Agam, O.; Braun, E.

Recent experimental investigations into Hydra regeneration revealed a remarkable phenomenon: the morphological transformation of a tissue fragment from the incipient spherical configuration to a tube-like structure - the hallmark of a mature Hydra - has the dynamical characteristics of a first-order phase-transition, with calcium field fluctuations within the tissue playing an essential role. This morphological transition was shown to be generated by activation over an energy barrier within an effective potential that underlies morphogenesis. Inspired by this intriguing insight, we propose a novel mechanism where stochastic fluctuations drive the emergence of morphological patterns. Thus, the inherent fluctuations determine the nature of the dynamics and are not incidental noise in the background of the otherwise deterministic dynamics. Instead, they play an important role as a driving force that defines the attributes of the pattern formation dynamics and the nature of the transition itself. Here, we present a simple model that captures the essence of this novel mechanism for morphological pattern formation. Specifically, we consider a one-dimensional tissue arranged as a closed contour embedded in a two-dimensional space, where the local curvature of the contour is coupled to a non-negative scalar field. An effective temperature parameter regulates the strength of the fluctuations in the system. The tissue exhibits fluctuations near a circular shape at sufficiently low coupling strengths, but as the coupling strength exceeds some critical value, the circular state becomes unstable. The nature of the transition to the new state, namely whether it is a first-order-like or a second-order-like transition, depends on the temperature and the effective cutoff on the wavelength of the spatial variations in the system. It is also found that entropic barriers separate the various metastable states of the system. 1. Introduction