The Biomechanical Basis of Biased Epithelial Tube Elongation

During lung development, epithelial branches expand preferentially in longitudinal direction. This bias in outgrowth has been linked to a bias in cell shape and in the cell division plane. How such bias arises is unknown. Here, we show that biased epithelial outgrowth occurs independent of the surrounding mesenchyme. Biased outgrowth is also not the consequence of a growth factor gradient, as biased outgrowth is obtained with uniform growth factor cultures, and in the presence of the FGFR inhibitor SU5402. Furthermore, we note that epithelial tubes are largely closed during early lung and kidney development. By simulating the reported fluid flow inside segmented narrow epithelial tubes, we show that the shear stress levels on the apical surface are sufficient to explain the reported bias in cell shape and outgrowth. We use a cell-based vertex model to confirm that apical shear forces, unlike constricting forces, can give rise to both the observed bias in cell shapes and tube elongation. We conclude that shear stress may be a more general driver of biased tube elongation beyond its established role in angiogenesis.


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Epithelial tubes are an essential component of many organs. During development, epithelial tubes 36 elongate (Fig. 1A). Tube elongation can be either isotropic or anisotropic, i.e. the tubes either lengthen as 37 much as they widen, or there is a bias in outgrowth (Fig. 1B). Growth is by default isotropic, and a bias in 38 elongation can therefore only arise if growth symmetry is broken in the epithelium. How this symmetry 39 break is achieved is largely elusive. We will focus here on the mouse embryonic lung and kidney. In the 40 mouse lung, epithelial tube expansion is anisotropic initially (E10.5-E11.5), but, at least in the trachea, 41 becomes isotropic at later stages (from E12.5) (Kishimoto et al., 2018;Tang et al., 2011; 42 2018). The biased outgrowth has been related to a bias in the orientation of the mitotic spindles of 43 dividing cells (Saburi et al., 2008;Tang et al., 2011;Tang et al., 2018;Yates et al., 2010). According to 44 Hertwig's rule (Hertwig, 1884), cells divide through their mass point and perpendicular to their longest 45 axis. Indeed, the bias in cell division is accompanied by a bias in cell shape  46 2018). The planar cell polarity (PCP) pathway plays an important role in regulating the mitotic spindle 47 angle distribution in many organs, including the embryonic renal tubes (Ciruna et al., 2006;Gong et al., 48 2004;Saburi et al., 2008), though no such involvement could be ascertained for the early stages of lung 49 development . Independent of whether the PCP pathway is involved, it remains an 50 open question how the elongation bias and its direction arise in the first place.

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In principle, a bias in outgrowth could originate from polarization along the tube, from a pulling force at 53 the tip, or from a mechanical constraint that limits expansion in the circumferential direction. Several 54 signalling pathways are known to affect the bias in lung tube elongation. Thus, hyperactive KRas 55 (KRasG12D) in the lung epithelium abrogates the bias in outgrowth during lung branching morphogenesis 56 , and pharmacological reagents that activate or inhibit fibroblastic growth factor (FGF) 57 signalling, sonic hedgehog (SHH) signalling, or L-type Ca2+ channels affect the width of cultured lung 58 buds (Goodwin et al., 2019). FGF10 and Glial cell line-derived neurotrophic factor (GDNF) signalling 59 are necessary for the formation of branches in the lung and kidney, respectively (Michos et al., 2010;Min 60 et al., 1998;Moore et al., 1996;Pichel et al., 1996;Rozen et al., 2009;Sanchez et al., 1996;Sekine et al., 61 1999). FGF10 has been proposed to act as chemoattractant because it is secreted from the submesothelial 62 mesenchyme, and isolated lung epithelia grow towards an FGF10 source (Park et al., 1998). However,

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Gdnf is expressed uniformly in the ureteric cap mesenchyme (Hellmich et al., 1996), and branching 64 morphogenesis is still observed when Fgf10 is expressed uniformly in the lung mesenchyme (Volckaert et In this paper, we sought to systematically analyse the minimal requirements for biased epithelial tube 89 elongation. To this end, we cultured mouse embryonic lungs and kidneys under different conditions and 90 quantified the length and width of the branches for up to 60h. We show that the mesenchyme is not 91 necessary as biased elongating outgrowth is still observed when epithelial buds are cultured on their own, 92 in the absence of mesenchyme, with uniformly dispersed growth factors. Furthermore, we show that 93 while ERK signalling concentrates at the tip of branching isolated epithelial tubes, there is no evidence 94 for the formation of actin-rich protrusions at the epithelial tips that could guide the biased elongating 95 outgrowth. In early lung and kidney development, epithelial tubes only have a narrow luminal space, and 96 tubular cross-sections are often elliptical rather than round. Despite the non-uniform curvature of such 97 closed tubes, tension, as monitored with actin staining, remains uniform in the epithelium. We show that 98 the predicted shear stress level in the narrow embryonic tubes is within the range that cells can, in 99 principle, sense, and a cell-based model confirms that a tangential apical force, as provided by shear 100 stress, can result in the reported bias in cell shape and elongating outgrowth. 101 102 103 104

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Biased epithelial lung tube elongation

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Given the reports that the trachea switches from anisotropic to isotropic expansion around E12.5 109 (Kishimoto et al., 2018), we sought to measure the length and circumference of the bronchus of the left 110 lobe (LL) between E10.5 and E14.5. For this, we used the ShhGC/+; ROSAmT/mG transgenic mouse line, 111 which expresses green fluorescent protein (GFP) in the cell membrane of the lung epithelium ( Fig. 1A, C, 112 D). Here, we averaged the circumference over the entire 3D bronchus, except for the parts where side 113 branches form (Fig. S1). We confirm the previously reported 2-fold stronger longitudinal than 114 circumferential expansion between E10.5 and E11.5 , and find that, much as in the 115 trachea, there is a switch to isotropic growth at later stages, though a day later (E13.5) than in the trachea.

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The substantial widening of the bronchus thus occurs after the emergence of cartilage and smooth 117 muscles (Hines et al., 2013;Schittny et al., 2000). Between E11.5 and E13.5, the bronchus still lengthens 118 more than it widens, even though the overall rate of growth declines (Fig. 1E).

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Each 3D length measurement in Fig. 1D,E comes from a different embryo, and we notice a certain level 121 of variability between the specimen. Part of the differences can be accounted to differences in 122 developmental progress, that is observed even in embryos from the same litter. To establish a reliable 123 time line of the growth process, we cultured E11.5 embryonic lungs for 48h on a filter and measured the 124 lengths and average diameter of the branches (Fig. 1F, Fig. S1). Given the development on a filter, there 125 are differences in the branch angles, and much as for the 3D specimens, there is considerable variability 126 between lungs. Nonetheless, in all specimens, we observe a similar biased expansion of the left bronchus 127 ( Fig. 1D,E, grey) as in the serially isolated embryonic lungs (Fig. 1D,E, green). The cultured lungs 128 elongate slightly less than in the embryo, and there is less of a reduction in the branch width, though this 129 difference may reflect differences in the analysis. The width in the 2D cultures was averaged along the 130 entire branch (Fig. 1F), while the averaged circumference of the 3D specimen excluded the parts where 131 branches emerge (Fig. S1). Overall, the cultured lungs recapitulate the growth process in the embryo very 132 well, and we will therefore use these to analyse the mechanisms that drives elongating outgrowth.

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Mesenchyme is not required for biased epithelial tube elongation during lung and kidney 136 development

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While smooth muscles have recently been shown to be dispensable for lung branching morphogenesis 139 (Young et al., 2020), the mesenchyme is well known to affect branch shapes (Blanc et al., 2012;Lin et al., 140 2003;Sakakura et al., 1976). We, therefore, sought to analyse the impact of the mesenchyme on biased 141 epithelial outgrowth. To this end, we cultured both control lungs and kidneys ( Fig. 2A, C, Video S1, S2) 142 as well as explants, where the epithelium was enzymatically separated from the mesenchyme (Fig. 2E, G,

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Video S3, S4). We used homogeneously distributed suitable growth factors in each case (Materials and 144 Methods), and analysed the three lateral domain branches in the left bronchus (LL1-LL3), and two 145 branches in the ureteric bud (UB). We find that these five branches all decrease in their average diameter 146 as they elongate ( Fig. 2A-D). As a result, the elongation bias is even more pronounced than for the left 147 lung bronchus. Both lung and ureteric buds still show biased elongating outgrowth when cultured in the 148 absence of mesenchyme ( Fig. 2F-H). This excludes a possible wall-like restrictive force, a pulling force, or 149 other polarity cues from the mesenchyme as a necessary driver of epithelial tube elongation. It also 150 confirms that smooth muscles are not necessary for biased elongating outgrowth. We note, however, that 151 in the case of the ureteric bud, the branches elongate less and remain wider in the absence of 152 mesenchyme. This shows that the mesenchyme impacts the elongation process, even though it is not 153 necessary for biased elongation.

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Biased outgrowth is not the result of FGF signalling at the tip

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Given that biased epithelial outgrowth occurs while isolated explants are exposed to uniform growth 159 factor concentrations (Fig. 2), a necessary polarity in the form of an external growth factor or morphogen 160 gradient can be ruled out. However, as branching is still observed with homogeneous distributions of

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To explore the possible mechanical effects that can lead to the observed collapse of epithelial tubes, and 184 whether this could provide cues for biased tube outgrowth, we conducted continuum-mechanical finite 185 element simulations in a two-dimensional cross-section perpendicular to the tube axis (Fig. 5A). In our 186 numerical model, the tubular epithelial tissue was represented by an isotropic, linearly viscoelastic 187 continuum, neglecting the cellular structure of the tissue. The epithelial material properties were therefore 188 characterized by a Young modulus E and a Poisson ratio . As an initial condition, we chose a tubular 189 shape with uniform radius R (measured from the cylinder axis to the middle of the tissue), and the relative 190 tissue thickness was set to t/R=0.5. The epithelium was set to be intrinsically uncurved, such that a stress-191 free configuration would be a flat tissue. We used a custom-built finite element simulation framework 192 (Vetter et al., 2013) (Materials and Methods).

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We considered three different collapse scenarios. In the first, a uniform net pressure difference P was 195 applied, corresponding to either a pressure drop in the lumen or an increased pressure exerted onto the 196 epithelium by the external environment. The pressure was increased until the critical point of collapse was 197 surpassed. In the second scenario, the epithelial tube was pinched by two rigid parallel clamps slowly 198 approaching one another, mimicking external spatial constraints imposed by a stiff surrounding medium.

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In the third scenario, the enclosed lumen volume V was controlled with a Lagrange multiplier and 6 drained over time until the tube was sufficiently collapsed. Figure 5B shows the equilibrated simulation 201 results for each of the three scenarios. In all cases, both the hoop stress and curvature profiles along the 202 tissue midline are highly nonuniform. Hoop stress is localized almost exclusively in the two extremal 203 points with large curvature. We conclude that, given their non-uniform distribution in the tube cross-204 section, the stress and curvature patterns that arise from the deformation cannot serve as cues for 205 uniform biased outgrowth.

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Stresses can be relaxed rapidly in tissues. We tested experimentally whether the most curved parts remain 208 under increased tension. We find that antibody staining for actin, a read-out for tension in a tissue, is 209 uniform in the closed lung tubes, indicating that there is no increased tension in the curved parts ( Fig.   210 5C,D). It remains possible that a wall-like constraint, in combination with rapid stress relaxation, enforces 211 the elliptic shape and elongating outgrowth. However, it is unclear how such an outer wall-like 212 constricting force would arise even in the absence of mesenchyme. Moreover, we have shown before that 213 a constricting force that results in the observed biased epithelial outgrowth in a cell-based model is 214 insufficient to generate the observed bias in cell shape and cell division (Stopka et al., 2019).

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Consequently, the mechanical constraints explored here are unlikely to drive the biased elongating 216 outgrowth of embryonic lung tubes.

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Shear stress in the developing lung

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The developing lung epithelium secretes fluid into the luminal space (George et al., 2015;Nelson et al.,

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Cells sense shear stress with their cilium (Weinbaum et al., 2011). Epithelial kidney cells are particularly 239 sensitive, with renal collecting duct chief cells responding to apical shear stress as low as 6.8•10-4 Pa 240 (Resnick and Hopfer, 2007), and cultured epithelial kidney epithelial cells responding to 0.075 Pa, but not

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The pressure gradient in the lumen could also, in principle, impact on tube width directly through a fluid-252 structure interaction (FSI). To obtain a flow from the bud tips to the opening of the trachea, the fluid 253 pressure must be highest at the tip and smallest at the tracheal opening (Fig. 6D). In case of a FSI, the 254 shape of the branches would then depend on the local fluid pressure, and buds should be wider than 255 stalks. While stalks are indeed thinner than buds, there is no direct dependency of branch width on the distance from the tracheal opening ( Fig. 6E, Fig. S4, Video S7). A simple way to modulate the pressure at 257 the tips is by altering the distance between the tips and the outlet by culturing lungs either with or without 258 their trachea (Fig. 6E). Removal of the trachea shortens the distance to the outlet, and thus, in case of a 259 constant pressure gradient and flow rate, reduces the pressure difference between the tips and the outlet.

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We find, however, that a removal of the trachea neither impacts branching morphogenesis nor tip shapes 261 ( Fig. 6E,F), which rules out a significant mechanical impact of the fluid pressure on the surrounding 262 epithelium.

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Shear stress forces can result in the observed bias in cell shape and outgrowth

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In a final step, we investigated whether shear stress, which results in a biased force in the longitudinal 268 direction (

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Shear stress does not directly deform cells, but rather cells sense shear stress via their primary cilium and 279 actively respond with cell shape changes (Galbraith et al., 1998;Weinbaum et al., 2011). However, also 280 this indirect shape change corresponds to a force that the cells generate intracellularly. Accordingly, we 281 represent the effect of shear stress by applying a constant force at the top and bottom of the simulated 282 tissue (Fig. 7A). This results in a uniform force field with uniform relative displacement of cells along the 283 tissue axis (Fig. 7E), as would be expected in case of shear stress. When we apply uniform growth, we 284 find an almost linear increase of the bias in outgrowth with such an external force (Fig. 7E,F). As shear 285 stress is actively sensed and translated by the cells into a change in cell shape (Galbraith et al., 1998), we 286 note, however, that there is not necessarily a linear correspondence between the extracellular shear force 287 and the intracellular force that reshapes the cell. Other force response curves could therefore result from 288 the intracellular regulatory processes that respond to the shear stress.

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Between E10.5 and E11.5, the lung tubes elongate twice more than they widen ( Fig. 1E) (Tang et al., 291 2011). We obtain this 2-fold bias in outgrowth with an elongation force of 1 a.u. (Fig. 7F). It has 292 previously been noted that this bias in outgrowth is accompanied by a bias in cell shape and cell division 293 Tang et al., 2018). Cell shape and the cell division axis are linked in that cells in the lung 294 epithelium divide perpendicular to their longest axis when their aspect ratios are greater than 1.53 (Tang 295 et al., 2018). With a force of 1 a.u. and cell division perpendicular to the longest axis, the simulations (

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The elongation of epithelial tubes is a key developmental process. We combined a quantitative analysis of 310 lung and kidney branching morphogenesis with computational modelling to evaluate candidate 311 mechanisms for the biased elongation of epithelial tubes. We show that biased elongation is an inherent 312 property of these epithelial tubes, and that it does not require contact with the mesenchyme or an 313 external chemotactic gradient. We note that the epithelial tubes are largely collapsed in early lung and 314 kidney development, and find that the fluid flow that has previously been estimated for early lung 315 development (George et al., 2015) could result in shear stress levels that epithelial cells can, in principle,

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sense with their primary cilium (Weinbaum et al., 2011). We evaluate the impact of shear stress in a cell-317 based tissue model, and find that shear stress, unlike constricting forces (Stopka et al., 2019), can explain 318 both the observed biased tube elongation and the observed bias in cell division. Shear stress may thus be 319 a more general driver of biased tube elongation beyond its established role in angiogenesis (Davies, 2009; 320 Galbraith et al., 1998;Galie et al., 2014).

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Consistent with a role for shear stress in biased lung tube elongation, the bias in cell division and . The cilium is necessary to respond to shear stress because shear stress does not directly deform 326 cells, but rather cells sense shear stress via their primary cilium and actively respond with cell shape 327 changes (Galbraith et al., 1998;Weinbaum et al., 2011). Cells then divide perpendicular to their longest 328 axis (Hertwig, 1884), and the bias in cell shape along the lung tube axis therefore translates into a bias in 329 cell division Tang et al., 2018).

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Given that shear stress is actively sensed and translated by the cells into a change in cell shape (

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KRas has previously also been linked to changes in cell shape and motility in airway epithelial cells by 348 affecting cortical actin (Fotiadou et al., 2007;Okudela et al., 2009), and the KRasG12D mutation has been 349 found to upregulate multiple ECM components in the pancreatic stroma (Tape et al., 2016).

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While biased tube elongation is observed in isolation, independent of the mesenchyme, we find that the

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Shear stress only has the potential to drive biased elongating outgrowth because the epithelial tubes are so 367 narrow in early lung and kidney development. In later stages, tubes are wide and open. The same level of 368 apical shear stress would then require much higher flow rates, and tube growth indeed becomes isotropic.

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It remains unclear why the tubes collapse in early developmental stages. Mechanical effects that could, in 370 principle, cause the collapse of the tubes would result in the highest mechanical stress levels in the curved 371 parts. Accordingly, neither curvature nor hoop stress (Hamant et al., 2008) could explain the biased 372 uniform outgrowth of the collapsed tubes. We note that staining for actin, a read-out for tension within 373 tissues, is uniform in the closed tubes, suggesting that any stress that may have been generated during the 374 collapse is quickly relaxed away. Going forward it will be important to identify the cause for tube collapse 375 and understand its potential impact in biasing elongating outgrowth.

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Similarly, measurements of the fluid velocity are required. In the mouse lung, fluid flow is well visible at

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The Shh-cre allele was used to drive Cre recombinase-mediated recombination of the ROSAmT/mG allele.

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As recombined EGFP localizes to the cell membrane, and Shh is only expressed in the lung bud epithelium, 420 individual cell morphology could be segmented.

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Immunofluorescence, optical clearing and light-sheet imaging

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Whole-mount tissue clearing of dissected embryonic explants was performed with the Clear Unobstructed

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In the meantime, LMP hollow agarose cylinders were prepared according to (Udan et al., 2014). Hollow 503 cylinders allow for unencumbered 3D embryonic growth, minimize tissue drift, enable imaging from 504 multiple orientations, and allow for better nutrients and gas perfusion. Within a hollow cylinder, a single 505 specimen was suspended in undiluted Matrigel (VWR International GmbH; 734-1101) to recapitulate the 506 in-vivo microenvironment. All cylinders were kept at 37ºC with 5% CO2 in culture media for 1h prior to 507 mounting.

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For an overnight culture, the imaging chamber was prepared first by sonication at 80ºC and subsequent 509 washes in ethanol and sterile PBS. After the chamber was assembled, culture medium and allowed to 510 equilibrate at 37ºC with 5% CO2 for at least 2h before a cylinder was mounted for imaging. Furthermore, 511 to compensate for evaporation over time and maintain a fresh culture media environment, peristaltic pumps 512 were installed to supply 0.4 ml and extract 0.2 ml of culture medium per hour. Each lung explant was then 513 aligned with the focal plane within the centre of a thin light-sheet to enable fine optical sectioning with 514 optimal lateral resolution. For this study, all samples were imaged using a 20x/1.0 Plan-APO water 515 immersion objective.

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Light-sheet datasets were transferred to a remote storage server and processed in a remote workstation 519 (Intel Xeon CPU E5-2650 with 512 GB memory). Deconvolution via Huygens Professional software (SVI) 520 improved overall contrast and resolution while Fiji (ImageJ v1.52t) (Schindelin et al., 2012) was used for 521 accentuating cell membranes, enhancing local contrast, and removing background fluorescence. To extract 522 3D morphological measurements, the length was measured along the centre of Imaris 9.1.2 (Bitplane, South

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Windsor, CT, USA) iso-surfaces, and cross-sections of tubular bronchial portions were masked and 524 exported into Fiji, where 2D circumference was calculated and averaged over the tube.

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Segmentation and skeletonization of 2D culture datasets

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Epifluorescence images of embryonic lung and kidney explants were processed in Fiji (ImageJ v1.52t) 528 (Schindelin et al., 2012). Before segmentation, local image contrast was increased, and image background 529 subtracted. Images were then binarized using a global thresholding method, and boundaries were

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Continuum-mechanical simulations of epithelial tube collapse

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A full technical description of the custom finite element simulation framework that we employed to 542 simulate epithelial tube collapse can be found in (Vetter et al., 2013). In brief, the shape of the epithelium  , and its mass density was set to that of water (1000 562 kg/m3). A no-slip condition was assumed at the interface between the fluid and the surface of the 563 epithelium. To generate fluid motion, the flow rate at the inlet was set to 420 µm3/s (George et al., 2015), 564 and the pressure at the outlet was maintained at 1 atm. The average wall shear stress value on the apical 565 surface was measured with a boundary probe.

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Cell-based simulations of shear stress effect

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We simulated the growth of the lung epithelium subjected to shear stress using a vertex model available in 569 the Chaste framework (Fletcher et al., 2013;Mirams et al., 2013). The dynamics of the vertices were derived from the potential energy of the system, as previously proposed (Nagai and Honda, 2009

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DI conceived the study. HG obtained the light-sheet microscopy data in Figures 1 and 4, and, together 598 with OM, the pERK staining in Figure 3B,C. MD obtained the 3D live imaging data in Figure 4, with 599 support from OM and HG. LC obtained and analysed the lung and kidney culture data in Figures 1 and 2