Transepithelial potential difference governs epithelial homeostasis by electromechanics

Studies of electric effects in biological systems, from the work on action potential to studies on limb regeneration or wound healing, commonly focus on transitory behaviour and not on addressing the question of homeostasis. Here we use a microfluidic device to study how the homeostasis of confluent epithelial tissues is modified when a transepithelial potential difference that is different from the natural one is imposed on an epithelial layer. When the field direction matches the natural one, we can restore perfect confluence in an epithelial layer turned defective either by E-cadherin knockout or by weakening the cell–substrate adhesion; additionally, the tissue pushes on the substrate with kilopascal stress, inducing active-cell response such as death and differentiation. When the field is opposite, the tissue pulls with similar strengths, whereas homeostasis is destroyed by the perturbation of junctional actin and cell shapes, increased cell division rate and formation of mounds. Most of these observations can be quantitatively explained by an electrohydrodynamic theory involving local cytoplasmic electro-osmotic flows. We expect this work to motivate further studies on the long-time effects of electromechanical pathways with important tissue engineering applications. Epithelial tissues such as those in the gut or skin are strongly polar, generating electric fields that play a role in wound healing and nutrient transport. Changing the field direction in a layer of tissue disrupts its homeostatic stability.

A mong the many bioelectric field effects observed previously [1][2][3][4] , the closest to our study concerns epithelial wound healing 4,5 . During wound healing, electric fields on the order of 1-10 V cm -1 can drive cell migration towards gaps, and this process is closely related to a field-induced cell migration mode called galvanotaxis 6,7 . In the case of single-cell galvanotaxis 6 , the electric field is a symmetry-breaking field acting parallel to the substrate. Intact tissues such as epithelia are strongly polar in the direction normal to the layer with a natural transepithelial potential difference (TEPD) of 1-10 mV (refs. [8][9][10]. The corresponding electric field is similar in magnitude to those observed around wounds, but its orientation is crucially different, being along the cell apicobasal polarity and substrate normal rather than orthogonal. Such fields are known to drive nutrient or ion transport in organs 11 and may even influence the migration of immune cells during intestinal bacterial infection 12 , but how they could play a more direct role in regulating collective cell behaviour and epithelial homeostasis is essentially unknown. Although interesting per se, what has been learned with galvanotaxis or wound healing cannot be straightforwardly translated to the homeostasis of epithelial tissues; new experiments have to be designed. To study the potential roles of TEPD in epithelial homeostasis, we used Madin-Darby canine kidney (MDCK) cells that are known to be apicobasally polarized in a monolayer, and first characterized their electrical properties on a Transwell system (Methods). Importantly, as the cells reached confluency and grew and matured, the TEPD/resistivity reached a steady state with the basal side of the epithelium becoming electrically positive (Extended Data Fig. 1), consistent with reported values for MDCK strain II (ref. 13 ). We then investigated whether the disruption of natural TEPD would lead to the perturbation of the epithelial monolayer, and conversely whether its reinforcement would maintain the normal epithelial characteristics. To answer this question, we fabricated a two-layered microfluidic device with a Collagen I surface-coated polyacrylamide (PA) gel. This allowed us to impose an average direct current (d.c.) with a physiological current density of ~10 µA cm -2 perpendicular to the monolayer plane, or an estimated intracellular electric field (E field) of ~15 V cm -1 and TEPD perturbation of ~15 mV (Methods, Supplementary Fig. 1 and Extended Data Fig. 2). An exogenous apical-to-basal (AtB) field opposes the original TEPD direction and disrupts it, whereas a basal-to-apical (BtA) field reinforces the TEPD (Fig. 1b).
With this setup amenable to optical imaging, we examined the effects of TEPD on the epithelium. Since the field was relatively uniform along the epithelium (Supplementary Information), we could obtain a large number of observations from a wide field of view (FoV), typically within ~2 mm from the field outlet. In no-field controls, the cells that had grown for a few days and had reached high cell densities exhibited low contrast cell-cell junctions under phase-contrast imaging (Methods, Fig. 1c,d (Ctrl) and Extended Data Fig. 3a). This corresponded to relatively flat apical surfaces throughout the epithelium (Methods, Fig. 1e (Ctrl) and Extended Data Fig. 3b), with strong junctional E-cadherin and actin localization indicative of strong cell-cell junctions (Methods, Fig. 1f-h (Ctrl) and Extended Data Fig. 3c-e (Ctrl)). Strikingly, clear changes to these normal characteristics were observed shortly after the AtB field was turned on to disrupt the natural TEPD. Cell-cell junctions brightened dramatically under phase contrast after ~10 min of field application (Fig. 1c,d (AtB) and Supplementary Video 1), reminiscent of the 'halo effect' observed around single cells. Such phenotype lasted as long as the field was applied (Extended Data Fig. 3f) and Transepithelial potential difference governs epithelial homeostasis by electromechanics Thuan Beng Saw 1,2,9 ✉ , Xumei Gao 3,9 , Muchun Li 1 , Jianan He 3 , Anh Phuong Le 2 , Supatra Marsh 2 , Keng-hui Lin 4 , Alexander Ludwig 5,6 , Jacques Prost 2,7 ✉ and Chwee Teck Lim 1,2,8 ✉ Studies of electric effects in biological systems, from the work on action potential to studies on limb regeneration or wound healing, commonly focus on transitory behaviour and not on addressing the question of homeostasis. Here we use a microfluidic device to study how the homeostasis of confluent epithelial tissues is modified when a transepithelial potential difference that is different from the natural one is imposed on an epithelial layer. When the field direction matches the natural one, we can restore perfect confluence in an epithelial layer turned defective either by E-cadherin knockout or by weakening the cell-substrate adhesion; additionally, the tissue pushes on the substrate with kilopascal stress, inducing active-cell response such as death and differentiation. When the field is opposite, the tissue pulls with similar strengths, whereas homeostasis is destroyed by the perturbation of junctional actin and cell shapes, increased cell division rate and formation of mounds. Most of these observations can be quantitatively explained by an electrohydrodynamic theory involving local cytoplasmic electro-osmotic flows. We expect this work to motivate further studies on the long-time effects of electromechanical pathways with important tissue engineering applications.
corresponded to the formation of convex apical cell shapes (Fig. 1e (AtB)). This was followed by a significant weakening of junctional E-cadherin and actin and thus a possible destabilization of cell-cell junctions 14 within a few hours ( Fig. 1f-h (AtB) and Extended Data Fig. 3c-e (AtB)). At the same time, the cells also adopted higher in-plane cell shape aspect ratios and movement speeds (Methods and Extended Data Fig. 3g,h), suggesting a weakening of collective cell constraints. Conversely, BtA fields maintained epithelial parameters that were usually more similar to those of the control or were in the opposite trend compared with AtB conditions (Fig. 1c-h (BtA), Extended Data Fig. 3c-h (BtA) and Supplementary Videos 2-4). These short-timescale observations from minutes to hours provided early evidence that a physiological TEPD is important in governing cell shapes and junctional properties depending on the field direction.
We wondered what constituted the main underlying mechanism driving these E-field-dependent cellular changes. Motivated by mechanobiology studies, we hypothesized that TEPD induces electromechanical stress leading to appreciable cell deformations. We examined the gel substrate deformations as done in traction force microscopy experiments, since this could inform us about the properties and origin of the stresses, if they existed 15 (Methods). After a field was imposed on a confluent monolayer, the gel started to significantly deform on average within a similar timescale for field-dependent cell shape changes to occur, and the gel deformation reached ~10 μm in magnitude in an hour ( Fig. 2a and Supplementary Information). Importantly, such gel deformations did not occur for bare gel surfaces (Fig. 2a) Fig. 1 | AtB field induces disruption to cell shape and cell-cell junctions, whereas BtA field maintains or reinforces normal epithelial characteristics. a, Schematic of the two-layered microfluidic setup to apply E fields perpendicular to the epithelial plane. The purple arrows show the AtB fields and the cell monolayer sits on the PA gel (cyan) coated with the ECM protein (Methods). b, Schematic shows the natural TEPD direction of MDCK, and how external fields disrupt or reinforce this parameter depending on their direction. c, Top-down view of the phase-contrast imaging of MDCK layers under the conditions of control (no field), AtB and BtA field. d, Quantification of the corresponding relative junctional intensities in c. Data are represented as mean ± standard error of the mean (s.e.m.). Ctrl: n = 730 junctions from three independent experiments in two biological replicates. AtB: n = 731 junctions from three independent experiments in three biological replicates. BtA: n = 980 junctions from three independent experiments in three biological replicates. Two-tailed, two-sample t-test between AtB-BtA, AtB-Ctrl and Ctrl-BtA; *p < 0.001 comparing the midpoints of graphs. n.s., not significant. e, Side-view, confocal images of fixed and phalloidin-stained epithelia under the three field conditions. 0.1 μm z-step size. f-h, Similar images and quantifications as c-e (f-h, respectively), but for fluorescent E-cadherin signals. The arrowheads in f point to junctions. Data are represented as average ± s.e.m. in g. Ctrl: n = 480 junctions from four independent experiments. AtB: n = 240 junctions from two independent experiments. BtA: n = 240 junctions from two independent experiments. Two-tailed, two-sample t-test between AtB-BtA, AtB-Ctrl and BtA-Ctrl; *p ≤ 0.001 comparing the midpoints of graphs. All scale bars, 10 μm. other direction. Such deformations translate into average electromechanical stresses (σ nn ≈ K(δL/L) ≈ 1.2 kPa) or force per cell of ~100 nN, knowing that the PA gel is elastic, with gel stiffness K ≈ 23 KPa, gel thickness L ≈ 200 μm and typical cell dimensions L cell ≈ 10 µm. Importantly, these stresses or force magnitudes are physiologically relevant stresses that are able to not only change the cell shapes but also induce active cellular responses 16,17 .
A typical hypothesis that accounts for tissue stresses may propose that stronger actomyosin contractility is activated by E fields. Yet, such mechanisms can only generate internal stresses that cannot explain the observed net forces 18 . Further, we found that actin stress fibers, which are local stress-bearing structures, only significantly deviated from controls under BtA fields but not AtB fields, and thus, they did not exhibit the same trend as the gel deformation data (Methods and Extended Data Fig. 4)  examined another hypothesis that involves electro-osmosis, a mechanism where hydrodynamic flow is induced by the interaction of E fields with counterions around charged constituents 19,20 . Since subcellular components are typically negatively charged [21][22][23] , such a hypothesis predicts that AtB fields would move the tissue away from the substrate and incur tensile tissue stresses, whereas BtA fields would push the cells towards the substrate leading to compressive forces, which is qualitatively consistent with the gel deformation data (Fig. 2a).
To quantitatively probe the electro-osmosis mechanism, we remark that the tight junctions between cells 24 can a priori force a substantial amount of extracellular ion current through the cell body, thus leading to the observed cell shapes ( Fig. 1e (AtB)). Taking this point into account, we used a two-component hydrodynamic theory of the cell body with local cytoplasmic electro-osmotic effects 20 , and derived expressions for the average total substrate stress and apical surface stress. Both are predicted to linearly scale with the E field and cell height, and the apical stress magnitude is expected to be roughly half the total substrate stress (Supplementary Information). To test the model's predictions, we first imposed different total ion currents across different monolayers and found that gel deformation (or stress) indeed scaled with the field approximately linearly as expected (Fig. 2b). Importantly, a fit of these data to the theoretical expression of stress produced an intracellular length scale (~14 nm), which reflects that expected in mammalian cells estimated from typical intracellular protein densities 25 (Supplementary Information).
Next, to test the linear cell height dependence of the stress equation, we took advantage of the highly curved, convex apical cell surfaces induced by AtB fields, and inferred the pressure difference across the cell membrane, δP, using Young-Laplace's law (Supplementary Information). For in-plane isotropic cells, δP = (2γcos(θ(z))/r(z)), where the cell surface tension γ can be approximated to be uniform based on F-actin staining, with typical cortex-membrane tension values of ~1 mN m -1 (ref. 26 ), whereas θ(z) is the angle of the membrane tangent with the substrate normal and r(z) is the distance of the cell surface to its axis (Fig. 2c). With this relation, δP was indeed inferred to increase linearly with the cell height (Methods and Fig. 2d), and a fit of δP produced theoretical cell heights and whole cell shapes that highly resembled the experimental measurements (Fig. 2e,f). The fit also allowed us to estimate the maximum pressure difference across the membrane at the tips of cells, namely, δP 0 , which is ~0.7 KPa on average (Fig. 2g), and this is again predicted by theory (Supplementary Information). The wide distribution of δP 0 of individual cells is a direct consequence of the natural variation in cell height (Supplementary Information). These quantitative results confirmed that electro-osmosis through the cell body directly governs the cell morphology in monolayers. Although the cell shape analysis has been primarily applied to cells under AtB fields, the geometry of the cells subjected to BtA fields are also consistent with this framework, but the effects are more subtle (Supplementary Information and Methods).
To further understand the role of TEPD in tissue homeostasis, we next examined the relevance of this electromechanical stress on the level of the whole epithelium over days. First, it has been reported that upward forces due to tensile stresses of a few hundred pascals, created by active processes involving actin or osmotic pumping, can lead to apical cell extrusion 27,28 or epithelial blisters 29 . We, thus, predicted that normal tensile stress induced by AtB fields at the cellular level could integrate over the whole MDCK monolayer and produce three-dimensional (3D) structures in the epithelium. To test this prediction, we applied E fields across the confluent monolayers for 2-3 days and examined the epithelial response by quantifying the heterogeneity of the spatial cellular distributions using the relative uniformity deviatory measure (RUDM), defined based on the spatial correlation function of the image intensity (Methods). Indeed, AtB fields induced the collective extrusion of live cells throughout the epithelium, which correlated with a significant increase in the RUDM value ( Fig. 3a-c (AtB) and Supplementary Video 5). The emergence of these extrusions resembled tumour-like structures previously observed in Src-oncoprotein-activated cells within MDCK monolayers 30 , and were not found in controls (Fig. 3a-c (Ctrl)). Interestingly, a synchronous burst of cell division events was initiated within a packed monolayer after ~1 day of field stimulation, and correlated with the timing of the initiation of extrusion events 20 (Extended Data Fig. 5). This massive proliferation provided cellular material in maintaining tissue integrity as cells extruded out of the epithelium, and may be related to stretch-induced cell-cycle re-entry 31 . The divisions could also provide steric repulsion that facilitated tissue remodelling and 3D mound formation. In contrast, BtA fields maintained cells within a single layer, similar to controls with low RUDM values ( Fig. 3a-c (BtA)). To demonstrate generality, similar observations were also made with immortalized N/ TERT-1 human keratinocyte cell lines 32 (Methods). Again, only AtB fields increased the heterogeneities of naturally stratified keratinocyte multilayers compared with controls, leading to the formation of more prominent 3D structures ( Fig. 3d-f and Supplementary Video 6). The latter is reminiscent of active, mechanically driven structures found in developing avian skin 33 . These results show that TEPD-induced stress is important in controlling cellular events and tissue morphologies on the order of days.
Having shown that the AtB field induces marked morphological changes compared with no-field conditions, we further examined the effects of BtA fields on long-term epithelial behaviour. Compressive stresses of few hundred pascals have been reported to induce programmed cell death or arrest proliferation in epithelial monolayers and spheroids 17,34 , as well as cell differentiation in keratinocyte cells 35 . We predicted, therefore, that BtA fields that impose similar compressive stresses, but not AtB fields, would exacerbate such events in MDCK and human N/TERT-1 layers. To test this, we quantified the frequency of cell nucleus fragmentation or condensation as an indicator of cell death rates in monolayers of MDCK cells expressing histone H1-GFP (H1-GFP) 27 (Fig. 4a). In addition, we analysed the cell differentiation rates in N/TERT-1 layers stably expressing the fluorescent ubiquitination-based cell-cycle indicator (FUCCI) reporter 36 . The differentiation rates were quantified by the number of nucleus condensation events with the absence   of the cell-cycle indicators, that is, Cdt1 (red) and geminin (green) expressions ( Fig. 4b and Methods). Consistent with our predictions, cell death and differentiation occurred with higher frequency in the MDCK and N/TERT-1 layers exposed to BtA fields, respectively, whereas the cells exposed to AtB fields were indistinguishable from control cells in this respect (Fig. 4c,d and Supplementary Videos 7 and 8). Such observations reinforce the idea that electromechanical stress is dependent on the field direction and induces different active-cell responses.
To check the extent of the influence of BtA fields on the epithelial fate, we studied if such fields may rescue layers with intrinsically haphazard organization. We searched for conditions that imposed high epithelial heterogeneity by modulating cell-substrate and cellcell adhesion strengths, which are important for determining epithelial morphologies 37,38 . We first sought to weaken cell-substrate adhesions that would destabilize epithelial structures by altering the type of extracellular matrix (ECM) coating. To this end, the PA gel support was coated with fibronectin (instead of Collagen I), which resulted in slower cell spreading after cell seeding, as expected. Intact epithelia on fibronectin-coated gels became more spatially heterogeneous over a few days at zero field, characterized by a large RUDM value leading to cell overlap and weak stratification (Extended Data Fig. 6a,b (Ctrl)). Intriguingly, BtA fields, but not AtB fields, prevented this heterogenization process (Extended Data Fig. 6a,b (BtA and AtB)). The former could even rescue tissues that had naturally developed high heterogeneity over time, demonstrated by the change in the sign of the average RUDM rate of change (Fig. 4e,f and Supplementary Video 9). This uniformity rescue was induced by higher cell death rates at denser cell regions (Fig. 4g), which are likely to be under larger pressures 27 that would favour compression-induced death. Unlike cell death, cell division rates were not significant functions of local cell densities (Extended Data Fig. 6c). We, thus, demonstrated that BtA fields can safeguard normal epithelial morphologies under non-favourable adhesive conditions expected from force conditions Finally, we tested the ability of BtA fields to restore the epithelial monolayer with a more severe phenotype by further weakening the cell-cell junctions. As E-cadherin was implicated in previous bioelectrical studies in non-trivial ways 39,40 , we used an E-cadherin knockout line (E-cad KO) for these experiments. The knockout of E-cadherin has been found to induce larger contractile force dipoles in cells, and the cells also still possess weakened, cadherin 6-mediated cell-cell connections 41 . Such monolayers ruptured globally after some time and exhibited dewetting transitions on the surface of the substrate 37 , forming multicellular clumps that compromised epithelial integrity (Methods and Fig. 4h,i (first image)). We hypothesized that compressive stresses from the BtA fields could prevent such epithelial disintegration or even rescue this process, as the pushing of cells on the substrate would increase cell-substrate contact times and adhesion strength 42 and thus facilitate cell spreading. Indeed, only BtA fields were able to impede the self-disruption of intact E-cad KO monolayers (Methods and Fig. 4h). Further, when the BtA fields were turned on only after the E-cad KO epithelium had disintegrated into disconnected patches, some areas regained confluency: in two out of six such experiments, some areas even regained close to 100% confluency over large millimetre-sized experimental FoVs. This was not achievable by AtB fields (Extended Data Fig. 7a).
The geometry of gapped epithelia is expected to incur more complex field distributions around cells. For sparse cell conditions, E fields may be expected to largely pass on the surface of single cells due to the low electrical resistivity of the cell medium. This may induce much lower mechanical stress compared with confluent layers where the fields are expected to substantially penetrate the cell bodies. This view was supported by the fact that there were no locally observable gel deformations around isolated cells during the rescue process (Extended Data Fig. 7b,c). However, we did find appreciable gel deformation around small epithelial gaps, in areas near confluency (Extended Data Fig. 7d). This showed that the rescue phenomenon can still be understood by electromechanical compression, at least partially when the local cell density is high. Along the same lines, reversing or halting the BtA field after the E-cad KO layer was rescued led to the quick release of gel deformation, followed by the formation of clumps and gaps again (Methods, Fig. 4i,j, Extended Data Fig. 7e and Supplementary Video 10). Overall, we showed that the BtA field induces cell spreading to recover normal Conversely, BtA conditions induce compressive stress and reinforced E-cadherin compared with control, but the flatness of the apical cell surface and junctional actin intensity are not statistically different from the control. In the long term (order of few tens of hours), the AtB fields induce more cell division and 3D mounds in the epithelium, which are normally monolayers, and the cells in the mounds remain largely alive. Conversely, the BtA fields not only maintain an epithelium that is similarly flat as the control but induce more cell deaths and even rescue defective, non-intact epithelia.
monolayer characteristics even without E-cadherin, but the electromechanical stress mechanism may depend on tissue confluency, cell density and other factors that can influence the E-field distribution around the cells. Altogether, our results converge to the conclusion that TEPD plays an important role in epithelial homeostasis driven by electro-osmosis through the cytoplasm. The natural TEPD is found to be in the same direction as BtA fields that not only reinforce cell-cell junctions and influence cell death and differentiation but also ensure flat, uniform and intact epithelial morphology through compressive stress (Fig. 5). This is a novel mechanism that could act in tandem with strong apical cortical F-actin previously found to integrate cells into epithelial layers 43 . This raises important questions about whether and how the original TEPD could influence embryonic development 44 and whether its disruption could lead to diseases such as the formation of carcinoma. The possibility of the latter is motivated by the fact that an AtB field with reverse TEPD and tensile stress buildup disrupts normal epithelial morphologies to induce cell divisions and 3D mound formation reminiscent of tumour structures (Fig. 5). Importantly, in vivo, the TEPD value is not necessarily a local property; thus, local pathologies could result from dysfunction in remote places of the organism. Note that the electromechanical stress effects of TEPD are fundamentally different from in-plane E-field effects that are thought to govern wound healing and cell migration due to the electrophoresis of membrane proteins on cell surfaces 6 . In essence, both effects could play combined roles to regulate tissue behaviour in more realistic conditions. Finally, the modulation of TEPD also demonstrates a strong functional aspect in controlling epithelial integrity and will find potential uses in tissue engineering applications.

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Methods
Cell culture and reagents. MDCK strain II was cultured in high-glucose Dulbecco's Modified Eagle's Medium culture medium (Gibco) with additional 10% heat-inactivated fetal bovine serum (Gibco), and 100 units ml -1 penicillin and 100 µg ml -1 streptomycin (Gibco) to prevent bacterial contamination. To study the function of specific proteins, visualize certain parts of the cell or to monitor cell division, death and cell-cycle events, stable cell lines with fluorescent expression or knockout variants of MDCK were used. Wild-type MDCK and stably transfected GFP-actin MDCK, GFP-E-cadherin MDCK and FUCCI cell-cycle reporter MDCK 45 (gifts from W. J. Nelson), histone-1-stable GFP (H1-GFP) MDCK (gift from S. Tlili) and stable E-cad KO MDCK (gift from B. Ladoux, Institut Jacques Monod) were used. GFP-actin and H1-GFP MDCK were maintained using media supplemented with 0.5 mg ml -1 geneticin (Gibco) to sustain their gene expression, whereas wild-type MDCK had additional 1 mM sodium pyruvate. N/ TERT-1 keratinocyte FUCCI cell lines stably transfected with Kusabira Orange 2 (mKO2)-Cdt1 and Azami Green 1 (mAG1)-geminin were cultured in keratinocyte serum-free medium supplemented with human recombinant epidermal growth factor and bovine pituitary extract (Gibco), 100 units ml -1 penicillin and 100 µg ml -1 streptomycin (Gibco). Experiments with MDCK used the same medium as the ones for passaging. For N/TERT-1, the passaging medium was used for the first day of cell culture on the chip and then changed to DNMedia (serum free, Denova Sciences) for improved cell differentiation. Mycoplasma testing was done every three months using the MycoAlert PLUS mycoplasma detection kit and assay control set (Lonza).
Immunofluorescence staining. For MDCK, the cells were fixed with methanol-free 4% paraformaldehyde (PFA) at 37 °C for 1 h and permeabilized with 0.1% Triton X-100 for 5 min. Actin filaments were then stained with Alexa Fluor 568 phalloidin (Life Technologies, A12380) at 1:100 dilution. The nucleus was labelled with Hoechst 33342 at 1 µg ml -1 concentration. For N/TERT-1, cells were fixed with methanol-free 4% PFA at room temperature for 3 h, permeabilized with 0.1% Triton X-100 and then blocked with 2% bovine serum albumin (BSA)/0.1% Triton for 1 h. Incubation with the primary antibody (Involucrin, mouse; Abcam ab68) diluted at 1:100 in 2% BSA was performed at 4 °C overnight. The secondary Alexa Fluor 647 goat anti-mouse antibody (Invitrogen A21235) was added at 1:100 in 2% BSA and maintained at room temperature for 3 h. Furthermore, ×1 phosphate-buffered saline (PBS) was used as the dilution buffer and for the gentle rinsing of samples between every step. Mounting was done with the ProLong glass antifade mountant (Invitrogen) at room temperature for a day before the samples were stored at 4 °C.

Microscopy imaging.
Wide-field, phase-contrast epifluorescence microscopy was performed using an Olympus IX81 inverted microscope. Confocal imaging was done either using spinning-disk confocal (CSU-W1 Yokogawa or X-light V2 head on a Nikon Eclipse Ti microscope body) or a Nikon A1R MP point-scanning microscope. All imaging was done at 37 °C and 5% CO 2 . For long-term experiments from a few days up to a week, the cell medium was refreshed daily on the microscope.

Natural TEPD and electrical resistance measurement on Transwell.
To estimate the electrical properties of epithelia and the timescale needed for growing epithelia to reach a sufficiently mature state, electrical measurements were done on Transwell systems. Cells were seeded at 0.9 million cells per square centimetre in a 12-well or 24-well Transwell system (Costar) with a permeable polyester membrane (0.4 µm pore size). The epithelial TEPD and resistance were measured (resistance measured at 12.5 Hz) using a Millicell-ERS voltohmmeter system, starting from the first day after the cells were seeded (this day is denoted as day 1). Based on the manufacturer's instructions, the Ag/AgCl electrodes were sanitized with 70% ethanol, calibrated (functional checking) and equilibrated in ×1 PBS and then placed in the culture medium before the measurements were taken. During this time, the cells that were taken out from the incubator were allowed to rest at room temperature for a few minutes and the electrode readings were only recorded when the readings stabilized. Several recordings were taken at different positions of the well and averaged. Also, the medium in the inner and outer compartments of the Transwell systems were fully isolated from the top such that only the electrical properties across the cells/membrane were measured. The samples were returned into the incubator after the measurements were done. The procedure was repeated daily for a week, during which the cells reached confluency at day 2 and continued to grow, and the medium was changed every two days. The monolayer resistance was obtained by subtracting off the resistance of a blank well (without cells).

Microfluidic chip and device design/fabrication and E-field experiment.
The custom electric-cell assay involved a two-layered microfluidic chip made of a UV-curable material NOA73. It was embedded with a neutral PA gel that had a surface coating of ECM of choice. The whole setup was connected to cartridges that held the cell medium (Extended Data Fig. 2a) and electrically linked to two platinum electrodes (Latech) through 60-cm-long Tygon tubings (formula 2375; inner diameter, 1.6 mm; outer diameter, 3.2 mm). A d.c. electric field or ion current was applied perpendicularly across the monolayer (Fig. 1a) with a sourcemeter (Keithley models 2400, 2450 or 2657A).
The experiments were done under constant current, as we could estimate the fixed average current density flowing through the epithelium due to current conservation. To achieve a field distribution that was spread more uniformly throughout the epithelium, the target gel height and design of the geometry of the second NOA73 layer were guided by simulations and different experiments (discussed later). Further, the channels within the chip were designed such that their electrical resistance was ~10 6 Ω (Extended Data Fig. 2b). This is orders of magnitude larger than the 12 Hz resistance of the epithelium on the chip (~10 2 Ω). The sample's resistance was, thus, fully determined by those of the channel, which was fixed (Extended Data Fig. 2a). The use of long tubing that separated the cell area from the electrode holder, the use of inert platinum electrodes and the refreshing of the medium at the cell region allowed the experiment to be performed for durations of up to a week without compromising the health of the cells. We also confirmed that the experimental results were solely due to the effects of the fields through different controls. Specifically, we measured that the pH of the cell medium at the cell region was similar between the no-field and field experiments at the end of experiments. Further, a field-conditioned medium (cell medium that was first passed with current without cells) did not induce cell behaviours related to the E fields.
The preparation of the electric assay involved the following processes in sequence, namely, the assembly of the microfluidic chip (Extended Data Fig. 2b), integration of the PA gel, coating of the PA gel surface with ECM proteins, assembly of the cartridges and connection to the electrodes, and finally cell seeding and E-field application. Briefly, to fabricate the microfluidic chip from a UV-curable adhesive NOA73 (Norland Products), 1-mm-thick glass slides (Marienfeld) that served as the base of the chip were pretreated with 0.3% acetic acid and 0.5% 3-(trimethoxysilyl)propyl methacrylate (Sigma) dissolved in 100% EtOH for good bonding with NOA73. The features of the first NOA73 layer, including channels, were moulded onto the pretreated glass using a 1:10 polydimethylsiloxane mould and lightly cured with 10 s, 365 nm UV treatment at 75 mW cm -2 to produce a solidified structure. The second NOA73 layer, which covers the channels and leaves small openings for the passage of ion current, was further moulded on a polydimethylsiloxane substrate and then transferred onto the first NOA73 layer. A 6 s UV treatment (75 mW cm -2 ) was done to allow the two layers to bond.
To fabricate the cell substrate (Extended Data Fig. 2b), a liquid PA mixture of 40% acrylamide solution (Bio-Rad), 2% bis-acrylamide solution (Bio-Rad) and water in a ratio of 0.25:0.11:0.64 with additional 1 µl crosslinker tetramethylethylenediamine (Bio-Rad) and 10 µl of 10% ammonium persulfate (Bio-Rad) was added to a 1 ml PA mixture for gelation. This ratio gave a final PA gel elasticity of ~20 kPa (ref. 46 ). Then, 10 µl of this mixture was added onto the opening of the second NOA73 layer, which also flowed into the bottom layer. The gel solution mixture was covered with a round coverslip of 12 mm diameter for polymerization to occur. Simultaneously, the sample was quickly treated with 365 nm UV for 8 min at 75 mW cm -2 that fully cured the chip and allowed the gel to bond to it. The sample was then left for more complete gelation for another 30 min. After that, the coverslip was peeled off, exposing the gel, and a pH 7.4, 0.1 M HEPES buffer was used to soak the gel for two days to rinse off the toxic, unpolymerized PA.
Next, to coat the PA gel with the ECM protein, a protocol using the Sulfo-SANPAH (SS, Pierce) crosslinker was followed 46 . Stock SS that was dissolved in anhydrous dimethyl sulfoxide (1 mg/50 µl) was diluted with cold HEPES buffer (pH 7.4, 0.1 M) at 1:40 dilution. This SS solution was pipetted onto the gel surface and treated with 365 nm UV for 5 min at 24.5 mW cm -2 for the activation of SS. This activation procedure was repeated once more with new SS solution after cold HEPES was used to rinse the sample. Finally, unattached SS was rinsed off with ×1 PBS. For ECM protein coating, we used either Collagen I (Corning, 50 µg ml -1 ) or fibronectin (Roche, 50 µg ml -1 ). Collagen I, dissolved in cold ×1 PBS to prevent initial gelation or fibronectin dissolved in ×1 PBS at room temperature was pipetted onto the substrate and incubated for 3 h at room temperature for the attachment of the ECM protein. We used fibronectin (Roche, 50 µg ml -1 ) at room temperature to coat the PA gel surface for the rescue experiments and cells were seeded at ~0.4-0.5 million cells per square centimetre on this substrate.
Further, to integrate the microfluidic chip with the cartridges, tubes and electrodes (Extended Data Fig. 2a), the chip (with Collagen-I-coated gel) was first dried and O rings were placed on it. The sample was then sandwiched between a custom-designed poly(methyl methacrylate) cartridge and an aluminium base, and screwed tight to isolate the different compartments from the top using pressure. This ensured that the ion current only flows through the channels in the bottom NOA layer and the opening of the second NOA layer. The gel was then quickly rehydrated with the cell medium, whereas the Tygon tubes were plugged into the cartridges and connected to 50 ml Falcon tubes with electrodes. The cell medium was then used to fill the whole setup. To determine whether a sample was well prepared, the total amount of current I with a certain value was checked to pass through the sample when a fixed voltage V was applied across the whole setup, such that the relation V ≈ IR was satisfied. Here R (~10 6 Ω), the resistance of the chip, was determined by the channel geometries and conductivity of the medium, which is ~1 S m -1 (refs. 47,48 ).
To perform the E-field experiment, MDCK or N/TERT-1 cells were seeded at ~0.2 million cells per square centimetre in each well and left in the incubator for three days for the cells to reach confluency. The setup was brought to the microscope for imaging and the E field was applied then (Extended Data Fig. 2a). After each experiment, the cartridges and accessories were cleaned and sonicated sequentially in detergent, water and 70% isopropyl alcohol. Finally, the materials were rinsed with 100% isopropyl alcohol and dried in a vacuum chamber before storing in a dry cabinet for the next experiment.
Also, to do live-cell experiments that were compatible with high-resolution imaging using a CFI Apochromat LWD Lambda S 40XC water-lens objective (×40; numerical aperture, 1.15; working distance, ~0.6), we replaced the 1-mm-thick glass slides with No. 1.5 precision slides (Marienfeld), which were ~170 µm thick. In this case, the O rings and pressure method could not be used to seal the compartments; therefore, a two-part dental silicone (twinsil, picodent) was used instead.
Estimation of E-field spatial distribution with bead electrophoresis. Fluorescent beads (carboxylated, 100 nm, Invitrogen) were injected at ~1:100 dilution into the chip with cells as the E field was applied. Since the beads are charged and will undergo electrophoresis along the field lines, the visualization of the accumulation of beads and their distribution throughout the epithelium gives us a rough estimate of the E-field distribution. An E-field magnitude that was five times larger than the usual one used for studying the cell behaviour was used to increase the electrophoresis of beads and to minimize the effects of bead diffusion.

Estimation of stress magnitude/spatial distribution with gel deformation.
To have a measure of the electromechanical stress magnitude, we consistently measured gel deformation at a location ~500 μm away from the microfluidic slit, which is the E-field outlet at the bottom of the epithelium. This location was chosen due to its better geometrical and optical properties over the one on top of the slit, as the fabricated substrate surface is intrinsically flatter here whereas its optical pathway is less obstructed, which is better for imaging. Importantly, the exact location of the measurement does not affect the interpretation of the result because the E-field magnitude is similar throughout the FoV (Supplementary Information). The normal stress with respect to the monolayer plane is in this geometry and given by σ nn ≈ K(δL/L) (ref. 49 ), where K is the PA gel stiffness determined by the gel component mixture ratios 46 , L is the gel thickness in our setup at the opening of the second NOA73 layer and δL is the gel deformation that can be negative (downward deformation) or positive (upward deformation). The typical gel thickness was visualized by infusing fluorescent beads (100 nm, Invitrogen) into the PA gel and imaging it on a confocal microscope. Manual refocusing of the microscopy images was done to track the z positions of the cells in real time under E fields, and the deformation of the gel surface was measured by subtracting the reference z position (height before the E field was turned on) from these real-time measurements.
When we needed to estimate the continuous spatial distribution of the stress, we used an open-source particle image velocimetry software (PIVlab version 4.13) implemented in MATLAB (version R2018b) to map the deformation field along the epithelia. The fast Fourier transform window deformation method was used with a single pass (and 50% overlap), and the tile size along the plane was ~200 μm.

Measurement of junctional intensity.
To determine the junctional intensity of phase-contrast images and z-projected fluorescent actin or E-cadherin signals from confocal imaging, the cutlines were manually drawn using ImageJ software, perpendicular to bicellular junctions, with the midpoint of the cutlines co-localizing with the centre of the junctions. The latter was found between two tricellular junctions that flanked the two ends of the bicellular junctions. The one-dimensional intensity along the cutline was normalized by the intensity of the endpoints of the cutline, which fell in the region of the cell body of the two neighbouring cells, and the process was repeated for different junctions. The averaging of all the junction intensities were done by aligning the centres of the cutlines in MATLAB. Whenever the junction signals were fuzzy, such as in the phase-contrast images under no-field and BtA-field conditions or in the fluorescent actin images under AtB-field conditions, the identification of junctions was aided by superimposing the fluorescent images of cell nuclei and by scrutinizing the dynamics of regions around the junctions.

Quantification of stress fibers.
To quantify the actin stress fibers that are mechanical stress-bearing structures at the basal side of cells, we cropped a square region (~3.7 × 3.7 μm 2 ) at the basal surface in the middle of each cell. The basal surface is chosen as the confocal z slice with the clearest phalloidin staining around the base. Two parameters, namely, coherency and strength, were used to quantify these cropped regions. Coherency quantifies the extent of orientation of the structures, given by the OrientationJ measure plugin 50 . The values range between values of 1 (fully aligned) and 0 (isotropic). Strength quantifies the average normalized brightness of the region. Normalization was done by dividing the pixel values with those of the background, defined by 5% pixels with the lowest intensities. Both quantities exhibited the same trend (Extended Data Fig. 4), and the larger these values, the more prominent were the stress fibers, which may, in turn, be related to larger cellular contractilities 51 .
Determination of different cell events. Cell death in MDCK was determined by the identification of nucleus condensation, fragmentation or disappearance in H1-GFP monolayers, the disappearance of Cdt1 (red) signal without the appearance of geminin (green) signal in FUCCI lines, or the sequential appearance and disappearance of a bright signal in GFP-actin cells. Cell division in MDCK was further identified by the appearance of two daughter cells replacing a mother cell in H1-GFP lines, or the disappearance of the geminin (green) signal in FUCCI cells. Finally, cell differentiation in FUCCI N/TERT-1 cells was determined by nucleus condensation under phase-contrast imaging, and the simultaneous disappearance of Cdt1 (red) and absence of geminin (green) expressions in fluorescent images. Such events were found to generally correlate with high involucrin expression.
Measure of homogeneity of epithelial cell distribution. First, the spatial correlation for coarse-grained image intensities, I , is defined as where | ⇀ r | is the distance, and <...> is the average. Here I is the average measure of local cell density and is coarse grained over a window size of 50 μm, with ~5 × 5 cells in each window. The step size between two neighbouring windows is 25 μm.
The uniformity deviatory measure (UDM) of each image is further defined as which measures the deviation of the average spatial correlation from a unity measure signifying the fully uniform situation. The larger the UDM, the more heterogeneous is the epithelium. The correlation function was averaged up to distances of ~150 μm, which is the typical correlation length of MDCK 52 and N/ TERT-1 epithelia in these conditions. Since C ⇀ r is calculated based on image intensities and would be sensitive to the imaging apparatus used, it may be difficult to directly compare the UDM of different samples. This difficulty is circumvented by calculating the RUDM for each image as which measures the relative change in the heterogeneity of the sample as a function of time t, with reference to the first image. Provided that different samples start at the same biological/physical conditions, this allows the objective comparison of different sample dynamics even when the imaging conditions may be slightly different.

Measure of tissue integrity for E-cad KO MDCK experiments.
The whole epithelium is partitioned into FoVs of ~460 μm × 460 μm squares. Each square is classified as 0 if it is determined to have a non-intact part of the epithelium and 1 for the opposite. The measure of tissue integrity is the percentage of all the squares valued as 1. The higher this value, the higher is the overall integrity of the layer. To determine whether a square has an intact part of the epithelium, we used ImageJ's variance filter with a radius of <1 pixel (typical cell size is ~5 pixels) to identify gaps within the epithelium as such areas had smoother local intensities. A smaller gap area shows an epithelial region with higher integrity. A gap area ratio threshold of ~0.0002 was used to classify each square, where a square was considered intact if the detected gap area ratio was below this threshold.
Cell speed measurement. Cell velocity and speed (magnitude of velocity) was calculated using PIVlab (version 4.13) implemented in MATLAB (version R2018b). The fast Fourier transform window deformation method was used with three passes, with window sizes of 64, 32 and 16 pixels (and 50% overlap). The images were taken with a resolution of 0.65 μm per pixel. The data were further smoothened by a rolling median every four frames.
COMSOL simulation for E-field distribution estimation. The 'a.c./d.c. ' module and 'electric currents' interface in COMSOL were used to simulate the experiments. We performed two-dimensional simulations because the experimental geometry of the slit (3 mm × 200 μm), which is the E-field outlet underneath the epithelium, has a 'length' dimension much larger than the 'width' dimension. The simulation geometries followed the cross section of the setup. Some other general specifics of the simulation include constant-potential boundary conditions at the inlet/ outlet and electrical insulation at the boundaries representing the walls of the microfluidic chip (Supplementary Information). The epithelium was simulated with a thin-layer approximation due to its small thickness compared with the other length scales of the system, with current conservation at its interface with the medium. A d.c. epithelial conductivity of σ = 3 × 10 -5 S m -1 was used based on reasonable estimations (Supplementary Information). Both gel and medium conductivities were inputted as 1 S m -1 (refs. 47,48 ) for simplicity.

Theoretical estimation of mechanical stress/cell shapes for comparison with experiments.
Young-Laplace's law was used to infer the pressure drop across apical cell surfaces. Standard electrophoresis/electro-osmosis theory 19,20 was used to estimate the stress generated by the E field on single attached cells and cells in confluent monolayers, keeping in mind the relevant field distributions around and within the cells (Supplementary Information).
Measurement of distance between apical surfaces of cell and nucleus. H1-GFP cells, subjected to fields or under control conditions, were fixed and stained with phalloidin. Dual-colour imaging was done using a ×60 objective with 100 nm z-step size on a Yokogawa spinning-disk system. This method allowed the measurement of distance around or below 500 nm, between the cell and nucleus apical surfaces. The cell surface is located by the 'Gaussian' peak of the phalloidin staining signals, whereas the nucleus surface is determined by the midpoint of the drop in nucleus fluorescent intensity.

Statistical analysis.
No statistical methods were used to predetermine the sample size. In the case where no statistical significance was observed, the sample size chosen was at least as big as those where the differences were observed. Blinding was achieved for determining the cell death rate as the datasets were independently analysed at two different institutes. One-tailed t-test was used to compare the distributions when the hypothesis was to test whether one of the distributions was larger. All the relevant statistics are reported in the corresponding legends.
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Data availability
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Code availability
Custom codes for image analysis are available from the corresponding authors upon reasonable request.   Line is mean ± s.t.d., scatter points are independent experiments. Ctrl: n = 6 independent experiments in 3 biological replicates. AtB: n = 3 independent experiments in 2 biological replicates. BtA: n = 5 independent experiments in 3 biological replicates. One-tailed, two-sample t-test. *p = 0.008 (Ctrl-BtA). *p = 0.01 (AtB-BtA). n.s. non-significant. c, Local division rates of dense and sparse regions under BtA fields. Line is mean ± s.t.d., scatter points are independent field-of-views. Dense/Sparse: n = 6 independent field-of-views, 3 independent experiments in 3 biological replicates. Two-tailed, paired t-test. p = 0.09. Fig. 7  Last updated by author(s): Apr 25, 2022 Reporting Summary Nature Portfolio wishes to improve the reproducibility of the work that we publish. This form provides structure for consistency and transparency in reporting. For further information on Nature Portfolio policies, see our Editorial Policies and the Editorial Policy Checklist.

Statistics
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Data analysis
All image analysis was done by ImageJ (updated 2019) or using custom written codes in MATLAB (R2019a). Graphs are plotted using MATLAB (R2019a) and Prism 9. Custom codes for image analysis are available upon reasonable request.
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