Spontaneous Spatial Correlation of Elastic Modulus in Jammed Epithelial Monolayers Observed by AFM

Abstract

For isolated single cells on a substrate, the intracellular stiffness, which is often measured as the Young’s modulus, E, by atomic force microscopy (AFM), depends on the substrate rigidity. However, little is known about how the E of cells is influenced by the surrounding cells in a cell population system in which cells physically and tightly contact adjacent cells. In this study, we investigated the spatial heterogeneities of E in a jammed epithelial monolayer in which cell migration was highly inhibited, allowing us to precisely measure the spatial distribution of E in large-scale regions by AFM. The AFM measurements showed that E can be characterized using two spatial correlation lengths: the shorter correlation length, l_S, is within the single cell size, whereas the longer correlation length, l_L, is longer than the distance between adjacent cells and corresponds to the intercellular correlation of E. We found that l_L decreased significantly when the actin filaments were disrupted or calcium ions were chelated using chemical treatments, and the decreased l_L recovered to the value in the control condition after the treatments were washed out. Moreover, we found that l_L decreased significantly when E-cadherin was knocked down. These results indicate that the observed long-range correlation of E is not fixed within the jammed state but inherently arises from the formation of a large-scale actin filament structure via E-cadherin-dependent cell-cell junctions.

Introduction

Epithelial cells form a cell monolayer in which cells tightly adhere to each other through cell-cell junctions (1, 2, 3, 4, 5). The cells in such a monolayer cooperatively migrate and perform various collective cell functions, including morphogenesis (1, 2, 3, 4, 5, 6, 7, 8, 9), wound healing (4, 5, 10, 11, 12, 13, 14, 15), and cancer progression (3, 4, 5, 11, 13, 14, 15). These functions are dominated by intercellular mechanical forces arising from structural changes in the cytoskeleton.

The intracellular stiffness is a fundamental cell mechanical property. Previous studies of isolated single cells adhered to a substrate revealed that the intracellular stiffness—that is, the Young’s modulus, E—measured by atomic force microscopy (AFM) is mainly dominated by actin cytoskeletal structures (16, 17, 18, 19) and can change in response to the rigidity of the substrate to which the cells adhere (20, 21); specifically, the intracellular stiffness increases with increasing substrate rigidity. However, little is known about how the intracellular stiffness changes in response to neighboring cells in a cell monolayer system. Furthermore, although single cells are known to exhibit large cell-to-cell variations in the cell stiffness (18, 19), the cell-to-cell variation in the intracellular stiffness in a cell monolayer system is not well understood.

To address these questions, using AFM, we investigated the E of cells in a type of jammed epithelial monolayer in which cell migration was highly inhibited, and the cell shape and height became rather homogeneous compared to those of an unjammed state (22, 23, 24, 25, 26, 27, 28, 29, 30). Recent studies have unveiled the characteristic features of cells in a jammed state in terms of cell migration and cell shape (27, 28, 29, 30). Thus, such a jammed cell monolayer system is useful for investigating cell-cell mechanical interactions. Moreover, the decrease in migration speed in jammed monolayers allows us to precisely measure the spatial distribution of E in large-scale regions by AFM. We observed that E exhibited long-range spatial correlations. The correlation length was longer than the distance between adjacent cells and decreased significantly when we used chemical treatments to disrupt actin filaments or relax cell-cell junctions. Importantly, the reduced spatial correlation length in the treated cell monolayer samples recovered to that in the control condition when the treatments were washed out. Furthermore, we found that the spatial correlation length also decreased when E-cadherin was knocked down. These results indicate that the long-range correlation of E observed by AFM is not frozen or jammed during the unjamming-jamming transition; instead, the cells in the jammed state inherently form a large-scale actin filament structure through E-cadherin-dependent cell-cell junctions.

Materials and Methods

Cell samples

We used two types of Madin-Darby canine kidney (MDCK) cells. One was MDCK cells from RIKEN (Tokyo, Japan), hereafter simply called MDCK cells. The MDCK cells were cultured at 37°C and 5% CO₂ in minimal essential medium (Sigma-Aldrich, St. Louis, MO) with 10% fetal bovine serum, 1% penicillin/streptomycin, and 1% nonessential amino acids (Sigma-Aldrich). The cells were trypsinized using 0.25% trypsin/EDTA (Sigma-Aldrich) and plated in culture dishes (Iwaki, Tokyo, Japan) at an initial concentration of 1.0 × 10⁴ cells/cm². After the MDCK cells reached confluence, the cell sample was further cultured for ∼3 days until an epithelial cell monolayer was formed with highly packed cells, whose migration almost halted with a translational speed of less than 3 μm/h (see Document S1. Supporting Materials and Methods and Figs. S1–S10, Video S1. MDCK Cell Monolayer in the Untreated Condition during a Jamming Transition, Video S2. MDCK Cell Monolayer in the Untreated Condition in a Confluent Unjammed State, Document S2. Article plus Supporting Material; Video S1). We confirmed that the MDCK cell monolayer was in a jammed state (see Fig. S1, b and c; Video S2).

The other type of cells was MDCK cells stably expressing E-cadherin short hairpin RNA (shRNA) (E-cadherin shRNA MDCK cells), in which the E-cadherin expression was knocked down by treatment with tetracycline (Sigma-Aldrich) (31). The E-cadherin shRNA MDCK cells were cultured at 37°C and 5% CO₂ in Dulbecco’s modified Eagle’s medium (Wako Chemicals, Tokyo, Japan) with 10% tetracycline-negative fetal bovine serum (Life Technologies, Boston, MA), 1% penicillin/streptomycin (Gibco, Boston, MA), 1% nonessential amino acids (GlutaMAX; Gibco), and antibiotic drugs (800 μg/mL G418 and 5 μg/mL blasticidin; InvivoGen, Carlsbad, CA). The cells were plated in culture dishes at an initial concentration of 3 × 10⁴ cells/cm². After the cells reached confluence, they were further cultured for 1 day to form an epithelial monolayer with highly packed cells at the same density as the jammed MDCK cells.

To inhibit actin filament polymerization, the cell samples were treated with 3 μM latrunculin A ((LatA) Sigma-Aldrich) for 30 min. For the washout experiments, the LatA-treated samples were washed three times with the culture medium and then incubated for 12 h. To chelate calcium ions (which are essential for regulating various types of cell-cell junctions in epithelial monolayers), the cell samples were treated with 4 mM EGTA for 6 h. For the washout experiments, the EGTA-treated samples were washed three times with the culture medium and then incubated for 12 h. For the E-cadherin knockdown experiments, the E-cadherin shRNA MDCK cells were incubated for 96 h in 2 μg/mL tetracycline (Sigma-Aldrich) before the AFM measurements. In the treated MDCK and E-cadherin shRNA MDCK cell monolayers, the cell migration speed was less than 3 μm/h, which was comparable to that of the jammed MDCK cell monolayer (see Fig. S2).

Immunofluorescence

The cell monolayer samples were fixed with 4% paraformaldehyde in phosphate-buffered saline for 30 min and then incubated with 0.1% Triton X-100 for 15 min and bovine serum albumin in phosphate-buffered saline for 1 h. The actin filaments were stained with Alexa Fluor 488-conjugated phalloidin (Invitrogen, Carlsbad, CA). E-cadherin was stained with E-cadherin monoclonal antibody (ECCD-2 primary antibody; Life Technologies) and Alexa Fluor 546 (secondary antibody; Life Technologies). For staining, the samples were incubated for 24 h at 4°C and subsequently imaged by scanning laser confocal microscopy (C1; Nikon, Tokyo, Japan).

AFM measurements

A customized AFM attached to an upright optical microscope (Eclipse FN1; Nikon) was used to map the Young’s modulus, E, of the cell monolayers (Fig. 1 a). A rectangular cantilever (BioLever mini, BL-AC40TS-C2; Olympus, Tokyo, Japan) with a nominal spring constant of less than 0.1 N/m was used. To achieve a well-defined contact geometry, a silica bead with a radius R of ∼2.5 μm (Funakoshi, Tokyo, Japan) was attached to the apex of the cantilever tip with epoxy (32). The loading force was determined using Hooke’s law by multiplying the cantilever deflection by the spring constant calibrated using a thermal fluctuation method.

Figure 1.

(a) Schematic of the AFM measurement of a jammed epithelial cell monolayer. (b) A typical AFM mapping image of E for a jammed MDCK cell monolayer is shown. (c) Spatial correlation function of E was estimated from the AFM mapping image (b). Solid line represents the fitted results using Eq. 1, and dotted lines represent two fitted exponential functions with a shorter correlation length l_S (blue) and a longer correlation length l_L (red). To see this figure in color, go online.

The force curve mapping measurements were performed in a scan region of 300 μm × 300 μm with a lateral interval of 3 μm with a piezo scanner with a closed loop (P-563.3CD; Physik Instruments, Karlsruhe, Germany) and a digital piezo controller (E-761; Physik Instruments), which was controlled with LabVIEW software (National Instruments, Austin, TX). In the force mapping measurements, the cells were indented at a maximal loading force of ∼1.5 nN. E was estimated from the observed force-distance curves with the Hertzian contact model (33), which is expressed as

$$F=\frac{4}{3}\frac{E{R}^{1/2}}{1-v^2}{\delta }^{3/2},$$ (1)

where F is the loading force, δ is the indentation depth, and ν is the Poisson’s ratio of the cell, assumed here to be 0.5 (16, 18, 19, 20, 34), which corresponds to a perfectly incompressible material (33). We estimated E from the force-indentation curve in the region of δ < 0.6 μm (see Fig. S3). We confirmed that the E measured in the cell monolayers exhibited a clear log-normal distribution (Fig. S3), which is commonly observed in single cells (18). The medium was replaced with CO₂-independent medium (Invitrogen) for the AFM measurements, and the temperature was kept at 30°C during the AFM measurements.

Data analysis

The spatial autocorrelation function of a quantity X with a normal distribution at a distance r, C(r), is defined as

$$C\left(r\right)=\sum _{i,j}\theta \left(r-\left|{\mathit{r}}_i-{\mathit{r}}_j\right|\right)\frac{\left(X\left({\mathit{r}}_i\right)-\langle X\rangle \right)\left(X\left({\mathit{r}}_j\right)-\langle X\rangle \right)}{\langle X^2\rangle -{\langle X\rangle }^2},$$ (2)

where θ(x) is 1 for x = 0 and 0 otherwise, r_i is the position vector at the i-th pixel in the AFM mapping image, and <X> is the arithmetic mean of X in the mapping image.

Results

Spatial correlation functions of E in the epithelial monolayer

Fig. 1 b shows a typical AFM image of E in a jammed MDCK cell monolayer. E is higher at the cell-cell boundaries than in the intracellular regions. Such a spatial distribution of E is commonly observed in confluent epithelial cell monolayers (34, 35). We noticed that E in the intracellular regions was not randomly distributed among the cells; rather, the cells were likely to have an E value similar to that of the neighboring cells. Indeed, as shown in Fig. 1 c, we found that the spatial autocorrelation function with logE as X in Eq. 2, C_E, estimated from a typical E map, exhibited a long-tail relaxation and was well fitted by the sum of two exponential functions with shorter and longer correlation lengths of l_S and l_L, respectively:

$$C_E\left(r\right)=a_S{e}^{-r/l_S}+a_L{e}^{-r/l_L},$$ (3)

where a_S and a_L represent the normalized amplitudes of the shorter and longer relaxations, respectively. The mathematical decomposition of Eq. 3 indicates that the shorter and longer correlation lengths originate from independent mechanical components of cells. Taking the experimental white noise into consideration (see Fig. S4), we estimated l_S to be ∼6.1 μm, which is less than the size of a single cell in the jammed MDCK cell monolayer (see Fig. S1). Thus, l_S corresponds to the intracellular correlation length of E. The estimated l_L, in contrast, was 25.4 μm, which is larger than the distance between adjacent cell centers of 15.3 μm (see Fig. S1), showing that l_L corresponds to the intercellular correlation length of E.

We first confirmed that l_L predominantly reflected the spatial extent of the elastic modulus in the apical cortical and/or medial regions rather than at the cell-cell boundary (see Fig. S5). Next, we confirmed that the jammed MDCK cell monolayer displayed no characteristic change in E during the mapping experiments (see Fig. S6). Moreover, when using an unmodified sharp tip, we observed a long-range correlation length close to that measured with colloidal probe cantilevers (see Fig. S7). Finally, we investigated the influence of thin film effects on l_L because in the case of thin compliant materials placed on solid substrates, the stiffness of the samples measured by AFM is often dependent on the sample thickness (36, 37). We estimated the cell thickness by analyzing side-view cell membrane images and confirmed that l_L was not influenced by thin film effects (see Fig. S8), even though E is slightly affected by the cell height (see inset of Fig. S8 e). These results indicate that the l_L of cell monolayer measured by AFM represents the intrinsic spatial dependence of E, which depends on the intracellular structural integrity and flexibility.

Influence of actin filaments

The elastic modulus of cells measured by AFM is dominated by actin filaments (17). Thus, we next investigated how the spatial distribution of E is altered when the actin filament structures in the jammed MDCK cell monolayer are depolymerized with LatA treatment (Fig. 2 a). The depolymerization of actin filaments caused a significant decrease in E (Fig. 2 c), which is commonly observed (17). Simultaneously, l_L exhibited a marked drop, although l_S was almost unchanged (Fig. 2 b). These results indicate that the actin filament network is correlated over adjacent cells in the jammed state. We also observed that when the culture medium with LatA was washed out and the actin filaments in cells repolymerized, l_L recovered to the value in the untreated condition (Fig. 2 b).

Figure 2.

(a) Fluorescence images of actin filaments in a jammed MDCK cell monolayer in the control (LatA(−)) and treated (LatA(+)) conditions. (b) Spatial correlation functions of E in the control (red), LatA-treated (blue), and washout (green) conditions are shown. The average l_S (left) and l_L (right) in these conditions (inset in b) is shown. (c) The average E in these conditions is shown (n = 9 control, n = 5 LatA, and n = 5 washout). ^∗p < 0.05, ^∗∗p < 0.005 (Student’s t-test), and n.s. indicates a nonsignificant difference. To see this figure in color, go online.

We found that the variation in E between the control and LatA washout conditions was significantly different (see Fig. S9, a and d). The results suggested that the spatial distribution of the reorganized actin filament structures after the washout is different from that in the untreated condition.

Influence of cell-cell junctions

In epithelial monolayers, actin filaments interact with various calcium-dependent junction proteins (9, 31, 38, 39, 40). To understand how the long-range network structure of actin filaments is stabilized by junction proteins, we first investigated E in jammed MDCK cell monolayers by chelating calcium ions with EGTA (Fig. 3 a), which disrupts cell-cell adherens junctions and tight junctions (38, 39). We observed that l_L significantly decreased after the EGTA treatment but recovered to the value in the untreated condition when the EGTA was washed out (Fig. 3 b). This result indicates that calcium-dependent cell-cell junctions play an important role in the spatial organization of actin filaments. The l_L value showed no significant difference between the EGTA washout and control cells (Fig. 3 b). This result shows that the spatial correlation of E does not significantly change as the calcium-dependent cell-cell binding proteins dissociate and then reassociate. Moreover, the average E remained unchanged even after the EGTA treatment, but the variation in E after the EGTA treatment significantly increased (Fig. 3 c; Fig. S9, b and c), showing that the cells in a monolayer have a characteristic feature of randomly changing their E but maintaining the average E even without the cell-cell interactions that occur via calcium-dependent cell-cell binding proteins.

Figure 3.

(a) Fluorescence images of E-cadherin junctions and actin filaments in a jammed MDCK cell monolayer in the control, EGTA-treated, and washout conditions. (b) The average l_L of E in these conditions is shown. (c) The average E in these conditions is shown (n = 9 control, n = 6 EGTA, and n = 5 washout). ^∗p < 0.05, ^∗∗p < 0.005 (Student’s t-test), and n.s. indicates a nonsignificant difference. To see this figure in color, go online.

Among the calcium-dependent junction proteins, E-cadherin has been extensively investigated in terms of the mechanical sensing and communication processes associated with various mechanobiological phenomena (3, 9, 11, 13, 40, 41, 42, 43). Using E-cadherin shRNA MDCK cell monolayers (Fig. 4 a), we also observed that l_L was reduced when E-cadherin was knocked down (Fig. 4 b). This result suggests that E-cadherin plays a decisive role in regulating the long-range network structure of actin filaments. We also observed that the average E showed no significant difference between cells in which E-cadherin was either expressed or knocked down (Fig. 4 c), but the variation in E significantly increased when E-cadherin was knocked down (see Fig. S9, c and f). This result suggests that E changes more randomly without the cell-cell interactions that occur through E-cadherin proteins.

Figure 4.

(a) Fluorescence images of E-cadherin junctions in a jammed E-cadherin shRNA MDCK cell monolayer in the control (tet(−)) and tetracycline-treated (tet(+)) conditions. (b) The average l_L of E in these conditions is shown. (c) The average E in these conditions is shown (n = 8 tet(−) and n = 5 tet(+)). ^∗∗p < 0.005 (Student’s t-test), and n.s. indicates a nonsignificant difference. To see this figure in color, go online.

Discussion

In a cell monolayer, the cell proliferation rate rapidly decreases at a critical cell density in the proximity of the unjamming-jamming transition (22, 23, 24, 25, 26, 27, 28, 29). This process raises questions regarding how the geometric heterogeneity of cells that are densely immobilized within cell monolayers influences the spatial distribution of E measured by AFM. In this context, first, we noted that the proliferation rate in this study was of the same order as the rate reported previously (i.e., the cell density in the jammed state in this study was beyond the critical value) (see Fig. S2). Second, we found that E was independent of the cell dimensions, such as the lateral cell area and the aspect ratio (see Fig. S10). These results suggest that the spatial changes in E measured with AFM are not associated with the geometric heterogeneities of spatial constraints existing at the unjamming-jamming transition.

In this study, we investigated how the E in jammed epithelial monolayers spatially varies in terms of actin filaments and cell-cell junction proteins (Fig. 5). For jammed MDCK cell monolayers, we found that l_L, which is related to the spatial extent of the actin filament network structure in the apical cortical and medial regions (see Fig. S5), exhibited a reversible change corresponding to the change between actin filament formation and disruption states (Fig. 2). This type of reversible change in l_L was also observed for calcium-dependent junction proteins (Fig. 3). The observed reversible changes suggest that the spatial change in E measured by AFM does not originate from a frozen mechanical structure formed during the unjamming-jamming transition but inherently arises from the formation of a large-scale actin filament structure through calcium-dependent cell-cell junctions. The observed behavior of E between adjacent cells is reminiscent of the behavior of isolated single cells cultured on a substrate that can regulate their intracellular stiffness by sensing the substrate rigidity through integrins (20, 21). It is known that in epithelial cell monolayers, actin network structures span multiple cells through calcium-dependent junction proteins (1, 2, 5). Thus, it is considered that epithelial cells in a monolayer have the ability to sense the stiffness of adjacent cells and alter their own stiffness via intercellular calcium-dependent junction proteins (Fig. 5).

Figure 5.

Schematic of the spatial distributions of E in a MDCK cell monolayer in response to the formation and disruption of actin filaments and E-cadherin knockdown. The top view of the cell model (top) shows that the spatially correlated distribution of the cell stiffness becomes nonuniform between neighboring cells upon the disruption of E-cadherin and becomes soft and individually nonuniform. The dotted line crossing the cells of the stiff population and the soft population (top) corresponds to the side view of the cell model (middle) and the plot of E as a function of position, x (bottom). To see this figure in color, go online.

Among the calcium-dependent junction proteins, E-cadherin has been most extensively investigated in terms of the mechanical response in epithelial cells and monolayers. Reports have indicated that the density of E-cadherin molecules is proportional to the intercellular stress or tension (43) and/or the rate of cell stress (13). Moreover, microrheological measurements with magnetic beads have shown that the cell elastic modulus increases when external stress or tension is applied to cells via the E-cadherin protein (13, 42). Fig. 4 indicates that a significant difference arises in l_L between the control and E-cadherin shRNA MDCK cells. The results indicate that the actin filaments associated with E-cadherin-connected adjacent cells are the predominant source of intracellular stiffness in epithelial monolayers, with a long-range correlation length longer than that in single cells (Fig. 5).

Furthermore, we found that the average E was unchanged when calcium ions were chelated or E-cadherin was knocked down (Fig. 4). This result implies that the MDCK cells in the jammed state have the ability to maintain a mechanical homeostasis that regulates the cell stiffness via physical cell-cell contacts rather than specific cell-cell junction proteins.

It has been reported that the intracellular stiffness is affected not only by the cytoskeleton but also by the osmotic pressure (44) and mechanical properties of the nucleus (45). However, we found that the longer correlation length largely disappeared by disruption of actin filaments (Fig. 2), and the average length was ∼10.6 μm, which was less than the cell size. The result indicates that the actin filamentous structures dominantly regulate the observed long-range correlation of the intracellular stiffness measured by AFM in a jammed cell monolayer. It should be here noted that an indentation depth less than 0.6 μm was used to prevent cell damage and was much smaller than the cell height, which was ∼8.4 μm (see Fig. S8). The experimental conditions may be one reason that the cell nucleus had a minor effect on E as measured by AFM.

It is illuminating to consider how E is related to the intercellular stress, which can be estimated using traction force microscopy (11, 13, 14, 15, 28, 41). As cells approach a jammed state, both the velocity and the intercellular stress (the latter of which is estimated from the traction force between the cells and the extracellular matrix) exhibit a long spatial correlation length of more than 100 μm (11, 26, 28), which is approximately one order of magnitude longer than that of the E measured by AFM. Moreover, we observed that the cell density is independent of the intracellular stiffness (see Fig. S10), whereas the intercellular stress is proportional to the cell density (46). These different features between E measured by AFM and the intercellular tensile stress measured by monolayer stress microscopy suggest that the measured mechanical quantities are not directly associated with each other.

To investigate how the intracellular stiffness is influenced by the stiffness of the surrounding cells, we used a type of jammed epithelial monolayer in which cell migration is highly inhibited, and the cell shape and height have become rather homogeneous compared to those of the unjammed state. This jammed cell monolayer allows us to precisely measure the spatial distribution of E in large regions with AFM. On the other hand, the mapping speed of AFM is slow for large-scan regions, making it difficult to precisely measure the spatial distribution of E in an unjammed state in which cells dynamically and cooperatively migrate over time. Thus, at present, we cannot determine whether the spatial distribution of E measured in this study is a universal feature of cell-cell mechanical interactions in confluent cell monolayers or a feature specific to jammed cell monolayers.

In studies on jammed epithelial cell monolayers, the intracellular stiffness is often assumed to be homogeneous (11). This study, however, shows that E in epithelial cell monolayers is broadly distributed with a large variation and long-range correlation, even when cell migration and proliferation are highly restricted. Thus, the determination of E is important not only to understand how cells change their stiffness with respect to the surrounding cells but also to more precisely estimate the intercellular tension and stress, which will facilitate the elucidation of the mechanism of cell mechanotransduction in a cell population system.

Conclusions

Using AFM, we observed a long-range correlation in the intracellular stiffness, which was evaluated as the Young’s modulus, E, of cells in a type of jammed epithelial monolayer. The cell behavior is reminiscent of the behavior of isolated single cells cultured on a substrate, in which cells can regulate their intracellular stiffness by sensing the substrate rigidity. In other words, the epithelial cells in the jammed state have the ability to sense the stiffness of adjacent cells and alter their own stiffness via intercellular calcium-dependent junction proteins. Importantly, the observed long-range correlation length exhibits a reversible change with respect to the formation and disruption of actin filaments and calcium-dependent cell-cell junction proteins. The results indicate that the spatial change in E measured by AFM does not originate from a frozen mechanical structure formed during the unjamming-jamming transition. Moreover, the E-cadherin knockdown experiment indicates that E-cadherin, which can regulate the magnitude and/or the rate of tensile stresses occurring at the cell vertex and the cell-cell contact region, plays a decisive role in regulating the intracellular stiffness measured by AFM. These findings suggest that a detailed understanding of the intracellular stiffness over a large region is crucial for extending our knowledge of cell-cell interactions in a cell population system.

Author Contributions

Y. Fujii, Y.O., and T.O. designed the study. Y. Fujii, Y.O., and M.T. performed the experiments and analyzed the data. M.K. and Y. Fujita contributed to the cell sample preparations. Y. Fujii, M.K., Y. Fujita, Y.I., and T.O. contributed to the discussion. Y. Fujii and T.O. wrote the article.

Editor: Jeffrey Fredberg.

Supporting Citations

Reference (47) appears in the Supporting Material.