Geodesic
Regime switching on the propagation speed of travelling waves of some size-structured myxobacteria population models
Vincent Calvez1 ; Adil El Abdouni2 ; Maxime Estavoyer1 ; Ignacio Madrid3 ; Julien Olivier4 ; Magali Tournus4
1Univ Lyon, CNRS, Université Claude Bernard Lyon 1, UMR5208, Institut Camille Jordan, F-69622 Villeurbanne, France
2Laboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 45 Avenue des États-Unis, 78035 Versailles cedex
3CMAP, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
4Aix Marseille Univ, CNRS, Centrale Marseille, I2M, UMR 7373, Turing Centre for Living systems, Marseille, France
ESAIM. Proceedings, Tome 77 (2024), pp. 195-212
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The spatial propagation of complex populations can depend on some structuring variables. In particular, recent developments in microscopy have revealed the impact of bacteria heterogeneity on the population motility. Biofilms of Myxococcus xanthus bacteria have been shown to be structured in clusters of various sizes, which remarkably, tend to move faster when they consist of a larger number of bacteria. We propose a minimal reaction-diffusion discrete-size structure model of a population of Myxococcus with two possible cluster sizes: isolated and paired bacteria. Numerical experiments show that this model exhibits travelling waves whose propagation speed depends on the increased motility of clusters, and the exchange rates between isolated bacteria and clusters. Notably, we present evidence of the existence of a characteristic threshold level θ*. on the ratio between cluster motility and isolated bacteria motility, which separates two distinct regimes of propagation speed. When the ratio is less or equal than θ*, the propagation speed of the population is constant with respect to the ratio. However, when the ratio is above θ*, the propagation speed increases. We also consider a generalised model with continuous-size structure, which also shows the same behaviour. We extend the model to include interactions with a resource population, which show qualitative behaviours in agreement to the biological experiments.
DOI : 10.1051/proc/202477195

Vincent Calvez  1   ; Adil El Abdouni  2   ; Maxime Estavoyer  1   ; Ignacio Madrid  3   ; Julien Olivier  4   ; Magali Tournus  4

1 Univ Lyon, CNRS, Université Claude Bernard Lyon 1, UMR5208, Institut Camille Jordan, F-69622 Villeurbanne, France
2 Laboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 45 Avenue des États-Unis, 78035 Versailles cedex
3 CMAP, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
4 Aix Marseille Univ, CNRS, Centrale Marseille, I2M, UMR 7373, Turing Centre for Living systems, Marseille, France 
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     author = {Vincent Calvez and Adil El Abdouni and Maxime Estavoyer and Ignacio Madrid and Julien Olivier and Magali Tournus},
     title = {Regime switching on the propagation speed of travelling waves of some size-structured myxobacteria population models},
     journal = {ESAIM. Proceedings},
     pages = {195--212},
     year = {2024},
     volume = {77},
     doi = {10.1051/proc/202477195},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202477195/}
}
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Vincent Calvez; Adil El Abdouni; Maxime Estavoyer; Ignacio Madrid; Julien Olivier; Magali Tournus. Regime switching on the propagation speed of travelling waves of some size-structured myxobacteria population models. ESAIM. Proceedings, Tome 77 (2024), pp. 195-212. doi: 10.1051/proc/202477195

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