Individual-Based Model for Quorum Sensing with Background Flow

Hannes Uecke, Johannes Müller, Burkhard A. Hense

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13 Scopus citations


Quorum sensing is a wide-spread mode of cell-cell communication among bacteria in which cells release a signalling substance at a low rate. The concentration of this substance allows the bacteria to gain information about population size or spatial confinement. We consider a model for N cells which communicate with each other via a signalling substance in a diffusive medium with a background flow. The model consists of an initial boundary value problem for a parabolic PDE describing the exterior concentration u of the signalling substance, coupled with N ODEs for the masses ai of the substance within each cell. The cells are balls of radius R in ℝ3, and under some scaling assumptions we formally derive an effective system of N ODEs describing the behaviour of the cells. The reduced system is then used to study the effect of flow on communication in general, and in particular for a number of geometric configurations.

Original languageEnglish
Pages (from-to)1727-1746
Number of pages20
JournalBulletin of Mathematical Biology
Issue number7
StatePublished - Jul 2014
Externally publishedYes


  • Dimension reduction
  • Drift
  • Parabolic PDE
  • Quorum sensing


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