Coarsening dynamics of chemotactic aggregates
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911267122315264 |
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| author | Weyer, Henrik Muramatsu, David Frey, Erwin |
| author_facet | Weyer, Henrik Muramatsu, David Frey, Erwin |
| contents | Auto-chemotaxis, the directed movement of cells along gradients in chemicals they secrete, is central to the formation of complex spatiotemporal patterns in biological systems. Since the introduction of the Keller--Segel model, numerous variants have been analyzed, revealing phenomena such as coarsening of aggregates, stable aggregate sizes, and spatiotemporally chaotic dynamics. Here, we consider general mass-conserving Keller--Segel models, that is, models without cell growth and death, and analyze the generic long-time dynamics of the chemotactic aggregates. Building on and extending our previous work, which demonstrated that chemotactic aggregation can be understood through a generalized Maxwell construction balancing density fluxes and reactive turnover, we use singular perturbation theory to derive the rates of mass competition between well-separated aggregates. We analyze how this mass-competition process drives coarsening in both diffusion- and reaction-limited regimes, with the diffusion-limited rate aligning with our previous quasi-steady-state analyses. Our results generalize earlier mathematical findings, demonstrating that coarsening is driven by self-amplifying mass transport and aggregate coalescence. Additionally, we provide a linear stability analysis of the lateral instability, predicting it through a nullcline-slope criterion that parallels the curvature criterion in spinodal decomposition. Overall, our findings suggest that chemotactic aggregates behave similarly to phase-separating droplets, providing a robust framework for understanding the coarse-grained dynamics of auto-chemotactic cell populations and a quantitative basis for comparing chemotactic coarsening to canonical non-equilibrium phase separation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20100 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coarsening dynamics of chemotactic aggregates Weyer, Henrik Muramatsu, David Frey, Erwin Soft Condensed Matter Pattern Formation and Solitons Biological Physics Auto-chemotaxis, the directed movement of cells along gradients in chemicals they secrete, is central to the formation of complex spatiotemporal patterns in biological systems. Since the introduction of the Keller--Segel model, numerous variants have been analyzed, revealing phenomena such as coarsening of aggregates, stable aggregate sizes, and spatiotemporally chaotic dynamics. Here, we consider general mass-conserving Keller--Segel models, that is, models without cell growth and death, and analyze the generic long-time dynamics of the chemotactic aggregates. Building on and extending our previous work, which demonstrated that chemotactic aggregation can be understood through a generalized Maxwell construction balancing density fluxes and reactive turnover, we use singular perturbation theory to derive the rates of mass competition between well-separated aggregates. We analyze how this mass-competition process drives coarsening in both diffusion- and reaction-limited regimes, with the diffusion-limited rate aligning with our previous quasi-steady-state analyses. Our results generalize earlier mathematical findings, demonstrating that coarsening is driven by self-amplifying mass transport and aggregate coalescence. Additionally, we provide a linear stability analysis of the lateral instability, predicting it through a nullcline-slope criterion that parallels the curvature criterion in spinodal decomposition. Overall, our findings suggest that chemotactic aggregates behave similarly to phase-separating droplets, providing a robust framework for understanding the coarse-grained dynamics of auto-chemotactic cell populations and a quantitative basis for comparing chemotactic coarsening to canonical non-equilibrium phase separation. |
| title | Coarsening dynamics of chemotactic aggregates |
| topic | Soft Condensed Matter Pattern Formation and Solitons Biological Physics |
| url | https://arxiv.org/abs/2409.20100 |