Mathematical Model of Quorum Sensing and Biofilm

  • Sarangam Majumdar
  • Sisir Roy


Bacteria are unicellular microorganism, which are found in nature quite often. They talk to each other using chemical signaling process (quorum sensing) and ion-channel mediated electrical signaling mechanism. Quorum sensing is a density dependent bacterial collective behaviour and/or cell-to -cell communication mechanism. This widespread bacterial behaviour is related with biofilm formation, gene expression, swarming, virulence and bioluminescence. In a recent realization (experimental and theoretical study), it was observed that bacteria can also talk to each other through the wave of potassium and an oscillatory dynamics was noticed in bacterial biofilms. In this present chapter, we present two different mathematical frameworks of bacterial communication system. The first model is based on the bacterial density dependent behaviour with up-regulation and down-regulation of the production of quorum sensing molecules. Second model, we introduce two different types of the bacterial communication process within a mathematical framework, which is also related to the biofilm formation. This mathematical framework combine quorum sensing mechanism as well as electrical signaling process. We discuss different spatiotemporal patterns and chaotic behaviour in this communication system. Moreover, it gives a significant and the fundamental role of noise in the complex biological conversation system. Finally we propose some open problem in the last section of this chapter, which are helpful for the future research of the bacterial communication system.


Quorum sensing Bioflim Noise Ion-channels Quantum biology Kinematic viscosity Pattern formations 



One of the authors (SR) greatly acknowledges Homi Bhabha Council, Mumbai for the grant under which the work has been done.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Sarangam Majumdar
    • 1
  • Sisir Roy
    • 2
  1. 1.Dipartimento di Ingegneria Scienze Informatiche e MatematicaUniversità degli Studi di L’ AquilaL’ AquilaItaly
  2. 2.National Institute of Advanced StudiesIndian Institute of Science CampusBangaloreIndia

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