Spontaneous strains in tissue mechanics: topologically driven morphogenesis

Growth processes are widely used by biological tissue in order to undergo shape changes. It has been determined that one of the reshaping mechanisms relies on the spontaneous strains that arise within the tissue as a result of gradients of growth. In some cases, the tissue can alleviate the induced internal stresses by adopting intricate 3D configurations as has been extensively reported, for example, in various plant tissue. However, less is understood about the formation of spontaneous strains in the much more dynamic animal tissue. Recent observations of morphogenic events together with single-cell resolution imaging have revealed that a variety of tissue such as the Drosophila melanogaster wing and embryo form as a result of cell elongation, proliferation, and division. The coupling of these cellular events is translated into gradients of the stress-field of the tissue that promote shape changes. Here, we seek to make a connection between cellular events and the physics of shape-changing materials based on the elongation and contraction of nematic elastomers. Furthermore, we discuss a coarse-grained model for morphogenesis a la physics of nematic liquid crystals that builds on the proliferation and dynamics of topological defects.