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Type: Journal article
Title: Mathematical modelling of quorum sensing in bacteria
Author: Ward, J.
King, J.
Koerber, A.
Williams, P.
Croft, J.
Sockett, R.
Citation: Mathematical Medicine and Biology, 2001; 18(3):263-292
Publisher: Oxford Univ Press
Issue Date: 2001
ISSN: 1477-8599
Abstract: The regulation of density-dependent behaviour by means of quorum sensing is widespread in bacteria, the relevant phenomena including bioluminescence and population expansion by swarming, as well as virulence. The process of quorum sensing is regulated by the production and monitoring of certain molecules (referred to as QSMs); on reaching an apparent threshold concentration of QSMs (reflecting high bacterial density) the bacterial colony in concert ‘switches on’ the density-dependent trait. In this paper a mathematical model which describes bacterial population growth and quorum sensing in a well mixed system is proposed and studied. We view the population of bacteria as consisting of down-regulated and up-regulated sub-populations, with QSMs being produced at a much faster rate by the up-regulated cells. Using curve fitting techniques for parameter estimation, solutions of the resulting system of ordinary differential equations are shown to agree well with experimental data. Asymptotic analysis in a biologically relevant limit is used to investigate the timescales for up-regulation of an exponentially growing population of bacteria, revealing the existence of bifurcation between limited and near-total up-regulation. For a fixed population of cells steady-state analysis reveals that in general one physical steady-state solution exists and is linearly stable; we believe this solution to be a global attractor. A bifurcation between limited and near-total up-regulation is also discussed in the steady-state limit.
Keywords: bacteria
quorum sensing
mathematical modelling
experimental validation
numerical solution
asymptotic analysis
steady-state analysis
Description: © 2001 by Institute of Mathematics and its Applications
DOI: 10.1093/imammb/18.3.263
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Appears in Collections:Applied Mathematics publications
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