# Developmental Cell

## Tight junctions control lumen morphology via hydrostatic pressure and junctional tension

### Graphical abstract

Molecular regulation of tight junctions

*Permeability*

<figure><img src="image_1.png" /></figure>

*Actomyosin*

<figure><img src="image_2.png" /></figure>

Lumen Morphology

<figure><img src="image_3.png" /></figure>

### Authors

Markus Mukenhirn, Chen-Ho Wang, Tristan Guyomar, ..., Tetsuya Hiraiwa, Daniel Riveline, Alf Honigmann

### Correspondence

riveline@unistra.fr (D.R.), alf.honigmann@tu-dresden.de (A.H.)

### In brief

Mukenhirn et al. show that epithelial cells use tight junctions to control lumen shape, and the depletion of the tight junction scaffold leads to lumen collapse and increased cortical tension. Claudin-depleted MDCK-II cysts maintain lumen pressure and shape despite high ion permeability.

### Highlights

* Depletion of ZO scaffold causes lumen collapse and apical membrane folding

* The claudin permeability barrier is not necessary for hydraulic lumen inflation

* Tight junctions promote lumen inflation by decreasing cortical tension

* Lumen shape controlled by pressure-tension force balance and apical area constraints

<figure><img src="image_4.png" /></figure>
## Article

# Tight junctions control lumen morphology via hydrostatic pressure and junctional tension

Markus Mukenhirn,<sup>1,2,14</sup> Chen-Ho Wang,<sup>2,14</sup> Tristan Guyomar,<sup>6,7,8,9,14</sup> Matthew J. Bovyn,<sup>2,4,5</sup> Michael F. Staddon,<sup>2,4,5</sup>

Rozemarijn E. van der Veen,<sup>13</sup> Riccardo Maraspini,<sup>2</sup> Linjie Lu,<sup>6,7,8,9</sup> Cecilie Martin-Lemaitre,<sup>1</sup> Masaki Sano,<sup>10</sup>

Martin Lehmann,<sup>13</sup> Tetsuya Hiraiwa,<sup>11,12</sup> Daniel Riveline,<sup>6,7,8,9,*</sup> and Alf Honigmann<sup>1,2,3,15,*</sup>

<sup>1</sup>Biotechnology Center, Center for Molecular and Cellular Bioengineering, Technische Universität Dresden, 01069 Dresden, Germany

<sup>2</sup>Max Planck Institute of Molecular Cell Biology and Genetics, 01309 Dresden, Germany

<sup>3</sup>Cluster of Excellence Physics of Life, TU Dresden, 01062 Dresden, Germany

<sup>4</sup>Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany

<sup>5</sup>Center for Systems Biology Dresden, 01307 Dresden, Germany

<sup>6</sup>Université de Strasbourg, IGBMC UMR 7104 - UMR-S 1258, 67400 Illkirch, France

<sup>7</sup>CNRS, UMR 7104, 67400 Illkirch, France

<sup>8</sup>Inserm, UMR-S 1258, 67400 Illkirch, France

<sup>9</sup>IGBMC, Institut de Génétique et de Biologie Moléculaire et Cellulaire, 67400 Illkirch, France

<sup>10</sup>Institute of Natural Sciences, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

<sup>11</sup>Mechanobiology Institute, National University of Singapore, Singapore 117411, Singapore

<sup>12</sup>Universal Biology Institute, The University of Tokyo, Hongo, Tokyo 113-0033, Japan

<sup>13</sup>Leibniz-Forschungsinstitut für Molekulare Pharmakologie (FMP), 13125 Berlin, Germany

<sup>14</sup>These authors contributed equally

<sup>15</sup>Lead contact

*Correspondence: riveline@unistra.fr (D.R.), alf.honigmann@tu-dresden.de (A.H.)

https://doi.org/10.1016/j.devcel.2024.07.016

## SUMMARY

Formation of fluid-filled lumina by epithelial tissues is essential for organ development. How cells control the hydraulic and cortical forces to control lumen morphology is not well understood. Here, we quantified the mechanical role of tight junctions in lumen formation using MDCK-II cysts. We found that the paracellular ion barrier formed by claudin receptors is not required for the hydraulic inflation of a lumen. However, the depletion of the zonula occludens scaffold resulted in lumen collapse and folding of apical membranes. Combining quantitative measurements of hydrostatic lumen pressure and junctional tension with modeling enabled us to explain lumen morphologies from the pressure-tension force balance. Tight junctions promote lumen inflation by decreasing cortical tension via the inhibition of myosin. In addition, our results suggest that excess apical area contributes to lumen opening. Overall, we provide a mechanical understanding of how epithelial cells use tight junctions to modulate tissue and lumen shape.

## INTRODUCTION

Luminal cavities are key structural components of organs, functioning as compartments for fluid transport, nutrient absorption, or waste secretion. Lumen establishment during development occurs via different morphogenetic mechanisms.¹ Lumina that form between existing cell contacts such as acini, blastocytes, or canaliculi require mechanisms that enable expansion of a fluid-filled cavity against the resistance of the surrounding cells.

On the molecular level, lumen formation is often coupled to the establishment of apical-basal polarity. In particular, formation of an apical membrane with a distinct composition that excludes cell-cell adhesion receptors and enriches ion transporters is important for lumen formation.² Molecular activities, such as ion pumping and acto-myosin constriction, have been linked to the mechanical forces that are required to open a luminal cavity

between cells.<sup>3,4</sup> Current physical models explain lumen shapes by considering osmotic, hydraulic, and cortical forces, with a special emphasis on luminal pressure.<sup>3,4</sup> Lumen inflation results from water influx that arises from ion gradients and hydrostatic pressure. However, luminal shape is a result of the competition between hydrostatic pressure and the mechanical properties of the surrounding cells. In addition to this hydraulic-based mechanism, it has been suggested that lumina can also grow in a pressure-independent way via forces that arise from the formation and maintenance of a constant apical membrane area per cell.⁵ Despite this progress, it remains challenging to link the control of mechanical forces that govern lumen growth and shape to the molecular regulation that happens on the cellular and tissue level.

Here, we investigated the role of epithelial tight junctions (TJs) in lumen growth and shape using MDCK-II cysts, an organotypic
A **Lumen expansion in MDCKII cysts**

<figure><img src="image_5.png" /></figure>

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j: active and passive flows of solutes and water

p : hydrostatic pressure

t : tissue tension

B Genetic perturbation of tight junctions

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C Dextran permeability of WT, TJ-mutant and rescue cysts

Permeability assay

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MDCK-II WT

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CLDN-KO

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ZO-KO

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+ CLDN2-Flag

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+ mCherry-ZO1

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cell-culture model for lumenogenesis. TJs control the paracellular flow of ions and water across the tissue by forming a trans-epithelial diffusion barrier via claudin strands.⁶ Knockout of claudins in MDCK-II cells (CLDN-KO) results in complete loss of TJ strands and CLDN-KO tissue is permeable for small molecules such as ions but remains impermeable to macro-molecules.⁷,⁸ Interestingly, the cytoplasmic TJ scaffold of ZO proteins remains largely unaffected by claudin depletion. An extensive body of work has shown that ZO-1 controls junctional contractility and epithelial cell shape by regulating the structure and activity of the acto-myosin cortex.⁹⁻¹¹ Depletion of ZO1/ZO2 in MDCK-II cells causes complete loss of all TJ proteins from the sub-apical belt, including claudins.⁷,¹²,¹³ In addition, the actin cytoskeleton is drastically remodeled.⁹⁻¹¹ Accordingly, ZO-KO tissue is highly permeable for small and large molecules.⁷,¹⁴ Because both trans-epithelial permeability and cytoskeletal tension are key mechanical parameters for controlling lumen formation, TJs are expected to be an important molecular regulator of lumen morphology.⁷,⁹⁻¹¹,¹⁴ Here, we studied lumen formation of genome-edited MDCK-II cysts mutated for key TJ proteins (wild type [WT], CLDN-KO, and ZO-KO) using quantitative microscopy and mechanical measurements of lumen pressure and junctional tension.

Surprisingly, we found that the opening of the trans-epithelial barrier to ions, using MDCK-II cells depleted of all expressed claudins (CLDN-KO<sup>7,8</sup>), did not result in a decrease in hydrostatic lumen pressure. Despite high ion leakage, lumen pressure is maintained close to WT levels and lumina expand to a round shape similar to WT tissue. This suggests that cells can compensate for paracellular leakage by increasing ion pumping. In contrast, depletion of the cytoplasmic tight scaffold (ZO-KO)¹³ resulted in lumen volume collapse, accompanied by a loss of hydrostatic pressure and a strong increase in junctional tension. Interestingly, the surface area of the collapsed lumina remained similar to WT tissue, causing strong deformations of the apical membrane, suggesting that the apical membrane area is largely independent of hydrostatic lumen pressure and cortical tension. Using a mechanical force balance model with a constrained apical area, we predicted lumen morphologies as a function of lumen pressure and junctional tension and found strong agreement with experimental phenotypes. Finally, we used perturbation of lumen pressure and junctional tension to verify the mechanical model using specific inhibitors and a pipette inflation assay. Taken together, our results revealed that an important function of TJs is to reduce the mechanical tension of cells, which enables lumen expansion at low hydrostatic pressure. We envision that the regulation of the pressure-tension

force balance by TJs is an important control node that allows the tuning of tissue and lumen shapes during morphogenesis.

## RESULTS

### TJ mutants used and their properties

To investigate the function of TJs in lumen formation (Figure 1A), we used genome-edited MDCK-II cells lacking either the cytoplasmic TJ scaffold proteins ZO1 and ZO2 (ZO-KO¹³) or the five major claudins expressed in MDCKs (CLDN-KO,⁷ Figure 1B). ZO1 and ZO2 as well as claudins are essential for the assembly of TJ strands and formation of a tissue permeability barrier. In addition, ZO proteins are involved in regulation of cell mechanics via interactions with the acto-myosin cortex.⁶,⁷,¹³,¹⁵

To study epithelial barrier formation in three dimensions (3D), we used MDCK-II cysts embedded in Matrigel and determined the permeability of a small molecular tracer (10 kDa dextran-647) to the luminal side of the tissue. We quantified dextran permeability as the percent of fluorescent signal in the lumen compared with the outside after 15–20 min incubation. In WT cysts, the soluble small molecule tracer was strongly excluded from the apical lumen with permeability < 5% (Figures 1C and 1D). In contrast, lumina of cysts grown from CLDN-KO and ZO-KO cells were permissive to the tracer, with 15% and 38% permeability, respectively (Figures 1C and 1D). We noted that CLDN-KO cysts were able to form a large, spherically inflated lumen despite being permissive to small solutes, whereas ZO-KO cysts had significantly smaller and more convoluted lumen shapes (Figure 1C). To test whether the observed permeability changes were indeed caused by the genetic depletions, we established rescue cell lines expressing FLAG-CLDN2 in CLDN-KO tissue and Cherry-ZO1 in ZO-KO tissue (Figure S1). Quantification of dextran permeability showed that the expression of FLAG-CLDN2 and mCherry-ZO1 both restored the permeability back to WT levels in the respective cell lines, verifying the specificity of the genetic perturbations (Figures 1C and 1D). In line with previous reports,⁷,¹⁶ these results demonstrate that loss of TJs causes increased epithelial barrier permeability and that loss of ZO1/ZO2 altered lumen morphology.

### Quantification of cyst and lumen morphology of TJ mutants

To quantify the impact of TJs on lumen formation, we compared changes in lumen and tissue morphology of WT, ZO-KO, and CLDN-KO during cystogenesis in Matrigel (Figure 2A). Immunofluorescence (IF) staining was performed on cysts at different stages of cyst development and a 3D image segmentation and

**Figure 1. Lumen formation in MDCK-II cysts and tight junction mutants used in this study**

(A) Scheme of lumen expansion in MDCK-II cysts. Polarized membrane domains and tight junctions are highlighted (right). Cysts are growing over time due to cell divisions. Osmotic gradients, due to the balance of active ion transport into the lumen and passive paracellular leaks, result in water influx and establishment of hydrostatic lumen pressure. Hydrostatic lumen pressure is balanced by cortical tension of the apical-junctional surface.

(B) Tight junction mutants used in this study. MDCK-II-WT tissue produces tight junctions that have very low permeability for ions and water. CLDN-KO tissue is permeable for small molecules and ZO-2KO tissue is permeable for small- and macro-molecules.

(C) Permeability assay in MDCK-II cysts for 10 kDa dextran AF647. Shown are midplane cross-sections of WT and TJ-mutant cysts; white is the dextran tracer and the cell membrane is magenta; scale bar, 20 µm. WT cysts are largely impermeable. CLDN-KO and ZO-KO cysts are permeable for dextran. However, CLDN-KO cysts produce a large lumen whereas ZO-KO cysts produce small, convoluted lumina. Re-expression of CLDN2 in CLDN-KO cysts or mCherry-ZO1 in ZO-KO cysts rescued the permeability barrier.

(D) Cyst diffusion quantification, WT (n = 34), CLDN-KO (n = 29), CLdn-KO Cldn2-FLAG (n = 24), ZO-KO cysts (n = 30), and ZO-KO ZO1-mCherry (n = 21). One-way ANOVA was used for statistical analysis against WT cysts.
A

Lumen morphology of WT and TJ-mutant cysts

<figure><img src="image_15.png" /></figure>

B

Scaling of morphological parameters with cell number

<figure><img src="image_16.png" /><figcaption>**Figure 2.** Lumen morphological differences between WT and TJ-mutant cell lines</figcaption></figure>

(A) Midplane cross-section of WT and TJ-mutant cysts as a function of cell number (indicated at the bottom of the panel). Lateral membranes are stained by E-cadherin (magenta) and apical membranes by podocalyxin (yellow). The right panels show 3D segmentation of the lumen at the later stage. WT and CLDN-KO

(legend continued on next page)
analysis pipeline was established to acquire morphometric parameters of lumina and cysts.

Overall, we observed that CLDN-KO and ZO-KO cells formed cysts with a single lumen and polarity markers, such as podocalyxin (apical) or E-cadherin (lateral), which were correctly polarized as in WT tissue (Figure 2A). Furthermore, lumen morphology at initial cyst stages (2–6 cells) was comparable between WT, CLDN-KO, and ZO-KO cysts (Figures 2A and 2B). Interestingly, at later stages of cyst development (>20 cells), clear differences in lumen morphology emerged: while both WT and CLDN-KO cysts developed large spherical lumina, ZO-KO cysts failed to inflate their lumen, which resulted in intricately folded apical membranes often bending into the cell bodies (see Video S1).

Quantification of lumen volume and apical surface area as a function of cell number revealed that the average lumen volume of WT and CLDN-KO cysts increased monotonically with cell number to a value of $8 \times 10^4 \mu m^3$ at 100 cells, with CLDN-KO lumen showing slightly faster growth than WT (Figure 2B). In contrast, the lumen volume of ZO-KO cysts inflated significantly slower and remained below $1 \times 10^4 \mu m^3$ even at 100 cells. Interestingly, despite ZO-KO cysts having a strongly reduced lumen volume, the apical surface area of lumina increased linearly with cell number, with the same slope as WT cysts. Thus, the apical surface area per cell was constant over time and comparable between WT and ZO-KO cells. This indicates that lumen volume and surface are not coupled; e.g., cells do not adapt their apical area according to changes in lumen volume.

To quantify the deviation from a spherical shape we calculated the sphericity of the lumen over time. After an initially irregular shape, sphericity of WT and CLDN-KO lumina quickly reached values close to a perfect sphere around the 10–20 cell stage. In contrast, sphericity of ZO-KO lumina dropped as a function of cell number, showing that the lumen surface to volume ratio increases as more and more cells compete for the relatively small lumen volume over time. To determine how the lumen volume grows in relation to the whole cyst volume, we calculated the lumen occupancy, i.e., the ratio of lumen to cyst volume. Lumen occupancy saturated around 50% for WT and CLDN-KO cysts. However, the latter had already reached saturation at the 20-cell stage while the WT cyst took 60–80 cells to reach a similar lumen occupancy, which indicates that lumen expansion in CLDN-KO cysts happens faster than WT despite higher trans-epithelial leakage. ZO-KO lumen occupancy was significantly lower than WT and saturated around 20%. The low lumen occupancy of ZO-KO cysts went along with a significant thickening of the epithelial cell layer, with cells having columnar shapes compared with the cuboidal shapes of WT cysts (see Figure 2A).

Taken together, the morphometric analysis revealed that perturbing TJs via claudin or ZO depletions has differential effects on lumen morphogenesis. First, lumen inflation is strongly

reduced by ZO-KO, while CLDN-KO cysts inflate spherical, lumen-like WT cysts. Second, the apical area of cells is largely constant and uncoupled from the collapse of lumen volume in ZO-KO tissue. Because both mutations produce a strong increase in trans-epithelial ion permeability compared with WT tissue, it is interesting that CLDN-KO cysts are able to inflate large spherical lumina whereas ZO-KO depletion caused a deflated lumen. To address this difference, we turned to the quantification of mechanical parameters, starting by designing a new method to measure the hydrostatic pressure of the lumen.

## Quantification of hydrostatic lumen pressure by lumen drainage

In many epithelial tissues, lumen inflation has been linked to the establishment of hydraulic forces.¹⁷ Apical secretion of chloride ions has been suggested to drive osmotic water influx into the lumen of MDCK cysts, producing a hydrostatic pressure difference that inflates the lumen.¹⁸ To test whether the morphological differences in lumen morphology between WT, CLDN-KO, and ZO-KO cysts are related to changes in hydrostatic pressure, we designed a lumen drainage experiment.

To measure the hydrostatic pressure difference between the lumen and the extracellular fluid, we used a two-photon laser to cut the cyst open via a short line scan through a single cell (Figure 3A). Cyst opening resulted in subsequent collapse of the lumen volume, which we quantified by segmenting the whole cysts and lumen from 3D confocal stacks over time (Figure 3A; Video S2). We found that the lumen volume of WT and CLDN-KO cysts decreased with an exponential-like kinetic to ≈20 % after 300 s, while ZO-KO showed significantly less decrease to ≈70 % of its initial volume (Figure 3D).

To check whether the lumen shrinkage was due to the equilibration of hydrostatic pressure caused by cutting the channel through the tissue, or whether active cellular responses induced by the laser cut could be responsible, we performed laser cuts only through the apical membrane (Figure S2C). In these cuts, the cytoplasm leaked into the lumen, but the tissue barrier remained tight. In contrast to cutting through the entire cell, cutting only the apical side did not lead to significant changes of cell shape and lumen volume change, indicating that the cell wounding alone did not cause the lumen collapse. In addition, we performed micropipette piercing experiments to check whether lumen collapse is reproducible by techniques complementary to laser cutting (Figure S3A). Micropipette piercing induced cyst collapse in a similar time period as laser cutting experiments, validating the results of laser cutting experiments (see Video S4).

We quantified the hydrostatic lumen pressure $\Delta P$ using the Hagen-Poiseuille law, which describes a flow $Q$ of a fluid with viscosity $\eta$ through a channel with radius $R$ and length $L$ due to a hydrostatic pressure difference $\Delta P$ (Figure 3B; STAR Methods). To

<footnote>cysts form large spherical lumina, ZO-KO cysts form a smaller, convoluted lumen with apical membranes curving into the cell bodies. Scale bar, 10 µm. See Video S1 for 3D representation of segmented lumen shapes.</footnote>

<footnote>(B) Quantification of lumen volume, surface area, sphericity, and occupancy based on 3D segmentation of lumen and cyst surfaces of WT (n = 114), CLDN-KO (n = 64), and ZO-KO cysts (n = 88) as a function of the total cell number per cyst. Bar graphs indicate quantification of lumen volume, surface area, sphericity, and occupancy for 55–65 cells (dashed box) and WT (n = 15), CLDN-KO (n = 6) and ZO-KO cysts (n = 9), error bars represent SEM. One-way ANOVA was used for statistical analysis against WT.</footnote>

<footnote>See also Video S1.</footnote>
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

measure the exit channel size of the luminal fluid, we expressed a fluorescently tagged, apically secreted sialomucin (Dendra2-CD164) in WT cysts, which provided strong staining of the luminal fluid. This allowed us to visualize the fluid outflow from the lumen after laser cutting the cyst and to confirm that the change in lumen volume corresponded to the actual flow of liquid (Video S3; Figures S3B–S3G). In addition, this analysis allowed us to determine the average length *L* and radius *R* of the exit channel (Figure 3C). The volume flow *Q* of lumen fluid was quantified via segmentation of the membrane channel providing the change in lumen volume from 3D confocal stacks over time (Figure 3A). The initial flow rate *Q* of luminal fluid was obtained from the initial change in lumen volume after cyst cutting (Figure 3D). Finally, to determine the viscosity of the luminal fluid, we measured the

<caption>**Figure 3.** Influence of TJ mutations on hydrostatic lumen pressure in MDCK-II cysts</caption>

(A) Lumen volume drainage of MDCK-II TJ-mutant cysts by laser cutting. Midplane cross-section of cysts before and after laser cutting. Positions of cuts are indicated by red lines. The lumina of WT and CLDN-KO cysts quickly collapsed after the cut, while the lumen of the ZO-KO cyst remained relatively constant. Scale bar, 20 µm. See Video S2 for an example of lumen drainage.

(B) Hagen-Poiseuille law used to determine initial hydrostatic pressure in the lumen: $\Delta P$ hydrostatic pressure difference, *Q* fluid flow, *L* and *R* channel length and radius, and $\eta$ fluid viscosity. Lumen fluid viscosity was measured using fluorescence correlation spectroscopy (FCS) (Figure S2).

(C) Geometry of the leak channel after laser cutting was determined by imaging the exit of the lumen fluid, which was stained by expression of Dendra2-CD164 (magenta). Scale bars, 10 µm.

(D) Lumen volume change after laser cutting determined from 3D segmentation of lumina over time. Values are normalized to the initial lumen volume before the cut. Right plot shows mean initial flow rate with standard error, calculated from the initial slope. WT ($n = 22$), CLDN-KO ($n = 14$), and ZO-KO cysts ($n = 10$).

(E) Hydrostatic lumen pressure of MDKC-II mutants and rescues. WT = 52 ± 29 Pa ($n = 22$), CLDN-KO = 66 ± 35 Pa ($n = 14$), CLDN-KO + CLDN2-FLAG = 23 Pa ($n = 13$), ZO-KO cysts = 1.6 ± 1.3 Pa ($n = 10$), and ZO-KO + mCherry-ZO1 = 19 ± 8 Pa ($n = 11$). Welch ANOVA was used for statistical tests against WT.

See also Videos S2, S3, and S4.

diffusion coefficient of Dendra2-CD164 in the lumen and in PBS buffer using fluorescence correlation spectroscopy. Lumen fluid viscosity was ≈5 times higher than water (Figure S2B).

Based on these four measured quantities (flow, radius, length, and viscosity), we calculated the average hydrostatic lumen pressure to be $\Delta P_{WT} = 52 \pm 29$ Pa, $\Delta P_{CLDN-KO} = 66 \pm 35$ Pa, and $\Delta P_{ZO-KO} = 1.7 \pm 1.3$ Pa (Figure 3E). FLAG-CLDN2 expression in CLDN-KO background signif-

icantly lowered the hydrostatic pressure $\Delta P_{CLDN-KO} + CLDN2 = 23 \pm 16$ Pa. mCherry-ZO1 expression in the ZO-KO cysts significantly increased lumen pressure to $\Delta P_{ZO-KO} + ZO1 = 19 \pm 8$ Pa. Both CLDN2 and ZO1 rescues showed the correct trend toward WT pressure; e.g., re-expression of CLDN2 lowered the pressure of CLDN2-KO tissue and re-expression of ZO1 increased the pressure of ZO-KO cysts, restoring round spherical lumen. However, CLDN2 expression overshot the pressure reduction below WT levels, and ZO1 did not fully increase the pressure back to WT levels.

Taken together, the hydrostatic pressure measurements revealed that WT cysts build up hydrostatic pressure of ≈52 Pa to inflate a spherical lumen, which is close to previously reported values.¹⁹ In addition, despite CLDN-KO cysts being permeable
<figure><img src="image_20.png" /></figure>

A

Myosin-IIa distribution in MDCKII WT, mutants and rescues

<figure><img src="image_21.png" /></figure>

C

Estimation of junctional tension via laser ablation

<figure><img src="image_22.png" /></figure>

D

Junctional recoil

<figure><img src="image_23.png" /></figure>

E

Recoil velocity

<figure><img src="image_24.png" /></figure>

F

Myosin vs recoil

<figure><img src="image_25.png" /><figcaption>**Figure 4. Quantification of junctional tension of MDCK-II mutants**</figcaption></figure>

(A) Distribution of endogenous myosin IIa tagged with mNeon in MDCK-II monolayers. In WT tissue, myosin is predominantly in the cytoplasm, with only minor punctae at cell junctions. CLDN-KO tissue showed significantly increased levels of myosin at the junctions, CLDN2-FLAG expression rescued myosin accumulation at cell-cell junctions and the ZO-KO monolayer had a strong accumulation of thick myosin bundles along cell-cell junctions; mCherry-ZO1 expression partially lowered myosin at cell-cell junctions. Scale bar, 20 µm.

(B) Quantification of myosin enrichment at the apical junction. WT (n = 125), CLDN-KO (n = 92), CLDN-KO + CLDN2 (n = 57), ZO-KO (n = 107), and ZO-KO + ZO1 (n = 107). Statistical analysis with one-way ANOVA against WT.

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to small molecules, they build up even higher lumen hydrostatic pressure than WT cysts ≈ 66 Pa. In contrast, ZO-KO cysts do not build up a significant hydrostatic pressure difference, which may explain why their lumina are collapsed. To understand how the changes in hydrostatic pressure are related to the morphological changes of the lumen, we next determined the corresponding changes of junctional tension of the TJ mutants.

## TJ mutations increase apical-junctional tension via myosin activation

To determine the influence of TJ mutations on mechanical tissue tension, we quantified endogenous myosin IIa distributions and performed laser ablation experiments. To visualize myosin distribution, we tagged endogenous myosin IIa with mNeonGreen in WT, CLDN-KO, and ZO-KO cells using CRISPR-Cas genome editing. We observed that in WT monolayers, Myo-IIa was mostly cytoplasmic, while in CLDN-KO and ZO-KO, Myo-IIa was clearly enriched at the apical-junctional complex (Figure 4A). Quantification of the enrichment of Myo-IIa at the junction with respect to the cytoplasm, i.e., the junction-to-cytoplasm ratio (JCR), showed that myosin in WT tissue was only slightly enriched at the junction (JCR ≈ 1), while in CLDN-KO, monolayers myosin was strongly enriched at the TJ (JCR ≈ 5). ZO-KO showed an even stronger enrichment with JCR ≈ 7 (Figure 4B). Re-expression of FLAG-CLDN2 fully rescued myosin distribution back to WT levels: JCR ≈ 1. Re-expression strongly reduced myosin enrichment, but the levels remained higher compared with WT tissue: JCR ≈ 2 (Figures 4A and 4B).

Increased junctional myosin levels suggest that cortical tension of the TJ mutants is increased. In order to estimate junctional tension, we laser dissected apical junctions and analyzed initial recoil velocities (Figures 4C–4E). WT tissue showed little recoil, with a velocity of v = 1.1 µm/s, indicating that the junctions are not under significant tension and the tissue is in a relaxed state. In contrast, we found that CLDN-KO recoil was 3× faster (v = 3.6 µm/s) and ZO-KO even 10× faster (v = 11 µm/s) compared with WT. In addition, re-expression of FLAG-CLDN2 decreased junctional recoil even below WT velocity v = 0.5 µm/s. Re-expression of ZO1-mCherry significantly lowered junctional recoil; however, as expected from the remaining myosin enrichment, the recoil velocity remained above WT levels v = 3.0 µm/s (Figure 4E).

Relating the junctional myosin levels to the junctional recoil velocities showed a strong positive correlation (Figure 4F), which suggests that depletion of CLDN—and even more so of ZO proteins—increases junctional tension via local myosin accumulation.

Taken together, myosin localization and junctional recoil quantification confirmed that TJs play an important role in regulating

junctional tension in MDCK tissue. ZO proteins and, to a lesser extent, claudins affect junctional myosin levels and, as a consequence, lower mechanical tension at the apical-junctional complex, effectively making the tissue softer. These results are in line with previous observations that loss of ZO1/ZO2 and loss of claudins are linked to myosin accumulation at the apical junction and increased tissue tension.⁹⁻¹¹ Increased junctional tension has also been linked to apical constriction of cells, which can induce folding of tissues.²⁰ In the context of lumen formation, apical constriction of cells is expected to counteract the hydrostatic pressure of the lumen (Figure 1A). Therefore, the combined loss of hydrostatic pressure together with the increased apical-junctional tension in ZO-KO cysts may explain the collapsed lumen volume and the folding of apical membranes.

The combined pressure and tension results suggest that TJs promote lumen inflation by two independent mechanisms. First, the junctional permeability barrier promotes the formation of hydrostatic pressure via maintaining ion gradients that drive osmotic water influx. Second, TJs inhibit myosin contractility, which reduces apical tension and allows lumen inflation at lower hydrostatic pressure.

## Minimal force balance model recapitulates and predicts lumen phenotypes

To better understand how the changes in hydrostatic pressure and junction tension relate to 3D shape changes of lumina, we used an analytical model to describe the force balance of the luminal cavity (Figure 5A; STAR Methods). We assumed that the volume and shape of the lumen are determined by the minimization of free energy of the lumen surface, which includes contributions from hydrostatic pressure and the junctional tension. In addition, we included in the model the finding that the apical surface per cell does not adapt to changes in lumen volume in our experiments (Figure 2). Therefore, we introduced a constant apical area per cell (experimental value). This surface also contributes to the force balance via a bending modulus (STAR Methods). Thus, deforming the apical surface is energetically costly.

Varying lumen pressure and junctional tensions in the regime of experimentally determined values resulted in two lumen states (Figure 5B). First, when junctional tension dominates, the lumen volume collapses. Second, when hydrostatic pressure dominates, the lumen volume inflates to a spherical shape. Introduction of a constant apical surface area with a bending modulus prevented full collapse of the lumen volume in the tension-dominated regime (Figures S4A and S4B). Thus, the bending energy of the constant apical surface area promotes lumen opening, especially in the regime when hydrostatic pressure is not sufficient to inflate the lumen (Figure S4C).

<footnote>(C) Laser ablation of cell-cell junctions of MDCK-II mutants. Position of cut is indicated by red arrow. Junctional recoil distance was measured by tracking the position of tricellular vertices over time.</footnote>

<footnote>(D) Dynamics of junctional recoil after laser ablation of MDCK-II WT and mutants. WT (n = 16), CLDN-KO (n = 21), and ZO-KO cysts (n = 14). Laser cut was done at 0 s. Initial distance before cut was subtracted to highlight the change due to recoil.</footnote>

<footnote>(E) Mean initial recoil velocities of MDCK-II mutants show that WT tissue is under low mechanical tension. CLDN-KO tissue has increased tension and ZO-KO tissue builds up strong junctional tension. Initial recoil velocities of MDCK-II mutants and rescues. Initial recoil velocities were determined from the slope of first data points after laser cutting. WT (n = 19), CLDN-KO (n = 31), CLDN-KO Cldn2-FLAG (n = 17), ZO-KO cysts (n = 22), and ZO-KO ZO1-mCherry (n = 21). Statistical analysis with one-way ANOVA against WT.</footnote>

<footnote>(F) Correlation between myosin junctional enrichment and initial recoil velocity, with a linear fit of WT, CLDN-KO, CLDN-KO Cldn2-FLAG, ZO-KO, and ZO-KO ZO1-mCherry data from (B) and (E) ($R^2$ = 0.73).</footnote>
<figure><img src="image_26.png" /></figure>

A

Lumen Model

Lumen Fluid

Apical Surface

<figure><img src="image_27.png" /></figure>

B

Pressure-Tension Space

<figure><img src="image_28.png" /></figure>

C

Predicted Lumen Shapes

<figure><img src="image_29.png" /><figcaption>Figure 5. Apical surface model recapitulates lumen phenotypes of TJ mutants</figcaption></figure>

(A) Schematics of the free-energy model of lumen surface. The shape of the lumen is obtained by minimizing the free energy *F* of its area *A*, computed with contributions from the hydrostatic pressure *P* of the lumen, the apical-junctional tension *T*, and the bending rigidity *K* of apical surface.

(B) Phase diagram of the inner lumen radius in the apical line tension-hydrostatic pressure parameter space. For this phase diagram, the bending energy is *K* = 2 × 10⁻¹⁶ J and the number of cells is *N*<sub>cells</sub> = 42 cells.

(C) Minimum energy 3D shapes of the lumen surface for the points labeled 1–12 in (B), calculated using Surface Evolver.
<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /><figcaption>**Figure 6.** Increasing hydrostatic lumen pressure promotes lumen opening</figcaption></figure>

(A) Schematic of pipette inflation assay.

(B) WT and ZO-KO cysts before and after lumen inflation. Fluorescently labeled dextran in the pipette solution was used to demonstrate entry of fluid into the lumen.

(C) Quantification of lumen volume change normalized to the volume values before inflation.

(D) Trajectories of lumen occupancy vs. cell height before and after inflation, represented by arrows, show that ZO-KO cysts cannot be inflated to the same level as WT cysts and cells remain more elongated. WT in blue and ZO-KO in red.

WT (n = 96) and ZO-KO (n = 96) for (C) and (D).

To compare the morphologies of lumina predicted by our model with the experimental observed shapes, we calculated the energy-minimized shape of a lumen surrounded by 42 cells (truncated icosahedron) for 12 positions in the pressure-tension range of our experiments with a vertrex model using Surface-Evolver²¹ (Figure 5B). The calculated shapes revealed a striking qualitative agreement with the experimental observations (Figure 5C). In the tension-dominated collapsed state, the excess apical membrane bends away from the lumen, forming the characteristic lobes that are observed in the ZO-KO cysts (Figure 5C states:1, 2, 4, 7). In the fully inflated state, the apical surface is a smooth sphere resembling WT cysts (states: 8, 9, 6). Close to the transition line, apical membranes bend slightly outward (states: 5 + 3), which resembles CLDN-KO cyst morphologies.

In summary, the force balance model is sufficient to recapitulate lumen morphologies of WT and TJ mutants of MDCK cysts in the experimentally determined parameter regime. Thus, the model supports the notion that TJs control lumen morphology by tuning the mechanical force balance of tension vs. pressure and bending of the apical surface. Mapping the pressure-tension parameter space showed how TJs in WT tissue promote efficient inflation of spherical lumina at relatively low hydrostatic pressure by decreasing apical-junctional tension. The model also highlights the mechanical role of the apical membrane that, due to its conserved area and resistance to bending, prevents full collapse of the lumen at high tensions and effectively facilitates lumen opening in the low tension vs. pressure regime, which is in line with findings from the Dunn lab.⁵

To further test the mechanical model, we performed perturbations experiments focusing on the rescue of the collapsed lumen phenotype of ZO-KO cysts. To facilitate lumen opening, we

reduced junctional tension via myosin inhibition and increased luminal pressure via micropipette inflation.

**Increasing hydrostatic lumen pressure partially reverses lumen collapse in ZO-KO cysts**

To increase luminal pressure of MDCK cysts, we developed a micropipette inflation approach. For this purpose, we grew cysts in shallow PDMS micro-cav-

ities,²²,²³ which allowed us to apply a fluid jet directly against the surface of cysts without detaching the cyst from the surface and the Matrigel. This setup enabled us to efficiently quantify morphological changes upon pipette inflation using confocal microscopy with high throughput (Figure 6A). We found that the fluid jet applied to the cyst surface was able to open TJs and press additional fluid into the lumen, increasing the hydrostatic lumen pressure. This was confirmed by observing fluorescent dextran entering the lumen from the pipette solution (Figure 6B).

Fluid addition to the lumen resulted in significant expansion of WT and ZO-KO cysts. In both cases, the lumen volume on average increased 7-fold (Figure 6C). However, because ZO-KO cysts started with much smaller lumina, the absolute volume after inflation remained smaller compared with inflated WT cysts. To quantify how the cell monolayer responded to the lumen volume increase, we quantified the change in cell height relative to the initial values (Figure 6D). We found that the average cell height decreased 0.7 ± 0.1-fold in the WT cyst and significantly less in the ZO-KO, with 0.9 ± 0.2-fold. Overall, ZO-KO cells started significantly more elongated compared with WT and even after lumen inflation did not reach the cell height of pre-inflation WT cysts. Relating the cell height change to the change in lumen occupancy after lumen inflation (Figure 6D) showed that WT and ZO-KO cysts follow the same trend, e.g., an increase in lumen occupancy and decrease in cell height. However, ZO-KO cysts could not be inflated to the same degree as WT cysts. Although lumen occupancy in WT cysts increased from 0.2 ± 0.1 to 0.5 ± 0.1, the cell height decreased from 10 ± 2 to 8 ± 2 µm. In contrast, lumen occupancy of ZO-KO cysts only increased from 0.08 ± 0.04 to 0.22 ± 0.1, while the cell height remained relatively high, with a change from 22 ± 2 to 19 ± 3 µm.
<figure><img src="image_32.png" /></figure>

A

Rho-kinase inhibition in MDCKII cysts

<figure><img src="image_33.png" /></figure>

B

Junctional myosin
enrichment

C

Lumen occupancy change

<figure><img src="image_34.png" /><figcaption>**Figure 7.** Release of junctional tension promotes lumen opening in CLDN-KO and ZO-KO cysts</figcaption></figure>

(A) Distribution of endogenous myosin IIa tagged with mNeon in MDCK-II cysts before and after addition of Rho kinase inhibitor Y-27632 (200 µM) in WT, CLDN-KO, and ZO-KO cysts. Scale bars, 20 µm. Fiji MQ-div-Magma LUT for visualization. A clear increase in lumen size is visible in ZO-KO cysts.

(legend continued on next page)
Taken together, increasing hydrostatic lumen pressure in WT and ZO-KO cysts via pipette inflation caused lumen expansion in both cases. However, cells in ZO-KO cysts remained significantly more elongated and lumen volume remained smaller compared with WT cysts. Thus, ZO-KO cells resisted lumen inflation and cell thinning in response to increased hydrostatic pressure significantly more than WT tissue, which is in line with the increased junctional tension of ZO-KO tissue.

## Reduction of junctional tension increases lumen volume in ZO-KO and CLDN-KO cysts

To reduce junctional tension, we inhibited Rho kinase (ROCK), an upstream myosin IIa activator, via the compound Y-27632.<sup>24,25</sup> Inhibition of ROCK via 200 µM Y-27632 resulted in efficient reduction of myosin accumulation at apical junctions after 120 min to almost WT levels in ZO-KO and CLDN-KO monolayers (Figures S5A and S5B). In line with the two-dimensional (2D) monolayer experiments, myosin IIa was mostly enriched at the basal membrane in WT cysts, at basal and apical-junctional membranes in CLDN-KO cysts, and at basal, lateral and apical-junctional membranes in ZO-KO cysts. Y-27632 treatment on 3D cysts resulted in qualitatively similar behavior as in 2D monolayers; e.g., myosin accumulation at the cell membrane, including the apical junction complex, was decreased (Figures 7A and 7B). Because junctional myosin levels strongly correlate with junctional tension (Figure 4F), Y-27632 treatment is expected to decrease junctional tension.

In WT cysts, addition of Y-27632 had no significant influence on cyst and lumen morphology (Figure 7C). In contrast, in ZO-KO cysts, we observed a significant increase in lumen volume starting 20 min after Y-27632 addition and reaching a plateau after 40 min. Overall, the lumen volume of ZO-KO cysts increased 1.2-fold after inhibition of myosin (Figure 7C). In CLDN-KO cysts, inhibition of myosin also resulted in an increase in lumen volume; however, with a slower kinetic and to a lesser extent compared with ZO-KO cysts.

In summary, ROCK inhibition resulted in the release of junctional myosin IIa accumulation in TJ-mutant tissues to almost WT levels. The release of myosin caused strong lumen expansion in ZO-KO and medium expansion in CLDN-KO cysts, while WT cysts were not affected. The perturbation results support the force balance model and show that releasing apical-junctional tension is an important function of TJs in promoting lumen inflation by hydrostatic pressure.

## DISCUSSION

In this work, we addressed the question of how TJs contribute to the formation of lumina in an organotypic 3D tissue culture model system (MDCK-II cysts). By measuring and modeling the force balance of hydrostatic lumen pressure and junctional tension of TJ mutants, we found that TJs have a strong impact

on the amount of apical-junctional tension and, to a lesser degree, on the amount of hydrostatic pressure established by solute pumping. In addition, our measurements revealed that cells control the area of the apical membrane independently from hydrostatic pressure, junctional tension, and lumen volume.

## Role of TJs in regulating tissue permeability and hydrostatic lumen pressure

Comparing hydrostatic lumen pressure of WT and TJ-mutant cysts revealed that the paracellular barrier for ions formed by claudin strands is not required to build up hydrostatic lumen pressure and inflate spherical lumina (CLDN-KO, Figures 2 and 3). Previous trans-epithelial permeability measurements of small molecule tracers showed that permeability for molecules with a size of ≈1 nm is ≈9-fold increased for CLDN-KO tissue and ≈12-fold increased in ZO-KO tissue compared with WT.<sup>7</sup> In addition, ZO-KO tissue is also permeable for larger macromolecules of up to ≈15 nm.<sup>7</sup> The significantly increased trans-epithelial leak for solutes of CLDN-KO and the ZO-KO tissue should, in principle, reduce the osmotic pressure difference between the lumen and the surrounding environment because the paracellular leak channels equilibrate concentration gradients established by active solute pumping into the lumen.<sup>17</sup> Indeed, previous work focusing on pressure-independent mechanisms of lumen formation assumed that, due to the increased solute permeability, CLDN-KO cysts have reduced hydrostatic pressure.<sup>5</sup> However, we found that despite the strongly increased permeability, CLDN-KO cysts establish a hydrostatic lumen pressure comparable with WT tissue and are able to inflate spherical lumina (Figures 2 and 3). This suggests that cells can compensate increased paracellular solute permeability. One mechanism could be that cells increase active ion pumping into the lumen to compensate the increased paracellular leak. On the other hand, our results showed that ZO-KO cysts are not able to establish significant hydrostatic pressure (Figure 3). This could imply that cells are not able to compensate the further increased solute permeability in the ZO-KO, which would suggest an upper limit for the pumping capacity. However, because the ZO-KO cysts also have strongly increased junctional tension and very convoluted lumen shapes, it is possible that our lumen volume analysis was not able to resolve small changes in volume after drainage, in particular, of the folded lobes of the lumen. Thus, it also remains possible that ZO-KO cysts can maintain an osmotic pressure in the lumen. Along these lines, it has been suggested that MDCK-II cysts grow in a regime in which the osmotic pressure ΔΠ is significantly larger than the hydrostatic pressure ΔP (ΔΠ ≫ ΔP). Under these conditions, buildup of high hydrostatic lumen pressure is limited by the relatively low water permeability through the epithelium.<sup>17</sup> Thus, a significant reduction of osmotic pressure due to increased paracellular leaks may still lead to conditions in which the lumen can expand

<footnote>(B) Quantification of junctional myosin enrichment at cell-cell junctions vs. cytoplasm and comparison between incubation with Y-27632 and the solvent DMSO 120 min after treatment, WT (n = 57), WT Y-27632 (n = 64), CLDN-KO (n = 41), CLDN-KO Y-27632 (n = 37), ZO-KO (n = 57), and ZO-KO Y-27632 (n = 42) cysts.
(C) (Left) Normalized lumen occupancy after Y-27632 addition. WT cysts showed no significant change in lumen volume. ZO-KO cysts significantly increased lumen occupancy 30 min after myosin inhibition. WT (n = 7), CLDN-KO (n = 6), and ZO-KO cysts (n = 9). (Right) Mean change in lumen occupancy after 120 min of Y-27632 addition. WT cysts show no significant change in lumen volume after tension release, while CLDN-KO and ZO-KO cysts show a 40% increase in their lumen volume. WT (n = 7), CLDN-KO (n = 6), and ZO-KO cysts (n = 9), Statistical analysis with one-way ANOVA against WT.</footnote>
by osmotic water influx (ΔΠ > ΔΡ). Because water permeability is also expected to increase when the paracellular barrier is opened, lumen volume could increase even faster and higher hydrostatic pressures could be reached than for the relatively tight WT tissue. This effect may explain our counter-intuitive results on the high pressure of CLDN-KO cysts, which is reduced to lower pressure when CLDN2 is overexpressed in these cells. Further development of methods that can directly measure luminal osmotic pressure will be required to understand the feedback between paracellular permeability, solute pumping, and hydrostatic pressure.

Overall, our results suggest that epithelial cells can maintain sufficient osmotic lumen pressure to drive water influx and promote lumen expansion even when TJs open the paracellular barriers. This points to a feedback mechanism that regulates solute pumping activity to maintain a certain luminal pressure. Recent work suggests that MDCK cells can sense the apical-basal pressure difference and modulate active fluid pumping via localization of the Na/K ATPase.¹⁹

## Role of TJs in regulating apical-junctional tension during lumen formation

The TJ scaffold proteins ZO1 and ZO2 have been shown to be important regulators of the apical actin cortex.⁹⁻¹¹ In addition, ZO1 is known to inhibit myosin activity via inhibition of the RhoA exchange factor GEF-H1,²⁶ and depletion of ZO1 leads to increased junctional tension.²⁷,²⁸ Our quantification of endogenous junctional myosin IIa levels in combination with junction tension measurements confirm the key role of ZO proteins in regulating apical-junctional contractility via myosin inhibition (Figures 4, 7, and S5). In addition, we found that claudins also play a critical role in tension regulation. Depletion of claudins causes an increase of myosin and junctional tension, albeit to a lesser extent than ZO1 depletion. Because junctional ZO1 levels are not affected by claudin depletion, myosin regulation via claudins is either regulated by changing ZO1 conformation or it involves a ZO1-independent pathway. Along these lines, recent work on transient TJ breaching via mechanical stretching has revealed that breaks in the TJ network cause local calcium bursts, which activate RhoA and lead to a contractile response via myosin.²⁹,³⁰ This response leads to efficient healing of TJ breaks and ensures active maintenance of the TJ barrier in a mechanically challenging tissue environment. Although the mechano-sensor that responds to TJ stretching has not been identified, we speculate that the same mechanical feedback may also be activated in ZO-KO and CLDN-KO tissue, which could explain the increase in junctional tension of CLDN-KO cells despite normal ZO1 levels.

Taken together, our results are in line with previous reports that TJs regulate junctional tension via control of acto-myosin activity.⁹⁻¹¹ Importantly, we found that a key role of TJs for lumen formation is to decrease apical-junctional tension, which promotes spherical lumen inflation at lower hydrostatic pressures.

## Tuning of lumen shapes by TJs and the role of the apical membrane cortex

In line with previous observations,⁵ we found that the apical surface area per cell is mostly constant during lumen growth

(Figure 2). Even when the lumen volume is collapsed in ZO-KO cysts, the apical area remains close to that of WT cells. This suggests that cells control the size of the apical membrane independently of hydrostatic pressure and tension, probably by tuning the balance of apical endo- and exocytosis³¹,³² and/or by independently regulating the apical actin cortex. This may also suggest that the size of the apical area is genetically encoded in a cell-type-specific manner rather than being a parameter that can freely adapt to morphological and mechanical changes of cells and tissues. Previous characterizations of apical polarity and the organization of the actin cortex in ZO1/2 KO cells have shown that polarity is partially compromised,⁷ the apical cortex and microvilli are disorganized,³³ and the viscoelastic properties of the apical cortex change.²⁷ How TJs and apical membrane formation are mechanistically connected remains an interesting question for future studies. To account for our apical area qualifications, we included an apical area constraint in our mechanical force balance model of lumen morphology (Figure 5). Our model is able to capture the key morphological changes of CLDN-KO and ZO-KO compared with WT cysts and, therefore, provides a useful tool to understand morphological transitions during lumen growth and remodeling.

We point out that the model we construct, which has only three parameters, has significant advantages in tractability over more complex models that take more geometry into account. This tractability allows us to explore the parameter space and compare 3D shapes to experimental phenotypes (Figures 5B and 5C). Our model also differs significantly from previous models of lumen size and shape by allowing for 3D spatial resolution over the surface of the lumen, with spatially separated contributions from junctional tension and from the mechanics of the rest of the apical surface. Previous models used spherical symmetry³⁴⁻³⁶ or did not separate the contributions of the junctions from those of other cell surfaces.³,⁵ This explicit spatial separation of junctional tension from the rest of the apical surface allows us to explain the ZO-KO phenotype. We finally note that our inclusion of a bending energy for the apical surface allows for smooth transitions from concave to convex curvatures at the junctions, a feature that would be hard to explain otherwise. The bending energy we used in our model effectively includes mechanical contributions from the whole tissue (basal, lateral, and cytoplasmic) and, therefore, should not be taken as a reference value for the properties of the apical membrane. In future work, it will be important to (1) further consolidate the role of the mechanical properties of the apical membrane and its area regulation, (2) include the contribution of lateral and basal surface mechanics also with anisotropic tension,³⁷ and (3) include the role of active pumping and osmotic pressure into the modeling framework to explore the dynamics of lumen formation.³,¹⁷,³⁸

## Limitations of the study

The quantification of hydrostatic lumen pressure from cyst laser cutting experiments using the Hagen-Poiseuille model provides a lower boundary for the lumen pressure because the model does not take viscoelastic properties of the tissue into account. In addition, the non-linear dependence of the quantified pressure on the geometry of the outflow channel created by the laser cut
limits the precision of the measurement. The mechanical model we use to describe the morphology of the apical surface of cysts is a minimal version that focuses on the experimentally accessible parameters of this study (junctional tension, hydrostatic pressure, and surface area constraints). In the future, it will be important to include the role of lateral and basal cell interface properties as well as changes in ion permeability and ion pumping of the tissue.

## STAR★METHODS

Detailed methods are provided in the online version of this paper and include the following:

* KEY RESOURCES TABLE

* RESOURCE AVAILABILITY

* Lead contact

* Materials availability

* Data and code availability

* EXPERIMENTAL MODEL AND STUDY PARTICIPANT DETAILS

* MDCK-II cells

* METHOD DETAILS

* Three-dimensional culture of MDCK cysts and drug treatment

* Trans-epithelial cyst permeability assay

* Lumen sphericity measurement

* Drainage of lumen and quantification of hydrostatic lumen pressure

* Measurement of lumen fluid viscosity

* Three-dimensional segmentation of MDCK cysts

* Junctional recoil measurement

* Immunostainings of MDCK tissue

* Confocal microscopy

* Cyst inflation in microfabricated cavities

* Lumen Model

* Apical surfaces with no bending energy

* Apical surfaces with a bending energy

* Differences between the two phase diagrams

* Parameter choice

* Shape calculation with Surface Evolver

* QUANTIFICATION AND STATISTICAL ANALYSIS

## SUPPLEMENTAL INFORMATION

Supplemental information can be found online at https://doi.org/10.1016/j.devcel.2024.07.016.

## ACKNOWLEDGMENTS

We thank Mikio Furuse, National Institute for Physiological Sciences (NIPS) Japan, for providing the CLDN-5KO MDCK-II cell line. We thank Byung Ho Lee for the help with the cyst segmentation. A.H.'s team thanks the light microscopy facility of the MPI-CBG as well as the light microscopy facility of the CMCB Dresden for help and support with imaging. D.R.'s team thanks the Imaging Platform of IGBMC for their support. D.R.'s team was supported by the Interdisciplinary Thematic Institute IMCBio, as part of the ITI 2021–2028 program of the University of Strasbourg, CNRS, and Inserm; IdEx Unistra (ANR-10-IDEX-0002); SFRI-STRAT'US project (ANR 20-SFRI-0012); and EUR IMCBio (ANR-17-EURE-0023) under the framework of the French Investments for the Future program. A.H. and M.M. were supported by the Volkswagen Foundation, project number A133289. M.J.B. and M.F.S. were funded by the Max Planck Society, including through an ELBE fellowship. T.H. was supported by the Mechanobiology Institute Seed fund. This project was funded by HFSP project number RGP0050/2018.

## AUTHOR CONTRIBUTIONS

A.H. conceived the project. M.M. performed all experiments, except those specifically attributed to other authors. D.R. and T.G. conceived the cyst

drainage assay for the estimate of luminal pressure, A.H. developed the experimental implementation, and M.M. and R.M. performed measurements. D.R. conceived the pipette assay with microfabricated substrate and the lumen inflation with T.G. and L.L., who performed the experiments and measurements. C.-H.W. performed morphological characterization of TJ mutants. T.H., M.S., D.R., M.M., and T.G. conceived the mechanical model and T.G. performed the associated numerical simulations. M.J.B. and M.F.S. implemented the model in Surface Evolver. A.H. and M.M. conceived ROCK inhibitor experiments. C.M.-L. and M.M. did the cell-culture work and created stable cell lines. R.E.v.d.V. and M.L. established CLDN2 rescue cell lines. A.H. and M.M. wrote the manuscript with input from all authors.

## DECLARATION OF INTERESTS

The authors declare no competing interests

Received: May 11, 2023

Revised: February 24, 2024

Accepted: July 16, 2024

Published: August 12, 2024

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## STAR★METHODS

### KEY RESOURCES TABLE

<table><thead><tr><th>REAGENT or RESOURCE</th><th>SOURCE</th><th>IDENTIFIER</th></tr></thead><tbody><tr><td colspan="3"><strong>Antibodies</strong></td></tr><tr><td>Mouse anti-E-Cadherin</td><td>MPI-CBG antibody facility</td><td>N/A</td></tr><tr><td>Rabbit anti-gp135/podocalyxin</td><td>Merck</td><td>Cat#MABS1327-3F2; RRID: AB_3102002</td></tr><tr><td>Goat anti-rabbit abberior STAR ORANGE</td><td>Abberior</td><td>Abberior Cat# STORAGE-1002-500UG; RRID:AB_3068622</td></tr><tr><td>Goat anti-mouse abberior STAR RED</td><td>Abberior</td><td>Abberior Cat# STRED-1001-500UG; RRID:AB_3068620</td></tr><tr><td colspan="3"><strong>Bacterial and virus strains</strong></td></tr><tr><td>Chemically competent Dh5alpha</td><td>Homemade</td><td>N/A</td></tr><tr><td>FLAG-Cldn2 retrovirus</td><td>Gonschior et al.<sup>16</sup></td><td>N/A</td></tr><tr><td colspan="3"><strong>Chemicals, peptides, and recombinant proteins</strong></td></tr><tr><td>MEM, GlutaMAX™ Supplement</td><td>Gibco™</td><td>Cat# 41090028</td></tr><tr><td>Fetal Bovine Serum</td><td>Gibco™</td><td>Cat# 10270106</td></tr><tr><td>Sodium pyruvate (100mM)</td><td>Gibco™</td><td>Cat# 11360070</td></tr><tr><td>MEM Non-Essential Amino Acids (100X)</td><td>Gibco™</td><td>Cat# 11140050</td></tr><tr><td>Puromycin Puromycin-Dihydrochlorid</td><td>Gibco™</td><td>Cat# A1113803</td></tr><tr><td>Geneticin™</td><td>Gibco™</td><td>Cat# 10131027</td></tr><tr><td>Lipofectamine™ 2000</td><td>Invitrogen™</td><td>Cat#11668019</td></tr><tr><td>Dextran, Alexa Fluor 647 10k</td><td>Invitrogen™</td><td>Cat#D22914</td></tr><tr><td>Halo Ligand JF646</td><td>Promega™</td><td>Cat#GA1120</td></tr><tr><td>Laminin</td><td>Roche</td><td>Cat#11243217001</td></tr><tr><td>Matrigel® Growth Factor Reduced (GFR)</td><td>Corning®</td><td>Cat#356231</td></tr><tr><td>Rock-Inhibitor Y-27632</td><td>Sigma-Aldrich</td><td>Cat#SCM075</td></tr><tr><td>CellMask™ Orange Plasma membrane stain</td><td>Invitrogen</td><td>Cat#C10045</td></tr><tr><td colspan="3"><strong>Other</strong></td></tr><tr><td>35 mm Dish | High Precision 1.5</td><td>Mattek</td><td>Cat#P35G-0.170-14-C</td></tr><tr><td>Coverslip | 14 mm Glass Diameter</td><td></td><td></td></tr><tr><td colspan="3"><strong>Experimental models: Cell lines</strong></td></tr><tr><td>MDCK-II</td><td>https://www.phe-culturecollections.org.uk</td><td>00062107</td></tr><tr><td>ZO1/2 knockout MDCK-II</td><td>Beutel et al.<sup>13</sup></td><td>N/A</td></tr><tr><td>Claudin quin-KO MDCK-II</td><td>Otani et al.<sup>7</sup></td><td>N/A</td></tr><tr><td colspan="3"><strong>Oligonucleotides</strong></td></tr><tr><td>dog MYH9 gRNA: ATCCACATAGAGATACTTAT</td><td>Integrated DNA Technologies (IDT)</td><td>N/A</td></tr><tr><td colspan="3"><strong>Recombinant DNA</strong></td></tr><tr><td>pOCC ZO1 mcherry</td><td>This study</td><td>N/A</td></tr><tr><td>pOCC CAAX HALO</td><td>This study</td><td>N/A</td></tr><tr><td>pOCC Dendra2-CD164</td><td>This study</td><td>N/A</td></tr><tr><td colspan="3"><strong>Software and algorithms</strong></td></tr><tr><td>Fiji</td><td>NIH</td><td>https://fiji.sc</td></tr><tr><td>MATLAB</td><td>Mathworks</td><td>https://www.mathworks.com/</td></tr><tr><td>Matlab Junctional recoil measurement</td><td>This study</td><td>https://github.com/Honigmann-Lab-BIOTEC/Tight-junctions-control-lumen-morphology-via-hydrostatic-pressure-and-junctional-tension/tree/main</td></tr><tr><td></td><td></td><td>https://doi.org/10.5281/zenodo.12168170</td></tr></tbody></table>

(Continued on next page)
**Continued**

<table><thead><tr><th>REAGENT or RESOURCE</th><th>SOURCE</th><th>IDENTIFIER</th></tr></thead><tbody><tr><td>LimeSeg</td><td>Machado et al.<sup>39</sup></td><td>https://imagej.net/plugins/limeseg</td></tr><tr><td>Limeseg Cyst/Lumen volume segmentation</td><td>This study</td><td>https://github.com/Honigmann-Lab-BIOTEC/Tight-junctions-control-lumen-morphology-via-hydrostatic-pressure-and-junctional-tension/tree/main<br>https://doi.org/10.5281/zenodo.12168170</td></tr><tr><td>Graphpad Prism</td><td>Graphpad</td><td>https://www.graphpad.com/features</td></tr><tr><td>Origin</td><td>Originlab</td><td>https://www.originlab.com/</td></tr><tr><td>Surface Evolver</td><td>Brakke<sup>21</sup></td><td>https://kenbrakke.com/evolver/evolver.html</td></tr></tbody></table>

## RESOURCE AVAILABILITY

### Lead contact

Further information and request for resources and reagents should be directed to and will be fulfilled by the lead contact, Alf Honigmann (alf.honigmann@tu-dresden.de).

### Materials availability

All unique/stable reagents generated in this study are available from the lead contact with a completed Materials Transfer Agreement.

### Data and code availability

Code to analyse lumen volume and Matlab code to analyse junctional recoil available at database: (https://github.com/Honigmann-Lab-BIOTEC/Tight-junctions-control-lumen-morphology-via-hydrostatic-pressure-and-junctional-tension)(https://doi.org/10.5281/zenodo.12168170). Any additional information required to reanalyze the data reported in this work paper is available from the lead contact upon request.

## EXPERIMENTAL MODEL AND STUDY PARTICIPANT DETAILS

### MDCK-II cells

MDCK-II cells were cultured in MEM (Gibco™), 5% FBS (Gibco™) with 1 mM of sodium pyruvate (Gibco™) and 1% of 100x MEM Non-Essential Amino Acids (Gibco™) at 37°C with 5% CO2. ZO1/2 knockout MDCK-II (ZO-KO) as well as MDCK-II WT-ZO1-mNeonGreen were created by Beutel et al.¹³ using Crispr/Cas13. As stated in Beutel et al.,¹³ immunostaining and Western blot analyses of the ZO1 and ZO2 dKO cell line showed a residual expression of 2-3% of the wild-type levels. Claudin quin-KO MDCK-II cells were obtained from the Furuse lab.⁷ For N-terminal endogenous labelling of myosin with mNeon in WT, ZO-KO, CLDN-KO cells, the myosin-2-A exon was targeted using Crispr/Cas. To generate stable CLDN-KO FLAG-Cldn2 cells, CLDN-KO cells were seeded and incubated at 50% confluency with a 50:50 mixture of retrovirus -containing and normal medium. After two days, successfully transduced cells were selected with 3 µg/mL puromycin and maintained in 2 µg/mL starting one day later. Retrovirus was produced as described in Gonschior et al.¹⁶ To generate stable CAAX-HALO, dendra2-CD164 or mCherry ZO1 cells, the gene of interest was incorporated into a mammalian expression plasmid (from the pOCC series) featuring the desired tag and a Neomycin-Geneticin resistance selection marker. Transfection was performed using Lipofectamine 2000 (Invitrogen™), followed by selection of transgenic cell lines in the presence of geneticin (400 µg/ml).

## METHOD DETAILS

### Three-dimensional culture of MDCK cysts and drug treatment

MDCK cysts were cultured as previously described,⁴⁰ in brief: MDCK monolayers were dissociated and either embedded in Matrigel (Corning, USA) for the pseudo-time-laps assay or seeded on 0.5 mg/ml laminin (Roche Diagnostics, Switzerland) coated 35-mm glass-bottom dish (MatTek Corp., USA) containing 5% of Matrigel for the other assays referred to in this manuscript. Cells were then cultured for 4-5 days and subsequently imaged. For perturbation of actomyosin contractility by ROCK inhibition, Y-27632 dissolved in DMSO was applied to the culture media with 200µM working concentration.
Trans-epithelial cyst permeability assay

3D adherent cysts were cultured as already described for 4 to 5 days in 37 °C 5% CO₂ until reaching 30 to 40 µm in diameter. To measure permeability of small solute (10kDa Dextran- Alexa Fluor 647 (Invitrogen™, D22914)), cyst medium was supplemented with CellMask Orange to visualize cell membranes, 4 hours prior Dextran addition. After washing, the medium was supplemented with 10µM Dextran-Alexa647. After 15min incubation, cysts were imaged on a confocal microscope to evaluate distribution of Dextran-Alexa647.

Lumen sphericity measurement

To determine how close the lumen shape resembles a sphere, the sphericity (Ψ) was calculated by comparing the surface area (A) and to the surface area of a perfect sphere with the measure lumen volume (V): $\psi = \frac{\pi^{1/3}(6V)^{2/3}}{A}$. A sphericity of 1 refers to a perfect sphere while a highly irregular lumen approaches a sphericity of 0.

Drainage of lumen and quantification of hydrostatic lumen pressure

WT, CLDN-KO and ZO-KO cells stably expressing HaloTag-CAAX were cultured with the laminin-based method for 5 days to form cysts. Prior to the experiment, cysts were incubated in culture media with 200 nM of Janelia Fluor® 646 HaloTag® ligand overnight to visualize the membranes.

The cysts were cut open by ablating one cell using a Zeiss LSM 780 NLO system (Zen Black software version 11.00) with a 2-photon laser (Titinium/Saphire) at 800 nm (Coherent, Santa Clara, USA) with a power of 3.2 W at the laser head and 100% laser output set in Zen Black. A line scan with a width of 3 µm and 5-line repetitions across the epithelium at the middle plane of a cyst was typically sufficient to open the lumen to the outside. Lumen collapse was imaged by taking 3D stacks of the cysts with a time resolution of 15 seconds.

To characterize the experiments quantitatively, we segmented the lumen in 3D over time and plotted the change of lumen volume as a function of time. These measurements allow us to calculate the initial flow as a key readout to evaluate hydrostatic luminal pressure. We also measured the channels dimensions using the passage of the fluorescent mucin (see Figure 3C).

To obtain the hydrostatic lumen pressure before the cut, we modelled the flow going out of the cyst as a Hagen-Poiseuille flow of a liquid of viscosity η at a flow rate Q in a channel of radius R and length L:

$$ \Delta P = P_{in} - P_{out} = \frac{8\etaQL}{\pi R^4} $$

We estimated the error on ΔP, based on the experimental measurement errors on the parameters:

$$ \delta_{exp}(\Delta P) = \sqrt{\left(\frac{(\delta\eta)^2(8QL)^2}{(\pi R^4)^2} + (\delta Q)^2\frac{(8\eta L)^2}{(\pi R^4)^2} + (\delta L)^2\frac{(8Q\eta)^2}{(\pi R^4)^2} + (\delta R)^2\frac{(32\eta QL)^2}{(\pi R^5)^2}\right)} $$

$$ \text{And: } \frac{\delta_{exp}(\Delta P)}{\Delta P} = \sqrt{\left(\frac{(\delta\eta)^2}{\eta} + \frac{(\delta Q)^2}{Q} + \frac{(\delta L)^2}{L} + \frac{(4\delta R)^2}{R}\right)} $$

Where we measured for WT cysts:

$$ -R \pm \delta R = 1.0 \pm 0.1 \mu m $$

$$ -L \pm \delta L = 3.2 \pm 0.1 \mu m $$

$$ -Q \pm \delta Q = 900 \pm 100 \mu m^3 \cdot s^{-1} $$

$$ -\eta \pm \delta\eta = 5.1 \pm 1.7 \text{ mPa}\cdot\text{s} $$

This yields: $\delta_{exp}(\Delta P) \approx 20 Pa$ and: $\frac{\delta_{exp}(\Delta P)}{\Delta P} \approx 30\%$. To compare to the statistical errorbars and the measured values for WT: $\Delta P_{WT} = 65 \pm 15$ Pa with a statistical error of 15 Pa. By combining the two sources of errors we get $\delta(\Delta P) = (\delta_{exp}^2(\Delta P) + \delta_{stat}^2(\Delta P))^{1/2} = \text{and} \Delta P_{WT} = 65 \pm 25$ Pa. And a relative error of 38%.

We note that this approach to measure the pressure difference between the lumen and the extracellular fluid may provide a lower boundary to the actual pressure difference, because we do not consider any contributions of deforming tissue (viscosity), which may slow down the outflow of fluid.
Measurement of lumen fluid viscosity

Viscosity of the luminal fluid was measured using fluorescence correlation spectroscopy (FCS) of dendra2-tagged soluble sialomucin (Dendra2-CD164) on an Abberior STED microscope (Abberior Instruments, Göttingen, Germany). The concentration of dendra2-mucin in the luminal fluid was typically too high for FCS. Therefore, we photo-converted a small fraction of dendra2 into the red-emit- ting form using a short scan of 405 nm light. FCS measurements were then performed using 561 nm excitation (20μW back focal plane) using a 60x water objective to measure the diffusion of the photo-converted dendra2-mucin in the lumen. FCS curves were fitted using a 3D diffusion model including triplet blinking as described previously.⁴¹ To determine the viscosity in the lumen the diffusion times of dendra2-mucin in the lumen were compared to diffusion times of the same molecule in standard 2D cell culture medium with µ (DMEM @ 37°C) = 0.9 mPa*s (MDCK monolayer on glass) (Figure S1).

Three-dimensional segmentation of MDCK cysts

Fluorescent Z-stacks of MDCK cysts were acquired by confocal microscopy. The images were processed with median filter to better
preserve the structures. All reconstructions of three-dimensional images were performed with LimeSeg³⁹ plugin from Fiji. The seg-
mentation on the 4-D recordings of lumen formation was performed using a groovy script that automatically operated LimeSeg to
multiple time points where segmented dots of present time point were applied to next time point as ROI for segmentation. The
geometrical information measured with segmented mesh was automatically saved. The number of cells of a cyst was quantified
with TrackMate of Fiji on the nuclei signals.

Junctional recoil measurement

Laser ablation was performed on Zeiss LSM 780 NLO system driven by Zen Black software version 11.00. Images pixel size was 0.268 µm x 0.2268 µm. Objective used was Zeiss C- Apochromat 40x/1.2 W. Ablation was performed with 800 nm Titanium/Sapphire femtosecond pulsed laser Chameleon from Coherent (Santa Clara, USA) with a power of 3.2 W at the laser head, 60% laser output set in Zen Black, reflected by MBS 760+, with pixel dwell time for photomanipulation of 7.2 µs, single iteration, ablation area was line scan, 10 pixels. For measuring the recoil velocity, the lateral junction of MDCK WT or CLDN-KO and ZO-KO cells was highlighted by ZO1-mNeonGreen or MyosinIIa-mNeon green respectively with the following settings: mNeonGreen was excited with 488 nm (Argon Laser) with MBS 488/561/633, emission filter used was 490-570 nm, pixel dwell time 2.83 µs, approximately 7.7 fps with GaAsP detector. Recoil distance was determined using a custom MATLAB script, which tracked the distance of the tri-cellular vertices over time. Initial recoil velocity was determined by dividing the initial change in vertex distance by the time interval.

Immunostainings of MDCK tissue

Samples were fixed with 4% w/v Paraformaldehyde (PFA) pH 7.25 in PBS for 10 minutes at room temperature. For pseudo time-lapse imaging samples were fixed with 4% PFA + 0.025% v/v Glutaraldehyde in PBS for 10 minutes at room temperature to prevent cells being washed away due to PFA incubation. Cells were then permeabilized with 0.5% v/v Triton X-100 in PBS for 10 minutes and blocked with the blocking buffer (2% w/v BSA, 0.02% v/v NaN3) in PBS for 1 hour at room temperature or overnight at 4°C followed by diluted secondary antibodies and labelled phalloidin incubation. Primary antibodies used were: Rabbit anti-gp135/podocalyxin (1:200; from Merck); Mouse anti-E-Cadherin (1:100; from MPI-CBG antibody facility).

Confocal microscopy

Live cell imaging: the images were acquired with a Zeiss Axio Observer.Z1 inverted microscope (ZEISS, Germany) equipped with a CSU-X1 spinning disc confocal scanning unit (Yokogawa, Japan), driving a Zeiss AxioCam MRm, Monochrome CCD camera. The images were acquired with a x63 1.2 NA water objective lens (ZEISS, Japan) and a x100 1.46NA alpha Plan-Apochromat oil objective lens (ZEISS, Japan) and ZEN blue software (ZEISS, Germany). Z-stacks were acquired with a distance of 300 nm.

Cyst inflation in microfabricated cavities

To increase the volume of the lumen, we applied a local liquid flow using a micro-pipette to cysts growing in microfabricated cavities, which prevented detachment and movements of cysts (see below). Application of liquid flow led to the rapid inflation of the cyst within seconds, which was reversible (see Figure 6). In addition, we found that fluorescent Dextran, present in the pipette solution, entered the lumen, which indicates that the liquid stream opened cell junctions and presses liquid into the lumen (see Figures 6A and 6B).

The inflation experiments were quantified by segmenting lumen and cyst shape before and after inflation to extract tissue and cell
shape changes in response to the hydrostatic pressure perturbations.

The micro-cavities were prepared by soft lithography.²² Briefly, a mask with 18 µm disks with 100 µm inter-distance was designed with Autocad, which was then printed on photomask. The pattern was transferred to SU8 silicon wafer by photolithography. Then a PMDS mold was generated by soft lithography. The PDMS pillar replica were transferred on a cover-glass using plasma activation and chlorotrimethylsilane for passivation and subsequently filled with liquid PDMS. With overnight polymerization at 65°C, the PMDS formed a solid membrane on the cover-glass, and cavities could be obtained by gentle removal of the PDMS stamp. After obtaining through-hole cavities on the cover-glass, the surface was activated by plasma and then incubated with 5 µg/ml laminin at room
temperature. Cells were seeded in cavities by centrifugation.⁴² Then 15µl Matrigel was added on the top of the cavities, which allowed MDCK to form cysts. Cysts were used 5 days after cell seeding for inflation experiments. To facilitate the experiments, Matrigel on top of micro-wells was removed using a needle.

The lumen was inflated by using a pipette pulled with a Sutter pipette puller (P 2000), the tip of the pipette was then broken using a scalpel under a binocular to the expected diameter. The flow was controlled with the Eppendorf Cell Tram Vario. We injected medium (MEM with 5% serum) containing fluorescent Dextran to track the localisation of the liquid. Finally, changes in cell and cyst shapes were monitored live by imaging by using Leica spinning disk (Spinning disk LEICA CSU W1).

## Lumen Model

The lumen shape was calculated based on the minimization of the free energy given by the sum of the contributions from the hydrostatic pressure in the lumen, the line tension at apical junctions of all neighbouring cell pairs and apical bending energy from the apical lumen surface.

$$F = F_{\text{hydr. press}} + F_{\text{line tension}} + F_{\text{bending}} \qquad (\text{Equation 1})$$

$$F = -PV + TL + N_k \int H(r)^2 \cdot dA \qquad (\text{Equation 2})$$

where P is the pressure of the lumen, V its volume, T the apical line tension, L the total apical line length, N is the number of cells, κ the effective bending energy of the apical membrane, H(r) its mean curvature.

To obtain an analytical solution to this problem, the following geometrical assumptions were made. We consider a spheroid composed of N cells surrounding a lumen filled with fluid. We set lumen surface area or the total apical surface area to be a constant S for a given number of cells N in a spheroid. We assume that the cells are organized approximately in a hexagonal tessellation. For each cell, the line perimeter of this hexagon is given by $P_{hex} = \sqrt{8\sqrt{3}S_{hex}}$. Next, we assume that the surface of this hexagon is close to the surface of the circle that is inscribed in: $S_{hex} = \pi r_a^2$ with $r_a$ the radius of this circle. Then the total line perimeter L for N cells is $L = \frac{1}{2}N\sqrt{8\sqrt{3}\pi r_a^2} = Nr_a\sqrt{\pi\sqrt{6}}$. We assume each cell has an apical surface that can be described as a paraboloid with a base circle of radius $r_a$ and of depth h. Note that h can be positive or negative. The volume of such paraboloid is $V_{paraboloid} = \frac{1}{2}\pi r_a^2 h$ and its surface is⁴³: $S_{paraboloid} = \frac{\pi r_a}{6h^2}[(r_a^2+4h^2)^{\frac{3}{2}} - r_a^3]$ and, by construction, the apical area of each cell is given by $S = \frac{S_{paraboloid}}{N}$. Then, the volume of the lumen is: $V = \frac{4}{3}\pi r_a^3 + \frac{N}{2}\pi r_a^2 h$ where $r_{int}$ is the radius of the sphere connecting all apical vertices.

$H(r)$ is the local mean curvature in Equation 2. We assume zero spontaneous curvature and considered only the lowest-order terms of curvatures i.e $O(H^2)$ and $O(K^1)$ with the Gaussian curvature K; the Gaussian-curvature term is omitted since $\int dA K$ is constant unless topology of the lumen surface changes due to Gauss-Bonnet Theorem.⁴⁴ We further assume that the minimization of F is given under the constraint that the total lumen surface S should be split equally on each individual cell:

$$\frac{S}{N} = S_{\text{paraboloid}} = \frac{\pi r_a}{6h^2} [(r_a^2+4h^2)^{\frac{3}{2}} - r_a^3] \qquad (\text{Equation 3})$$

## Apical surfaces with no bending energy

We first consider the simpler case where the lumen morphology is determined by minimizing the free energy of the lumen surface, $F_1$.

$$F_1 = F_{\text{hydr. press.}} + F_{\text{apical junctional tension}} = -PV + TL$$

In this case, we can derive the existence of a transition line between two states: an inflated lumen or a fully collapsed lumen (Figures S4A and S4B). With the above parametrization it is possible to compare the free energy of an observed flower lumen shape with a spherical lumen. If we set the free energy of the flower shape to 0:

$$F_{\text{spherical lumen}} - F_{\text{flower lumen}} = -P \frac{S^2}{6\sqrt{\pi}} + T \sqrt{2SN\sqrt{3}}$$

We have $F_{\text{spherical lumen}} < F_{\text{flower lumen}}$ (spherical lumen shape stable) if:

$$T < \frac{PS}{\sqrt{72\pi N\sqrt{3}}}$$

The line $T = \frac{PS}{\sqrt{72\pi N\sqrt{3}}}$ defines two regions in the $(P, T)$ phase diagram for lumen surface. If $T < \frac{PS}{\sqrt{72\pi N\sqrt{3}}}$, then $F_{\text{spherical lumen}} < F_{\text{flower lumen}}$ and spherical lumen is stable. Otherwise, the flower shape is stable.
## Apical surfaces with a bending energy

To compute the bending energy of the apical surface, one needs to express its mean curvature, with $r$, parametrizing the radius at height $z$, the paraboloid is parametrized as $z = S(r) = \frac{r^2}{2\rho}$, with $\rho = \frac{r_a^2}{2h}$. Then the mean curvature of this paraboloid can be computed as:

$$2H(r) = \frac{\frac{\partial^2 S}{\partial r^2}}{\left(1 + \left(\frac{\partial S}{\partial r}\right)^2\right)^{\frac{3}{2}}} + \frac{\frac{\partial S}{\partial r}}{r\left(1 + \left(\frac{\partial S}{\partial r}\right)^2\right)^{\frac{1}{2}}}$$

so that

$$H(r) = \frac{\frac{1}{2\rho}\left(2+\left(\frac{r}{\rho}\right)^2\right)}{\left(1+\left(\frac{r}{\rho}\right)^2\right)^{\frac{3}{2}}}$$

We can now compute the free energy corresponding to the bending of the apical surface of cells:

$$\iint dA \cdot H(r)^2 = \int_0^{2\pi} d\theta \int_0^{r_a} dr \left[ r \left(1 + \left(\frac{r}{\rho}\right)^2\right)^{\frac{1}{2}} \frac{1}{4\rho^2} \frac{\left(2 + \left(\frac{r}{\rho}\right)^2\right)^2}{\left(1 + \left(\frac{r}{\rho}\right)^2\right)^3} \right] = \frac{\pi}{2} \left[ \frac{4}{3} + \frac{1}{3\rho} \frac{3r_a^4 - 4\rho^4}{3} \right] = \frac{\pi}{6} \left[ 4 + \frac{\left(\frac{6h}{r_a} - \frac{r_a^3}{2h^3}\right)}{\left(1 + \left(\frac{r_a}{2h}\right)^2\right)^2} \right]$$

Altogether, we obtain for the total free energy $F$:

$$F(r_a, h, P, T, \kappa, N) = -P \left[ \frac{4}{3} \pi \left(\frac{N}{4}\right)^{\frac{3}{2}} r_a^3 + \frac{N}{2} \pi r_a^2 \right] + T N r_a \sqrt{\pi \sqrt{6} + \frac{\pi N \kappa}{6}} \left[ 4 + \frac{\left(\frac{6h}{r_a} - \frac{r_a^3}{2h^3}\right)}{\left(1 + \left(\frac{r_a}{2h}\right)^2\right)^2} \right] \quad (\text{Equation 4})$$

In addition, for a given $r_a$, it is possible to compute the corresponding $h$ from Equation 3, which can be rewritten as:

$$64 h^4 + h^2 \left(48 r_a^2 - \frac{36 S^2}{\pi^2 N^2 r_a^2}\right) + 12 \left(r_a^4 - \frac{S r_a^2}{\pi N}\right) = 0 \quad (\text{Equation 5})$$

In summary, one can compute $F(r_a, h, P, T, \kappa, N)$ from Equation 4 with $h$ given as a solution of Equation 5 and compute a phase diagram in the $(P, T)$ parameter space for the inner lumen radius. Ranges of parameters are taken from experimental values (see parameter table) and are consistently used in Figure S4 and in Figure 5 with the vertex model.

## Differences between the two phase diagrams

The linear relation described in paragraph 2 can be seen in Figure S4 with the addition of bending energy of the apical side, the slope of the transition line shifts towards higher values. This analytical model also allows to probe the influence of the total number of cells and of the total lumen surface as illustrated in Figure S4C. When the total apical surface $S$ increases the slope of the transition line scales up as well. Similarly, when the total number of cells $N$ in the cyst increases the slope of the transition line decreases. This is consistent with the estimation of the transition line from the simplified model obtained in paragraph 2. The region of the phase diagram where the folded shape is more stable increases in size when $N$ increases. When $N$ increases, the inner lumen radius also increases for a given set of $(P, T)$ values.

## Parameter choice

To estimate the junctional line tension $T = \zeta v$ from the recoil velocities $v$ determined by laser ablation experiments (Figure 4) we used a damping coefficient of $\zeta = \eta_{\text{cortex}} \eta_{\text{cortex}} = 50pN \cdot s/\mu m$. For this we take the typical value of $\eta_{\text{cortex}} = 200$ Pa. s$^{45}$ and a cortical length of $l_{\text{cortex}}=500$nm. Using these values with $v = 10$ $\mu m/s$ gives line tensions in the range of $T = 1000$ pN (see parameter table below), which corresponds to about $10^4$ myosin motors applying a 0.1pN mean force,$^{46}$ We assume the same $\zeta$ damping coefficient for the different MDCK-II-mutants because the change in myosin expression levels is related to the changes in tension and not in viscosity of the cortex.
In our model, the complex mechanics of cell bulk, surfaces, and adhesions which in principle conspire to resist protrusion of apical surface into the cell interior⁴⁷ are collapsed into a single penalty for bending of the apical surface, quantified by an effective bending modulus. Through a manual parameter search, we found 2.10-16J is a good match to the experimental results. This value (~50,000 kBT) is much higher than what has been estimated for actin cortex (e.g. 400 kBT in Dictyostelium⁴⁸) because it effectively includes contributions from other mechanics.

## Shape calculation with Surface Evolver

3D shapes of lumen were calculated using Surface Evolver²¹ by minimizing the energy:

$$F = -PV + TL + K \int dA \cdot H^2 + \sum_{i=1}^{N} M(A_i - A_0).$$

By term, the contributions are: the contribution from the fluid inside the lumen, where *P* is the pressure and *V* is the volume, contribution from the junctions, where *T* is the tension and *L* is the total junction length, bending of the apical surface, where *K* is the bending modulus and *H* is the mean curvature which we integrate over the surface, and finally area conservation, where *M* is the area modulus, *A*<sub>i</sub> is the area of cell *i* and *A*<sub>0</sub> is the preferred cell area (equal to *S*/*N*, where *S* is the total surface area and *N* is the total number of cells). Energy minimization was accomplished using the Surface Evolver programming language.²¹ Briefly, a surface consisting of 42 polygonal faces was imported into Surface Evolver. These 42 faces consist of a mixture of pentagons and hexagons, as dictated by Euler's formula. The edges between the polygonal faces were marked to represent junctions. The surface was then triangulated and transformed into a sphere of surface area *S*. The energy function above was then applied and the surface evolved toward minimum energy with Surface Evolver's gradient descent tools. A high area modulus was used to ensure cell areas remain approximately constant.

Parameters taken for computation of the phase diagram of Figure 5:

<table><thead><tr><th>Common to all parameter sets</th><th>Value</th></tr></thead><tbody><tr><td>Total surface area <i>S</i></td><td>2,500 µm<sup>2</sup></td></tr><tr><td>Number of cells <i>N</i></td><td>42</td></tr><tr><td>Effective Bending energy <i>K</i></td><td>2·10<sup>-16</sup> J = 200 pN µm</td></tr><tr><th>Parameter with ranges</th><th>Range</th></tr><tr><td>Hydrostatic Pressure</td><td>From 0 to 100 Pa</td></tr><tr><td>Apical Line Tension</td><td>From 0 to 3,000 pN</td></tr></tbody></table>

Parameters taken for computation of the lumen shapes (surface evolver) of Figure 5:

<table><thead><tr><th>Common to all parameter sets</th><th>Values</th></tr></thead><tbody><tr><td>Total surface area <i>S</i></td><td>2,500 µm<sup>2</sup></td></tr><tr><td>Number of cells <i>N</i></td><td>42</td></tr><tr><td>Bending energy <i>K</i></td><td>2·10<sup>-16</sup> J = 200 pN µm</td></tr><tr><td>Area modulus <i>M</i></td><td>1·10<sup>-14</sup> J/µm<sup>2</sup>= 10,000 pN /µm</td></tr></tbody></table>

<table><thead><tr><th>Parameter set label</th><th>Tension <i>T</i> (pN)</th><th>Pressure <i>P</i> (Pa = pN/micron<sup>2</sup>)</th></tr></thead><tbody><tr><td>1</td><td>3,000</td><td>10</td></tr><tr><td>2</td><td>3,000</td><td>50</td></tr><tr><td>3</td><td>3,000</td><td>90</td></tr><tr><td>4</td><td>2,000</td><td>10</td></tr><tr><td>5</td><td>2,000</td><td>50</td></tr><tr><td>6</td><td>2,000</td><td>90</td></tr><tr><td>7</td><td>1,000</td><td>10</td></tr></tbody></table>

(Continued on next page)
**Continued**

<table><thead><tr><td>Parameter set label</td><td>Tension T (pN)</td><td>Pressure P (Pa = pN/micron<sup>2</sup>)</td></tr></thead><tbody><tr><td>8</td><td>1,000</td><td>50</td></tr><tr><td>9</td><td>1,000</td><td>90</td></tr><tr><td>10</td><td>0</td><td>10</td></tr><tr><td>11</td><td>0</td><td>50</td></tr><tr><td>12</td><td>0</td><td>90</td></tr></tbody></table>

**QUANTIFICATION AND STATISTICAL ANALYSIS**

Images were analyzed using FIJI (https://fiji.sc/) and MATLAB (MathWorks). Statistical analyses were conducted with GraphPad Prism and Origin. Data are presented as mean ± standard deviation (SD), mean ± standard error of the mean (SEM), or mean ± 95% confidence intervals, as indicated in the figure legends and results from three or more independent experiments. The value of n and its representation are specified in the figure legends and results. One-way ANOVA was used to compare means of more than two groups with one independent variable and one dependent variable. Welch's ANOVA was used for one-way analysis of variance with repeated measures.