Skip Navigation

Mathematical Medicine and Biology 2001 18(3):263-292; doi:10.1093/imammb/18.3.263
© 2001 by Institute of Mathematics and its Applications
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Ward, J. P.
Right arrow Articles by Sockett, R. E.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Ward, J. P.
Right arrow Articles by Sockett, R. E.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Mathematical modelling of quorum sensing in bacteria

J. P. Ward1, J.R. King1, A. J. Koerber1, P. Williams2, J. M. Croft3 and R. E. Sockett3

1 Division of Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK. Email: john.ward{at}nottingham.ac.uk 2 School of Pharmaceutical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK 3 Division of Genetics, School of Clinical Laboratory Sciences, Queens Medical Centre, University of Nottingham, Nottingham, NG7 2UH, UK

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

Received 26 July 2000. Revised 13 July 2001.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.