Elasticity, stability, and quasi-oscillations of cell-cell junctions in solid confluent epithelia

Abstract

Macroscopic properties and shapes of biological tissues depend on remodelling of cell-cell junctions at the microscopic scale. We propose a theoretical framework that couples a vertex model of solid confluent tissues with the dynamics describing generation of local force dipoles in the junctional actomyosin. Depending on the myosin-turnover rate, junctions preserve stable length or collapse to initiate cell rearrangements. We find that while the elasticity of solid tissues does not meet the conditions for a stable limit cycle of junctional movements, junctional noise can amplify and sustain transient oscillations to the fixed point, yielding quasi-periodic junctional dynamics. We also discover that junctional stability is affected by cell arrangements and junctional rest tensions, which may explain junctional collapse during convergence and extension in embryos.