Quorum Sensing pp 253-271 | Cite as

Differential Equations Models to Study Quorum Sensing

  • Judith Pérez-Velázquez
  • Burkhard A. Hense
Part of the Methods in Molecular Biology book series (MIMB, volume 1673)


Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

Key words

Quorum sensing Differential equations Derivatives Ordinary differential equations Partial differential equations Mathematical models 


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Copyright information

© Springer Science+Business Media LLC 2018

Authors and Affiliations

  1. 1.Mathematical Modeling of Biological Systems, Centre for Mathematical ScienceTechnical University of MunichGarchingGermany
  2. 2.Institute of Computational BiologyHelmholtz Zentrum MünchenNeuherbergGermany

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