Journal of Mathematical Biology

, Volume 53, Issue 4, pp 672–702 | Cite as

Cell–cell communication by quorum sensing and dimension-reduction

  • Johannes MüllerEmail author
  • Christina Kuttler
  • Burkard A. Hense
  • Michael Rothballer
  • Anton Hartmann


Several bacterial taxa change their behavior if the population density exceeds a certain threshold. This phenomenon is the consequence of a communication system between the bacteria and is called quorum sensing (QS). Up to now, this phenomenon is mostly modeled at population level. However, new experimental techniques allow for single cell analysis. We introduce a modeling approach for the description of this QS system, including a discussion of the regulatory network and its bistable behavior. Based on this single-cell model we develop and analyze a spatially structured model for a cell population. Special attention is given to the scaling behavior w.r.t. the cell size (leading to an approximation theorem for stationary solutions) and its consequences for the interpretation of cell communication (QS versus diffusion sensing). Concluding, we apply the modeling approach to spatially structured experimental data.


Quorum sensing Single cell analysis Bistability Dimension reduction Partial differential equation 

Mathematics Subject Classification (2000)

92C15 35A35 


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  1. 1.
    Adams R., Fournier J. (2003). Sobolev Spaces. Elsevier, AmsterdamzbMATHGoogle Scholar
  2. 2.
    Bassler B. (1999). How bacteria talk to each other: regulation of gene expression by quorum sensing. Curr. Opin. Microbiol. 2:582–587CrossRefGoogle Scholar
  3. 3.
    Daniels R., Vanderleyden J., Michiels J. (2004). Quorum sensing and swarming migration in bacteria. FEMS Microbiol. Rev. 28:261–289CrossRefGoogle Scholar
  4. 4.
    Dockery J., Keener J. (2001). A mathematical model for quorum sensing in Pseudomonas aeruginosa. Bull. Math. Biol. 63:95–116CrossRefGoogle Scholar
  5. 5.
    Eberhard A., Burlingame A., Eberhard C., Kenyon G., Nealson K., Oppenheimer N. (1981). Structural identification of autoinducer of Photobacterium fischeri luciferase. Biochemistry 20:2444–2449CrossRefGoogle Scholar
  6. 6.
    Fuqua C., Greenberg P.E. (2002). Listening on bacteria: acyl-homoserine lactone signalling. Nat. Rev. 3:685–695CrossRefGoogle Scholar
  7. 7.
    Gantner, S.: Mikrobielle Ökologie N-Acyl-L-Homoserinlacton-produzierender Bakterien in der Rhizosphäre von Tomatenpflanzen. PhD Thesis, Ludwig-Maximilian-Universität München (2003)Google Scholar
  8. 8.
    Gray K., Greenberg E. (1992). Physical and functional maps of the luminescence gene cluster in an autoinducer-deficient Vibrio fischeri strain isolated from a squid light organ. J. Bacteriol. 174:4384–4390Google Scholar
  9. 9.
    Kaplan H., Greenberg E. (1985). Diffusion of autoinducers is involved in regulation of the Vibrio fischeri luminescence system. J. Bacteriol. 163:1210–1214Google Scholar
  10. 10.
    Koerber A., King J., Williams P. (2005). Deterministic and stochastic modelling of endosome escape by Staphylococcus aureus: “quorum” sensing by a single bacterium. J. Math. Biol. 50:440–488zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Kuo A., Blough N., Dunlap P. (1994). Multiple N-acyl-L-homoserine lactone autoinducers of luminescence in the marine symbiotic bacterium Vibrio fischeri. J. Bacteriol. 176:7558–7565Google Scholar
  12. 12.
    Lupp C., Ruby E. (2004). Vibrio fischeri LuxS and AinS: comparative study of two signal synthases. J. Bacteriol. 186:3873–3881CrossRefGoogle Scholar
  13. 13.
    Lupp C., Ruby E. (2005). Vibrio fischeri uses two quorum-sensing systems for the regulation of early and late colonization factors. J. Bacteriol. 187:3620–3629CrossRefGoogle Scholar
  14. 14.
    Lupp C., Urbanowski M., Greenberg E., Ruby E. (2003). The Vibrio fischeri quorum-sensing systems ain and lux sequentially induce luminescence gene expression and are important for persistence in the squid host. Mol. Microbiol. 50:319–331CrossRefGoogle Scholar
  15. 15.
    Miller M., Bassler B. (2001). Quorum sensing in bacteria. Annu. Rev. Microbiol. 55:165–199CrossRefGoogle Scholar
  16. 16.
    Nealson K., Platt T., Hastings J. (1970). Cellular control of the synthesis and activity of the bacterial luminescent system. J. Bacteriol. 104:313–322Google Scholar
  17. 17.
    Ravn L., Christensen A., Molin S., Givskov M., Gram L. (2001). Methods for detecting acylated homoserine lactones produced by Gram-negative bacteria and their application in studies of AHL-production kinetics. J. Microbiol. Methods 44:239–251CrossRefGoogle Scholar
  18. 18.
    Redfield R.J. (2002). Is quorum sensing a side effect of diffusion sensing? Trends Microbiol. 10:365–370CrossRefGoogle Scholar
  19. 19.
    Renardy M., Rogers R.C. (1992). An Introduction to Partial Differential Equations. Springer, Berlin Heidelberg New YorkGoogle Scholar
  20. 20.
    Riedel K., Hentzer M., Geisenberger O., Huber B., Steidle A., Wu H., Hoiby N., Givskov M., Molin S., Eberl L. (2001). N-acylhomoserine-lactone-mediated communication between Pseudomonas aeruginosa and Burkholderia cepacia in mixed biofilms. Microbiology 147:3249–3262Google Scholar
  21. 21.
    Ruby E., Lee K.-H. (1998). The Vibrio fischeri-Euprymna scolopes light organ association: current ecological paradigms. Appl. Environ. Microbiol. 64(3):805–812Google Scholar
  22. 22.
    Schaefer A., Val B., Hanzelka B., Cronan J., Greenberg E. (2000). Detection, purification and structural elucidation of acylhomoserine lactone inducer of Vibrio fischeri luminescence and other related molecules. Method. Enzymol. 305:288–301CrossRefGoogle Scholar
  23. 23.
    Sharma A., Sahgal M., Johri B. (2003). Microbial communication in the rhizosphere: operation of quorum sensing. Curr. Sci. 85:1164–1172Google Scholar
  24. 24.
    Steidle A., Sigl K., Schuhegger R., Ihring A., Schmid M., Gantner S., Stoffels M., Riedel K., Givskov M., Hartmann A., Langebartels C., Eberl L. (2001). Visualization of N-Acylhomoserine lactone-mediated cell-cell communication between bacteria colonizing the tomato rhizosphere. Appl. Environ. Microbiol. 67:5761–5770CrossRefGoogle Scholar
  25. 25.
    Steidle A., Allesen-Holm M., Riedel K., Berg G., Givskov M., Molin S., Eberl L. (2002). Identification and characterization of an N-Acylhomoserine Lactone-dependent quorum-sensing system in Pseudomonas putida strain IsoF. Appl. Environ. Microbiol. 68:6371–6382CrossRefGoogle Scholar
  26. 26.
    Thyson J., Othmer H. (1978). The dynamics of feedback control circuits in biochemical pathways. Progr. Theor. Biol. 5:1–62Google Scholar
  27. 27.
    Walter W. (1964). Differential- und Integral-Ungleichungen. Springer, Berlin Heidelberg New YorkzbMATHGoogle Scholar
  28. 28.
    Ward J., King J., Koerber A., Croft J., Socket R., Williams P. (2004). Cell-signalling repression in bacterial quorum sensing. Math. Med. Biol. 21:169–204zbMATHCrossRefGoogle Scholar
  29. 29.
    Waters C., Bassler B. (2005). Quorum sensing: Cell-to-cell communication in bacteria. Annu. Rev. Cell. Dev. Biol. 21:319–346CrossRefGoogle Scholar
  30. 30.
    Whitehead N., Barnard A., Slater H., Simpson N., Salmond G. (2001). Quorum-sensing in Gram-negative bacteria. FEMS Microbiol. Rev. 25:365–404CrossRefGoogle Scholar
  31. 31.
    You L., Cox R.S. III, Weiss R., Arnold F.A. (2004). Programmed population control by cell-cell communication and regulated killing. Nature 428:868–871CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Johannes Müller
    • 1
    Email author
  • Christina Kuttler
    • 2
  • Burkard A. Hense
    • 2
  • Michael Rothballer
    • 3
  • Anton Hartmann
    • 3
  1. 1.Centre for Mathematical SciencesTechnical University MunichGarching/MunichGermany
  2. 2.Institute of Biomathematics and BiometryGSF - National Research Center for Environment and HealthOberschleißheimGermany
  3. 3.Institute of Soil Ecology, Department of Rhizosphere BiologyGSF - National Research Center for Environment and HealthOberschleißheimGermany

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