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Experts develop a simpler mathematical model for reproducing bacterial growth patterns

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The expansion of bacterial colonies is one of the classic research areas in biology. In a recent study, Ignasi Pagonabarraga, from the UB Department of Fundamental Physics, and researchers from the University of Edinburgh consider a new model that uses two parameters to reproduce the growth patterns of these microorganisms.


The mathematical model described in the study, which has been published in the Proceedings of the National Academy of Science (PNAS), takes into account the basic movements of which bacteria are capable: motility, directional movement and diffusion, which is less regular and harder to model. "Eventually we decided on two adimensional parameters that describe the way motility changes according to aspects such as the density of the bacteria and the rate of diffusion", explains Pagonabarraga. Current research into bacterial growth is based on the combined evolution of bacterial density and chemical stimulants and requires up to ten parameters to be adjusted.

In nature, bacteria are often found concentrated on surfaces in structures that form spectaular patterns viewable under a microscope. In the laboratory, these patterns can be reproduced in a Petri dish containing agar gel, which acts as a culture. The specialist biologists behind the study have developed a series of equations that account for the changes in directional movement in response to chemical stimuli such as food sources, in a phenomenon known as chemotaxis. As Pagonabarraga explains, "The model we propose does not take into account chemotaxis but does predict the formation of patterns that are surprisingly similar to those considered to reflect chemotactic behaviour". The two parameters have a physical component, allowing them to be adjusted for use in future experiments.
One of the most commonly observed growth patterns in bacterial colonies consists of concentric rings. Patterns of this type can be predicted by taking into account that bacterial motility changes according to density. This change causes the bacteria to separate into two phases of different thicknesses due to the coexistence of two densities. Cell division is predominant in the regions with lower density and cell death in the denser regions. The development of simplified models that identify a minimum number of parameters for describing the growth patterns observed under experimental conditions will facilitate identification of the basic mechanisms underlying bacterial dynamics.



M. E. Cates, D. Marenduzzo, I. Pagonabarraga, J. Tailleur. "Arrested phase separation in reproducing bacteria creates a generic route to pattern formation". Proceedings of the National Academy of Sciences of the United States of America. DOI: 10.1073/pnas.1001994107 (2010).

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