Statistics of noisy growth with mechanical feedback in elastic tissues

Abstract

Tissue growth is a fundamental aspect of development and is intrinsically noisy. Stochasticity has important implications for morphogenesis, precise control of organ size, and regulation of tissue composition and heterogeneity. However, the basic statistical properties of growing tissues, particularly when growth induces mechanical stresses that can in turn affect growth rates, have received little attention. Here, we study the noisy growth of elastic sheets subject to mechanical feedback. Considering both isotropic and anisotropic growth, we find that the density-density correlation function shows power law scaling. We also consider the dynamics of marked, neutral clones of cells. We find that the areas (but not the shapes) of two clones are always statistically independent, even when they are adjacent. For anisotropic growth, we show that clone size variance scales like the average area squared and that the mode amplitudes characterizing clone shape show a slow 1/n decay, where n is the mode index. This is in stark contrast to the isotropic case, where relative variations in clone size and shape vanish at long times. The high variability in clone statistics observed in anisotropic growth is due to the presence of two soft modes-growth modes that generate no stress. Our results lay the groundwork for more in-depth explorations of the properties of noisy tissue growth in specific biological contexts. tissue mechanics | noisy growth | clonal dynamics | mechanical feedback G rowth is central to biology and usually involves a level of stochasticity (1-3). The presence of such noise can have significant consequences for developmental processes like morphogenesis and the regulation of organ size. However, relatively little is known about quantitative aspects of stochastic growth. Our goal here is to understand the interplay between noise and mechanical feedback in growing elastic tissues. To that end, we present a generic, continuum model of such tissues and use it to study measurable features of tissue architecture like density fluctuations and statistics of marked, neutral clones. Our model makes a number of unexpected predictions, including the presence of power law correlations in space and the existence of soft modes that allow clone sizes to grow diffusively, evading the effects of mechanical feedbacks that might otherwise be expected to limit clone size variability.In experiments, noise in growth has most often been probed through the size and spatial distribution of clones of cells (4-10), especially of neutral clones that are genetically identical to surrounding tissue except for a clone marker. Cell density variation has also been observed directly in culture (11-15) and in fixed tissues (16), as have correlations in positions of mitotic cells (1), and size asymmetry between contralateral organs can be used as an indirect readout of noise levels (17).Theoretically, the most thoroughly explored area is the noisy dynamics of stem cell populations (4,5,9), where zerodimensional descriptions are often appropriat...

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Cellular organization in lab-evolved and extant multicellular species obeys a maximum entropy law

“…The success of multicellular organisms is due in part to their ability to assemble cells into complex, functional arrangements. Self-assembly, however, is fundamentally subject to random noise (Zeravcic and Brenner, 2014;Szavits-Nossan et al, 2014;Damavandi and Lubensky, 2019) that affects the final emergent structure (Michel and Yunker, 2019). The physiology of multicellular organisms can depend sensitively on the geometry of cellular packing (Bi et al, 2015b;Drescher et al, 2016;Jacobeen et al, 2018b;Larson et al, 2019;Schmideder et al, 2021), and such noise may therefore have direct consequences on organismal fitness.…”