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The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion

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  • Leyva, J. Francisco
  • Málaga, Carlos
  • Plaza, Ramón G.

Abstract

This paper studies a reaction–diffusion–chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (1997) [5] and it includes a suitable nutrient chemotactic term compatible with such type of diffusion, as suggested by Ben-Jacob et al. (2000) [20]. An asymptotic estimation predicts the growth velocity of the colony envelope as a function of both the nutrient concentration and the chemotactic sensitivity. It is shown that the growth velocity is an increasing function of the chemotactic sensitivity. High resolution numerical simulations using Graphic Processing Units (GPUs), which include noise in the diffusion coefficient for the bacteria, are presented. The numerical results verify that the chemotactic term enhances the velocity of propagation of the colony envelope. In addition, the chemotaxis seems to stabilize the formation of branches in the soft-agar, low-nutrient regime.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:22:p:5644-5662
    DOI: 10.1016/j.physa.2013.07.022
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    References listed on IDEAS

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    1. 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.
    2. Golding, Ido & Kozlovsky, Yonathan & Cohen, Inon & Ben-Jacob, Eshel, 1998. "Studies of bacterial branching growth using reaction–diffusion models for colonial development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 260(3), pages 510-554.
    3. Ben-Jacob, Eshel & Cohen, Inon & Golding, Ido & Gutnick, David L. & Tcherpakov, Marianna & Helbing, Dirk & Ron, Ilan G., 2000. "Bacterial cooperative organization under antibiotic stress," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 247-282.
    4. David A. Kessler & Herbert Levine, 1998. "Fluctuation-induced diffusive instabilities," Nature, Nature, vol. 394(6693), pages 556-558, August.
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    Cited by:

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