Inflationary Embryology and the Statistical Physics of Noisy Tissue Growth

Tissue growth is fundamental to biology and is noisy. Noise has important implications for morphogenesis and tissue integrity, yet a basic theoretical description of noisy tissue growth has been lacking. Growth nonuniformity leads to a build-up of mechanical stresses, and many tissues respond to stress by modulating their growth. Then, how does the interplay between noise and stress feedback affect tissue growth, and what can we predict about the statistical properties of experimentally accessible quantities? We model the tissue as a continuum, elastic sheet undergoing exponential growth with mechanical feedback and find that the density-density correlations show power-law scaling in space. In anisotropic growth, the standard deviation in clone sizes is comparable to the mean, in contrast to the isotropic case where relative variations in clone size vanish at long times. The high variability in clone statistics observed in anisotropic growth is due to the presence of two soft growth modes, which generate no stress. Our work analyzes the simplest model of noisy growth of elastic tissues. It thus both introduces a new class of nonequilibrium growth models and represents a first step towards understanding specific biological contexts.