Tissue morphogenesis comprises the self-organized creation of various patterns and shapes. Although detailed underlying mechanisms are still elusive in many cases, an increasing amount of experimental data suggests that chemical morphogen and mechanical processes are strongly coupled. Here, we develop and test a minimal model of the axis-defining step (i.e., symmetry breaking) in aggregates of the Hydra polyp. Based on previous findings, we combine osmotically driven shape oscillations with tissue mechanics and morphogen dynamics. We show that the model incorporating a simple feedback loop between morphogen patterning and tissue stretch reproduces a wide range of experimental data. Finally, we compare different hypothetical morphogen patterning mechanisms (Turing, tissue-curvature, and self-organized criticality). Our results suggest the experimental investigation of bigger (i.e., multiple head) aggregates as a key step for a deeper understanding of mechanochemical symmetry breaking in Hydra.

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A free-boundary approach is applied to derive universal relationships between the excitability and the velocity and the shape of stabilized wave segments in a broad class of excitable media. In the earlier discovered low excitability limit wave segments approach critical fingers. We demonstrate the existence of a second universal limit (a motionless circular shaped spot) in highly excitable media. Analytically obtained asymptotic relationships and interpolation formula connecting both excitability limits are in good quantitative agreement with results from numerical simulations.

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