Mathematical Model of Quorum Sensing and Biofilm
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.
KeywordsQuorum 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.
- 10.Majumdar, S., Datta, S., & Roy, S. (2012). Mathematical modelling of quorum sensing and bioluminescence in bacteria. International Journal of Advance and Applied Science, 1(3), 139–146.Google Scholar
- 11.Majumdar, S. (2013). Hydrodynamic conditions of quorum sensing in bacteria. International Journal of Biochemistry and Biophysics, 2(1), 1–4.Google Scholar
- 12.Majumdar, S. (2016). Math behind quorum sensing. Society for Industrial and Applied Mathematics (SIAM).Google Scholar
- 14.National Institutes of Health. (2007). Immunology of biofilms (R01). http://grants.nih.gov/grants/guide/pa-files/PA-07-288.html.
- 23.Majumdar, S.(2017). Experimental evidence of coherence in bacterial communication system. Science (eLetter).Google Scholar
- 24.Majumdar, S., & Roy, S. (2017). The role of coherence in bacterial communication. bioRxiv. https://doi.org/10.1101/119503.
- 26.Majumdar, S., & Roy, S. (2018). Relevance of quantum mechanics in bacterial communication. Neuro Quantology, 16(3), 1–6.Google Scholar
- 27.Roy, S., & Llinas, R. (2016). Non-local hydrodynamics of swimming bacteria and self-activated process., BIOMAT 2015 Proceedings of the International Symposium on Mathematical and Computational Biology. World Scientific 153–165.Google Scholar
- 28.Majumdar, S., & Roy, S. (2017). Spatiotemporal patterns and chaos in non-equilibrium bacterial communication. 17th International symposium on mathematical and computational biology, at Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia.Google Scholar
- 29.Majumdar, S., Roy, S., & Llinas, R. (2017). Bacterial conversations and pattern formation. bioRxiv. https://doi.org/10.1101/098053.
- 30.Majumdar, S. (2016). Mathematical model of talking bacteria. Workshop on industrial and applied mathematics. Hamburg: University of Hamburg.Google Scholar
- 32.Majumdar, S. (2017). Bacterial communication: classical and quantum aspects. AquaDiva Recruitment Symposium, Friedrich-Schiller-Universitat Jena, Germany.Google Scholar