Illustrations and equations can be used to make sense of biology.

Guillaume Salbreux : Tissue mechanics and self-organisation

Introduction

The primary goal of morphogenesis is to establish animal shape.

Dramatic tissue deformations occur during morphogenesis, such as invagination of epithelia, formation of furrows and tissue growth and shrinkage. These events are controlled by patterns of gene expression but are also powered by mechanical forces that induce transient deformations, as well as maintain the shape of cells and tissues over long time scales.

In order to understand the deformations of tissues in 3D, we have developed a 3D vertex model, where the tissue geometry is represented by a set of vertices. The volume enclosed by triangulated surfaces joining the vertices corresponds to an epithelial cell. The cell apical surfaces, cell basal surfaces and cell-cell interfaces are subjected to different interfacial tensions, the edges joining vertices are subjected to line tensions, and a pressure constrains the total cell volume. These forces arise from the cytoskeleton and their relative magnitudes depend on the localisation of actin and myosin or other force-producing elements in the cell. We use the 3D vertex model as a tool to understand the mechanics of morphogenesis during development.

On larger length scales, we are developing a continuum theory for epithelial tissues, in order to establish a general framework for how tissues deform and flow on large spatial scales. Cell mechanics, cell rearrangements allowed by T1 transitions and cell division and apoptosis are taken into account to derive constitutive equations, describing how forces in the tissue depend on cell shape and other quantities characterising the state of the tissue.