Active wetting of epithelial tissues

TL;DR

This study demonstrates that tissue wetting transitions in epithelial tissues are governed by active cellular forces, revealing a new physical framework that explains morphological changes during development and disease.

Contribution

It introduces an active wetting model for epithelial tissues, highlighting the role of active forces and a critical size in tissue morphology transitions.

Findings

Wetting transition depends on traction and contractile stresses.

Identifies a critical tissue size for wetting behavior.

Active shape fluctuations are amplified during dewetting.

Abstract

Development, regeneration and cancer involve drastic transitions in tissue morphology. In analogy with the behavior of inert fluids, some of these transitions have been interpreted as wetting transitions. The validity and scope of this analogy are unclear, however, because the active cellular forces that drive tissue wetting have been neither measured nor theoretically accounted for. Here we show that the transition between 2D epithelial monolayers and 3D spheroidal aggregates can be understood as an active wetting transition whose physics differs fundamentally from that of passive wetting phenomena. By combining an active polar fluid model with measurements of physical forces as a function of tissue size, contractility, cell-cell and cell-substrate adhesion, and substrate stiffness, we show that the wetting transition results from the competition between traction forces and contractile intercellular stresses. This competition defines a new intrinsic lengthscale that gives rise to a critical size for the wetting transition in tissues, a striking feature that has no counterpart in classical wetting. Finally, we show that active shape fluctuations are dynamically amplified during tissue dewetting. Overall, we conclude that tissue spreading constitutes a prominent example of active wetting --- a novel physical scenario that may explain morphological transitions during tissue morphogenesis and tumor progression.

Tables

Table 1. Table 1 : Estimates of model parameters.

Symbol	Description	Estimate
$h$	monolayer height	$5$ $\mu$m
$\xi$	friction coefficient	$100$ Pa$\cdot$s/$\mu$m2
$T_0$	maximal traction	$0.2-0.8$ kPa
$L_c$	nematic length	$25$ $\mu$m
$-\zeta$	contractility	$5-50$ kPa
${\gamma }_1$	rotational viscosity	$10$ kPa$\cdot$s
$a$	polarity restoring coefficient	$20$ Pa
$K$	Frank constant	$10$ nN
$\eta$	monolayer viscosity	$3-30$ MPa$\cdot$s
$\lambda$	hydrodynamic screening length	$0.2-0.6$ mm
$D$	noise intensity of monolayer shape fluctuations	$0.05-1.5$ $\mu$m2/h

Equations

$$F=\int \left[\frac{a}{2}{p}_{\alpha }{p}_{\alpha }+\frac{K}{2}({\partial }_{\alpha }{p}_{\beta })({\partial }_{\alpha }{p}_{\beta })\right]{\text{differential}}^3\vec{r}.$$

$$L_c^2{\nabla }^2{p}_{\alpha }=p_{\alpha },$$

$${\partial }_{\beta }{\sigma }_{\alpha \beta }=T_{\alpha },$$

$${\sigma }_{\alpha \beta }^{\text{s}}=\frac{{\sigma }_{\alpha \beta }}{h}=\eta ({\partial }_{\alpha }{v}_{\beta }+{\partial }_{\beta }{v}_{\alpha })-\zeta p_{\alpha }{p}_{\beta },$$

$$f_{\alpha }=-\frac{T_{\alpha }}{h}=-\xi v_{\alpha }+{\zeta }_i{p}_{\alpha }.$$

$$S\approx \frac{T_0{L}_c}{h}R+\left(\zeta -\frac{3T_0{L}_c}{h}\right)\frac{L_c}{2}.$$

$$R^{\ast }\approx \frac{1}{2}\left(3L_c-\frac{\zeta h}{T_0}\right)\sim -\frac{1}{2}\frac{\zeta }{{\zeta }_i}$$

$${\omega }_0\approx \frac{T_0{L}_c}{2\eta h}$$

$$S_n(t)=⟨|\delta {\tilde{R}}_n(t){|}^2⟩=\frac{D}{{\omega }_n}\left[e^{2{\omega }_n(t-t^{\ast })}-1\right],$$

$$R(t)=a+\frac{b}{1+\exp [(d+\ln (2-\sqrt{3}))t/c+d]}$$

$$T_r(r)=-T_0{p}_r(r)=-T_0\frac{I_1(r/L_c)}{I_1(R/L_c)},$$

$$-\zeta =2T_0\frac{L_c}{h}\frac{I_2\left(R/L_c\right)}{I_1\left(R/L_c\right)-I_0\left(R/L_c\right)\left[\frac{I_0\left(R/L_c\right)}{I_1\left(R/L_c\right)}-\frac{2L_c}{R}\right]}.$$

$$\begin{gathered} {\sigma }_{rr}\left(r\right)=T_0{L}_c\left[\frac{I_0^2\left(R/L_c\right)}{I_1^2\left(R/L_c\right)}-\frac{L_c}{R}\right]-T_0{L}_c\frac{I_0\left(r/L_c\right)}{I_1\left(R/L_c\right)} \\ +\frac{\zeta h}{2}\left[1+\frac{L_c}{R}\frac{I_0\left(R/L_c\right)}{I_1\left(R/L_c\right)}-\frac{I_0^2\left(R/L_c\right)}{I_1^2\left(R/L_c\right)}\right]+\frac{\zeta h}{2}\frac{1}{I_1^2\left(R/L_c\right)} \\ \left[\frac{1}{2}{I}_0\left(r/L_c\right)\left[I_0\left(r/L_c\right)+I_2\left(r/L_c\right)\right]-I_1^2\left(r/L_c\right)\right]. \end{gathered}$$

$$\begin{gathered} \sigma =\frac{1}{\pi R^2}{\int }_0^{2\pi }d\theta {\int }_0^R{\sigma }_{rr}rdr= \\ {T}_0{L}_c\left[\frac{I_0\left(R/L_c\right)}{I_1\left(R/L_c\right)}-3\frac{L_c}{R}+2\frac{L_c^2}{R^2}\frac{I_0\left(R/L_c\right)I_1\left(R/L_c\right)-1}{I_1^2\left(R/L_c\right)}\right] \\ -\frac{\zeta h}{2}[1-\frac{I_0^2\left(R/L_c\right)}{I_1^2\left(R/L_c\right)} \\ +\frac{L_c}{R}\frac{I_0\left(R/L_c\right)}{I_1\left(R/L_c\right)}+\frac{L_c^2}{R^2}\frac{I_0^2\left(R/L_c\right)-1}{I_1^2\left(R/L_c\right)}] \end{gathered}$$

$$\frac{\partial p_{\alpha }}{\partial t}=-\frac{1}{{\gamma }_1}\frac{\delta F}{\delta p_{\alpha }},$$

$$F={\int }_V\left[\frac{a}{2}{p}_{\alpha }{p}_{\alpha }+\frac{K}{2}\left({\partial }_{\alpha }{p}_{\beta }\right)\left({\partial }_{\alpha }{p}_{\beta }\right)\right]d^3\mathbf{r},$$

$${\partial }_t{p}_{\alpha }=\frac{1}{{\gamma }_1}\left(-a{p}_{\alpha }+K{\nabla }^2{p}_{\alpha }\right).$$

$$L_c^2{\nabla }^2{p}_{\alpha }=p_{\alpha },$$

$$0={\partial }_{\beta }\left({\sigma }_{\alpha \beta }^s+{\sigma }_{\alpha \beta }^a+{\sigma }_{\alpha \beta }^{E,s}\right)+f_{\alpha },$$

$${\sigma }_{\alpha \beta }^E=-P{\delta }_{\alpha \beta }-\frac{\partial f}{\partial \left({\partial }_{\beta }{p}_{\gamma }\right)}{\partial }_{\alpha }{p}_{\gamma },$$

$$0=-{\partial }_{\alpha }P+{\partial }_{\beta }\left({\sigma }_{\alpha \beta }^s+{\sigma }_{\alpha \beta }^a\right)+f_{\alpha }.$$

$$0={\partial }_{\beta }\left({\sigma }_{\alpha \beta }^s+{\sigma }_{\alpha \beta }^a\right)+f_{\alpha }.$$

$$0={\partial }_{\beta }{\sigma }_{\alpha \beta }^s+f_{\alpha }.$$

$${\partial }_{\beta }{\sigma }_{\alpha \beta }=T_{\alpha },$$

$$T_{\alpha }=-f_{\alpha }h,{\sigma }_{\alpha \beta }={\sigma }_{\alpha \beta }^{s}h.$$

$${\sigma }_{\alpha \beta }^s=2\eta {\tilde{v}}_{\alpha \beta }+\frac{{\nu }_1}{2}\left(p_{\alpha }{h}_{\beta }+h_{\alpha }{p}_{\beta }-\frac{2}{d}{p}_{\gamma }{h}_{\gamma }{\delta }_{\alpha \beta }\right)-\zeta q_{\alpha \beta }+\left(\bar{\eta }d{v}_{\gamma \gamma }+{\bar{\nu }}_{1}d{p}_{\gamma }{h}_{\gamma }-\bar{\zeta }-{\zeta }^{\prime }{p}_{\gamma }{p}_{\gamma }\right){\delta }_{\alpha \beta },$$

$$f_{\alpha }=-\xi v_{\alpha }+{\nu }_i{\dot{p}}_{\alpha }+{\zeta }_i{p}_{\alpha },$$

$${\sigma }_{\alpha \beta }^s=\eta \left({\partial }_{\alpha }{v}_{\beta }+{\partial }_{\beta }{v}_{\alpha }\right)-\zeta p_{\alpha }{p}_{\beta },$$

$$f_{\alpha }=-\xi v_{\alpha }+{\zeta }_i{p}_{\alpha },$$

$$r^2{p}^{\prime \prime }\left(r\right)+r{p}^{\prime }\left(r\right)-\left[1+\frac{r^2}{L_c^2}\right]p\left(r\right)=0.$$

Full text

Living tissues are active materials with the ability to undergo drastic transitions in shape and dimensionality1. When properly controlled, such morphological transitions enable development and regeneration. When regulation fails, however, aberrant morphological transitions underlie developmental defects and tumour formation2; 3. Transitions in tissue shape are regulated by a myriad of molecular processes that act upon a limited number of physical properties to ultimately determine tissue dynamics. To understand the nature of these physical properties and their impact on tissue shape, extensive research has focused on how a three-dimensional cell aggregate spreads on a substrate4; 5; 6; 7; 8. Besides mimicking biological processes such as epiboly in zebrafish9; 10; 11; 12, the spreading of a cell aggregate is amenable to theoretical and experimental access, and has become a widespread model process.

Given the fluid behaviour of cell aggregates at long times, their spreading on a substrate has been studied as a wetting problem1. In analogy with the case of a fluid drop, the extent to which the aggregate spreads on the substrate has been proposed to rely on a competition between cell-cell ($W_{\text{cc}}$) and cell-substrate ($W_{\text{cs}}$) adhesion energies4; 5 encoded in the so-called spreading parameter $S=W_{\text{cs}}-W_{\text{cc}}$. This parameter changes sign at the wetting transition that separates tissue spreading ($S>0$) from retraction into a droplet-like aggregate ($S<0$)5; 6; 13; 14. This analogy with the classical theory of wetting has successfully explained aspects of tissue wetting such as changes in contact angle as a function of cell-cell and cell-extracellular matrix (ECM) adhesion15. However, this conceptual framework overlooks the active nature of living tissues and, hence, it does not explicitly account for the ability of cells to polarize, generate traction forces, and couple such forces with adhesion dynamics. To a great extent, this limitation stems from the lack of direct measurements of cell-cell and cell-matrix forces during tissue wetting and dewetting.

To overcome these experimental and theoretical limitations, we performed a systematic quantitative study of the mechanics of tissue wetting as a function of cell-cell and cell-matrix adhesion, ECM ligand density, ECM stiffness, tissue size, and contractility. Our results cannot be explained solely in terms of the physics of passive fluids. Instead, we show that the tissue wetting transition and dewetting dynamics are well captured by a new framework for active wetting based on an active polar fluid model of tissue spreading.

E-cadherin expression induces dewetting of a cell monolayer

We designed an experimental assay to study wetting transitions of epithelial clusters induced by controlled changes in tissue mechanics. The idea behind the experimental approach is to progressively increase cell-cell adhesion in an epithelial monolayer while measuring its effect on cellular forces and tissue spreading. To this end, we use human breast adenocarcinoma cells (MDA-MB-231) transfected with a dexamethasone-inducible vector containing human E-cadherin mRNA16. In the absence of dexamethasone, these metastatic cells do not express significant levels of cell-cell adhesion proteins. Upon adding dexamethasone, the concentration of E-cadherin increases almost linearly in time for $\sim 24$ h and plateaus thereafter (Figs. 1 and S1). To study tissue wetting, MDA-MB-231 cells are seeded on a $12$ kPa polyacrylamide gel coated with collagen I (Fig. 1). Initially, the cells form a monolayer within a circular opening of a PDMS membrane deposited on the gel. 8 hours after E-cadherin induction, the confining membrane is removed and the monolayer spreads. However, after $\sim 20$ hours, the monolayer often starts retracting, eventually becoming a spheroidal cell aggregate (Figs. 1 and S2; Supplementary Movies 1, 2). Thus, the monolayer undergoes a transition from wetting to dewetting, which we refer to hereafter generically as wetting transition.

To reproducibly study this transition, we seed cells on adherent (collagen I-coated) circular islands of controlled size ($100$ $\mu$m in radius) surrounded by an uncoated surface that cells cannot invade (Fig. 1). We use Traction Force Microscopy to measure traction forces on the substrate (Fig. 1)17, and Monolayer Stress Microscopy to measure tension within and between cells (Fig. 1)18; 19. A few hours after E-cadherin induction, monolayers become cohesive (Fig. 1). Cells at the edge polarize by extending lamellipodia towards the exterior of the island, generating radially-oriented inwards-pointing tractions (Figs. 1 and S3)20; 21. Monolayer tension increases from the edge of the monolayer and reaches a maximum at the center (Fig. 1). Note that monolayer tension is a bulk property and should not be confused with the interfacial surface tension that plays a central role in classical wetting phenomena. During the first $\sim 25$ hours of the experiment, tractions (Fig. 1) and tension (Fig. 1) rise in parallel with the increase in E-cadherin. As for unconfined spreading monolayers, the monolayer eventually retracts, decreasing its area (Fig. 1) and dewetting the substrate to form a spheroidal aggregate, thus completing a transition from 2D to a 3D tissue geometry (Fig. S4; Supplementary Movies 3, 4).

Formation of E-cadherin junctions activates myosin

To study the mechanisms underlying the increase of tension we measure myosin levels and activity. During the first 24 hours of E-cadherin expression, myosin levels remain constant but diphosphorylated myosin light chain (ppMLC) exhibits a $\sim 3$-fold increase (Figs. 2 and 2). Untransfected cells (CT) or transfected cells lacking dexamethasone in their medium (labelled E-cad) show constant ppMLC levels (Fig. 2), indicating that the observed response is not attributable to a secondary effect of dexamethasone addition or to transfection artifacts. Unlike in cohesive monolayers, expression of E-cadherin does not lead to an increase of tension in single cells (Fig. 2). Consistently, monolayers show higher levels of ppMLC than single cells several hours after induction (Fig. S5). Moreover, abrogating cell-cell adhesions with EGTA (2 mM) prevents the buildup of traction and tension, as well as the wetting transition (Fig. S6, Supplementary Movie 5). Thus, we conclude that E-cadherin regulates myosin-generated contractility through a mechanism dependent on cell-cell junction formation. Notably, E-cadherin not only affects intercellular forces but also tractions, ultimately determining the global mechanics of the monolayer22; 23; 24; 25.

Tissue tension induces the wetting transition

Next, we study the reorganization of adhesive and cytoskeletal structures in the monolayer. Upon induction of its expression, E-cadherin progressively accumulates at cell-cell contacts (Fig. 2) and colocalizes with $\beta$-catenin (Figs. 2 and 2), confirming the formation of adherens junctions. In parallel, the focal adhesion protein paxillin redistributes to the periphery of the monolayer (Fig. 2), and supracellular stress fibers rich in active myosin massively form (Figs. S7, 2 and 2). These results suggest that dewetting is not directly caused by an increase in cell-cell adhesion, but rather by an increase in tension, which eventually causes the failure of cell-substrate adhesions. To test this hypothesis, we incubate the cells with blebbistatin (25 $\mu$M) to hinder the increase in contractility without impairing the over-expression of E-cadherin (Fig. 2). This treatment reduces cellular forces (Fig. S8) and delays dewetting (Fig. 2; Supplementary Movie 6). Conversely, the addition of the ROCK inhibitor Y27632 (25 $\mu$M) during dewetting causes the monolayer to rewet the substrate (Figs. 2 and 2; Supplementary Movie 6), thus demonstrating the active origin and reversibility of the transition. Together, these results show that the wetting transition results from a competition between active cellular forces, rather than simply between cell-cell and cell-substrate adhesion energies.

An active polar fluid model of tissue wetting

To understand how the wetting transition emerges from active cellular forces, we build upon a continuum mechanical model of epithelial spreading26. Given the long time scales of the wetting/dewetting processes, we neglect the elastic response of the tissue21; 27; 28; 29, assuming that it has a purely viscous behavior26; 30; 31; 32; 33; 34; 35. Thus, taking a coarse-grained approach, the model describes the cell monolayer as a two-dimensional (2D) active polar fluid36; 37; 38; 39, namely in terms of a polarity field $\mathbf{p}(\mathbf{r},t)$ and a velocity field $\mathbf{v}(\mathbf{r},t)$ (Supplementary Note). Our 2D model does not aim at describing the out-of-plane flows and shape of the tissue, nor the dynamics of the contact angle. However, it allows us to predict the onset and initial dynamics of the wetting transition, which is the focus of our study.

The cell monolayer is unpolarized in the bulk and polarized at the edge (see Figs. 1 and 1). Hence, we take a free energy for the polarity field that favours the unpolarized state $\mathbf{p}=0$ with a restoring coefficient $a>0$, and that introduces a cost for polarity gradients, with $K$ the Frank constant of nematic elasticity in the one-constant approximation40:

[TABLE]

We assume that the polarity field is set by flow-independent mechanisms, so that it follows a purely relaxational dynamics, and that it equilibrates fast compared to the spreading dynamics. Hence, $\delta F/\delta p_{\alpha}=0$, which yields

[TABLE]

where $L_{c}=\sqrt{K/a}$ is the characteristic length with which the polarity decays from $p_{r}(R)=1$ at the edge of the monolayer of radius $R$ to $p_{r}(0)=0$ at the center (red shade in Fig. 3).

Then, force balance imposes

[TABLE]

where $\sigma_{\alpha\beta}$ and $T_{\alpha}$ are the components of the monolayer tension and traction stress fields, respectively. We relate these forces to the polarity and velocity fields via the following constitutive equations for a compressible active polar fluid41:

[TABLE]

[TABLE]

Here, $h$ is the monolayer height, $\eta$ is the monolayer viscosity, $\zeta$ is the active stress coefficient, $\xi$ is the cell-substrate viscous friction coefficient, and $\zeta_{i}$ is the contact active force coefficient. These parameters are assumed to be time-dependent to account for the evolving mechanical properties of the monolayer. Note that $\zeta<0$ for contractile behaviour, and hence we call $-\zeta$ ‘contractility’. In addition, we define the maximal traction stress exerted by polarized cells, $T_{0}=\zeta_{i}h$.

Assuming radial symmetry, neglecting cell-substrate viscous friction, and imposing stress-free boundary conditions, we analytically solve the model (Supplementary Note). Thus, we obtain the spreading velocity $V=v_{r}(R)=\differential R/\differential t$ and, hence, the spreading parameter7 $S=\eta V$. In the experimentally relevant limit $L_{c}\ll R$, it reads

[TABLE]

Strikingly, the spreading parameter depends on the monolayer radius $R$, which entails the existence of a critical radius

[TABLE]

above which the tissue spreads ($S>0$) driven by traction forces $T_{0}>0$ and below which it retracts ($S<0$) driven by tissue contractility $\zeta<0$ (Fig. 3). The competition between bulk and contact active forces defines a novel intrinsic lengthscale $L_{p}\equiv-\zeta/\zeta_{i}$ of active polar fluids that naturally gives rise to the critical radius for the wetting transition, a striking property that has no counterpart in the classical wetting scenario.

Unlike for ordinary fluids, the wetting properties of tissues are not determined by local forces at the contact line but by the balance of forces across the entire monolayer, which results in the size-dependent wetting. Specifically, the internal, unpolarized region of the monolayer is subject to almost no external forces, and hence it is under a uniform tension set by traction forces at the polarized boundary layer. Because of the viscous rheology of the tissue, this uniform tension generates an outwards-directed flow with a linearly increasing velocity profile (Figs. S9 and S10; Supplementary Movie 7). Thus, larger monolayers exhibit a larger velocity right behind the boundary layer, which requires a higher contractility to induce monolayer dewetting (Fig. 3; Supplementary Note). Finally, we suggest that the predicted non-monotonous flow profiles might induce the formation of 3D cell rims observed at the edge of epithelial monolayers42; 43.

Tissue wetting depends on tissue size and substrate properties

The model predicts that the wetting transition depends on monolayer size and tissue forces (Figs. 3 and 3). To assess the role of these variables in the experiments, we generate circular islands of different radii ($50$, $100$, $150$, and $200$ $\mu$m) on substrates of different ECM ligand densities ($100$, $10$, and $1$ $\mu$g/mL of collagen in the coating solution) (Figs. 4 and 4). We also study cell monolayers on substrates of different rigidities ($3$, $12$, and $30$ kPa) (Fig. S11). With the only exception of $30$ kPa gels, on which dewetting does not occur in the time scale of the experiment, monolayers in all conditions feature a tension buildup phase and a dewetting phase (Figs. S11 to S11, Figs. S12 to S12; Supplementary Movies 8, 9). However, the duration of each phase presents large quantitative differences (Figs. 4, 4 and S11). To assess these differences, we implement a robust user-blind method to measure the time $t^{*}$ at which dewetting starts (Fig. S13; see Methods). This analysis establishes that smaller monolayers dewet earlier than larger ones, and so do monolayers on softer and/or less densely coated substrates (Figs. 4 and S11). Therefore, tissue size as well as substrate adhesion and stiffness are key parameters in determining the wetting transition (Supplementary Movie 10). Of note, transition times span from $7$ to $40$ h after E-cadherin induction and monolayers on stiff substrates do not dewet in the experimental time window ($85$ h), which implies that changes in E-cadherin levels alone (Fig. 1) cannot account for tissue dewetting.

In our experiments, tissue forces increase with time until the wetting transition takes place. As a consequence, larger monolayers not only dewet later than smaller ones but also at higher tension (Figs. S12 to S12). This finding is consistent with our prediction (Fig. 3) that larger monolayers require higher contractility to dewet or, equivalently, that for a given contractility only sufficiently large monolayers will wet. Thus, our experimental results do not directly establish but support the existence of a critical radius for tissue wetting. Future work should further assess the size dependence of the wetting transition using direct control of cell contractility.

To infer the values of model parameters, we fit the predicted traction profiles to the experimental data (Fig. 3, see Methods). Hence, we obtain the time evolution of the model parameters $T_{0}(t)$ and $L_{c}(t)$. In addition, by imposing that the velocity of the tissue boundary vanishes during the wetting phase, we obtain the time evolution of the contractility $-\zeta(t)$ (Eq. 12, see Supplementary Note). The maximal traction $T_{0}$ and the contractility $-\zeta$ experience a $~{}3$-fold increase, whereas the nematic length $L_{c}$ remains constant (Figs. 3 to 3). This analysis is performed for all experimental conditions (Fig. S14, Figs. S11 to S11), from which we obtain the critical values of the parameters at the wetting transition, namely at time $t^{*}$. The nematic length has a similar value of $L_{c}\approx 25$ $\mu$m for all the experimental conditions (Fig. S11, Figs. S14 to S14), suggesting that, as considered in our model, it is an intrinsic property of the cell monolayer. Critical tractions $T_{0}^{*}=T_{0}(t^{*})$ are largely independent of monolayer radius (Fig. 4), but they increase with substrate rigidity (Fig. S11). Critical tractions also increase linearly with measured substrate ligand density (Figs. 4 and S12), suggesting that collagen is fully saturated with integrins at the wetting transition. The critical traction $T_{0}^{*}$ should thus be interpreted as the maximum force that cells can withstand before focal adhesions fail44, and hence tissue spreading is not possible above it. Like critical tractions, the critical contractility $-\zeta^{*}=-\zeta(t^{*})$ increases with substrate rigidity (Fig. S11) and with ligand density (Fig. 4). However, unlike critical tractions, the critical contractility also increases with monolayer radius (Fig. 4). We summarize our results in a phase diagram for the tissue wetting transition as a function of contractility, substrate ligand density, and monolayer radius (Fig. 4).

Active forces govern tissue morphology during dewetting

Our analysis thus far shows that an active polar fluid model captures the onset of dewetting as a function of the material properties and geometry of the tissue. Next, we focus on the early dynamics of tissue dewetting. Immediately after the onset of dewetting, the monolayer loses its circular symmetry, acquiring an elliptic-like shape before collapsing into a spheroidal cell aggregate (Fig. 5; Supplementary Movie 11). This striking symmetry breaking is in stark contrast with the known isotropic dewetting of passive fluids45; 46; 47. Although pinning of the contact line46; 47; 48 may contribute to breaking the circular symmetry, the fact that monolayer retraction systematically tends to start at diametrically opposed points of the tissue boundary (Supplementary Movie 11) suggests the presence of a morphological instability of active origin. Indeed, from our active polar fluid model, we analytically predict a long-wavelength instability of monolayer shape during dewetting (Supplementary Note).

To test the predictions, we characterize the evolution of tissue morphology by tracking the contour of the monolayer (Fig. 5). The local radius perturbation $\delta R(\theta,t)=R(\theta,t)-R_{0}$ quantifies the loss of circular symmetry (Fig. 5), and its Fourier transform dissects the contribution of each perturbation mode to the overall shape of the monolayer (Fig. 5). Consistent with the predicted instability, the amplitudes $|\delta\tilde{R}_{n}|$ of the long-wavelength modes increase with time upon the onset of dewetting (Fig. 5). Their predicted growth rates $\omega_{n}$ depend on a single yet-unmeasured parameter, the monolayer viscosity at the wetting transition, $\eta^{*}$. Its value can be inferred from the retraction rate of the monolayer, $\omega_{0}$, which we experimentally measure by fitting the exponential growth of the zeroth perturbation mode: $\delta\tilde{R}_{0}(t)=\delta\tilde{R}_{0}(t^{*})\,e^{\omega_{0}(t-t^{*})}$ (Figs. 5 and S15). Comparing with the theoretical prediction (Supplementary Note)

[TABLE]

we obtain viscosities that increase with monolayer radius and substrate ligand density, spanning from $3$ to $30$ MPa·s (Fig. 5). The tendency exhibited by the viscosity is similar to that of transition times (Fig. 4). In fact, these two quantities linearly correlate (Fig. 5), which suggests that monolayer viscosity increases with time in our experiment, likely due to a combination of cell-cell junction formation26; 49, increasing contractility50, and increasing cell density49.

Once the theoretical growth rates $\omega_{n}$ are known, we can predict the amplitudes of the different shape modes. Assuming that monolayer shape fluctuations are fast compared to the dewetting dynamics, we compute the structure factor of the monolayer boundary

[TABLE]

where $D$ is the noise intensity of mode amplitudes (Supplementary Note). By fitting this prediction to the experimental data (Figs. 5 and S16), we infer the value of $D$, which increases with tissue size but decreases with substrate ligand density (Fig. 5). This behavior is consistent with active shape fluctuations driven by the total traction force in the tissue, which scales linearly with monolayer radius (see Eq. 6), and damped by cell-substrate friction, which increases with substrate ligand density. Finally, we obtain experimental growth rates from the structure factors (Figs. 5 and S16; Supplementary Note). Despite their expected variability, our experimental results agree with the predictions, confirming that the growth of shape-changing perturbations, especially of mode $n=2$, is responsible for the elliptic-like shape of the monolayer (Figs. 5 and 5). Overall, these results show that active forces and shape fluctuations determine the morphological evolution during monolayer dewetting.

Discussion and outlook

Our results illustrate how E-cadherin adhesion regulates tissue mechanical properties and forces and, in turn, how these forces determine tissue shape, dynamics, fluctuations and dimensionality as a function of tissue size, contractility, substrate stiffness, and cell-cell and cell-substrate adhesion. In vivo, transitions in tissue morphology are characterized by changes in cell contractility51; 52, cell adhesion53; 54 and ECM composition55; 56. It is appealing to think that these changes translate into different wetting states. For example, this could explain increased tumor invasiveness when contractility decreases or critical traction increases due to an enhanced cell-substrate adhesion, ECM deposition or ECM stiffening. This scenario is supported by previous experiments associating E-cadherin-dependent epithelial retraction and suppression of tumor invasion in vivo57. Furthermore, tumor growth per se implies an increase in tissue radius, possibly leading to a dewetting-wetting transition even if contractility and critical traction remain unaltered. In this line, the nucleation of a spreading monolayer from a growing cell aggregate has been previously reported43.

Our analysis unveils fundamental features of tissue wetting that differ qualitatively from the classical wetting paradigm. We account for these differences by developing a theoretical framework for active wetting, which explicitly relates the wetting properties of tissues to active cellular forces. This framework, based on active gel theory, captures the mechanics of the wetting transition as well as the dynamics of monolayer morphology during the early stages of tissue dewetting. Furthermore, it allows the quantification of active stresses, viscosity, and active fluctuations in the tissue. In light of these results, we propose that tissue spreading can be understood as the wetting process of an active polar fluid, constituting the defining example of the general phenomenon of active wetting.

.1 Active polar fluid model of epithelial spreading

Instead of formulating a model based on adhesion energies, similar to those previously proposed to describe tissue wetting 5, our aim is to see how the wetting transition arises from mechanical models of collective cell migration. To this end, we extend a previously introduced continuum model of epithelial spreading 26 to the present problem. This continuum model takes a coarse-grained approach that describes the long-time and large-scale dynamics of the tissue as those of an active polar liquid, namely in terms of a polarity field $\bm{p}\left(\bm{r},t\right)$ and a flow field $\bm{v}\left(\bm{r},t\right)$. Below, we briefly justify this description, which has already been applied to the spreading of tissue monolayers26; 30; 31; 32. A very similar model was also proposed for traction force and velocity profiles of single crawling cells 60.

.1.1 Polarity dynamics

In our monolayer, cells at the center exert weak and random traction forces. In contrast, cells at the edge extend large lamellipodia towards the outside and exert strong inward-pointing traction forces on the substrate, indicating that they are polarized (Figs. 1 and S3). The outwards polarization of cells at the border is likely due to contact inhibition of locomotion, a cell-cell interaction whereby cells repolarize in opposite directions upon contact 61; 62. In fact, this interaction is mediated by cell-cell adhesion, with front-rear differences in cadherin-based junctions acting as a cue for the repolarization 63; 64; 65; 66; 67; 68. Although originally proposed for mesenchymal cells, contact inhibition of locomotion is being increasingly recognized to play a key role in orchestrating the collective migration of epithelial monolayers 61; 66; 67; 68; 69; 70; 71; 72; 14. In a cohesive monolayer, this interaction naturally leads to polarization of cells at the edge towards free space, leaving the inner region of the monolayer unpolarized. Such a polarity profile, in turn, explains the localization of traction forces at the edge and the build-up of tension at the center of epithelial monolayers 71; 72. Therefore, upon the expression of E-cadherin, we expect the polarity field $\bm{p}\left(\bm{r},t\right)$ to be set by an autonomous cellular mechanism such as contact inhibition of locomotion, which polarizes cells within a time scale $\tau_{\text{CIL}}\sim 10$ min 14; 65. Hence, $\bm{p}\left(\bm{r},t\right)$ should remain essentially independent of flows in the monolayer, which occur over a longer time scale given by the strain rate, at least of order $\tau_{s}\sim 100$ min 26; 73. Consequently, within a phenomenological approach, we propose the polarity field to follow a purely relaxational dynamics given by

[TABLE]

where $F\left[\bm{p}\right]$ is the coarse-grained free energy functional of the orientational degrees of freedom, and $\gamma_{1}$ is a kinetic coefficient (the rotational viscosity for the angular degrees of freedom). With respect to the most general dynamics of the polarity field in an active polar fluid, Eq. S1 neglects polarity advection and corotation, as well as flow alignment and active spontaneous polarization effects.

Then, since the bulk of the monolayer remains mechanically unpolarized, the coarse-grained free energy $F$ includes a Landau expansion around the isotropic state $\bm{p}=0$, and gradient terms resulting from nematic elasticity 40:

[TABLE]

where $a>0$ is a restoring coefficient of the polarity, and $K$ is the Frank elastic constant in the usual one-constant approximation. The dynamics of the polarity is thus given by

[TABLE]

In the limit of fast polarity dynamics compared to the spreading dynamics, the polarity field is always at equilibrium, $\partial_{t}p_{\alpha}=0$, adiabatically adapting to the shape of the monolayer. Under this approximation, the polarity field is given by

[TABLE]

where we have defined the characteristic length $L_{c}\equiv\sqrt{K/a}$ of the polar order in the monolayer.

.1.2 Force balance

Flows in cell monolayers occur at very low Reynolds numbers. Therefore, inertial forces are negligible, and hence momentum conservation reduces to the force balance condition

[TABLE]

where $\sigma_{\alpha\beta}^{s}$ and $\sigma_{\alpha\beta}^{a}$ are the symmetric and antisymmetric parts of the deviatoric stress tensor, and $f_{\alpha}$ is the external force density. Respectively, $\sigma_{\alpha\beta}^{E,s}$ is the symmetric part of the Ericksen tensor. This tensor generalizes the pressure $P$ to include anisotropic elastic stresses associated to the orientational degrees of freedom in liquid crystals 40:

[TABLE]

where $f$ is the Frank free energy density, namely the integrand of Eq. S2. Thus, the orientational contribution to the Ericksen tensor is of second order in gradients of the polarity field, and hence we neglect it, so that force balance reads

[TABLE]

Then, the pressure is related to the cell number surface density $\rho$ by the equation of state of the monolayer. For the sake of an estimate, we assume the simplest form for an equation of state, $P\left(\rho\right)=B\left(\rho-\rho_{0}\right)/\rho_{0}$, where $B$ is the bulk modulus of the monolayer, and $\rho_{0}$ is a reference density defined by $P\left(\rho_{0}\right)=0$. Taking the pressure origin at the monolayer edge, $\rho_{0}\sim 3\cdot 10^{3}$ cells/mm2 (Fig. S10). Respectively, density differences in the monolayer are, at most, $\rho-\rho_{0}\sim 10^{3}$ cells/mm2 (Fig. S10). Then, the monolayer is expected to be highly compressible because area changes can in principle be accommodated by changes in height, resisted only by the shear modulus of the tissue. Hence, we estimate the bulk modulus of the monolayer by typical shear moduli of cell aggregates, which are in the range $G\sim 10^{2}-10^{3}$ Pa 74; 75; 76. Thus, the pressure in the monolayer should be $P\lesssim 30-300$ Pa. In fact, isotropic compressive stresses (pressures) of $\sim 50$ Pa were shown to induce cell extrusion 33. In conlusion, if tissue spreading is not dominated by cell proliferation 77; 78; 79, the magnitude of the pressure in the monolayer is expected to be much smaller than the tensile stress (tension) induced by traction forces, as measured by monolayer stress microscopy, which is of the order of several kPa (Fig. 1), with a monolayer height of $h\sim 5$ $\mu$m. Hence, we neglect the pressure in the force balance:

[TABLE]

Now, for a nematic medium, the antisymmetric part of the stress tensor is given by $\sigma_{\alpha\beta}^{a}=1/2\left(p_{\alpha}h_{\beta}-h_{\alpha}p_{\beta}\right)$, where $h_{\alpha}=-\delta F/\delta p_{\alpha}$ is the molecular field. From Eq. S1, the adiabatic approximation for the polarity dynamics, $\partial_{t}p_{\alpha}=0$, implies $h_{\alpha}=0$. Therefore, the antisymmetric part of the stress tensor vanishes under this approximation, $\sigma_{\alpha\beta}^{a}=0$. Thus, force balance reduces to

[TABLE]

Finally, multiplying Eq. S9 by the height $h(t)$ of the monolayer, the force balance can be rewritten in terms of the experimentally measured traction stress $T_{\alpha}\left(\bm{r},t\right)$ and monolayer tension $\sigma_{\alpha\beta}\left(\bm{r},t\right)$ fields:

[TABLE]

from where

[TABLE]

.1.3 Constitutive equations

Next, constitutive equations must be given to specify the deviatoric stress tensor $\sigma_{\alpha\beta}^{s}$ and the external force $f_{\alpha}$ in terms of the polarity and velocity fields. The generic constitutive equations of an active liquid crystal are provided by active gel theory 36; 37; 38; 39. Here, based on the previous assumptions for the dynamics of the polarity field, we propose a simplified version of the generic constitutive equations of an active polar gel to describe epithelial spreading.

First, the spreading occurs on timescales of the order of $\tau_{s}\sim 100$ min 26, at which the tissue should have a fluid rheology. This time scale is much slower than the turnover time scales of proteins in the cytoskeleton or in cell-cell junctions, which are of the order of tens of minutes at most 80; 81. Intra- or intercellular processes such as cytoskeletal reorganizations or cell-cell slidings dissipate energy over these time scales, so that elastic energy may only be stored in the tissue at shorter times. Therefore, to describe the slow spreading dynamics, we will not consider the elastic response of the tissue at short time scales. Note that incessant cell-cell sliding and neighbour exchanges are observed throughout the experiments (Supplementary Movie 7), which provides further support to the fluid behaviour of the monolayer at the experimentally relevant time scales.

Then, in the viscous limit, the constitutive equations for the internal stress and the interfacial force of an active polar medium are:

[TABLE]

[TABLE]

where, $q_{\alpha\beta}=p_{\alpha}p_{\beta}-p_{\gamma}p_{\gamma}/d\;\delta_{\alpha\beta}$ is the traceless symmetric nematic order parameter tensor, with $d$ the system dimensionality, and $v_{\alpha}$ is the velocity of the fluid with respect to the substrate. The coefficients $\eta$ and $\bar{\eta}$ are the shear and bulk viscosities of the medium, $\zeta$ is the anisotropic active stress coefficient, and $\bar{\zeta}$ and $\zeta^{\prime}$ are two isotropic active stress coefficients. Finally, $\xi$, $\nu_{i}$, and $\zeta_{i}$ are the corresponding interfacial versions of the viscosity (viscous friction), flow alignment (polar friction), and active stress (active force) coefficients. The constitutive equation for the internal stress, Eq. S12, is that of an active polar gel with a variable modulus of the polarity 37. In turn, the constitutive equation for the interfacial force, Eq. S13, is less conventional 82, but it was derived from a mesoscopic model of an active polar gel 41.

Now, the adiabatic approximation for the polarity dynamics implies $\dot{p}_{\alpha}=h_{\alpha}=0$, so that flow alignment terms contribute neither to the stress tensor nor to the interfacial force. Next, we assume that polarized cells generate much larger active stresses than unpolarized cells. Hence, we neglect the active stress coefficient $\bar{\zeta}$ in front of $\zeta$ and $\zeta^{\prime}$. Note that, to capture the wetting transition with a model for a two-dimensional fluid layer, the fluid must be compressible, meaning that bulk coefficients must be retained. Then, for simplicity, we assume $\zeta=\zeta^{\prime}\,d=2\zeta^{\prime}$ and $2\eta=\bar{\eta}\,d=2\bar{\eta}$. Under these simplifications, the constitutive equations reduce to

[TABLE]

[TABLE]

which close the set of equations defining the active polar fluid model of the spreading of an epithelial monolayer.

.2 Traction and flow profiles

In this section, the model is solved in a circular geometry. There are two unknown fields: the polarity field $\bm{p}\left(\bm{r},t\right)$ and the flow field $\bm{v}\left(\bm{r},t\right)$. The polarity field is completely specified by Eq. S4. Once the polarity profile is known, introducing the constitutive equations Eqs. S14 and S15 into the force balance condition Eq. S9 sets a closed equation for the flow field. The equations for both the polarity and the flow field are time-independent. Therefore, the time dependence of these fields arises solely from the boundary conditions at the free interface, which moves according to $dR/dt=v_{r}\left(R\right)$.

.2.1 Traction profile

Since traction forces are mainly along the radial direction (Fig. 1, Fig. S3), we assume the polarity field to be radial: $\bm{p}=p\left(r\right)\bm{r}$. Hence, in polar coordinates, Eq. S4 reads

[TABLE]

Because of the strong outwards polarization of cells at the edge of the cell island, we impose $p\left(R\right)=1$, namely the maximal polarity value, as a boundary condition. Finitude and symmetry of the profile also require $p\left(0\right)=0$. Hence, the solution for the radial polarity profile is

[TABLE]

where $I_{1}$ is the modified Bessel function of the first kind and first order. Therefore, the nematic length $L_{c}$ characterizes the decay of the tissue polarity from its maximal value at the boundary towards its vanishing value in the bulk (red gradient in Fig. 3).

Next, we may compare the two sources of dissipation, the viscosity and the friction coefficient, whose ratio defines the hydrodynamic screening length $\lambda=\sqrt{\eta/\xi}$. For monolayers smaller than this length, $R<\lambda$, viscosity dominates over friction, and the monolayer stress profile features a central plateau of maximal stress. In contrast, for monolayers larger than this length, $R>\lambda$, friction dominates over viscosity, and the monolayer stress decays at the center, thus featuring its maximum close to the monolayer edge 26. In our case, the stress is always maximal at the center of the monolayer (Fig. 1), meaning that $R>\lambda$. Hence, we neglect cell-substrate friction hereafter. This corresponds to the so-called wet limit, $\lambda\rightarrow\infty$, in which the flows in the monolayer are fully hydrodynamically coupled, with no screening effects due to the release of stress to the substrate through friction 38. In this limit, the force balance reduces to

[TABLE]

where we have defined the active traction stress coefficient $T_{0}=\zeta_{i}h$, which gives the maximal traction stress exerted at the edge of the monolayer.

Then, we fit the predicted radial traction force profile $T_{r}\left(r\right)=-T_{0}p\left(r\right)$ to the experimentally measured profiles at different times, as represented in kymographs as in Fig. S3 (see Fig. 3 and Methods). From the fits, we obtain the time evolution of the maximal traction stress $T_{0}\left(t\right)$ and the nematic length $L_{c}\left(t\right)$ (Fig. 3,Fig. 3). After an initial transient, the nematic length remains essentially constant throughout the experiment (Fig. 3), taking a value $L_{c}\sim 25$ $\mu$m. This gives support to the assumption that the polarity field is set by a flow-independent mechanism, and that its dynamics is quasi-static.

Now, by combining the inferred value of the nematic length $L_{c}$ with estimates for typical traction forces and cell migration velocities, we can estimate all the parameters of the polarity dynamics, namely the rotational viscosity $\gamma_{1}$, the restoring force coefficient $a$, and the Frank elastic constant $K$. To this end, we start by estimating the cell-substrate friction coefficient as $\xi\sim T/\left(vh\right)$. Taking typical values of traction stresses $T\sim 100$ Pa and speeds $v\sim 10$ $\mu$m/min for cell migration 77, and estimating the cell height $h\sim 5$ $\mu$m (Fig. S4), we get $\xi\sim 100$ Pa$\cdot$s/$\mu$m2, consistent with previous estimates 83. Then, we assume that the rotational viscosity mainly arises from the friction between the substrate and polarized cytoskeletal structures such as the lamellipodia 30. Thus, considering the polarized structures to be rods of length $\ell\sim 10$ $\mu$m comparable to cell length, the rotational friction may be estimated as $\gamma_{1}\sim\xi\ell^{2}\sim 10$ kPa$\cdot$s. Now, together with the restoring force coefficient $a$, the rotational friction $\gamma_{1}$ determines the time scale of the polarity field: $\tau_{p}\sim\gamma_{1}/a$. As argued above, the polarity field should be essentially set by contact inhibition of locomotion interactions, so that the time scale of the polarity field may be estimated by that of contact inhibition events, $\tau_{p}\sim\tau_{\text{CIL}}\sim 10$ min 14; 65. This gives an estimate for the polarity restoring force coefficient $a\sim 20$ Pa. Finally, we estimate the Frank constant as $K=aL_{c}^{2}\sim 10$ nN. The estimates of model parameters are collected in Table 1.

Finally, knowing the value of $K$ allows to check that the orientational contribution of the Ericken tensor in Eq. S6 is negligible as argued above. Using Eq. S2 and the polarity profile in Eq. S17, this contribution can be estimated as $K\left(p^{\prime}\right)^{2}\sim K/L_{c}^{2}=a\sim 20$ Pa. Therefore, it is much smaller than the typical tensile stresses measured in the monolayer, of the order of several kPa, and it can be safely neglected.

.2.2 Flow profile

The next step is to solve the force balance equation to obtain the velocity field. As for the traction field, we also consider a radial velocity field, $\bm{v}=v\left(r\right)\bm{r}$. Thus, in polar coordinates, the nonvanishing components of the stress tensor are

[TABLE]

and the force balance reads

[TABLE]

Hence, the equation for the velocity profile is

[TABLE]

Finitude and symmetry of the velocity profile impose $v\left(0\right)=0$. In addition, in agreement with the experimental measurements, we impose normal stress-free boundary conditions at the tissue boundary: $\left.n_{\alpha}\sigma_{\alpha\beta}n_{\beta}\right|_{r=R}=0$. This translates into $\sigma_{rr}\left(R\right)=0$, which is the same condition employed to compute the monolayer tension via monolayer stress microscopy. Under these conditions, the velocity profile reads

[TABLE]

which is plotted in Fig. S9 (red curve).

Now, the previous solution is general for a freely spreading cell monolayer. However, the monolayers in our experiments are confined within circular adherent regions. In the wetting phase, this confinement imposes $v\left(R\right)=0$. With no integration constants left, this extra boundary condition sets a relationship between model parameters. Since the values of $T_{0}\left(t\right)$ and $L_{c}\left(t\right)$ are set by traction profiles, this condition directly determines the active stress coefficient $\zeta\left(t\right)$ in terms of the other parameters:

[TABLE]

Thus, whereas all model parameters are free in a spreading or retracting monolayer, they are not independent in a confined monolayer. Equation S23 shows that, under confinement, the active stress coefficient is negative, hence corresponding to a so-called contractile active stress. Accordingly, the coefficient $-\zeta$ is called contractility hereinafter. During the dewetting phase, the confinement restriction is released, and hence the contractility becomes an independent parameter, not governed by Eq. S23 anymore.

Both for confined and free monolayers, a general feature of the predicted velocity profiles is their nonmonotonicity (Fig. S9). The model predicts an outwards flow at a velocity that, close to the center, has a linearly increasing profile, with a slope controlled by traction forces: $v\left(r\right)\approx T_{0}L_{c}/(\eta h)\;r$; $r\ll R$, as obtained from Eq. S22 in the limit $L_{c}\ll R$. In contrast, through Eq. S19, the stress-free boundary condition $\sigma_{rr}\left(R\right)=0$ imposes the slope of the velocity at the boundary to be $v^{\prime}\left(R\right)=\zeta/\eta<0$. Hence, the contractility causes the velocity to drop at the peripheral polarized region of width $L_{c}$. Therefore, the velocity a bit behind the boundary is always higher than at the very boundary (Fig. S9). As a consequence, cells are expected to accumulate close to the monolayer edge as they flow outwards. Experimentally, a gradient of increasing cell density towards the edge develops in the monolayer (Fig. S10), consistently with the predicted flow profile.

The increase in peripheral cell number density might promote the extrusion of live cells from the monolayer 84; 85; 86, eventually leading to the formation of 3D structures at the monolayer edge. This is indeed what seems to occur in our monolayers (Fig. S4, Supplementary Movie 4). In fact, 3D structures in the form of cell rims were previously observed both in confined and unconfined monolayers 42; 43. We suggest that the formation of these structures might partially stem from the predicted flow-induced accumulation of cells at the tissue edge.

.3 Critical size for tissue wetting

We now focus on deriving the wetting transition, defined by a vanishing spreading parameter, $S=0$. The spreading parameter is directly related to the spreading velocity 7 $V=v\left(R\right)$ by $S=\eta V$, so that using Eq. S22 it reads

[TABLE]

In the experimentally relevant limit $L_{c}\ll R$, it reduces to

[TABLE]

This result gives the spreading parameter in terms of the active forces responsible for collective cell migration, showing that the wetting transition results from a competition between traction forces and tissue contractility. Thus, note that, in contrast to other studies of wetting phenomena in active liquid crystal films 87; 88, our treatment of the wetting transition in tissues based on an active polar fluid model crucially accounts for active traction forces, which give rise to the distinct physics of the active wetting transition.

From Eq. S24, monolayer dewetting will occur whenever the contractility exceed the critical value

[TABLE]

which increases with the radius of the monolayer as shown in Fig. 3. Therefore, larger monolayers require a higher contractility to induce the dewetting. This can be understood by looking at the velocity profiles of monolayers of different radii. As explained above, traction forces at the edge impose a linearly increasing velocity profile at the central region of the monolayer. As a result, larger monolayers reach higher velocities right behind the narrow polarized peripheral region of width $L_{c}$ (Fig. S9). In turn, the wetting transition condition imposes a vanishing velocity at the boundary. As also explained above, the contractility is responsible for the velocity drop across the strongly polarized peripheral layer. Thus, larger monolayers require a higher contractility to bring the velocity down to zero at the boundary.

Note that the critical contractility $-\zeta^{*}$ is precisely the contractility under confinement (Eq. S23), since confinement also imposes the condition $V=0$ in the wetting phase. Therefore, while fully spread, our confined monolayers are in a resting state ($V=0$) maintained by the parallel increase of traction $T_{0}\left(t\right)$ and contractility $-\zeta\left(t\right)$, continuously fulfilling Eq. S26.

.4 Morphological instability during monolayer dewetting

.4.1 Linear stability analysis

In this section, we study the morphological stability of the retracting tissue front during monolayer dewetting. To allow for the loss of the circular tissue shape, we include the ortoradial components of the polarity and velocity fields. Thus, Eq. S4 reads

[TABLE]

Force balance is expressed as

[TABLE]

with the components of the stress tensor given by

[TABLE]

The solution for the unperturbed state, which preserves circular symmetry, is given by Eqs. S17 and S22:

[TABLE]

[TABLE]

where the superindex indicates the zeroth order in the front perturbations, and $R_{0}$ is the monolayer radius, which changes according to $dR_{0}/dt=v_{r}^{0}\left(R_{0}\right)$.

Next, we introduce small-amplitude perturbations of the circular monolayer boundary (Fig. 5):

[TABLE]

Then, the polarity and velocity fields are correspondingly perturbed:

[TABLE]

[TABLE]

To impose boundary conditions, we define the normal and tangential vectors at the boundary,

[TABLE]

where $\alpha$ is the angle between the normal directions of the perturbed and unperturbed interfaces. In terms of the normal and tangential vectors, the conditions that impose a normal and maximal polarity at the boundary read

[TABLE]

For the radial component, these conditions imply $p_{r}\left(R\right)\approx 1$, which expands into

[TABLE]

so that

[TABLE]

For the ortoradial component,

[TABLE]

In turn, the boundary conditions on the stress impose a vanishing normal and shear stress at the interface:

[TABLE]

The condition on the normal stress gives $\sigma_{rr}\left(R\right)=0$ which, after expanding as previously, yields

[TABLE]

Finally, the condition on the shear stress imposes $\sigma_{r\theta}\left(R\right)=0$, which translates into

[TABLE]

Next, we decompose the perturbations in their Fourier modes, identified by an index $n$ (Fig. 5):

[TABLE]

In terms of the Fourier modes, the equations for the polarity components read

[TABLE]

In turn, the components of the force balance, once the constitutive equation has been introduced, are expressed as

[TABLE]

Finally, in Fourier space, the boundary conditions read

[TABLE]

[TABLE]

At this point, the four coupled ordinary differential equations Eqs. S44 and S45 are solved for $\delta\tilde{p}_{\alpha,n}\left(r\right)$ and $\delta\tilde{v}_{\alpha,n}\left(r\right)$. The solution is completely analytical for mode $n=0$ and almost analytical for the rest of modes, meaning that it has an analytical expression that involves two integrals that need to be numerically evaluated. Then, from the Fourier modes of the velocity field, the perturbed spreading velocity can be obtained as

[TABLE]

which implies

[TABLE]

Thus, the growth rate $\omega_{n}$ of the tissue shape perturbations follows from

[TABLE]

Hence,

[TABLE]

The resulting growth rate is a purely real number under any conditions, showing that there is no oscillatory instability. At the onset of dewetting, namely using typical critical parameter values $T_{0}^{*}$, $L_{c}^{*}$, and $-\zeta^{*}$ that define the tissue wetting transition (Figs. 4, 4 and S14), the cell monolayer exhibits a long-wavelength morphological instability (Fig. 5). Several modes corresponding to deformations of the tissue shape ($n\geq 2$, Fig. 5) are unstable. Hence, we propose that this instability is at the root of the observed shape changes during monolayer dewetting (Fig. 5, Supplementary Movie 11).

.4.2 Monolayer viscosity

At the wetting transition point, all the model parameters are known except for the monolayer viscosity. This allows us to estimate the monolayer viscosity at the wetting transition $\eta^{*}$ from the retraction rate of the monolayer (Fig. 5):

[TABLE]

which is approximated by

[TABLE]

in the limit $L_{c}\ll R_{0}$.

.4.3 Structure factor of monolayer shape

To compute the structure factor, we add a noise term to the dynamics of the perturbation modes, Eq. S50. Thus, the corresponding Langevin equation reads

[TABLE]

Assuming that shape fluctuations are fast compared to the dewetting dynamics, we consider that they are temporally uncorrelated and hence we take a Gaussian white noise:

[TABLE]

where $D$ is the noise intensity, which we assume independent of the mode number $n$. Now, under the approximation of a constant growth rate $\omega_{n}$ in the short time span $t_{f}-t^{*}=7$ h, the solution to Eq. S54 can be formally expressed as

[TABLE]

Considering no shape perturbations at the onset of dewetting, $\delta\tilde{R}_{n}\left(t^{*}\right)=0$, the equal-time structure factor reads

[TABLE]

where we have employed Eq. S55.

Finally, once the experimental value for $\omega_{0}$ is known, the experimental growth rate is determined from the structure factor by numerically inverting the relation

[TABLE]

which is independent of the noise intensity $D$.

Supplementary Figures

Supplementary Movies

Movie 1. Unconfined monolayer exhibiting a transition from wetting to dewetting. Representative example of a spreading monolayer (shown in Fig. 1) undergoing a wetting transition. The release of confinement at $t=0$ h allows the monolayer to freely spread. At $\sim 25$ h, the monolayer spontaneously starts retracting until it collapses into a spheroidal aggregate.

Movie 2. Another example of a wetting transition in a spreading monolayer. Another spreading monolayer (shown in Fig. S2) undergoing a wetting transition.

Movie 3. Evolution of traction and tension fields during wetting and dewetting. Videos of phase contrast images (left), maps of traction (center) and monolayer tension (right) in a monolayer with increasing concentration of E-cadherin. A wetting transition is observed at time $t=22$ h.

Movie 4. Orthogonal views of monolayer dewetting. Time lapse of MDA-MB-231 cells stably expressing a cell membrane marker (CAAX-iRFP). The tissue-substrate contact area decreases pronouncedly during dewetting, while the tissue evolves from a monolayer to a spheroidal cell aggregate, resembling a droplet.

Movie 5. Calcium chelation hinders the increase of tissue forces and prevents dewetting. Phase contrast, and maps of traction forces and monolayer tension of control (left) and EGTA-treated (right) cell islands. Cells treated with EGTA move individually rather than forming a cohesive monolayer, suggesting that cell-cell junctions are efficiently abrogated. In the presence of EGTA, both tractions and monolayer tension increase much more slowly than in control islands, and the wetting transition does not occur.

Movie 6. Dewetting is inhibited and reversed when tissue contractility is externally decreased. Dewetting (left), dewetting inhibition (center) and reversibility (right) assays. Partial inhibition of contractility with blebbistatin clearly delays the wetting transition. A sudden inhibition of contractility with Y27632 ($t=46$ h) is enough to revert dewetting, inducing a rewetting of the substrate. The name of the drug indicates its presence in the cell medium.

Movie 7. Cell rearrangements in the monolayer. Phase contrast (left) and cell nuclei (right) in a $200$ $\mu$m radius island during the wetting phase of the experiment. Cells incessantly exchange neighbors, a fact that provides support to the fluid behavior of the monolayer. Moreover, cells progressively accumulate at the edge of the monolayer, which develops a gentle cell density gradient.

Movie 8. Evolution of traction and monolayer tension fields in islands of different radii. For all sizes, the magnitude of tractions and monolayer tension increase in time as E-cadherin is progressively expressed. Tractions accumulate at the edges of the monolayers, while monolayer tension has a maximum at the center. Red frames indicate monolayer dewetting.

Movie 9. Evolution of traction and monolayer tension fields in islands on substrates of different stiffnesses. For monolayer on substrates of Young’s modulus $3$ and $12$ kPa, tissue forces increase in time, eventually triggering monolayer dewetting. This transition occurs earlier for the softest substrate. For the stiffest substrate ($30$ kPa), tissue forces keep increasing until the end of the experiment, suggesting that the critical contractility to induce dewetting is not reached. Red frames indicate monolayer dewetting.