Active tension network model suggests an exotic mechanical state realized in epithelial tissues

Abstract

Mechanical interactions play a crucial role in epithelial morphogenesis, yet understanding the complex mechanisms through which stress and deformation affect cell behaviour remains an open problem. Here we formulate and analyse the active tension network (ATN) model, which assumes that the mechanical balance of cells within a tissue is dominated by cortical tension and introduces tension-dependent active remodelling of the cortex. We find that ATNs exhibit unusual mechanical properties. Specifically, an ATN behaves as a fluid at short times, but at long times supports external tension like a solid. Furthermore, an ATN has an extensively degenerate equilibrium mechanical state associated with a discrete conformal—‘isogonal’—deformation of cells. The ATN model predicts a constraint on equilibrium cell geometries, which we demonstrate to approximately hold in certain epithelial tissues. We further show that isogonal modes are observed in the fruit fly embryo, accounting for the striking variability of apical areas of ventral cells and helping understand the early phase of gastrulation. Living matter realizes new and exotic mechanical states, the study of which helps to understand biological phenomena.

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Figure 1: Force balance in a tension net defines a triangulation of the ‘tension plane’.
Figure 2: Role of myosin motors in the ATN model.
Figure 3: Mechanical properties of an ATN.
Figure 4: Experimental tests of ATN model predictions.

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Acknowledgements

The authors gratefully acknowledge stimulating discussions with K. Irvine, T. Lecuit and E. Wieschaus, and thank K. Irvine for sharing the wing imaginal disc data. This work was supported by the NSF PHY-1220616 (B.I.S., N.N.) and PHY-1125915 (M.M.), GBMF grant #2919 (B.I.S./I.H.) and NICHD 5K99HD088708-02 (S.J.S.).

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Model formulation and analysis: B.I.S., I.H., M.M. and N.N. Experimental data: S.J.S. Numerical simulations and data analysis: N.N. Manuscript: B.I.S. and N.N. All authors discussed the results and implications of the work as well as provided critical comments on the manuscript at all stages.

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Correspondence to Boris I. Shraiman.

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The authors declare no competing financial interests.

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Noll, N., Mani, M., Heemskerk, I. et al. Active tension network model suggests an exotic mechanical state realized in epithelial tissues. Nature Phys 13, 1221–1226 (2017). https://doi.org/10.1038/nphys4219

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