Mechanical stress plays an intricate role in gene expression in individual cells and sculpting of developing tissues. However, systematic methods of studying how mechanical stress and feedback help to harmonize cellular activities within a tissue have yet to be developed. Motivated by our observation of the cellular constriction chains (CCCs) during the initial phase of ventral furrow formation in the Drosophila melanogaster embryo, we propose an active granular fluid (AGF) model that provides valuable insights into cellular coordination in the apical constriction process. In our model, cells are treated as circular particles connected by a predefined force network, and they undergo a random constriction process in which the particle constriction probability P is a function of the stress exerted on the particle by its neighbors. We find that when P favors tensile stress, constricted particles tend to form chain-like structures. In contrast, constricted particles tend to form compact clusters when P favors compression. A remarkable similarity of constricted-particle chains and CCCs observed in vivo provides indirect evidence that tensile-stress feedback coordinates the apical constriction activity. We expect that our particle-based AGF model will be useful in analyzing mechanical feedback effects in a wide variety of morphogenesis and organogenesis phenomena.
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