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arXiv 2409.13129cond-mat.softq-bio.TO
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上皮组织主动塑性流动的均场模型

A Mean-Field Model for Active Plastic Flow of Epithelial Tissue

Nikolas H. Claussen, Fridtjof Brauns

AI总结:

本研究结合对称性论证与随机均场模型,利用弹性弛豫与形态发生动力学的时间尺度分离,建立了上皮组织主动塑性流动的粗粒化模型,解释了自限性行为及外部场对定向重排的维持作用。

摘要:

动物形态发生常涉及上皮组织片层的显著形状变化。在理解潜在的细胞驱动力及其通过生物力学反馈环路的协调方面已取得重大进展。然而,关于细胞水平动力学如何转化为大规模形态发生流动的定量理解仍然有限。一个关键挑战是找到能够保留细胞尺度结构关键信息的相关宏观变量(序参量)。为应对这一挑战,我们将对称性论证与考虑相关微观动力学的随机均场模型相结合。与先前关于组织被动流体和固体性质的研究互补,我们聚焦于主动产生的内部应力的作用。核心地,我们利用弹性弛豫与形态发生动力学之间的时间尺度分离,来描述组织片层内准静态力平衡下的组织形状变化。由此产生的几何结构——与多边形细胞平铺对偶的张力空间中的三角剖分——被证明是发展均场模型的理想框架。粗粒化模型的所有参数均从底层微观动力学计算得出。核心地,该模型解释了由自主主动细胞重排驱动的主动塑性流动如何变得自限性,正如先前在实验和模拟中观察到的那样。此外,该模型定量预测了组织在与外部场(如平面细胞极性和外力)耦合时的行为。我们展示了此类场如何维持定向的主动细胞重排,从而克服纯自主主动塑性流动的自限特性。这些发现证明了局部自组织和自上而下的遗传指令如何共同决定内部驱动的组织动力学。

英文摘要:

Animal morphogenesis often involves significant shape changes of epithelial tissue sheets. Great progress has been made in understanding the underlying cellular driving forces and their coordination through biomechanical feedback loops. However, quantitative understanding of how cell-level dynamics translate into large-scale morphogenetic flows remains limited. A key challenge is finding the relevant macroscopic variables (order parameters) that retain the essential information about cell-scale structure. To address this challenge, we combine symmetry arguments with a stochastic mean-field model that accounts for the relevant microscopic dynamics. Complementary to previous work on the passive fluid- and solid-like properties of tissue, we focus on the role of actively generated internal stresses. Centrally, we use the timescale separation between elastic relaxation and morphogenetic dynamics to describe tissue shape change in quasi-static balance of forces within the tissue sheet. The resulting geometric structure - a triangulation in tension space dual to the polygonal cell tiling - proves ideal for developing a mean-field model. All parameters of the coarse-grained model are calculated from the underlying microscopic dynamics. Centrally, the model explains how active plastic flow driven by autonomous active cell rearrangements becomes self-limiting as previously observed in experiments and simulations. Additionally, the model quantitatively predicts tissue behavior when coupled with external fields, such as planar cell polarity and external forces. We show how such fields can sustain oriented active cell rearrangements and thus overcome the self-limited character of purely autonomous active plastic flow. These findings demonstrate how local self-organization and top-down genetic instruction together determine internally-driven tissue dynamics.

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