Abstract
The vertex model is a mesoscopic model in that it considers the properties of individual cells. To describe the macroscopic properties of the tissue, the cell properties must be locally averaged to define the cell deformation rate or local velocity gradient in the tissue. The local averaging procedure is quite subtle and has been carried out by two groups : Frank Jülicher's Dresden group and Boris Guirao's in Yohann Bellaïche's team at the Institut Curie. Locally, F. Jülicher's group triangulates the surface around each vertex, and studies the deformation of each triangle with respect to a reference equilateral triangle. This defines a deformation tensor and a cell elongation tensor. These tensors can then be averaged locally, and the rate of deformation linked to the rate of elongation.
The effect of topological transitions must then be taken into account. This enables the strain rate to be decomposed as a function of the variation in the elongation rate and the contributions of topological transitions.
The two teams then carried out the actual averaging procedure on Drosophila epithelial tissue to identify each of the contributions. The Dresden team described experiments on the Drosophila wing. Experiments by the Institut Curie group were described in the seminar by Y. Bellaïche's seminar.
