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Mapping cell cortex rheology to tissue rheology and vice versa

Étienne Moisdon1, Pierre Seez1, François Molino2, Philippe Marcq3, and Cyprien Gay1,*

  • 1Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université Paris Cité, 75205 Paris cedex 13, France
  • 2Laboratoire Charles Coulomb, UMR 5221, CNRS and Université de Montpellier, Place Eugène Bataillon, F-34095 Montpellier, France
  • 3PMMH, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université Paris Cité, F-75005 Paris, France

  • *Corresponding author: cyprien.gay@univ-paris-diderot.fr
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Phys. Rev. E 106, 034403 – Published 15 September, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.034403

Abstract

The mechanics of biological tissues mainly proceeds from the cell cortex rheology. A direct, explicit link between cortex rheology and tissue rheology remains lacking, yet would be instrumental in understanding how modulations of cortical mechanics may impact tissue mechanical behavior. Using an ordered geometry built on 3D hexagonal, incompressible cells, we build a mapping relating the cortical rheology to the monolayer tissue rheology. Our approach shows that the tissue low-frequency elastic modulus is proportional to the rest tension of the cortex, as expected from the physics of liquid foams as well as of tensegrity structures. A fractional visco-contractile cortex rheology is predicted to yield a high-frequency fractional visco-elastic monolayer rheology, where such a fractional behavior has been recently observed experimentally at each scale separately. In particular cases, the mapping may be inverted, allowing to derive from a given tissue rheology the underlying cortex rheology. Interestingly, applying the same approach to a 2D hexagonal tiling fails, which suggests that the 2D character of planar cell cortex-based models may be unsuitable to account for realistic monolayer rheologies. We provide quantitative predictions, amenable to experimental tests through standard perturbation assays of cortex constituents, and hope to foster new, challenging mechanical experiments on cell monolayers.

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Phys. Rev. E 106, 034403– Published 15 September, 2022
  • Received 22 April 2022
  • Revised 25 July 2022
  • Accepted 11 August 2022
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