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

J. Francisco Leyva, Carlos Malaga, Ramon G. Plaza
Posgrado en Ciencias Matematicas, Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Circuito Exterior s/n, Ciudad Universitaria, C.P. 04510 Mexico D.F. (Mexico)
arXiv:1301.5058 [q-bio.CB], 2013

@article{2013arXiv1301.5058F,

   author={Francisco Leyva}, J. and {Malaga}, C. and {Plaza}, R.~G.},

   title={"{The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1301.5058},

   primaryClass={"q-bio.CB"},

   keywords={Quantitative Biology – Cell Behavior, Nonlinear Sciences – Pattern Formation and Solitons, Physics – Biological Physics},

   year={2013},

   month={jan},

   adsurl={http://adsabs.harvard.edu/abs/2013arXiv1301.5058F},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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This paper introduces 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. (J. of Theor. Biol. 188(2) 1997) and it includes a suitable nutrient chemotactic term compatible with such type of diffusion. High resolution numerical simulations using Graphic Processing Units (GPUs) of the new model are presented, showing that the chemotactic term enhances the velocity of propagation of the colony envelope for dense-branching morphologies. In addition, the chemotaxis seems to stabilize the formation of branches in the soft-agar, low-nutrient regime. An asymptotic estimation predicts the growth velocity of the colony envelope as a function of both the nutrient concentration and the chemotactic sensitivity. For fixed nutrient concentrations, the growth velocity is an increasing function of the chemotactic sensitivity.
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