Fluctuation-driven morphological patterning: An unconventional approach to morphogenesis

Recent experimental investigations into regeneration revealed a remarkable phenomenon: the morphological transformation of a tissue fragment from the incipient spherical configuration to a tubelike structure—the hallmark of a mature —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 a barrier within an effective morphological potential that underlies morphogenesis. Inspired by this intriguing insight, we propose an unconventional 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 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 second-order-like transition, depends on the effective temperature and the effective cutoff on the wavelength of the spatial variations in the system. The former sets the level of noise, while the latter determines the height of the potential barrier between the initial circular state and the final deformed state of the tissue. It is also found that entropic barriers separate various metastable states of the system. Published by the American Physical Society 2024