Applied Mathematics and Nonlinear Sciences
Journal license

Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 2, Issue 1


Published
on

May 16, 2017


Pages

157-172


DOI

Article

On the stabilizing effect of chemotaxis on bacterial aggregation patterns

Check for updates


Authors

J. Alejandro Butanda Affiliation:
Centro de Investigación en Matemáticas A. C., Jalisco s/n, La Valenciana, C.P. 36023 Guanajuato, Gto., Mexico
, Carlos Málaga Affiliation:
Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior s/n, Ciudad Universitaria, C.P. 04510 Cd. de México, Mexico
and Ramón G. Plaza Affiliation:
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Circuito Escolar s/n, Ciudad Universitaria, C.P. 04510 Cd. de México, Mexico


Abstract

We consider a chemotaxis-reaction-diffusion system that models the dynamics of colonies of Bacillus subtilis on thin agar plates. The system of equations was proposed by Leyva et al. [14], based on a previous non-chemotactic model by Kawasaki and collaborators [9], which reproduces the dense branching patterns observed experimentally in the semi-solid agar, low-nutrient regime. Numerical simulations show that, when the chemotactic sensitivity toward nutrients is increased, the morphology of the colony changes from a dense branched pattern to a uniform envelope that propagates outward. Here, we provide a quantitative argument that explains this change in morphology. This result is based on energy estimates on the spectral equations for perturbations around the envelope front, suggesting the suppression of colony branching as a result of the stabilizing effect of the increasing chemotactic signal.


Keywords

Nutrient chemotaxis, non-linear cross diffusion, stability of fronts, 92C17, 92D25, 35B35, 35C07


Citation

Butanda, J. A., Málaga, C., & Plaza, R. G. (2017). On the stabilizing effect of chemotaxis on bacterial aggregation patterns. Applied Mathematics and Nonlinear Sciences, 2(1), 157–172. https://doi.org/10.21042/AMNS.2017.1.00013

Published by: Engineering Journals

Engineering Journals Logo