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Mathematical Modeling of Quorum-Sensing Control in Biofilms

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Control of Biofilm Infections by Signal Manipulation

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

Abstract

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.

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References

  1. Anguige K, King JR, Ward JP, Williams P (2004) Mathematical modeling of therapies targeted at bacterial quorum sensing. Math Biosci 192:39–83

    Article  PubMed  CAS  Google Scholar 

  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 51:557–594

    Article  PubMed  CAS  Google Scholar 

  3. Anguige K, King JR, Ward JP (2006) A multi-phase mathematical model of quorum sensing in a maturing Pseudomonas aeruginosa biofilm. Math Biosci 203:240–276

    Article  PubMed  CAS  Google Scholar 

  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 52:260–268

    Google Scholar 

  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 52:248–259

    CAS  Google Scholar 

  6. Bakke R, Trulear MG, Robinson JA, Characklis WG (1984) Activity of Pseudomonas aeruginosa in biofilms: steady state. Biotech and Bioeng 26:1418–1424

    Article  CAS  Google Scholar 

  7. Boyle JD, Dodds I, Lappin-Scott H, Stoodley P (1999) Limits to growth and what keeps a biofilm finite. Anitmicrobial Agents Chemo 38:303–315

    Google Scholar 

  8. Chaudhry MAS, Beg SA (1998) A review on the mathematical modeling of biofilm processes: advances in fundamentals of biofilm modeling. Chem Eng Technol 21:701–710

    Article  CAS  Google Scholar 

  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 29:339–346

    Article  CAS  Google Scholar 

  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 65:1053–1079

    Article  PubMed  CAS  Google Scholar 

  11. Cogan NG, Cortez R, Fauci L (2005) Modeling physiological resistance in bacterial biofilms. Bull Math Biol 67:831–853

    Article  PubMed  CAS  Google Scholar 

  12. Cogan NG, Keener JP (2004) The role of the biofilm matrix in structural development. Math Med Biol 21:147–166

    Article  PubMed  CAS  Google Scholar 

  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 280:295–297

    Article  PubMed  CAS  Google Scholar 

  14. Dockery JD, Keener JP (2001) A mathematical model for quorum sensing in Pseudomonas aeruginosa. Bull Math Biol 63:95–116

    Article  PubMed  CAS  Google Scholar 

  15. Dockery J, Klapper I (2001) Finger formation in biofilms layers. SIAM J Appl Math 62:853–869

    Google Scholar 

  16. Dillon R, Fauci L, Fogelson A, Gaver D III (1996) Modeling biofilm processes using the immersed boundary method. J Comp Phys 129:57–73

    Article  CAS  Google Scholar 

  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 68:1754–1759

    Article  PubMed  CAS  Google Scholar 

  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 55:6209–6222

    Article  CAS  Google Scholar 

  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 80:201–213

    Article  PubMed  CAS  Google Scholar 

  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 6:88–100

    Article  PubMed  CAS  Google Scholar 

  21. Freter R, Brickner H, Fekete J, Vickerman M, Carey K (1983) Survival and implantation of Escherichia coli in the intestinal tract. Infect Immun 39:686–703

    PubMed  CAS  Google Scholar 

  22. Fuqua C, Greenberg EP (2002) Listening in on bacteria: acyl-homosering lactone signalling. Mol Cell Biol 3:685–695

    CAS  Google Scholar 

  23. Gonpot P, Smith R, Richter A (2000) Diffusion limited biofilm growth. Mod Simul Mater Sci Eng 8:707–726

    Article  CAS  Google Scholar 

  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 83:178–187

    Article  PubMed  CAS  Google Scholar 

  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 183:5395–5401

    Article  PubMed  CAS  Google Scholar 

  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 22:3803–3815

    Article  PubMed  CAS  Google Scholar 

  27. Hudson MC, Ramp WK, Nicholson NC, Williams AS, Nousiainen MT (1995) Internalisation of Staphylococcus aureus by cultured osteoblasts. Microb Pathog 19:409–419

    Article  PubMed  CAS  Google Scholar 

  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 296:1127–1137

    Article  PubMed  CAS  Google Scholar 

  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 64:239–259

    Article  PubMed  CAS  Google Scholar 

  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 50:440–488

    Article  PubMed  CAS  Google Scholar 

  31. Kreft JU (2004) Biofilms promote altruism. Microbiology 150:2751–2760

    Article  PubMed  CAS  Google Scholar 

  32. Kreft JU, Booth G, Wimpenny JWT (1998) BacSim, a simulator for individual-based modeling of bacterial colony growth. Microbiology 144:3275–3287

    Article  PubMed  CAS  Google Scholar 

  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 68:3919–3924

    Article  PubMed  CAS  Google Scholar 

  34. Lewandowski Z, Walser G, Characklis WG (1991) Reaction Kinetics in Biofilms. Biotech and Bioeng 38:877–882

    Article  CAS  Google Scholar 

  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 145:283–291

    Article  PubMed  CAS  Google Scholar 

  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 148:1119–1127

    PubMed  CAS  Google Scholar 

  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 309:631–640

    Article  PubMed  CAS  Google Scholar 

  38. Noguera DR, Pizarro G, Stahl DA, Rittmann BE (1999) Simulation of multispecies biofilm development in three dimensions. Wat Sci Tech 39:123–130

    Article  Google Scholar 

  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 181:1203–1210

    PubMed  CAS  Google Scholar 

  40. Picioreanu C, Kreft JU, van Loosdrecht MCM (2004) Particle-based multidimensional multispecies biofilm model. Appl Environ Microbiol 70:3024–3040

    Article  PubMed  CAS  Google Scholar 

  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 57:718–731

    Article  CAS  Google Scholar 

  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 58:101–116

    Article  CAS  Google Scholar 

  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 69:504–515

    Article  CAS  Google Scholar 

  44. Pritchett LA, Dockery J (2001) Steady state solutions of a one-dimensional biofilm model. Math Comput Model 33:255–263

    Article  Google Scholar 

  45. Rittmann BE, Manem JA (1992) Development and experimental evaluation of a steady-state, multispecies biofilm model. Biotech Bioeng 39:914–922

    Article  CAS  Google Scholar 

  46. Sloane NJA (1998) Kepler's conjecture confirmed. Nature 395:435–436

    Article  CAS  Google Scholar 

  47. Stewart PS (1994) Biofilm accumulation model that predicts antibiotic resistance of Pseudomonas aeruginosa biofilms. Anitmicrobial Agents Chemo 38:1052–1058

    CAS  Google Scholar 

  48. Szego S, Cinnella P, Cunningham AB (1993) Numerical simulation of biofilm growth in closed conduits. J Comp Phys 108:246–263

    Article  CAS  Google Scholar 

  49. Tiwari SK, Bowers KL (2001) Modeling biofilm growth and porous media applications. Math Comput Model 33:299–319

    Article  Google Scholar 

  50. Ulrich RL (2004) Quorum quenching:enzymatic disruption of N-acylhomoserine lactone-mediated bacterial communication in Burkholderia thailandensis. Appl Environ Microbiol 70:6173–6180

    Article  PubMed  CAS  Google Scholar 

  51. Viretta AU, Fusseneggar M (2004) Modeling the quorum sensing regulatory network of human-pathogenic Pseudomonas aeruginosa. Biotechnol Prog 20:670–678

    Article  PubMed  CAS  Google Scholar 

  52. Wanner O, Gujer W (1986) A Multispecies Biofilm Model. Biotech and Bioeng 28:314–328

    Article  CAS  Google Scholar 

  53. Wanner O, Reichert P (1995) Mathematical modeling of mixed culture biofilms. Biotech and Bioeng 49:172–184

    Article  Google Scholar 

  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 47:23–55

    PubMed  Google Scholar 

  55. Ward JP, King JR, Koerber AJ, Williams P, Croft JM, Sockett RE (2004) Cell-signalling repression in bacterial quorum sensing. Math Med Biol 21:169–204

    Article  PubMed  CAS  Google Scholar 

  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 18:263–292

    Article  PubMed  CAS  Google Scholar 

  57. Wimpenny JWT, Colasanti R (1997) A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models. FEMS Microbiol Ecol 22:1–16

    Article  CAS  Google Scholar 

  58. Xu F, Byun T, Dussen HJ, Duke KR (2003) Degradation of N-acylhomoserine lactones, the bacterial quorum-sensing molecules, by acylase. Biotechnology 101:89–96

    Article  CAS  Google Scholar 

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Correspondence to John Ward .

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Naomi Balaban

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Ward, J. (2008). Mathematical Modeling of Quorum-Sensing Control in Biofilms. In: Balaban, N. (eds) Control of Biofilm Infections by Signal Manipulation. Springer Series on Biofilms, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/7142_2007_010

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