Effects of time delays and viscoelastic parameters in oscillatory response of cell monolayers

Abstract Oscillatory response of cellular tissues has been observed in multiple embryogenetic developmental stages. The source of these oscillations has been attributed to imbalance of instabilities in the chemo-mechanical signaling and delayed cell activity. Although the relation of these oscillations with further drastic tissue deformation remains uncertain, it is apparent that intracellular remodeling events seem to drive the viscoelastic properties and the measured pulsatile deformations. We here resort to a viscoelastic model that is based on a variable rest-length of the cell. We include a delay between the measured elastic strain and the evolution of the rest-length which dynamically adapts to the cell strain. This law is not only able to reproduce the relaxation phenomena observed in embryonic tissues in vitro and in vivo, but also to give rise to oscillatory cell responses. We analyze the stability of the resulting oscillations on minimal systems with two cells, and also on planar or out of plane deformation modes of monolayers. We conclude that in all cases, the stability decreases with an increasing delay or with the ability to adapt in a faster manner.