Abstract
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.
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References
Nealson, K. H., Platt, T., & Hastings, J. W. (1970). Cellular control of the synthesis and activity of the bacterial luminescent system. Journal of Bacteriology, 104, 313–322.
Gray, K. M., Passador, L., Iglewski, B. H., & Greenberg, E. P. (1994). Interchangeability and specificity of components from the quorum-sensing regulatory systems of Vibrio fischeri and Pseudomonas aeruginosa. Journal of Bacteriology, 176, 3076–3080.
Fuqua, C., Winans, S. C., & Greenberg, E. P. (1996). Census and consensus in bacterialecosystems: The LuxRLuxI family of quorum-sensing transcriptional regulators. Annual Review of Microbiology, 50, 727–751.
Shapiro, J. A. (1998). Thinking about bacterial populations as multicellular organisms. Annual Review of Microbiology, 52, 81–104.
Miller, M. B., & Bassler, B. L. (2001). Quorum sensing in bacteria. Annual Review of Microbiology, 55(1), 165–199.
Shapiro, J. A. (2007). Bacteria are small but not stupid: Cognition, natural genetic engineering and socio-bacteriology. Studies in History and Philosophy of Science Part C. Studies in History and Philosophy of Biological and Biomedical Sciences, 38(4), 807–819.
Williams, P., Winzer, K., Chan, W. C., & Camara, M. (2007). Look who’s talking: Communication and quorum sensing in the bacterial world. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 362(1483), 1119–1134.
Majumdar, S., & Mondal, S. (2016). Conversation game: Talking bacteria. Journal Cell Communication Signal, 10(4), 331–335.
Majumdar, S., & Pal, S. (2016). Quorum sensing: A quantum perspective. Journal of Cell Communication and Signaling, 10(3), 173–175.
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.
Majumdar, S. (2013). Hydrodynamic conditions of quorum sensing in bacteria. International Journal of Biochemistry and Biophysics, 2(1), 1–4.
Majumdar, S. (2016). Math behind quorum sensing. Society for Industrial and Applied Mathematics (SIAM).
Klapper, I., & Dockery, J. (2010). Mathematical description of microbial biofilms. SIAM Review, 52(2), 221–265.
National Institutes of Health. (2007). Immunology of biofilms (R01). http://grants.nih.gov/grants/guide/pa-files/PA-07-288.html.
Majumdar, S., & Pal, S. (2017). Cross-species communication in bacterial world. Journal Cell Communication and Signaling, 11(2), 187–190.
Doyle, D. A., Cabral, M. J., Pfuetzner, A. R., Kuo, A., Gulbis, M. J., Cohen, L. S., Chait, T. B., & MacKinnon, R. (1998). The structure of the potassium channel: Molecular basis of K+ conduction and selectivity. Science, 280(5360), 69–77.
Prindle, A., Jintao, L., Munehiro, A., San, L., Jordi, G.-O., & Süel, G. M. (2015). Ion channels enable electrical communication in bacterial communities. Nature, 527(7576), 59–63.
Beagle, S. D., & Lockles, S. W. (2015). Electrical signaling goes bacterial. Nature, 527, 44.
Liu, J., Arthur, P., Jacqueline, H., Maral, G.-S., Munehiro, A., Lee Dong-yeon, D., San, L., Jordi, G.-O., & Süel, G. M. (2015). Metabolic co-dependence gives rise to collective oscillations within biofilms. Nature, 523(7562), 550–554.
Humphries, J., Xiong, L., Liu, J., Prindle, A., Yuan, F., Arjes, H. A., Tsimring, L., & Süel, G. M. (2017). Species-independent attraction to biofilms through electrical signaling. Cell, 168(1), 200–209.
Majumdar, S., & Pal, S. (2017). Bacterial intelligence: Imitation games, time-sharing and long- range quantum coherence. Journal Cell Communication and Signaling, 11(3), 281–284.
Liu, J., Corral, M. R., Prindle, A., Dong-yeon, L. D., Larkin, J., Sagarra, G. M., Ojalvo, G. J., & Süel, M. G. (2017). Coupling between distant biofilms and emergence of nutrient time-sharing. Science, 356(6338), 638–642.
Majumdar, S.(2017). Experimental evidence of coherence in bacterial communication system. Science (eLetter).
Majumdar, S., & Roy, S. (2017). The role of coherence in bacterial communication. bioRxiv. https://doi.org/10.1101/119503.
Ward, P. J., King, R. J., Koerber, J. A., Williams, P., Croft, M. J., & Sockett, E. R. (2001). Mathematical modelling of quorum sensing in bacteria. IMA Journal of Mathematics Applied in Medicine and Biology, 18(3), 263–292.
Majumdar, S., & Roy, S. (2018). Relevance of quantum mechanics in bacterial communication. Neuro Quantology, 16(3), 1–6.
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.
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.
Majumdar, S., Roy, S., & Llinas, R. (2017). Bacterial conversations and pattern formation. bioRxiv. https://doi.org/10.1101/098053.
Majumdar, S. (2016). Mathematical model of talking bacteria. Workshop on industrial and applied mathematics. Hamburg: University of Hamburg.
Roy, S., & Llinas, R. (2009). Relevance of quantum mechanics on some aspects of ion channel function. Comptes Rendus Biologies, 332(6), 517–522.
Majumdar, S. (2017). Bacterial communication: classical and quantum aspects. AquaDiva Recruitment Symposium, Friedrich-Schiller-Universitat Jena, Germany.
Acknowledgement
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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Majumdar, S., Roy, S. (2018). Mathematical Model of Quorum Sensing and Biofilm. In: Pallaval Veera Bramhachari (eds) Implication of Quorum Sensing System in Biofilm Formation and Virulence. Springer, Singapore. https://doi.org/10.1007/978-981-13-2429-1_24
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DOI: https://doi.org/10.1007/978-981-13-2429-1_24
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