Résumé
The mechanics of biological tissuesmainly 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 relatingthe cortical rheology to the monolayer tissue rheology.Our approach shows that the tissue low frequency elastic modulusis proportional to the rest tension of the cortex,as expected from the physics of liquid foamsas well as of tensegrity structures.A fractional visco-contractile cortex rheologyis 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 toderive 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 ofcortex constituents, and hope to foster new, challenging mechanicalexperiments on cell monolayers.