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Simple models for quorum sensing: nonlinear dynamical analysis.

Wei-Yin Chiang¹, Yue-Xian Li, Pik-Yin Lai

¹Department of Physics, Graduate Institute of Biophysics and Center for Complex Systems, National Central University, Chungli, Taiwan 320, Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 21, 2011

Summary

Quorum sensing describes how cell behavior changes with population density. This study models how quiescent cells become oscillatory, with synchronized dynamics observed at the onset of these oscillations.

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Area of Science:

Mathematical Biology
Systems Biology
Nonlinear Dynamics

Background:

Quorum sensing involves population density-dependent cooperative behaviors in cells.
This phenomenon is driven by chemical signaling within the environment.
Focus is on transitions from quiescent to oscillatory dynamics with changing cell populations.

Purpose of the Study:

To develop and analyze simple models of quorum sensing.
To investigate the transition from quiescent to oscillatory behavior.
To explore synchronization phenomena in coupled elements.

Main Methods:

Construction of two mathematical models: an excitable/oscillatory phase model and a FitzHugh-Nagumo element model.
Application of mean-field approximation for analytical insights.
Nonlinear dynamical analysis, including bifurcation analysis.
Numerical verification of analytical results.

Main Results:

The phase model identified parameter regimes for quorum sensing and yielded analytical phase diagrams.
The FitzHugh-Nagumo model exhibited diverse dynamics like Hopf and fold bifurcations.
Synchronization of elements was observed concurrently with the onset of oscillations in both models.

Conclusions:

The developed models effectively capture key quorum sensing dynamics.
Population density significantly influences system dynamics, leading to oscillations and synchronization.
The findings offer insights into collective cell behavior and potential model extensions.