Active surface models for the mechanics of biological tissues

Biological tissues are complex materials made, most of the time, of one confluent layer of living cells. The main originality of these materials is that they are active: they can extract energy from their environment to self-generate internal stresses. Moreover, cells or subcellular elements can self-organize on large scale, subsequently influencing the mechanics of the tissue. Modelling the mechanics of these materials and understanding how biological phenomenon influence it is of prime importance in many domains like developmental biology, medecine or bioengeeniring… To this purpose, many efforts have been done this last decade to adapt the framework of surface mechanics to biological tissues. This allows for a continuous description where we introduce active stresses whose dynamics aims to capture the tissue biology. In this talk, I will present different active surface models and the insights they bring on some biological systems.

I will first introduce an active tube model for the mechanics of the endothelium, the main cell layer of blood vessels. This model reproduces the experimental response of an in vitro endothelium to a step of pressure and highlights the key role of actin fibers orientational order in this response.

I will then present an active shell model that I used to investigate the gastrulation of sea urchin, a specific stage of development where the embryo, that is initially a spherical monolayer of cell, generates an inward folding. By implementing in vivo observations in numerical simulations of this model, I was able to identify the key mechanisms driving this dramatic deformation of the tissue.

Finally, I will show how the previous active shell model can be adapted to study the larval shape diversity of cnidarians, a wide family of sea animals. I will explain how, combining in vivo microscopy data for different species to simulations of this model, I identified three common biomechanical features controlling the shape of cnidarian larvae.