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Reaction–diffusion modelling of bacterial colony patterns

Author

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  • Mimura, Masayasu
  • Sakaguchi, Hideo
  • Matsushita, Mitsugu

Abstract

It is well known from experiments that bacterial species Bacillus subtilis exhibit various colony patterns. These are essentially classified into five types in the morphological diagram, depending on the substrate softness and nutrient concentration. (A) diffusion-limited aggregation-like; (B) Eden-like; (C) concentric ring-like; (D) disk-like; and (E) dense branching morphology-like. There arises the naive question of whether the diversity of colony patterns observed in experiments is caused by different effects or governed by the same underlying principles. Our research has led us to propose reaction–diffusion models to describe the morphological diversity of colony patterns except for Eden-like ones.

Suggested Citation

  • Mimura, Masayasu & Sakaguchi, Hideo & Matsushita, Mitsugu, 2000. "Reaction–diffusion modelling of bacterial colony patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 283-303.
    • Handle: RePEc:eee:phsmap:v:282:y:2000:i:1:p:283-303
    DOI: 10.1016/S0378-4371(00)00085-6
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    Citations

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    Cited by:

    1. Kaoru Sugimura & Kohei Shimono & Tadashi Uemura & Atsushi Mochizuki, 2007. "Self-organizing Mechanism for Development of Space-filling Neuronal Dendrites," PLOS Computational Biology, Public Library of Science, vol. 3(11), pages 1-12, November.
    2. Leyva, J. Francisco & Málaga, Carlos & Plaza, Ramón G., 2013. "The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5644-5662.
    3. Gafiychuk, V.V. & Datsko, B.Yo., 2006. "Pattern formation in a fractional reaction–diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 300-306.
    4. Lin Chen & Javad Noorbakhsh & Rhys M Adams & Joseph Samaniego-Evans & Germaine Agollah & Dmitry Nevozhay & Jennie Kuzdzal-Fick & Pankaj Mehta & Gábor Balázsi, 2014. "Two-Dimensionality of Yeast Colony Expansion Accompanied by Pattern Formation," PLOS Computational Biology, Public Library of Science, vol. 10(12), pages 1-14, December.
    5. Mansour, M.B.A., 2007. "Traveling wave solutions of a reaction–diffusion model for bacterial growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 466-472.
    6. Chapwanya, Michael & Dumani, Phindile, 2023. "Stationary and oscillatory patterns in microbial population under environmental stress," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 370-383.
    7. Badoual, M. & Derbez, P. & Aubert, M. & Grammaticos, B., 2009. "Simulating the migration and growth patterns of Bacillus subtilis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 549-559.
    8. Samvel Sarukhanian & Anna Maslovskaya & Christina Kuttler, 2023. "Three-Dimensional Cellular Automaton for Modeling of Self-Similar Evolution in Biofilm-Forming Bacterial Populations," Mathematics, MDPI, vol. 11(15), pages 1-18, July.
    9. Banitz, Thomas & Fetzer, Ingo & Johst, Karin & Wick, Lukas Y. & Harms, Hauke & Frank, Karin, 2011. "Assessing biodegradation benefits from dispersal networks," Ecological Modelling, Elsevier, vol. 222(14), pages 2552-2560.

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