Mathematical Modeling of Quorum-Sensing Control in Biofilms

Part of the Springer Series on Biofilms book series (BIOFILMS, volume 2)


This chapter begins with an overview of the relevant literature on theoretical approaches to modeling biofilms, quorum sensing in bacteria, and anti-quorum-sensing treatment. Following this, new mathematical models are proposed to investigate anti-quorum-sensing treatment in batch cultures and in biofilm environments. Details for the models' derivation are aimed so that readers with a nonmathematical background will have a good idea of how such models are constructed and studied. Three anti-quorum-sensing targets are investigated, and a wide variety of outcomes in terms of successful treatment are predicted depending on treatment type, strength, and timing. The many interesting conclusions that can be drawn from the presented results are discussed in detail, including ideas for new experiments, many of which would be considered routine, that will provide deeper insights into how anti-quorum-sensing treatments could be highly effective means of controlling bacterial behavior in a variety of situations and environments.


Batch Culture Pretreated Medium Total Population Density Downregulated Cell Rapid Jump 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Anguige K, King JR, Ward JP, Williams P (2004) Mathematical modeling of therapies targeted at bacterial quorum sensing. Math Biosci 192:39–83PubMedCrossRefGoogle Scholar
  2. 2.
    Anguige K, King JR, Ward JP, Williams P (2005) Modeling antibiotic- and anti-quorum sensing treatment of a Pseudomonas aeruginosa biofilm. J Math Biol 51:557–594PubMedCrossRefGoogle Scholar
  3. 3.
    Anguige K, King JR, Ward JP (2006) A multi-phase mathematical model of quorum sensing in a maturing Pseudomonas aeruginosa biofilm. Math Biosci 203:240–276PubMedCrossRefGoogle Scholar
  4. 4.
    Atkinson B, Davies IJ (1974a) The overall rate of substrate uptake (reaction) by microbial film. Part I – a biological rate equation. Trans Inst Chem Eng 52:260–268Google Scholar
  5. 5.
    Atkinson B, Davies IJ (1974b) The overall rate of substrate uptake (reaction) by microbial film. Part II – effect of concentration and thickness with mixed microbial films. Trans Inst Chem Eng 52:248–259Google Scholar
  6. 6.
    Bakke R, Trulear MG, Robinson JA, Characklis WG (1984) Activity of Pseudomonas aeruginosa in biofilms: steady state. Biotech and Bioeng 26:1418–1424CrossRefGoogle Scholar
  7. 7.
    Boyle JD, Dodds I, Lappin-Scott H, Stoodley P (1999) Limits to growth and what keeps a biofilm finite. Anitmicrobial Agents Chemo 38:303–315Google Scholar
  8. 8.
    Chaudhry MAS, Beg SA (1998) A review on the mathematical modeling of biofilm processes: advances in fundamentals of biofilm modeling. Chem Eng Technol 21:701–710CrossRefGoogle Scholar
  9. 9.
    Chopp DL, Kirisits MJ, Moran B, Parsek MR (2002) A mathematical model of quorum sensing in a growing bacterial biofilm. J Indust Microbiol Biotech 29:339–346CrossRefGoogle Scholar
  10. 10.
    Chopp DL, Kirisits MJ, Moran B, Parsek MR (2003) The dependence of quorum sensing on the depth of a growing biofilm. Bull Math Biol 65:1053–1079PubMedCrossRefGoogle Scholar
  11. 11.
    Cogan NG, Cortez R, Fauci L (2005) Modeling physiological resistance in bacterial biofilms. Bull Math Biol 67:831–853PubMedCrossRefGoogle Scholar
  12. 12.
    Cogan NG, Keener JP (2004) The role of the biofilm matrix in structural development. Math Med Biol 21:147–166PubMedCrossRefGoogle Scholar
  13. 13.
    Davies DG, Parsek MR, Pearson JP, Iglewski BH, Costerton JW, Greenberg EP (1998) The involvement of cell-to-cell signals in the development of a bacterial biofilm. Science 280:295–297PubMedCrossRefGoogle Scholar
  14. 14.
    Dockery JD, Keener JP (2001) A mathematical model for quorum sensing in Pseudomonas aeruginosa. Bull Math Biol 63:95–116PubMedCrossRefGoogle Scholar
  15. 15.
    Dockery J, Klapper I (2001) Finger formation in biofilms layers. SIAM J Appl Math 62:853–869Google Scholar
  16. 16.
    Dillon R, Fauci L, Fogelson A, Gaver D III (1996) Modeling biofilm processes using the immersed boundary method. J Comp Phys 129:57–73CrossRefGoogle Scholar
  17. 17.
    Dong YH, Gusti AR, Zhang Q, Xu JL, Zhang LH (2002) Identification of quorum-quenching N-acyl homoserine lactonases from Bacillus species. Appl Environ Microbiol 68:1754–1759PubMedCrossRefGoogle Scholar
  18. 18.
    Eberl HJ, Picioreanu C, Heijnen JJ, van Loosdrecht MCM (2000) A three-dimensional numerical study on the correlation of spatial structure, hydrodynamic conditions, and mass transfer and conversion in biofilms. Chem Eng Sci 55:6209–6222CrossRefGoogle Scholar
  19. 19.
    Fagerlind MG, Nilsson P, Harlén M, Karlsson S, Rice SA, Kjelleberg S (2005) Modeling the effect of acylated homoserine lactone antagonists in Pseudomonas aeruginosa. Biosystems 80:201–213PubMedCrossRefGoogle Scholar
  20. 20.
    Fagerlind MG, Rice SA, Nilsson P, Harlén M, James S, Charlton T, Kjelleberg S (2003) The Role of Regulators in the Expression of Quorum-Sensing Signals in Pseudomonas aeruginosa. J Mol Microbiol Biotechnol 6:88–100PubMedCrossRefGoogle Scholar
  21. 21.
    Freter R, Brickner H, Fekete J, Vickerman M, Carey K (1983) Survival and implantation of Escherichia coli in the intestinal tract. Infect Immun 39:686–703PubMedGoogle Scholar
  22. 22.
    Fuqua C, Greenberg EP (2002) Listening in on bacteria: acyl-homosering lactone signalling. Mol Cell Biol 3:685–695Google Scholar
  23. 23.
    Gonpot P, Smith R, Richter A (2000) Diffusion limited biofilm growth. Mod Simul Mater Sci Eng 8:707–726CrossRefGoogle Scholar
  24. 24.
    Goryachev AB, Toh DJ, Lee T (2006) Systems analysis of a quorum sensing network: design constraints imposed by the functional requirements, network topology and kinetic constants. Biosystems 83:178–187PubMedCrossRefGoogle Scholar
  25. 25.
    Hentzer M, Teitzel GM, Balzer GJ, Heydorn A, Molin S, Givskov M, Parsek MR (2001) Alginate overproduction affects Pseudomonas aeruginosa biofilm structure and function. J Bacteriol 183:5395–5401PubMedCrossRefGoogle Scholar
  26. 26.
    Hentzer M, Wu H, Andersen JB, Riedel KB, Rasmussen T, Bagge N, Kumar N, Schembri MA, Song Z, Kristoffersen P, Manefield M, Costerton JW, Molin S, Eberl L, Steinberg P, Kjelleberg S, Hoiby N, Givskov M (2003) Attenuation of Pseudomonas aeruginosa virulence by quorum sensing inhibitors. EMBO J 22:3803–3815PubMedCrossRefGoogle Scholar
  27. 27.
    Hudson MC, Ramp WK, Nicholson NC, Williams AS, Nousiainen MT (1995) Internalisation of Staphylococcus aureus by cultured osteoblasts. Microb Pathog 19:409–419PubMedCrossRefGoogle Scholar
  28. 28.
    James S, Nilsson P, James G, Kjelleberg S, Fagerstrøm T (2000) Luminescence control in the marine bacterium Vibrio fischeri: an analysis of the dynamics of lux regulation. J Mol Biol 296:1127–1137PubMedCrossRefGoogle Scholar
  29. 29.
    Koerber AJ, King JR, Ward JP, Williams P, Croft JM, Sockett RE (2002) A mathematical model of partial-thickness burn-wound infection by Pseudomonas aeruginosa: quorum sensing and the build-up to invasion. Bull Math Biol 64:239–259PubMedCrossRefGoogle Scholar
  30. 30.
    Koerber AJ, King JR, Williams P (2005) Deterministic and stochastic modeling of endosome escape by Staphylococcus aureus: ``quorum'' sensing by a sungle bacterium. J Math Biol 50:440–488PubMedCrossRefGoogle Scholar
  31. 31.
    Kreft JU (2004) Biofilms promote altruism. Microbiology 150:2751–2760PubMedCrossRefGoogle Scholar
  32. 32.
    Kreft JU, Booth G, Wimpenny JWT (1998) BacSim, a simulator for individual-based modeling of bacterial colony growth. Microbiology 144:3275–3287PubMedCrossRefGoogle Scholar
  33. 33.
    Lee S, Park S, Lee J, Yum D, Koo B, Lee J-K (2002) Genes encoding the N-Acyl Homoserine Lactone-Degrading Enzyme Are Widespread in Many Subspecies of Bacillus thuringiensis. Appl Environ Microbiol 68:3919–3924PubMedCrossRefGoogle Scholar
  34. 34.
    Lewandowski Z, Walser G, Characklis WG (1991) Reaction Kinetics in Biofilms. Biotech and Bioeng 38:877–882CrossRefGoogle Scholar
  35. 35.
    Manefield M, De Nys R, Kumar N, Read R, Givskov M, Steinberg P, Kjelleberg S (1999) Evidence that halogenated furanones from Dlisea pulchra inhibit acylated homoserine lactone (AHL)-mediated gene expression by displacing the AHL signal from its receptor protein. Microbiology 145:283–291PubMedCrossRefGoogle Scholar
  36. 36.
    Manefield M, Rasmussen TB, Hentzer M, Andersen JB, Steinberg P, Kjelleberg S, Givskov M (2002) Halogenated furanones inhibit quorum sensing through accelerated LuxR turnover. Microbiology 148:1119–1127PubMedGoogle Scholar
  37. 37.
    Nilsson P, Olofsson A, Fagerlind MG, Fagerstrøm T, Rice S, Kjelleberg S, Steinberg P (2001) Kinetics of the AHL regulatory system in a model biofilm system: how many bacteria constitute a ``quorum''. J Mol Biol 309:631–640PubMedCrossRefGoogle Scholar
  38. 38.
    Noguera DR, Pizarro G, Stahl DA, Rittmann BE (1999) Simulation of multispecies biofilm development in three dimensions. Wat Sci Tech 39:123–130CrossRefGoogle Scholar
  39. 39.
    Pearson JP, van Dalden C, Iglewski BH (1999) Active efflux and diffusion are involved in transport of Pseudomonas aeruginosa cell-to-cell signals. J Bacteriol 181:1203–1210PubMedGoogle Scholar
  40. 40.
    Picioreanu C, Kreft JU, van Loosdrecht MCM (2004) Particle-based multidimensional multispecies biofilm model. Appl Environ Microbiol 70:3024–3040PubMedCrossRefGoogle Scholar
  41. 41.
    Picioreanu C, van Loosdrecht MCM, Heijnen JJ (1998a) A new combined differential-discrete cellular automaton approach for biofilm modeling: application for growth in gel beads. Biotech and Bioeng 57:718–731CrossRefGoogle Scholar
  42. 42.
    Picioreanu C, van Loosdrecht MCM, Heijnen JJ (1998b) Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotech and Bioeng 58:101–116CrossRefGoogle Scholar
  43. 43.
    Picioreanu C, van Loosdrecht MCM, Heijnen JJ (2000) Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study. Biotech and Bioeng 69:504–515CrossRefGoogle Scholar
  44. 44.
    Pritchett LA, Dockery J (2001) Steady state solutions of a one-dimensional biofilm model. Math Comput Model 33:255–263CrossRefGoogle Scholar
  45. 45.
    Rittmann BE, Manem JA (1992) Development and experimental evaluation of a steady-state, multispecies biofilm model. Biotech Bioeng 39:914–922CrossRefGoogle Scholar
  46. 46.
    Sloane NJA (1998) Kepler's conjecture confirmed. Nature 395:435–436CrossRefGoogle Scholar
  47. 47.
    Stewart PS (1994) Biofilm accumulation model that predicts antibiotic resistance of Pseudomonas aeruginosa biofilms. Anitmicrobial Agents Chemo 38:1052–1058Google Scholar
  48. 48.
    Szego S, Cinnella P, Cunningham AB (1993) Numerical simulation of biofilm growth in closed conduits. J Comp Phys 108:246–263CrossRefGoogle Scholar
  49. 49.
    Tiwari SK, Bowers KL (2001) Modeling biofilm growth and porous media applications. Math Comput Model 33:299–319CrossRefGoogle Scholar
  50. 50.
    Ulrich RL (2004) Quorum quenching:enzymatic disruption of N-acylhomoserine lactone-mediated bacterial communication in Burkholderia thailandensis. Appl Environ Microbiol 70:6173–6180PubMedCrossRefGoogle Scholar
  51. 51.
    Viretta AU, Fusseneggar M (2004) Modeling the quorum sensing regulatory network of human-pathogenic Pseudomonas aeruginosa. Biotechnol Prog 20:670–678PubMedCrossRefGoogle Scholar
  52. 52.
    Wanner O, Gujer W (1986) A Multispecies Biofilm Model. Biotech and Bioeng 28:314–328CrossRefGoogle Scholar
  53. 53.
    Wanner O, Reichert P (1995) Mathematical modeling of mixed culture biofilms. Biotech and Bioeng 49:172–184CrossRefGoogle Scholar
  54. 54.
    Ward JP, King JR, Koerber AJ, Croft JM, Sockett RE, Williams P (2003) Early development and quorum sensing in bacterial biofilms. J Math Biol 47:23–55PubMedGoogle Scholar
  55. 55.
    Ward JP, King JR, Koerber AJ, Williams P, Croft JM, Sockett RE (2004) Cell-signalling repression in bacterial quorum sensing. Math Med Biol 21:169–204PubMedCrossRefGoogle Scholar
  56. 56.
    Ward JP, King JR, Koerber AJ, Williams P, Croft JM, Sockett RE (2001) Mathematical modeling of quorum sensing in bacteria. IMA J Math Appl Med Biol 18:263–292PubMedCrossRefGoogle Scholar
  57. 57.
    Wimpenny JWT, Colasanti R (1997) A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models. FEMS Microbiol Ecol 22:1–16CrossRefGoogle Scholar
  58. 58.
    Xu F, Byun T, Dussen HJ, Duke KR (2003) Degradation of N-acylhomoserine lactones, the bacterial quorum-sensing molecules, by acylase. Biotechnology 101:89–96CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  1. 1.Department of Mathematical SciencesLoughborough UniversityLeicestershireUK

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