The biomechanical basis of biased epithelial tube elongation in lung and kidney development

Abstract

During lung development, epithelial branches expand preferentially in a longitudinal direction. This bias in outgrowth has been linked to a bias in cell shape and in the cell division plane. How this bias arises is unknown. Here, we show that biased epithelial outgrowth occurs independent of the surrounding mesenchyme, of preferential turnover of the extracellular matrix at the bud tips and of FGF signalling. There is also no evidence for actin-rich filopodia at the bud tips. Rather, we find epithelial tubes to be collapsed during early lung and kidney development, and we observe fluid flow in the narrow tubes. By simulating the measured 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. This article has an associated 'The people behind the papers' interview.

Keywords: Cell-based tissue simulations; Computational model; Directional growth; Epithelial tube; Light-sheet imaging; Shear stress.

Fig. 1.

Biased epithelial lung tube elongation. (A) Developmental timeline of serial dissections from mouse embryonic lungs expressing the Shh^GC/+; ROSA^mT/mG reporter (green, epithelium). (B) Schematic of isotropic and anisotropic tube expansion. (C) 3D morphometric measurements of epithelial tube length and circumference for an E10.5 left bronchus. (D) 3D length and average circumference measurements of the left bronchus of embryonic lungs (E10.5-E14.5 in green), and 2D length and diameter measurements for E11.5 lungs cultured on a filter over 48 h (grey). (E) Relative width and length for 3D serial dissections (green) and 2D filter-cultured lungs (grey), normalized to their average size at E11.5. (F) 2D morphometric measurements of length and diameter for a filter-cultured E11.5 lung. Width scale (colour bar) in µm. Scale bars: 200 µm (A,F); 50 µm (C).

Fig. 2.

Mesenchyme is not required for biased epithelial tube elongation during lung and kidney development. (A,C,E,G) Epifluorescence (A,C) and brightfield (inverted) (E,G) microscopy images of the lung and kidney epithelium expressing mGFP (A,E) or myr-Venus (C,G), cultured for up to 60 h with (left panels) and without (right panels) mesenchyme. Coloured lines mark the branches analysed in B, D, F and H. Scale bars: 100 µm. (B,D,F,H) Relative width and length measurements of lung and kidney epithelial branches. Data points above and away from the orange line show biased tube elongation. Dot size increases with culture time.

Fig. 3.

Biased outgrowth is not the result of FGF signalling or ECM turnover at the tip. (A) Concentrated growth factor signalling at the tip. (B-D) pERK antibody staining shows localized spots at the tips of an E12.5 embryonic lung (B), an E12.5 kidney (C) and a cultured isolated ureteric bud (UB) (D). Uniform contrast-limit adjustment was applied to 3D-rendered volumes. (E) A pulling force due to cytoskeletal protrusions could drive biased outgrowth. (F,G) Actin staining of E11.5 embryonic lungs shows enrichment at the apical, but not at the basal, tissue boundary. Arrows point to regions of high actin intensity. (H) Relative width and length measurements for the first secondary branch of the left lobe (LL1) of E11.5 control and FGFR inhibitor-treated lungs over 48 h. Different colour shades distinguish different lung samples (n=3 for each condition). (I) Enhanced ECM degradation by MMPs at the tip. (J) Epifluorescence microscopy images of E11.5 control and MMP inhibitor-treated lung epithelium, expressing mGFP, after culture on a filter for 60 h (top). Dashed boxes mark the region of LL1 branches. Fibronectin (FN) antibody staining of LL1 branches (bottom) shows low intensity at the tips, but high intensity in cleft regions of control lungs. Lungs treated with 2.5 µM MMP inhibitor have high fibronectin intensity in both tip and cleft regions. In lungs treated with 20 µM MMP inhibitor, fibronectin is deposited between mesenchymal cells rather than in the basement membrane. Asterisks mark branch tips. (K) Relative width and length measurements for the first secondary branch of the left lobe (LL1) of E11.5 control and MMP inhibitor-treated lungs over 60 h. Different colour shades distinguish the data for different lung samples (n=3 for each condition). Scale bars: 100 µm (B-D); 20 µm (F,G); 200 µm (J, top); 50 µm (J, bottom).

Fig. 4.

Collapsed epithelial tubes in embryonic mouse lungs and kidneys. (A) Tubular sections (yellow dashed outlines) of embryonic lungs have narrow, elliptical luminal spaces, whereas tips and branch points (blue dashed outlines) have wider luminal spaces. (B) Light-sheet microscopy time-lapse imaging of embryonic lung development. Iso-surface overlays highlight shape changes; overall domain volumes are given on the lower left. Cross-sections in boxed regions (shown in lower panels) corroborate dynamic collapsed morphologies in elongating epithelial tubes (yellow dashed outlines). The specimen was imaged for over 40 h every 20 min. (C) Embryonic kidney epithelia display narrowed tubular architectures (yellow outlines in bottom panels). Scale bars: 50 µm (A,B); 25 µm (C).

Fig. 5.

Mechanically forced tube collapse unlikely to result in directional cues for uniform biased outgrowth. (A) Initial tubular configuration and simulated two-dimensional cross-section (red). (B) Collapsed shapes for three scenarios: a uniform pressure difference ΔP (top row, arrows), rigid external clamps (middle row, grey bars) and a reduced lumen volume V (bottom row, hatched area). Colours indicate the hoop stress (left column) in units of Young's modulus E, and the midline curvature (right column) in units of the inverse initial tube radius, 1/R. (C,D) Actin staining is higher at the apical side, but otherwise uniform in cross-sections of closed epithelial tubes from an E11.5 mouse lung. Scale bars: 30 µm.

Fig. 6.

Shear stress in the developing lung. (A) Wall shear stress |τ| for Hagen-Poiseuille flow in a tubular lumen with elliptical cross-section is maximal in weakly curved regions (minor ellipse axis) and minimal in strongly curved regions (major ellipse axis) of the luminal surface. (B) Measurements of flow velocity in the lumen of an E11.5 lung by following injected beads in the right lobe that show directional movement towards the trachea (representative image, n=5). (C) Estimated wall shear stress levels at the apical surface of a 400 µm epithelial tube segment that was extracted between the carina and the first branch of the left lung lobe (LL1) (inset). The lumen geometry after numerical rescaling had an average cross-sectional opening of 2 µm. (D) The lumen geometry presented in Fig. 6B was rescaled with different scaling factors. For each scaling factor, the semi-axis a of the lumen was measured. The average wall shear stress on the apical surface, τ, was calculated for a flow with an average velocity of 0.36±0.13 µm/s (black dots) or a flow rate of 420 µm³/s (blue squares). The error bars correspond to the standard deviation in the flow velocity. The average level of wall shear stress for a given flow velocity can be well approximated from a Hagen-Poiseuille flow profile in an elliptical tube of equivalent size (red line); shaded region corresponds to measured standard deviation. (E) For flow to exist, the fluid pressure must be higher at the tips than at the trachea opening. In the case of a fluid-structure interaction (FSI), the luminal fluid pressure would widen the branches at the tips more than the branches near the trachea. The existence of such an FSI can be tested by reducing the pressure difference between the tips and the outlet. This was achieved by culturing the lungs without their trachea. (F) Epifluorescence microscopy images of E11.5 lung epithelium, expressing mGFP, after culture on a filter for 48 h. The distance of the branches from the tracheal opening was altered by cutting the trachea either below the larynx or above the carina before the culture. Control lungs maintained an intact trachea. (G) Branch width and distance measurements for all branches of the left lobe of the lung cultures in F at the culture endpoint. Different symbol types mark the different culture conditions regarding trachea length. Different colour shades distinguish the data for different lung samples (n=3 for each condition). Branch width does not depend on the distance from the tracheal opening, reflected by low Pearson correlation coefficients (R). Scale bars: 70 µm (B); 200 µm (F).

Fig. 7.

Longitudinally biased forces can result in the observed bias in cell shape and outgrowth. (A) The apical surface of the lung epithelium was simulated with a 2D vertex model. Longitudinally biased external forces were applied to the vertices of the cells at the top-most and bottom-most layers of the tissue. (B) Schematic of the cell-based model. The potential energy of the system is comprised of three contributions. The area elasticity energy U_A penalizes any deviation of the cell area A_k from its target area A_0,k. The constant λ defines how resistant the cells are to deformations. Similarly, the circumference elasticity energy U_C aims to emulate the contractility of the actomyosin ring by penalizing any deviation of the cell circumference C_k from its target circumference C_0,k. The line tension U_L energy gives rise to a force associated with cell-cell adhesion. Low values of γ characterize stable and favourable contacts between cells. (C,D) The cell area (C) and cell shape (D) distributions of E11.5 lung epithelial cells were measured at their apical (green) and basal (yellow) sides. All parameters in the vertex model (purple) were set so that simulated tissues reproduce the measured distributions (n=3 for experimental tissues and n=5 for simulated tissues, error bars show standard deviations). (E) Relative displacement of the cells as a function of their initial positions in the simulated tissues. Regardless of the magnitude of the elongation force applied, the cells are displaced uniformly along the tissue axis. (F) Bias in outgrowth as a function of the elongation forces applied. A force of 1.0 a.u. yields the measured (Tang et al., 2011, 2018) 2-fold elongation bias of lung tubes (n=5, error bars show standard deviations). (G) Distribution of the cell division angles in the simulated tissues in the presence or absence of an elongation force. The elongation force 1.0 a.u. yields a bias in cell division orientation equivalent to the bias reported by Kadzik et al. (2014) and Tang et al. (2011); n=5 for simulated tissues, error bars show standard deviations. (H) Bias in outgrowth of tissues subjected to an elongation force of 1.5 a.u. as a function of their surface tensions or line tensions. High cortical tensions result in reduced biased outgrowth.