Journal article
Spatial segregation across travelling fronts in individual-based and continuum models for the growth of heterogeneous cell populations
- Abstract:
- We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they are less compressed, and thus their movement occurs down the gradient of the cellular pressure. The cellular pressure is defined as a weighted sum of the densities (i.e. the volume fractions) of cells with different phenotypes. To translate into mathematical terms the idea that cells with distinct phenotypes have different morphological and mechanical properties, both the cell mobility and the weighted amount the cells contribute to the cellular pressure vary with their phenotype. We formally derive this model as the continuum limit of an on-lattice individual-based model, where cells are represented as single agents undergoing a branching biased random walk corresponding to phenotype-dependent and pressure-regulated cell division, death, and movement. Then, we study travelling wave solutions whereby cells with different phenotypes are spatially segregated across the invading front. Finally, we report on numerical simulations of the two models, demonstrating excellent agreement between them and the travelling wave analysis. The results presented here indicate that inter-cellular variability in mobility can support the maintenance of spatial segregation across invading fronts, whereby cells with a higher mobility drive invasion by occupying regions closer to the front edge.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 1.9MB, Terms of use)
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- Publisher copy:
- 10.1007/s11538-025-01452-y
Authors
+ European Research Council
More from this funder
- Funder identifier:
- https://ror.org/0472cxd90
- Grant:
- 883363
- Programme:
- Advanced Grant Nonlocal-CPD (Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization)
+ Engineering and Physical Sciences Research Council
More from this funder
- Funder identifier:
- https://ror.org/0439y7842
- Grant:
- EP/V051121/1
- Publisher:
- Springer
- Journal:
- Bulletin of Mathematical Biology More from this journal
- Volume:
- 87
- Article number:
- 77
- Publication date:
- 2025-05-19
- Acceptance date:
- 2025-04-15
- DOI:
- EISSN:
-
1522-9602
- ISSN:
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0092-8240
- Language:
-
English
- Keywords:
- Pubs id:
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2072026
- Local pid:
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pubs:2072026
- Deposit date:
-
2025-04-16
Terms of use
- Copyright holder:
- Carrillo et al.
- Copyright date:
- 2025
- Rights statement:
- © The Author(s) 2025. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
- Licence:
- CC Attribution (CC BY)
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