Journal of Mathematical Biology

, Volume 53, Issue 4, pp 672–702 | Cite as

Cell–cell communication by quorum sensing and dimension-reduction

  • Johannes Müller
  • Christina Kuttler
  • Burkard A. Hense
  • Michael Rothballer
  • Anton Hartmann
Article

Abstract

Several bacterial taxa change their behavior if the population density exceeds a certain threshold. This phenomenon is the consequence of a communication system between the bacteria and is called quorum sensing (QS). Up to now, this phenomenon is mostly modeled at population level. However, new experimental techniques allow for single cell analysis. We introduce a modeling approach for the description of this QS system, including a discussion of the regulatory network and its bistable behavior. Based on this single-cell model we develop and analyze a spatially structured model for a cell population. Special attention is given to the scaling behavior w.r.t. the cell size (leading to an approximation theorem for stationary solutions) and its consequences for the interpretation of cell communication (QS versus diffusion sensing). Concluding, we apply the modeling approach to spatially structured experimental data.

Keywords

Quorum sensing Single cell analysis Bistability Dimension reduction Partial differential equation 

Mathematics Subject Classification (2000)

92C15 35A35 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Johannes Müller
    • 1
  • Christina Kuttler
    • 2
  • Burkard A. Hense
    • 2
  • Michael Rothballer
    • 3
  • Anton Hartmann
    • 3
  1. 1.Centre for Mathematical SciencesTechnical University MunichGarching/MunichGermany
  2. 2.Institute of Biomathematics and BiometryGSF - National Research Center for Environment and HealthOberschleißheimGermany
  3. 3.Institute of Soil Ecology, Department of Rhizosphere BiologyGSF - National Research Center for Environment and HealthOberschleißheimGermany

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