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Mathematical modelling of quorum sensing in bacteria
J P Ward1, J R King, A J Koerber
1Division of Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, UK. john.ward@nottingham.ac.uk
IMA Journal of Mathematics Applied in Medicine and Biology
|January 31, 2002
Summary
This study models bacterial quorum sensing, revealing how bacteria coordinate behaviors like swarming and virulence. Mathematical analysis shows how bacterial density triggers collective action, with findings aligning with experimental data.
Area of Science:
- Microbiology
- Mathematical Biology
- Systems Biology
Background:
- Quorum sensing regulates density-dependent bacterial behaviors like bioluminescence, swarming, and virulence.
- This process involves producing and detecting signaling molecules (QSMs) that trigger collective action at high bacterial densities.
Purpose of the Study:
- To propose and analyze a mathematical model for bacterial population growth and quorum sensing in a well-mixed system.
- To investigate the dynamics of bacterial up-regulation and density-dependent trait expression.
Main Methods:
- Developed a mathematical model representing bacterial populations as down-regulated and up-regulated sub-populations.
- Utilized curve fitting for parameter estimation and ordinary differential equations to model system dynamics.
- Employed asymptotic and steady-state analyses to explore bacterial up-regulation and bifurcation phenomena.
Main Results:
- Model solutions showed good agreement with experimental data.
- Asymptotic analysis revealed bifurcations between limited and near-total up-regulation in exponentially growing populations.
- Steady-state analysis identified a single, stable physical steady-state solution, likely a global attractor.
Conclusions:
- The mathematical model accurately captures bacterial population growth and quorum sensing dynamics.
- Bifurcation phenomena are critical in determining the extent of bacterial collective behavior up-regulation.
- The identified stable steady-state solution provides insights into bacterial population regulation.