Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations
Americo Marrocco,Hervé Henry,I. B. Holland,Mathis Plapp,S. J. Seror,Benoît Perthame,Benoît Perthame +6 more
TLDR
A critical anal ysis of the validity of the model based on recent observations of the swarming bacteria which show that nutrients are not limitating but distinct subpopulations growing at different rates are lik ely present is presented.Abstract:
Bacillus subtilis swarms rapidly over the surface of a synthetic medium creating remarkable hyperbranched dendritic communities. Models to reproduce such effects have been proposed under the form of parabolic Partial Differential Equations representing the dynamics of the active cells (both motile and multiplying), the passive cells (non-motile and non-growing) and nutrient concentration. We test the numerical behavior of such models and compare them to relevant experimental data together with a critical analysis of the validity of the models based on recent observations of the swarming bacteria which show that nutrients are not limitating but distinct subpopulations growing at different rates are likely present.read more
Citations
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On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives
Nicola Bellomo,Christian Dogbe +1 more
TL;DR: A review and critical analysis of the mathematical literature concerning the modeling of vehicular traffic and crowd phenomena and a critical analysis focused on research perspectives that consider the development of a unified modeling strategy are presented.
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Branching instability in expanding bacterial colonies
TL;DR: An analytical and computational analysis is performed to study pattern formation during the spreading of an initially circular bacterial colony on a Petri dish, finding the spreading colony is found to be always linearly unstable to perturbations of the interface, whereas branching instability arises in finite-element numerical simulations.
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Traveling plateaus for a hyperbolic Keller-Segel system with attraction and repulsion: existence and branching instabilities
TL;DR: In this paper, the authors studied the branching instability in the hyperbolic Keller-Segel system with logistic sensitivity, where repulsive and attractive forces, acting on a conservative system, create stable traveling patterns or branching instabilities.
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Congestion-driven dendritic growth
TL;DR: In this paper, a simple model where a given population evolves feeded by a diffusing nutriment, but is subject to a density constraint is proposed, where particles (e.g., cells) of the population spontaneously stay passive at rest, and only move in order to satisfy the constraint by choosing the minimal correction velocity so as to prevent overloading.
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Modelling of surfactant-driven front instabilities in spreading bacterial colonies.
TL;DR: It is shown that variations in the wettability and surfactant production are sufficient to reproduce four different types of colony growth, which have been described in the literature, namely, arrested and continuous spreading of circular colonies, slightly modulated front lines and the formation of pronounced fingers.
References
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Phase transition of traveling waves in bacterial colony pattern
TL;DR: In this paper, the wave form as a function of the initial nutrient concentration was studied and two distinct types of solution were found, and the velocity of traveling wave also showed sharp transition in nonlinear diffusion model.
2D simulation of chemotactic bacteria aggregation
TL;DR: In this paper, a new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi-Fermi level in the framework of semiconductor modelling).
Posted Content
Existence result for a model of Proteus mirabilis swarm
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Aggrégation de bactéries. Simulations numériques de modèles de réaction-diffusion à l'aide des éléments finis mixtes
TL;DR: The work of J.D. Murray (Mathematical biology) constitue d'un systeme de trois equations aux derivees partielles as discussed by the authors, i.e., densite de bacteries, concentration de chemoattractants and concentration of stimulants (nourriture).