Universal calcium fluctuations in hydra morphogenesis.

Understanding the collective physical processes that drive robust morphological transitions in animal development necessitates the characterization of the relevant fields involved in morphogenesis. Calcium (Ca2+) is recognized as one such field. In this study, we demonstrate that the spatial fluctuations of Ca2+ during Hydra regeneration exhibit universal characteristics. To investigate this phenomenon, we employ two distinct controls, an external electric field and Heptanol, a gap junction-blocking drug. Both lead to the modulation of the Ca2+ activity and a reversible halting of the regeneration process. The application of an electric field enhances Ca2+ activity in the Hydra's tissue and increases its spatial correlations, while the administration of Heptanol inhibits its activity and diminishes the spatial correlations. Remarkably, the statistical characteristics of Ca2+ spatial fluctuations, including the coefficient of variation and skewness, manifest universal shape distributions across tissue samples and conditions. We introduce a field-theoretic model, describing fluctuations in a tilted double-well potential, which successfully captures these universal properties. Moreover, our analysis reveals that the Ca2+ activity is spatially localized, and the Hydra's tissue operates near the onset of bistability, where the local Ca2+ activity fluctuates between low and high excited states in distinct regions. These findings highlight the prominent role of the Ca2+ field in Hydra morphogenesis and provide insights into the underlying mechanisms governing robust morphological transitions.