The Strange Maths of Cellular Materials

par François Graner (Complex Systems and Matter, CNRS & Université Paris Cité)

lundi 9 mars 2026, 11:30 → 12:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Each living animal or human originates from a single cell, which divides several times, then cells differentiate and robustly self-organize into tissues and organs. This talk will discuss mechanisms governing such tissue development. Forces, shapes, movements, shape changes, all obey the laws of mechanics. But cellular materials (made of cells tiling the space) have peculiar mechanical properties.
Our example is the Drosophila metamorphosis: within a few days, the fly strikingly changes from a rather simple maggot shape to a refined adult shape with wings, legs, antennas, waist, neck, and compound eyes. We film the fly's dorsal structure (the thorax, see Figure), and its wing. We characterize quantitatively each geometrical or topological change at cell scale: cell divisions, cell neighbour changes, cell size and shape changes, and programmed cell deaths. Our unified description respects tensorial symmetry and is thus built to be valid in any dimension. It enables us to coarse-grain the discrete description, at the cell scale, to link it with a continuum mechanics description, which encompasses the information useful at the tissue scale. Such rigorous multi-scale

approach applies to a large class of disordered systems, including aggregates of living cells, or collectively migrating cells.
In addition, measuring mechanical stresses in situ in the developing tissues evidences unexpected interplays between patterns of tissue elongation, cell division and mechanical stress. The complex regulation of tissue morphology, based on feedbacks betwen physics and genetics, is the subject of active researches: open questions and perspectives will be presented.