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

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

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 22, 5644-5662

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.

Keywords: Nutrient chemotaxis; Bacillus subtilis; Non-linear degenerate diffusion; Front propagation (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:22:p:5644-5662

DOI: 10.1016/j.physa.2013.07.022

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