we show that there exists a strong correlation between cellular stiffness and the cells’ projected apical area, i.e., the occupied space within a cell monolayer. Our finding points toward a regulation of cell size in a confluent layer driven by cortical tension. Knowledge of this correlation between cell stiffness and projected cell area permits us to estimate and potentially also to eliminate the often-observed variation in mechanical measurements due to a variation in cell size. We suggest following a precise protocol to ensure that comparable data sets are gathered, in which variations in seeding density and incubation time are kept at a minimum.

Materials and Methods

Cell culture

Madin Darby canine kidney cells (MDCK II; Health Protection Agency, Salisbury, UK) were cultivated in minimal essential medium (MEM with Earl’s salts, 2.2 g/L NaHCO₃; Biochrom, Berlin, Germany) containing 4 mM l-glutamine (Lonza, Basel, Switzerland) and 10% (v/v) fetal calf serum (FCS; BioWest, Nuaillé, France). Stem and samples were kept at 37°C and 7.5% CO₂ (Heracell 150i; Thermo Fisher Scientific, Waltham, MA). Subcultivation was performed using standard culture flasks (TPP, Trasadingen, Switzerland) by addition of 0.05% trypsin and 0.02% EDTA (Biochrom) and short incubation to remove the adherent cells from the culture surface. Suspended cells were mixed with FCS and centrifuged, and the pellet was dissolved in MEM and seeded into fresh flasks.

Cells destined to serve in experiments of confluent cells were taken in the last step. 220 cells per square millimeter (c/mm²) were seeded into petri dishes (Ibidi, Martinsried, Germany) and kept at 37°C and 7.5% CO₂ for 48 h, unless stated otherwise. Before experiments, cell media were exchanged to MEM containing HEPES (15 mm on confluent cells, 40 mm on single cells, 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid; Biochrom) as well as 0.2 mg/mL penicillin/streptomycin (PAA, Pasching, Germany) and 0.25 mg/mL amphotericin B (Biochrom).

Cell patterning

To create micrometer-scale patterns on culture dishes, plasma-induced protein patterning was used. First, patterns were drawn in AutoCAD (Autodesk, San Rafael, CA), and the corresponding mask was created (Compugraphics, Jena, Germany). The passivated, microstructured wafers were then used to cast polydimethylsiloxane (SYLGARD 184; Dow Corning, Wiesbaden, Germany) molds by mixing polymer and curing agent in a 10:1 ratio and curing it at 70°C for 4 h. The finished stamp was peeled off the wafer.

Glass-bottomed petri dishes (Ibidi) were cleaned by washing with ultrapure water and ethanol and dried in nitrogen stream. The freshly cured polydimethylsiloxane stamp was cut into 5 × 5 mm pieces and placed onto the glass surface. While in contact, the dish was placed in a plasma cleaner and exposed to oxygen plasma for 90 s. Immediately after plasma treatment, a solution of poly-l-lysine-graft-poly-ethyleneglycol (0.5 μL, PLL (20)-g[3.5]-PEG (2)/ tetramethylrhodamine; SuSoS, Dübendorf, Switzerland) was added to each individual stamp, and the sample rested for 1 h at 23°C under exclusion of light. Within the given time period, the solvent evaporated. After incubation, the stamps were removed, and the dish was washed three times with phosphate-buffered saline (PBS; Biochrom) without Mg²⁺ or Ca²⁺ and a solution of bovine collagen I (0.2 mg/mL; Thermo Fisher Scientific) in PBS was added and incubated for another 2 h. Finally, the dish was again washed three times with PBS and twice with MEM, and 100,000 MDCK II cells suspended in 2.5 mL M10F40 (MEM containing 10% FCS (Biowest), 4 mM l-glutamine (Lonza), penicillin/streptomycin (0.2 mg/mL; PAA, Pasching, Germany), 0.25 mg/mL amphotericin B (Biochrom), and 40 mM HEPES (Biochrom)) were added and incubated at 37°C. After 60 min, the sample was rinsed with M10F40 to remove any nonadherent cells, and atomic force microscopy (AFM) measurements were started.

AFM

Experiments were performed using MLCT cantilevers (k_norm = 0.01 pN/nm; Bruker AFM Probes, Camarillo, CA) on an atomic force microscope (either MFP-3D Origin; Asylum Research, Santa Barbara, CA or NanoWizard III; JPK, Berlin, Germany). Samples were kept at 37°C in pH-buffered media during all experiments. Force maps with a resolution of 1–8 μm² per force-distance curve (FDC) were acquired. To determine the Young’s moduli, cells were indented up to a force of 0.5–1 nN at vertical speeds of 2–5 μm/s. To receive the size of individual cells and correlate that to their Young’s modulus, slope maps were calculated from the force-distance data by baseline correcting and linear fitting of the lowest 20 nm of the data. In confluent cells, cell-cell contacts are much stiffer than central cell regions, and high slopes therefore mark contact lines (see Figs. S1 and S2). These boundaries of cell-cell contacts were then chosen manually and used for cell segmentation. In single-cell studies, cell bodies were chosen in a similar fashion based on the substrate showing extremely steep slopes in the FDCs.

To determine viscoelastic properties, the cantilever, which has been indented into the cellular cortex to a depth of about 1 μm, was actively oscillated to examine the impact of the cytoskeleton (9, 25, 26). The cantilever was exited to sinusoidal oscillations at different frequencies ranging from 5 to 100 Hz with small amplitudes. The complex shear modulus G^∗(ω) can then be obtained by the amplitude diminution and the phase shift between the in- and output signal. The real part of the resulting complex shear modulus, the storage modulus G′(ω), describes the frequency-dependent elastic properties, whereas the imaginary part, the loss modulus G″(ω), displays the energy dissipation in the system and represents its viscous properties. The fraction η(ω) = G″(ω)/G′(ω) is the so-called loss tangent, a model free parameter describing the material properties of the cell (9).

The complex shear modulus G^∗ increases with frequency following a weak power law with an exponent β usually in between 0.2 and 0.4. The loss modulus G″ exhibits lower values than G′ in the low-frequency regime (<50 Hz). Hence, in this regime, MDCK II cells behave more elastically rather than viscous. The mild power law and the elastic nature of the cell justifies our approach using Young’s moduli from fitting a purely elastic model to the data. In contrast, at larger frequencies, the cells display more fluid-like properties. A successful attempt to explain this power law behavior in G^∗ in the sense of an active soft glassy material has been suggested by Fabry and co-workers (27, 28). The idea is based on the soft glassy rheology model, assuming that the cytoskeleton of the cell is held together by weak attractive forces between neighboring elements (28, 29). Therefore, the complex shear modulus G^∗ of living cells is fitted with the power law structural damping (Eq. 1) using a complex, nonlinear, least-squares fitting routine:

$$G^{\text{∗}}=G_0\mathit{\Gamma }\left(1-\beta \right)\text{cos}\left(\frac{\pi }{2}\beta \right)\left(1+i\tan \left(\frac{\beta \pi }{2}\right)\right){\left(\frac{\omega }{{\omega }_0}\right)}^{\beta }+i\omega \mu ,$$ (1)

with G₀ the scaling factor describing the stiffness of the sample; β, the power-law coefficient; ω₀, the scaling factor of the frequency (set to 1 rad/s); and the viscosity μ. G₀ can be easily converted in the apparent Young’s modulus E₀ by E₀ = 2G₀(1 + ν), where ν is Poisson’s ratio (assumed to be 0.3 because cells consist predominately of water, which is incompressible). Notably, the scaling factor of the frequency is set arbitrarily, which prevents a direct comparison between the Young’s modulus obtained from force indentation data using a purely elastic contact mechanics model.

Theory

Cellular mechanics measured by external probes is often described in terms of contact mechanics such as the Hertz model, considering the deformation of a semi-infinite fully elastic space by a rigid indenter. Such deformations are usually characterized by a single parameter describing the elastic response, the so-called Young’s modulus E. Employing a conical indenter with half-opening angle θ results in the following approximate relationship between the force f and the indentation depth δ (30):

$$f=\frac{2E\text{tan}\left(\theta \right)}{\pi \left(1-{\nu }^2\right)}{\delta }^2.$$ (2)

In typical force spectroscopy experiments, a force setpoint f_SP is given, and indentation is continued until the specified force setpoint is reached; hence, all acquired data share roughly the same maximal force but different indentation depths. The equation above is only true during contact between probe and samples and does not apply to regions of the FDC without contact. To evaluate FDCs without knowledge of the contact point, which is usually difficult to determine automatically, we use the integral of the whole curve, which is invariant to the length of the noncontact region.

$$W_{\text{elast}}={\int }_0^{{\delta }_{\text{SP}}}\frac{2E\text{tan}\left(\theta \right)}{\pi \left(1-{\nu }^2\right)}{\delta }^2\text{d}\delta$$ (3)

We know that indentation depth at the force setpoint equals

$${\delta }_{\text{SP}}=\sqrt{\frac{f_{\text{SP}}\pi \left(1-{\nu }^2\right)}{2E\text{tan}\left(\theta \right)}}.$$ (4)

Together with Eq. 3, the Young’s modulus can be obtained from the elastic energy W_elast via

$$E=\frac{f_{\text{SP}}^3}{18W_{\text{elast}}^2\text{tan}\left(\theta \right)}\pi \left(1-{\nu }^2\right).$$ (5)

This idea of obtaining the elastic modulus automatically from FDCs without determining the contact point is similar to the force integration to equal limits, which has been applied to extract relative values (31). However, here, we actually obtain the absolute Young’s modulus. The procedure is strictly correct for ideal data, but the addition of noise might lead to a biased modulus even for large sampling. For typical FDCs, at least, as they occur in our experiments, we can show that from simulated and noise-decorated FDCs, the correct modulus is found with high precision (see Fig. S3).

Results

Cell mechanics as a function of seeding density

Our first approach was to seed different amounts of MDCK II cells on equally sized petri dishes to obtain confluent cell monolayers with different individual cell size. Seeding high numbers of cells leads to an early and dense confluent layer and consequently to a small average cell size. To verify that a confluent monolayer was formed at each cell-seeding density, fluorescence stainings of important cell-cell interconnecting proteins such as ZO-1, F-actin, or E-cadherin were visually inspected (see Fig. S4). The mechanical properties of the cells were obtained from microrheology experiments as described previously (9, 32).

We investigated layers originating from three different seeding densities (270, 540, and 815 c/mm²). Each sample was incubated for 48 h, with a clear tendency of smaller cell sizes for higher seeding densities. On these samples, AFM-based microrheology was performed to probe the elastic and viscous responses as a function of cell size. Essentially, two parameters were obtained from the microrheological spectra: the apparent Young’s modulus, E₀, which describes the elastic stiffness (Fig. 1, top), and the loss tangent η, which provides information about the relation of the viscous and elastic properties at a given frequency (Fig. 1, bottom). We have chosen 100 Hz because it turned out in a previous study that at this frequency, differences between different cell lines are most pronounced (9). The loss tangent is a quantitative measure of to what extent the viscous properties (G″) prevail over the elastic properties (G′). For a seeding density of 540 c/mm², a median Young’s modulus of E₀(540 c/mm²) = 850 Pa was found, which is in good agreement with previously reported Young’s moduli of the same cell line under similar culture conditions (E₀(330–540 c/mm²) = 560 Pa (32)). For higher seeding densities, the Young’s modulus decreased to E₀(815 c/mm²) = 460 Pa, whereas lower seeding densities resulted in a higher elastic modulus of E₀(270 c/mm²) = 1.0 kPa. Hence, higher seeding densities generate smaller cells correlating with lower Young’s moduli. Notably, E₀ obtained from rheological data is not directly comparable with the Young’s modulus from fitting a pure elastic contact model to the data because E₀ scales with the arbitrarily set time t₀, here set to 1 s.

Figure 1.

Young’s modulus E₀ (top) and loss tangent at 100 Hz (bottom) of MDCK II seeded at different cell densities. Box plots extend from the 25th to the 75th percentile, and whiskers from the 10th to the 90th. Individual data points are shown as dots; some outliers are not shown. Four different cell-seeding densities were used, these being 190, 270, 540 and 815 c/mm². Cells were allowed to grow for 48 h before measurement, and in the case of 190 c/mm², for 72 h. Number of viscoelastic spectra: n = 4092 (>20 cells), 7789 (>20 cells), 2027 (>20 cells), and 1622 (>12 cells), respectively. A rank-sum test was performed to test the null hypothesis that the data of the indicated data sets are from populations with equal medians. Asterisks indicate that the null hypothesis was rejected at the 0.05% (^∗∗∗) significance level. To see this figure in color, go online.

The loss tangent computed at 100 Hz does not follow a systematic trend. For all samples, the loss tangent was found to be η > 1; thus, G″ > G′. Comparing the lowest and highest cell-seeding densities used in this study, we observed a slight increase from η(270 c/mm²) = 2.04 to η(815 c/mm²) = 2.14. However, intermediate seeding densities showed an overall lower loss tangent of η(540 c/mm²) = 1.86.

To further explore this relationship, we decided to perform additional experiments with a seeding density of only 190 c/mm². Here, the cells grow so sparsely that an incubation time of 3 days was necessary to obtain a confluent monolayer. However, after incubation, we found even larger cells compared to the other seeding conditions, and the Young’s modulus was indeed increased in these samples (Fig. 1). We also observed a significant drop of the loss tangent to η(190 c/mm²) = 1.68, which indicates a more solid-like behavior of these larger cells. This is expected because more prestressed cells are exhibiting a smaller power-law factor, which indicates a less fluid behavior. The elastic modulus follows the general trend that larger cells display a larger stiffness, i.e., E₀(190 c/mm²) = 1.3 kPa. We rationalize this trend by considering that neighboring cells pull more strongly at larger cells, forcing them into a highly prestressed state.

These findings underline the importance of adhering rigidly to established protocols with respect to both cell-seeding density and growth time when extracting mechanical properties from cell culture samples. In fact, we suggest that evaluation of cell density at the time of experiments should be performed and the data supplied in biomechanical studies. The question was now whether the observed effect was due to variations in cell size or, for instance, polarity of the cells.

Size-dependent elasticity of confluent cells

The variation in mechanical behavior of cells in monolayers could be caused by several aspects that might change during layer maturation. Even after establishment of a confluent monolayer, cell density still increases for days, continuously decreasing the mean area that cells occupy within the layer (21, 23). To test whether the difference in area on its own is responsible for the variation in stiffness, we conducted experiments in which we acquired force maps across multiple cells within one particular sample and determined the area of each individual cell. By doing so, we can circumvent effects that are caused by different lengths of postconfluent incubation periods. However, because this includes the acquisition and evaluation of large data sets, we used a fully automated analysis in the following, yielding solely the Young’s modulus as the description of the cellular elastic behavior. This is further justified by the finding that viscous contribution did not change much with seeding density.

To determine the size distribution of cells under our experimental conditions as precisely as possible, we stained for the tight junction protein ZO-1 to facilitate cell segmentation. Employing automated analysis of fluorescence micrographs over large areas of a culture dish, we receive reliable and well-resolved data on cell areas, with the majority of cells taking up between 150 and 350 μm² (see Fig. 2). This distribution corresponds well to previous studies conducted by Puliafito et al. (21).

Figure 2.

Kernel density estimates of projected cell areas obtained from ZO-1 stainings of confluent MDCK II cells (n = 506). An average cell area of 278 μm² is found.

The determination of Young’s moduli of individual cells as a function of cell area was performed by AFM indentation experiments. In these experiments, cell area and Young’s modulus were extracted concomitantly from the acquired force maps. Therein, cell-cell contacts are marked by narrow bands of exceptionally stiff behavior, as is confirmed by overlay with optical phase-contrast images (see Fig. S1). We decided to use the force data for determination of cell borders instead of fluorescence images of fixed samples because cell position and area change dynamically and could easily vary between the force map acquisition and successful fixation.

Binning the results of cells in bands of 50 μm², Fig. 3 shows that for increasing cell area within a monolayer, the Young’s modulus indeed increases monotonically from 1 kPa to ∼3 kPa within sizes ranging from about 100 μm² up to about 600 μm². Considering that the ratio between circumference/area decreases for larger areas and because the circumference usually marks the stiffest region of such cells, larger areas should systematically decrease in median stiffness. However, the contrary was observed in our experiments, underlining the actual size-dependent stiffening. Because the increase in stiffness with occupied area of cells within a confluent cell monolayer corresponds to our observation of stiffness changes depending on initial seeding cell density (Fig. 1), we suggest that the cell area plays a pivotal role in cell-stiffness homeostasis. Interestingly, the Young’s modulus increases in a nonlinear fashion and seems to saturate for very large cell sizes.

Figure 3.

Plot of the cells’ Young’s modulus (median) as a function of projected apical cell area. Cells within a range of 50 μm² were collected and represented in points; error bars represent the standard error of the mean for all condensed cells’ values. The dotted line (smoothed spline) serves as a guide to the eye, showing the saturation effect for large areas. Data include 14,326 FDCs taken on 105 cells.

Single-cell studies

Our experiments concerning size-stiffness correlation of cells that are part of a confluent layer rely on the natural size distribution, which is, among other factors, also a result of seeding density and time. This brings up the question as to what extent the size dependence of cell stiffness is a feature of confluent cells and originates from neighboring cells pulling more strongly to enlarge the area or is, instead, a generic property. Moreover, the number of cells exhibiting sizes at the lower or upper end of this distribution is very low. To force a larger number of cells into extreme sizes and thereby increase the significance of results, we used micropatterned culture substrates. These substrates consist of well-defined areas coated with collagen I to foster adhesion of cells surrounded by coatings with nonadhesive polymer, forcing the cells to occupy and adapt their shape to that of the extracellular matrix patterns. MDCK II cells have shown that if the patterns are packed densely enough for cells to form cell-cell contacts and form a confluent layer, the cell-cell adhesion dominates, and cells essentially disregard the matrix patterns (unpublished data). Therefore, instances of the patterned grids were separated far enough to allow for only a single MDCK II cell per instance to adhere, in which case cells successfully adapt to the matrix pattern.

Single-spread MDCK II cells show a different size distribution compared to confluent ones. They are lower in height but produce larger adhesion areas. Therefore, we investigated cells with adhesion areas of 900, 1200, and 1500 μm². This approach not only enabled us to enforce a particular cell size but also an exact adhesion geometry. Using highly symmetric patterns—here, disks—we can average results by using the four symmetry axes when analyzing parameter maps. By doing so and averaging locally over all investigated cells, we receive parameter maps with high statistical accuracy to generate a distribution of stiffness values on different areas of the cell surfaces. See the recent work of Garcia and Garcia for a detailed discussion on this topic (33).

As shown in Fig. 4, circular cells show a small ring around their perimeter of high Young’s moduli, surrounding a larger central region that is rather soft. Although the central region with a Young’s modulus of ∼1.2 kPa is quite similar to values of other studies on confluent cells, the stiffer perimeter shows moduli that are up to two orders of magnitude larger (11, 34). The width of this ring differs slightly depending on the total adhesion area, but the general pattern is strikingly similar between all three tested sizes. Notably, the modulus depends also on the distance to underlying substrate. The numbers are therefore rather apparent ones in the context of the corresponding experiment.

Figure 4.

Elasticity of micropatterned cells. Parameter maps of the logarithmic Young’s modulus (top) at a resolution of 1.5 × 1.5 μm show softer central regions and stiffer peripheries. For all adhesion areas (blue = 900 μm², red = 1200 μm², green = 1500 μm²), the Young’s modulus of the central region is almost the same at 1.2 kPa. The stiffer perimeter has no dedicated peak in the one-dimensional distribution, with values up to two orders of magnitude larger than the softer interior part. N_blue = 2834, N_red = 2924, N_green = 2362. To see this figure in color, go online.

The central region on the patterned cells, apart from the circumference ring, represents the majority of the cell surface. As seen in the one-dimensional kernel density distribution (Fig. 4, bottom), the Young’s modulus is very similar for all investigated cell sizes, with virtually no effect from the different adhesion areas. The stiffer perimeter of the cells, however, displays a size-dependent Young’s modulus, i.e., E₉₀₀ = 73.0 kPa, E₁₂₀₀ = 18.6 kPa, and E₁₅₀₀ = 29.9 kPa. In contrast to the confluent studies, this is not a simple stiffening with increased size because the intermediate adhesion area results in the softest cell periphery, whereas the smallest adhesion area leads to the softest cell periphery. These results suggest that the mechanical behavior of MDCK II cells follow distinctively different rules depending on whether or not a confluent layer is present, which further supports the idea of cell mechanics playing a role in layer organization and vice versa. Still, these results are surprising, given recent studies by Efremov et al. who compared the stiffness of vero cells either in single-spread or confluent stages and observed stiffer behavior for single cells in a setup similar to ours (35). Also, similar studies of single cells on adhesive islands (human mesenchymal stem cells and lung human microvascular endothelial cells) showed size stiffening in the respective studies, which we did not observe in our experiments on MDCK II cells (36, 37).

Discussion

The mechanical properties of epithelial cells are of major importance for their biological function as efficient barrier tissue. Therefore, epithelia have to ensure that their structural integrity is not compromised. One prime example for such cells is the MDCK II cell line, which forms a rather flexible and fluid two-dimensional layer of cells where intercellular gaps are tightly closed to provide control over the transepithelial flow. In this study, we used MDCK II cells grown on standard culture surfaces and performed site-specific nanoindentation experiments to probe the repulsive force in response to deformation. This permitted us to gain information about the apical mechanics of these cells. We employ simple Hertzian mechanics here and refrain from more complex viscoelastic models to keep the matter simple. Essentially, more sophisticated models based on shell mechanics also generate the same qualitative picture. The goal of this work was to elaborate on the distribution of mechanical properties between multiple cells within confluent layers and to search for correlations between cellular mechanics and the occupied area of cells within these layers. From a tensegrity point of view, we expect larger structures if neighboring cells exert stress through adherens junctions, leading to larger restoring forces upon indentation.

Therefore, we initially performed rheological experiments on samples derived from cells seeded at different initial cell densities. Force indentation curves were subjected to a theoretical framework that has been well established before (9), and we found Young’s moduli that are comparable to those found in previous studies (11, 15, 38). However, by comparing the results of samples with different cell densities, we found that there is a significant trend to decreasing stiffness for higher amounts of cells seeded. Higher amounts of seeded cells do also result in higher cell density after an equal amount of incubation time and therefore lead to smaller cell areas (see Fig. S4). Apart from the decreasing Young’s modulus, we also found that the loss tangent at 100 Hz drops moderately with decreasing cell-seeding density. This means that cells behave more like solids if larger. This corresponds well to the general behavior of cells in the framework of soft glassy materials in which stiffer cells also generate less energy dissipation. However, care needs to be taken when cell densities are very low because polarization of cells might not be completed yet (39). These findings once more underline the importance of using equal incubation conditions for all samples to provide correct comparability between measurements.

Further, given the correlation between seeding and incubation conditions with both elasticity and cell adhesion area, we wanted to elucidate whether we can also find a correlation between cell size and elasticity in a single confluent layer independent of seeding density or other factors. Fortunately, even monoclonal cultures show cells with a broad size distribution, and although the exact regulatory mechanisms involved in size homeostasis are still under debate, influence of cell size on processes like division rates has been shown to exist (24, 40, 41). Alterations of cell mechanics depending on size may pose a way for cells to recognize their current size and alter their biochemistry appropriately. This is especially interesting because different stiffness and thereby actomyosin network architectures can carry information even from mother to daughter cells and should therefore contribute to the ongoing discussion on how cells could be aware of their very own size (42).

We have shown that for MDCK II cells, a decently broad size distribution can be obtained, and by determining the exact size and median Young’s modulus of individual cells, we were able to show that larger cells tend to have higher stiffness even if originating from the same cell layer. Interestingly, we found a trend including saturation effects for large sizes. Such saturation has also been observed when investigating cells seeded on gels of different elasticity, where cell stiffness correlates with substrate stiffness (37). Interestingly, we did not find a window of optimal size compared to Miettinen et al., who observed a peak metabolic activity for an optimal cell size (43). This shows that the way cellular properties correlate with cell size is diverse and complex in nature, and cell stiffness is one of these properties.

Lastly, we tested whether or not we can use single patterned cells to find the same correlations we found in the confluent samples already. In other words, we wanted to find out whether the size-dependent stiffness is a universal feature or only occurs in confluent layers. Although we had to rely on much larger adhesion areas for single-cell studies, this approach provided better reproducibility of exact cell sizes and yielded laterally resolved parameter maps of the apical mechanics of cells (44). The Young’s moduli of the stiffer, peripheral region of single patterned MDCK II cells do depend on the total adhesion area, whereas the central region shows similar Young’s moduli regardless of the adhesion area. Previous studies by Tee et al. and Roca-Cusachs et al. did not consider this difference in behavior depending on the exact location on the cell surface and could not report such bimodal distribution because the authors did not acquire force maps across the complete cell surface. It is therefore even more surprising that neither of the surface regions, which we managed to distinguish by mechanical behavior, show the same changes that have been observed on other cell lines in the respective studies. This emphasizes how fundamentally different the mechanical behavior of cells is regulated depending on cell type and how strongly it is influenced by the environmental conditions.

In larger cells, contractile forces and internal stresses are presumably enhanced. A similar trend was previously found when cells were cultured on pores. Cells on larger pores were smaller and softer (32).

Conclusion

We scrutinized the connection between the size of cells and their apical mechanics, showing that in confluent MDCK II cells, stiffness is increased in samples with lower initial cell-seeding density. Even in one cell monolayer, the stiffness of individual cells is increased with increasing apical surface area. This shows that special caution is required when comparing mechanical studies of cells carried out under different culture conditions.

Interestingly, this behavior could not be observed for single patterned cells, where we found that mechanics differ between certain locations on a cell’s surface, but the stiffness obtained from the cell’s center does not depend on the cell’s size. This emphasizes the importance of cell-cell contacts for the elastic response of cells, as recently shown (38). Taken together, these findings show that cellular mechanics react to environmental conditions in complex ways and that tension homeostasis and cell size are inherently coupled. The further understanding of the correlation between mechanical and biochemical properties of cells should ultimately lead to a better understanding of how these cells are able to respond appropriately to a large variety of different environmental conditions and still maintain performance.

Author Contributions

H.N. and F.R. performed experiments and analysis of the experiments regarding different cell-seeding densities. S.N., H.N., and S.K. performed experiments on confluent cells related to individual cell size. S.N. performed analysis on these data sets. Single-cell studies were performed and analyzed by S.N. S.N. and A.J. wrote the manuscript.

Editor: Christopher Yip.