Séminaire Doctorants
organisé par l'équipe DOCT
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Roxana Sublet
Modelling collective cell dynamics
8 octobre 2026 - 16:30Salle de conférences IRMA
This work focuses on the mathematical modeling of cellular tissue dynamics. We first propose an individual-based model that provides the dynamics of the positions, velocities, and polarities of the cells, idealized as hard spheres. Cells interact with each other through contact forces, smooth attraction, and polarity alignment. The present work is an extension of the model proposed in [3] and validated by experiments on cellular rings. We will study the well-posedness of a regularized version. We are particularly interested in the congested regime and the impact of apoptosis on the jammed state. Indeed, cell apoptosis corresponds to programmed cell death: when cells leave the tissue, they induce local contractions but also enable cellular rearrangements. To this end, we add to the previous model a microscopic description of apoptotic and proliferation events. Numerical simulations are performed to show the impact of apoptosis on collective cell dynamics. Next, we derive a macroscopic description, following the methodology proposed in [1] and [2]. We start from a mean-field dynamics of the kinetic distribution function in phase space (position, polarity, radius), where contact forces have been replaced with repulsion forces. We then introduce a specific time and space rescaling and identify the equilibrium distribution functions, which are parameterized by two macroscopic quantities: the density and the mean polarity. Based on the Generalized Collision Invariant (GCI) method [2], we are then able to identify their dynamics: the resulting description can be seen as a modified Self-Organized Hydrodynamics (SOH) model. We finally discuss the obtained model and highlight the effect of the apoptotic events on the dynamics. This is a joint work with Laurent Navoret (Université de Strasbourg) and Marcela Szopos (Université Paris Cité). It has also been carried out in collaboration with Romain Levayer (Institut Pasteur) and Daniel Riveline (IGBMC, Université de Strasbourg) in the context of the ANR project MAPEFLU. References [1] Degond, P., Dimarco, G., Mac, T. B. N., and Wang, N. Macroscopic models of collective motion with repulsion. Communications in Mathematical Sciences, 13(6), 1615–1638 (2015). [2] Degond, P., and Motsch, S. Continuum limit of self-driven particles with orientation interaction. Mathematical Models and Methods in Applied Sciences, 18(supp01), 1193–1215 (2008). [3] Vecchio, S. L., Pertz, O., Szopos, M., Navoret, L., and Riveline, D. Spontaneous rotations in epithelia as an interplay between cell polarity and boundaries. Nature Physics (2024).