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Multiphase field models have emerged as an important computational tool for understanding biological tissue while resolving single-cell properties. While they have successfully reproduced many experimentally observed behaviors of living tissue, the theoretical underpinnings have not been fully explored. We show that a two-dimensional version of the model, which is commonly employed to study tissue monolayers, can be derived from a three-dimensional version in the presence of a substrate. We also show how viscous forces, which arise from friction between different cells, can be included in the model. Finally, we numerically simulate a tissue monolayer and find that intercellular friction tends to solidify the tissue. Published by the American Physical Society2024
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This content will become publicly available on April 1, 2026
Mean-Field Model for Active Plastic Flow of Epithelial Tissue
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, our 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 solidlike 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 the quasistatic 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 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. Published by the American Physical Society2025
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- Award ID(s):
- 2210612
- PAR ID:
- 10617662
- Publisher / Repository:
- APS
- Date Published:
- Journal Name:
- PRX Life
- Volume:
- 3
- Issue:
- 2
- ISSN:
- 2835-8279
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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