Coupling osmosis and mechanics in vertex-based models for plant tissue growth - Guillaume Mestdagh (INRIA Montbonnot)

Understanding plant growth is fundamental to address global challenges such as food security, biodiversity, and soil‑erosion control. The development of plants involves many interconnected physical processes, occurring at various spatial and temporal scales, making modeling an indispensable complement to experiments. In particular, discrete vertex-based models have successfully described the coupling between inter-cell water fluxes and mechanical deformations of cell walls, in response to a prescribed inner water pressure.

A two-dimensional vertex-based model represents a group of cells as a tiling of polygons, with the edges between polygons representing cell walls. Existing vertex-based models postulate a fixed water pressure inside cells as the force driving growth. In reality, this inner pressure itself is the consequence of osmosis, a chemical process by which water is attracted into cells with a higher concentration of solute. However, capturing the interplay between mechanics and solute dynamics in plant tissues into one model remains a challenge that requires novel mathematical frameworks.

In this talk, I will present a new approach to couple solute and water fluxes with mechanics and growth in vertex-based models. The proposed approach is based on a variational formalism where the system physics is described in terms of free energy and dissipation function. After building the model and deriving the evolution equations of the system, I will show that the resulting formulation can be turned into a numerical method. Finally, I will illustrate the model properties through a few numerical simulations and discuss its interest for the study of plant growth.

Contact: Philippe Marmottant