ArticleProceedings. Mathematical, physical, and engineering sciences2020
From a discrete model of chemotaxis with volume-filling to a generalized Patlak-Keller-Segel model.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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12 citing papers in PubMed, 27 citations in OpenAlex.
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- Designing reaction-cross-diffusion systems with Turing and wave instabilities.Journal of mathematical biology · 2025Article
- Spatial Segregation Across Travelling Fronts in Individual-Based and Continuum Models for the Growth of Heterogeneous Cell Populations.Bulletin of mathematical biology · 2025Article
- Agent-Based and Continuum Models for Spatial Dynamics of Infection by Oncolytic Viruses.Bulletin of mathematical biology · 2023Article
- Microbial Cells as a Microrobots: From Drug Delivery to Advanced Biosensors.Biomimetics (Basel, Switzerland) · 2023Review
- Modeling Receptor Motility along Advecting Lipid Membranes.Membranes · 2022Review
- Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework.Proceedings. Mathematical, physical, and engineering sciences · 2022Article
- Collective self-optimization of communicating active particles.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
- Treatment-induced shrinking of tumour aggregates: a nonlinear volume-filling chemotactic approach.Journal of mathematical biology · 2021Article
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3 authors at 2 institutions in 3 countries.
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Abstract
We present a discrete model of chemotaxis whereby cells responding to a chemoattractant are seen as individual agents whose movement is described through a set of rules that result in a biased random walk. In order to take into account possible alterations in cellular motility observed at high cell densities (i.e. volume-filling), we let the probabilities of cell movement be modulated by a decaying function of the cell density. We formally show that a general form of the celebrated Patlak-Keller-Segel (PKS) model of chemotaxis can be formally derived as the appropriate continuum limit of this discrete model. The family of steady-state solutions of such a generalized PKS model are characterized and the conditions for the emergence of spatial patterns are studied via linear stability analysis. Moreover, we carry out a systematic quantitative comparison between numerical simulations of the discrete model and numerical solutions of the corresponding PKS model, both in one and in two spatial dimensions. The results obtained indicate that there is excellent quantitative agreement between the spatial patterns produced by the two models. Finally, we numerically show that the outcomes of the two models faithfully replicate those of the classical PKS model in a suitable asymptotic regime.
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