ArticleJournal of mathematical biology2018
A space-jump derivation for non-local models of cell-cell adhesion and non-local chemotaxis.
Article in Journal of mathematical biology, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 16 papers.
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Who cites it
16 citing papers in PubMed.
- Modelling and Simulation of Collective Cell Migration with Non-Local Interactions on Time-Dependent Spatial Domains.Bulletin of mathematical biology · 2026Article
- Pattern Formation in Agent-Based and PDE Models for Evolutionary Games with Payoff-Driven Motion.Bulletin of mathematical biology · 2026Article
- Actin network heterogeneity tunes activator-inhibitor dynamics at the cell cortex.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Self-generated chemotaxis of mixed cell populations.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Modelling non-local cell-cell adhesion: a multiscale approach.Journal of mathematical biology · 2024Article
- Derivation of continuum models from discrete models of mechanical forces in cell populations.Journal of mathematical biology · 2021Article
- Comparative analysis of continuum angiogenesis models.Journal of mathematical biology · 2021Article
- Nonlocal and local models for taxis in cell migration: a rigorous limit procedure.Journal of mathematical biology · 2020Article
- Multi-bit Boolean model for chemotactic drift ofIET systems biology · 2020Article
- Mathematical models for cell migration: a non-local perspective.Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 2020Review
- A Coupled Mass Transport and Deformation Theory of Multi-constituent Tumor Growth.Journal of the mechanics and physics of solids · 2020Article
- From a discrete model of chemotaxis with volume-filling to a generalized Patlak-Keller-Segel model.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Modelling physical limits of migration by a kinetic model with non-local sensing.Journal of mathematical biology · 2020Article
- Kinetic models with non-local sensing determining cell polarization and speed according to independent cues.Journal of mathematical biology · 2020Article
- Modelling collective cell migration: neural crest as a model paradigm.Journal of mathematical biology · 2020Article
- Bridging the gap between individual-based and continuum models of growing cell populations.Journal of mathematical biology · 2020Article
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4 authors.
Funding
Abstract
Cellular adhesion provides one of the fundamental forms of biological interaction between cells and their surroundings, yet the continuum modelling of cellular adhesion has remained mathematically challenging. In 2006, Armstrong et al. proposed a mathematical model in the form of an integro-partial differential equation. Although successful in applications, a derivation from an underlying stochastic random walk has remained elusive. In this work we develop a framework by which non-local models can be derived from a space-jump process. We show how the notions of motility and a cell polarization vector can be naturally included. With this derivation we are able to include microscopic biological properties into the model. We show that particular choices yield the original Armstrong model, while others lead to more general models, including a doubly non-local adhesion model and non-local chemotaxis models. Finally, we use random walk simulations to confirm that the corresponding continuum model represents the mean field behaviour of the stochastic random walk.
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