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快乐十分杀号技巧:Statistics of noisy growth with mechanical feedback in elastic tissues
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Tissue growth is often a noisy process, and control of this noise is vital to the integrity of growth and development. However, a basic theoretical understanding of how noise affects growth, especially in tissues with mechanical feedback, is lacking. Here, we consider the simplest model of stochastic tissue growth and show that it predicts nontrivial behavior for observable quantities like density correlations and the sizes of marked clones. The former, in particular, exhibits power laws analogous to those seen in models of the early universe, hinting at a hitherto unexplored richness in the physics of “inflationary embryology.”
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 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.
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Author contributions: O.K.D. and D.K.L. designed research; O.K.D. performed research; and O.K.D. and D.K.L. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1816100116/-/DCSupplemental.
Published under the PNAS license.