  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.
