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Mathematical modelling of the agr operon in Staphylococcus aureus

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Abstract

Staphylococcus aureus is a pathogenic bacterium that utilises quorum sensing (QS), a cell-to-cell signalling mechanism, to enhance its ability to cause disease. QS allows the bacteria to monitor their surroundings and the size of their population, and S. aureus makes use of this to regulate the production of virulence factors. Here we describe a mathematical model of this QS system and perform a detailed time-dependent asymptotic analysis in order to clarify the roles of the distinct interactions that make up the QS process, demonstrating which reactions dominate the behaviour of the system at various timepoints. We couple this analysis with numerical simulations and are thus able to gain insight into how a large population of S. aureus shifts from a relatively harmless state to a highly virulent one, focussing on the need for the three distinct phases which form the feedback loop of this particular QS system.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  • Anguige K, King JR, Ward JP (2005) Modelling antibiotic- and anti-quorum sensing treatment of a spatially-structured Pseudomonas aeruginosa population. J Math Biol 51: 557–594

    Article  MATH  MathSciNet  Google Scholar 

  • Cámara M, Williams P, Hardman A (2002) Controlling infection by tuning in and turning down the volume of bacterial small-talk. Lancet Infect Dis 2: 667–676

    Article  Google Scholar 

  • Chan WC, Coyle BJ, Williams P (2004) Virulence regulation and quorum sensing in staphylococcal infections: competitive AgrC antagonists as quorum sensing inhibitors. J Med Chem 47: 4633–4641

    Article  Google Scholar 

  • Cheung AL (2001) Global regulation of virulence determinants in Staphylococcus aureus. In: Honeyman AL, Friedman H, Bendinelli M (eds) Staphylococcus aureus infection and disease. Kluwer Academic/Plenum Publishers, Dordrecht, pp 295–322

    Google Scholar 

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

    Article  Google Scholar 

  • 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  Google Scholar 

  • Finch R (2006) Gram-positive infections: lessons learnt and novel solutions. Clin Microbiol Infect 12: 3–8

    Article  Google Scholar 

  • Fujii T, Ingham C, Nakayama J, Beerthuyzen M, Kunuki R, Molenaar D, Sturme M, Vaughan E, Kleerebezem M, de Vos W (2009) Two homologous agr-like quorum-sensing systems cooperatively control adherence, cell morphology, and cell viability properties in Lactobacillus plantarum WCFS1. J Bacteriol 190: 7655–7665

    Article  Google Scholar 

  • George EA, Muir TW (2007) Molecular mechanisms of agr quorum sensing in virulent Staphylococci. ChemBioChem 8: 847–855

    Article  Google Scholar 

  • Gustafsson E, Nilsson P, Karlsson S, Arvidson S (2004) Characterizing the dynamics of the quorum-sensing system in Staphylococcus aureus. J Mol Microbiol Biotechnol 8: 232–242

    Article  Google Scholar 

  • Hense BA, Kuttler C, Müller J, Rothballer M, Hartmann A, Kreft J (2007) Does efficiency sensing unify diffusion and quorum sensing?. Nature Rev Mirobiol 5: 230–239

    Article  Google Scholar 

  • Hiramatsu K, Aritaka N, Hanaki H, Kawasaki S, Hosoda Y, Hori S, Fukuchi Y, Kobayashi I (1997) Dissemination in Japanese hospitals of strains of Staphylococcus aureus heterogeneously resistant to vancomycin. Lancet 350: 1670–1673

    Article  Google Scholar 

  • Jabbari S (2004) Computational modelling of quorum sensing in Staphylococcus aureus. Qualifying dissertation, University of Nottingham

  • Jabbari S (2007) Mathematical modelling of quorum sensing and its inhibition in Staphylococcus aureus. Ph.D. thesis, University of Nottingham

  • James S, Nilsson P, James G, Kjelleberg S, Fagerström T (2007) Luminescence control in the marine bacterium Vibrio fischeri: an analysis of the dynamics of lux regulation. J Mol Biol 296: 1127–1137

    Article  Google Scholar 

  • Ji G, Beavis RC, Novick RP (1995) Cell density control of staphylococcal virulence mediated by an octapeptide pheromone. Proc Natl Acad Sci USA 92: 12055–12059

    Article  Google Scholar 

  • Kevorkian J, Cole JD (1981) Perturbation methods in applied mathematics. Springer, New York

    MATH  Google Scholar 

  • Koenig RL, Ray JL, Maleki SJ, Smeltzer MS, Hurlburt BK (2004) Staphylococcus aureus AgrA binding to the RNAIII-agr regulatory region. J Bacteriol 186: 7549–7555

    Article  Google Scholar 

  • Koerber AJ, King JR, Williams P (2005) Deterministic and stochastic modelling of endosome escape by Staphylococcus aureus: “quorum sensing” by a single bacterium. J Math Biol 50: 440–488

    Article  MATH  MathSciNet  Google Scholar 

  • Lazazzera BA, Palmer T, Quisel J, Grossman AD (1999) Cell density control of gene expression and development in Bacillus subtilis. In: Dunny GM, Winans SC (eds) Cell-cell signaling in bacteria. American Society for Microbiology, pp 27–46

  • Mayville P, Ji G, Beavis R, Yang H, Goger M, Novick RP, Muir TW (1999) Structure-activity analysis of synthetic autoinducing thiolactone peptides from Staphylococcus aureus responsible for virulence. Proc Natl Acad Sci USA 96: 1218–1223

    Article  Google Scholar 

  • McDowell P, Affas Z, Reynolds C, Holden MTG, Wood SJ, Saint S, Cockayne A, Hill PJ, Dodd CER, Bycroft BW, Chan WC, Williams P (2001) Structure, activity and evolution of the group I thiolactone peptide quorum-sensing system of Staphylococcus aureus. Mol Microbiol 41: 503–512

    Article  Google Scholar 

  • Miller MB, Bassler BL (2001) Quorum sensing in bacteria. Annu Rev Microbiol 55: 165–199

    Article  Google Scholar 

  • Müller J, Kuttler C, Hense BA, Rothballer M, Hartmann A (2006) Cell-cell communication by quorum sensing and dimension-reduction. J Math Biol 53: 672–702

    Article  MATH  MathSciNet  Google Scholar 

  • Novick RP (2003) Autoinduction and signal transduction in the regulation of staphylococcal virulence. Mol Microbiol 48: 1429–1449

    Article  Google Scholar 

  • Novick RP, Geisinger E (2008) Quorum sensing in Staphylococci. Annu Rev Genet 42: 541–564

    Article  Google Scholar 

  • Otto M (2004) Quorum-sensing control in Staphylococci—a target for antimicrobial drug therapy?. FEMS Microbiol Lett 241: 135–141

    Article  Google Scholar 

  • Pearson H (2002) ‘Superbug’ hurdles key drug barrier. Nature 418: 469

    Article  Google Scholar 

  • Redfield RJ (2002) Is quorum sensing a side effect of diffusion sensing?. Trends Microbiol 10: 365–370

    Article  Google Scholar 

  • Riedel CU, Monk IR, Casey PG, Waidmann MS, Gahan CGM, Hill C (2009) AgrD-dependent quorum sensing affects biofilm formation, invasion, virulence and global gene expression profiles in Listeria monocytogenes. Mol Microbiol 71: 1177–1189

    Article  Google Scholar 

  • Salmond GPC, Bycroft BW, Stewart GSAB, Williams P (1995) The bacterial ‘enigma’: cracking the code of cell-cell communication. Mol Microbiol 16: 615–624

    Article  Google Scholar 

  • Sebaihia M, Peck MW, Minton NP et al (2007) Genome sequence of a proteolytic (Group I) Clostridium botulinum strain Hall A and comparative analysis of the clostridial genomes. Genome Res 17: 1082–1092

    Article  Google Scholar 

  • Ward JP, King JR, Koerber AJ, Williams P, Croft JM, Sockett RE (2001) Mathematical modelling of quorum sensing in bacteria. IMA J Math Appl Med 18: 263–292

    Article  MATH  Google Scholar 

  • Wilson M, McNab R, Henderson B (2002) Bacterial disease mechanisms, an introduction to cellular microbiology. Cambridge University Press, Cambridge

    Google Scholar 

  • Wright III JS, Jin R, Novick RP (2005) Transient interference with staphylococcal quorum sensing blocks abscess formation. Proc Natl Acad Sci USA 102: 1691–1696

    Article  Google Scholar 

  • Yarwood JM, Schlievert PM (2003) Quorum sensing in Staphylococcus infections. J Clin Invest 112: 1620–1625

    Google Scholar 

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Authors and Affiliations

  1. Division of Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK

    Sara Jabbari & John R. King

  2. School of Mathematical Sciences, University of Adelaide, Adelaide, SA, 5005, Australia

    Adrian J. Koerber

  3. Centre for Biomolecular Sciences, University of Nottingham, Nottingham, NG7 2RD, UK

    Paul Williams

Authors
  1. Sara Jabbari
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  2. John R. King
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  3. Adrian J. Koerber
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  4. Paul Williams
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Correspondence to Sara Jabbari.

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Jabbari, S., King, J.R., Koerber, A.J. et al. Mathematical modelling of the agr operon in Staphylococcus aureus . J. Math. Biol. 61, 17–54 (2010). https://doi.org/10.1007/s00285-009-0291-6

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  • DOI: https://doi.org/10.1007/s00285-009-0291-6

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