Many epithelial developmental processes like cell migration and spreading, cell sorting, or T1 transitions can be described as planar deformations. As such, they can be studied using two-dimensional tools and vertex models that can properly predict collective dynamics. However, many other epithelial shape changes are characterized by out-of-plane mechanics and three-dimensional effects, such as bending, cell extrusion, delamination, or invagination. Furthermore, during planar cell dynamics or tissue repair in monolayers, spatial intercalation between the apical and basal sides has even been detected. Motivated by this lack of symmetry with respect to the midsurface, we here present a 3D hybrid model that allows us to model differential contractility at the apical, basal or lateral sides. We use the model to study the effects on wound closure of solely apical or lateral contractile contributions and show that an apical purse-string can be sufficient for full closure when it is accompanied by volume preservation.
Cells and tissues exhibit sustained oscillatory deformations during remodelling, migration or embryogenesis. Although it has been shown that these oscillations correlate with intracellular biochemical signalling, the role of these oscillations is as yet unclear, and whether they may trigger drastic cell reorganisation events or instabilities remains unknown. Here, we present a rheological model that incorporates elastic, viscous and frictional components, and that is able to generate oscillatory response through a delay adaptive process of the rest-length. We analyse its stability as a function of the model parameters and deduce analytical bounds of the stable domain. While increasing values of the delay and remodelling rate render the model unstable, we also show that increasing friction with the substrate destabilises the oscillatory response. This fact was unexpected and still needs to be verified experimentally. Furthermore, we numerically verify that the extension of the model with non-linear deformation measures is able to generate sustained oscillations converging towards a limit cycle. We interpret this sustained regime in terms of non-linear time varying stiffness parameters that alternate between stable and unstable regions of the linear model. We also note that this limit cycle is not present in the linear model. We study the phase diagram and the bifurcations of the non-linear model, based on our conclusions on the linear one. Such dynamic analysis of the delay visco-elastic model in the presence of friction is absent in the literature for both linear and non-linear rheologies. Our work also shows how
Cells and tissues exhibit oscillatory deformations during remodelling, migration or embryogenesis. Although it has been shown that these oscillations correlate with cell biochemical signalling, it is yet unclear the role of these oscillations in triggering drastic cell reorganisation events or instabilities, and the coupling of this oscillatory response with tested visco-elastic properties.We here present a rheological model that incorporates elastic, viscous and frictional components, and that is able to generate oscillatory response through a delay adaptive process of the rest-length. We analyse its stability properties as a function of the model parameters and deduce analytical bounds of the stable domain. While increasing values of the delay and remodelling rate render the model unstable, we also show that increasing friction with the substrate destabilise the oscillatory response. Furthermore, we numerically verify that the extension of the model to non-linear strain measures is able to generate sustained oscillations that alternate between stable and unstable regions.
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