Speaker
Description
Cell migration is regulated by the ability of cells to sense their surroundings over distances of several cell diameters and adjust both their direction and speed accordingly. We study the stability of a kinetic model for cell migration \cite{loy_kinetic_2020} that incorporates such non-local sensing mechanisms. In the model, cell density is perceived through sensing kernels that may differ for directional and speed regulation. To investigate their combined effects, we assume that cell–cell adhesion influences cell orientation, while volume-filling effects regulate cell speed. By deriving the dispersion relation, we show that the stability of the homogeneous equilibrium depends on three dimensionless parameters: one measuring the stiffness of the system (related to the turning rate, equilibrium speed, and sensing radius), and two associated with the sensitivity of the speed and directional bias to changes in cell density. Extending previous studies \cite{loy_stability_2021,loy_stability_2020}, we derive conditions for instability to both long- and short-wave perturbations in specific scenarios. Finally, numerical simulations are performed to illustrate the system’s behaviour and the possible emergence of spatial patterns.
Bibliography
@article{loy_kinetic_2020,
title = {Kinetic models with non-local sensing determining cell polarization and speed according to independent cues},
volume = {80},
issn = {0303-6812, 1432-1416},
url = {http://link.springer.com/10.1007/s00285-019-01411-x},
doi = {10.1007/s00285-019-01411-x},
language = {en},
number = {1-2},
urldate = {2026-03-11},
journal = {Journal of Mathematical Biology},
author = {Loy, Nadia and Preziosi, Luigi},
month = jan,
year = {2020},
pages = {373--421},
}
@article{loy_stability_2020,
title = {Stability of a non-local kinetic model for cell migration with density dependent orientation bias},
volume = {13},
copyright = {http://creativecommons.org/licenses/by/3.0/},
issn = {1937-5093},
url = {https://www.aimsciences.org/en/article/doi/10.3934/krm.2020035},
doi = {10.3934/krm.2020035},
language = {en},
number = {5},
urldate = {2026-03-11},
journal = {Kinetic and Related Models},
author = {Loy, Nadia and Preziosi, Luigi},
month = aug,
year = {2020},
pages = {1007--1027},
}
@article{loy_stability_2021,
title = {Stability of a non-local kinetic model for cell migration with density-dependent speed},
volume = {38},
copyright = {https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model},
issn = {1477-8599, 1477-8602},
url = {https://academic.oup.com/imammb/article/38/1/83/6041785},
doi = {10.1093/imammb/dqaa013},
language = {en},
number = {1},
urldate = {2026-03-11},
journal = {Mathematical Medicine and Biology: A Journal of the IMA},
author = {Loy, Nadia and Preziosi, Luigi},
month = mar,
year = {2021},
pages = {83--105},
}
