Speaker
Description
Cell–cell adhesion is a key organiser of tissue structure, in both healthy and cancerous environments, and plays a crucial role in regulating cancer cell migration. In this talk, we introduce a multiscale modelling framework for the dynamics of a moving self‑adhesive cell population \cite{ZR}. The approach links a detailed microscopic description of deterministic adhesion‑driven motion with a standard mesoscopic representation of a stochastic velocity‑jump process, leading to a kinetic transport equation that features several nonlocal terms. Passing to the macroscopic scale yields continuum equations that couple nonlocal adhesion with myopic diffusion.
The framework lends itself conveniently to representing the underpinning binding dynamics of adhesion molecules such as cadherins. When these microscopic effects are translated to the macroscopic level, they generate a novel nonlinear integral equation coupled to the cell‑density equation. For a rigorous mathematical analysis of models of this type, we refer to \cite{RZ} and the talk “A cell–cell adhesion model: local well‑posedness” in this conference.
Bibliography
@article{ZR, title={Modelling non-local cell-cell adhesion: a multiscale approach}, author={Anna Zhigun and Mabel Lizzy Rajendran}, archivePrefix = "arXiv", eprint = {2308.05676}, doi={10.1007/s00285-024-02079-8}, url={https://doi.org/10.1007/s00285-024-02079-8}, volume={88}, number={55}, year={2024}, JOURNAL = {J. Math. Biol.}, FJOURNAL = {Journal of Mathematical Biology} }
@article{RZ, author = {Rajendran, Mabel Lizzy and Zhigun, Anna}, title = {Local Well-Posedness for a Novel Nonlocal Model for Cell-Cell Adhesion via Receptor Binding}, journal = {SIAM Journal on Mathematical Analysis}, volume = {57}, number = {4}, pages = {4016-4067}, year = {2025}, doi = {10.1137/24M1667518}, URL = {https://epubs.siam.org/doi/abs/10.1137/24M1667518}, eprint = {https://epubs.siam.org/doi/pdf/10.1137/24M1667518} }
