ArticleJournal of mathematical biology2006
A structured-population model of Proteus mirabilis swarm-colony development.
Article in Journal of mathematical biology, 2006. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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Who cites it
13 citing papers in PubMed.
- Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods.Journal of mathematical biology · 2025Review
- Adjustment in the Composition and Organization ofInternational journal of molecular sciences · 2023Article
- Structured models of cell migration incorporating molecular binding processes.Journal of mathematical biology · 2017Article
- Mathematics as a conduit for translational research in post-traumatic osteoarthritis.Journal of orthopaedic research : official publication of the Orthopaedic Research Society · 2017Article
- A random graph model of density thresholds in swarming cells.Journal of cellular and molecular medicine · 2016Article
- Linking Cellular and Mechanical Processes in Articular Cartilage Lesion Formation: A Mathematical Model.Frontiers in bioengineering and biotechnology · 2016Article
- Proteus mirabilis and Urinary Tract Infections.Microbiology spectrum · 2015Review
- A validated model of the pro- and anti-inflammatory cytokine balancing act in articular cartilage lesion formation.Frontiers in bioengineering and biotechnology · 2015Article
- Modeling and simulation of the effects of cyclic loading on articular cartilage lesion formation.International journal for numerical methods in biomedical engineering · 2014Article
- Radial and spiral stream formation in Proteus mirabilis colonies.PLoS computational biology · 2011Article
- Patterning of mutually interacting bacterial bodies: close contacts and airborne signals.BMC microbiology · 2010Article
- An explanatory model to validate the way water activity rules periodic terrace generation in Proteus mirabilis swarm.Journal of mathematical biology · 2009Article
- Bacterial Swarming: A Model System for Studying Dynamic Self-assembly.Soft matter · 2009Article
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Abstract
In this paper we present continuous age- and space-structured models and numerical computations of Proteus mirabilis swarm-colony development. We base the mathematical representation of the cell-cycle dynamics of Proteus mirabilis on those developed by Esipov and Shapiro, which are the best understood aspects of the system, and we make minimum assumptions about less-understood mechanisms, such as precise forms of the spatial diffusion. The models in this paper have explicit age-structure and, when solved numerically, display both the temporal and spatial regularity seen in experiments, whereas the Esipov and Shapiro model, when solved accurately, shows only the temporal regularity. The composite hyperbolic-parabolic partial differential equations used to model Proteus mirabilis swarm-colony development are relevant to other biological systems where the spatial dynamics depend on local physiological structure. We use computational methods designed for such systems, with known convergence properties, to obtain the numerical results presented in this paper.
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