Mapping cell cortex rheology to tissue rheology, and vice-versa

TL;DR

This paper establishes a theoretical link between cell cortex rheology and tissue rheology using a 3D hexagonal cell model, predicting how cortical mechanics influence tissue behavior and providing testable experimental predictions.

Contribution

It introduces a novel mapping between cortex and tissue rheology based on a 3D cell geometry, highlighting the importance of 3D models over 2D for realistic tissue mechanics.

Findings

Tissue elastic modulus is proportional to cortex rest tension.

Fractional cortex rheology predicts high-frequency tissue rheology.

Inversion of the mapping allows deriving cortex rheology from tissue rheology.

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 behaviour. 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 behaviour 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.