Mechanochemical patterning localizes the organizer of a luminal epithelium

Abstract

The spontaneous emergence of tissue patterns is often attributed to biochemical reaction-diffusion systems. In Hydra tissue regeneration, the formation of a Wnt signaling center exemplifies this process. However, a strictly biochemical mechanism for self-organization in Hydra remains elusive. In this study, we investigated mechanical stimuli and identified a positive feedback loop between Wnt signaling and tissue stretching. We developed a mathematical model of mechanochemical pattern formation in a closed elastic shell, representing regenerating Hydra epithelial spheroids. Our model explains how mechanical forces drive axis formation and predict the organizer's location under various perturbations. Validation by partially confining regenerating tissues showed that the organizer forms in regions with the greatest stretching potential. This work highlights a versatile mechanochemical mechanism for luminal epithelium patterning, which is relevant across various biological systems.

Fig. 1.. Wnt signaling enhances tissue stretching during Hydra spheroid regeneration.

(A) Representative trajectories showing the size of regenerating, wild-type, and Wnt3-overexpressing (Wnt3-OE) spheroids over the first 24 hours of regeneration. Quantification of maximum radius (B), average period (C), and average slope (D) of the initial oscillations from regenerating, wild-type, and Wnt3-OE spheroids (for both conditions, n = 9). (E) Representative trajectories showing the size of regenerating spheroids grown in Hydra medium (HM) supplemented with 0.2% dimethyl sulfoxide or 5 μM AP during the first 24 hours of regeneration. (F) Snapshots of the regenerating spheroids in (E). Shown are the initial time points and time points at which the spheroids have reached their peak size. Data in [(B) to (D)] were analyzed using an unpaired, two-tailed t test. ****P < 0.0001. Scale bars, 200 μm. n.s., not significant.

Fig. 2.. Surface tension is reduced in Wnt3-OE spheroids.

Representative images showing how the surface tension was measured for a control (A) and Wnt3-OE (B) spheroid. The critical pressure required to obtain a hemispherical deformation for each measurement is indicated. (C and D) Using the ectodermal green fluorescent protein (GFP) signal, the hemispheres inside the pipette of the same spheroids represented in (A) and (B), respectively, can be visualized more clearly. (E) Quantification of the surface tension for control and Wnt3-OE spheroids (for each genotype, n = 15, with five measurements per sample). Data were analyzed using generalized linear mixed models. ****P < 0.0001. Scale bars, 100 μm [(A) and (B)] and 50 μm [(C) and (D)].

Fig. 3.. Mechanochemical model for symmetry breaking in Hydra spheroids.

(A) Local activation through a positive feedback loop coupling strain and morphogen concentration. (B) Nonlocal inhibition mechanism driven by volume and cell count conservation. (C) Simulation of spontaneous pattern formation starting from spherical initial shape with randomly perturbed constant morphogen concentration. Over time, morphogen concentration and strain colocalize, (D) leading to a local protrusion with high morphogen concentration (E). (F) Simulated trajectories showing the size dynamics of control and Wnt3-OE spheroids (additional constant production rate of $0.05{\text{hour}}^{-1}$ on the right-hand side of the morphogen concentration equation).

Fig. 4.. Pipette aspiration mechanically biases the angle of axis formation.

Snapshots of Hydra spheroids regenerating while undergoing micropipette aspiration at the start (A) and end (B) of the regeneration process. (C) Distribution of axis formation angles in spheroids regenerating under pipette aspiration (n = 9). Angles were measured as indicated by the yellow lines in (B). The simulation of pattern formation under pipette aspiration begins at time t₀, with a patch of nodes on the spheroid immobilized as if held in a pipette (D). By time t₁, high morphogen expression localizes at a distinct angle from the immobilized nodes (E). (F) Distribution of axis formation angles in simulations mimicking pipette aspiration (n = 18). Angle distributions were compared using a Kolmogorov-Smirnov test: (C) versus (F): P = 0.617; (C) versus theoretically expected random distribution: P = 0.066. Scale bars, 100 μm.

Fig. 5.. The organizer arises in regions with the highest level of tissue stretching.

(A) Optical section of a β-catenin::GFP Hydra spheroid at 19.2 hours, illustrating the variability in tissue thickness across its surface, with the organizer indicated by a localized patch of β-catenin⁺ nuclei (blue arrowheads). (B) Tissue thickness compared across the surface of regenerating spheroids at the first time point that clustered β-catenin⁺ nuclei are visible. Tissue thickness was measured relative to the area containing β-catenin⁺ nuclei, as indicated by the yellow lines in (A) (n = 9). Data were analyzed using a Kruskal-Wallis test, with Dunn’s multiple comparisons test for post hoc analysis. ***P < 0.001, **P < 0.01, and *P < 0.05. Scale bar, 100 μm.

Fig. 6.. The location of the organizer can be biased by mechanical confinement.

(A) Simulation of pattern formation under mechanical confinement where stretch is restricted in a single plane. (B) The final location of the protrusion associated with high levels of morphogen is significantly dependent on the immobilization plane. (C) Distribution of angles resulting from simulations of spheroids with confined stretch in a single plane (n = 70). (D) Schematic of the experimental setup mimicking mechanical confinement as shown in (A) and (B), where spheroids were partially embedded in 2% agarose, causing local confinement of stretch by the ring-shaped edge of the agarose upon inflation. Snapshots illustrate a confined, regenerating spheroid at maximum inflation (E) and after successful regeneration (F). (G) Distribution of angles of axis formation in spheroids experiencing local confinement in agarose (n = 27). (H) Schematic of the control setup with spheroids fully embedded in 2% agarose. Snapshots depict a fully embedded, regenerating spheroid at maximum inflation (I) and after successful regeneration (J). (K) Distribution of angles of axis formation in control spheroids fully embedded in 2% agarose (n = 36). Distributions were compared using a Kolmogorov-Smirnov test: (C) versus (G): P = 0.592; (G) versus theoretically expected distribution: P = 0.001; (K) versus theoretically expected distribution: P = 0.439. Scale bars, 250 μm.