Abstract
In a process called quorum sensing, bacteria monitor their population density via extracellular signaling molecules and modulate gene expression accordingly. In this paper, a one-dimensional model of a growing Pseudomonas aeruginosa biofilm is examined. Quorum sensing has been included in the model through equations describing the production, degradation, and diffusion of the signaling molecules, acyl-homoserine lactones, in the biofilm. From this model, we are able to make some important observations about quorum sensing. First, in order for quorum sensing to initiate near the substratum, in accordance with experimental observations, the model suggests that cells in oxygen-deficient regions of the biofilm must still be synthesizing the signal compound. Second, the induction of quorum sensing is related to a critical biofilm depth; once the biofilm grows to the critical depth, quorum sensing is induced. Third, the critical biofilm depth varies with the pH of the surrounding fluid. Of particular interest is the prediction of a critical pH threshold, above which quorum sensing is not possible at any depth. These results highlight the importance of careful study of the relationship among metabolic activity of the bacterium, signal synthesis, and the chemistry of the surrounding environment.
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Atkinson, B. and I. J. Davies (1974). The overall rate of substrate uptake (reaction) by microbial films. Trans. Inst. Chem. Eng. 52, 248–259.
Bakke, R., W. G. Characklis, M. H. Turakhia and A. Yeh (1990). Biofilms, Chapter Modeling a Monopopulation Biofilm System: Pseudomonas aeruginosa, New York: John Wiley and Sons.
Chopp, D. L., M. J. Kirisits, B. Moran and M. R. Parsek (2002). A mathematical model of quorum sensing in a growing bacterial biofilm. J. Ind. Microbiol. Biotech. 29, 339–346.
Costerton, J. W., Z. Lewandowski, D. E. Caldwell, D. R. Korber and H. M. Lappin-Scott (1995). Microbial biofilms. Annu. Rev. Microbiol. 49, 711–745.
Costerton, J. W., P. S. Stewart and E. P. Greenberg (1999). Bacterial biofilms: a common cause of persistent infections. Science 284, 1318–1322.
Davies, D. G., M. R. Parsek, J. P. Pearson, B. H. Iglewski, J. W. Costerton and E. P. Greenberg (1998). The involvement of cell-to-cell signals in the development of a bacterial biofilm. Science 280, 295–298.
De Kievit, T. R., R. Gillis, S. Marx, C. Brown and B. H. Iglewski (2001). Quorum-sensing genes in Pseudomonas aeruginosa biofilms: their role and expression patterns. Appl. Environ. Microbiol. 67, 1865–1873.
Dockery, J. D. and J. P. Keener (2001). A mathematical model for quorum sensing in Pseudomonas aeruginosa. Bull. Math. Biol. 63, 95–116.
Fuqua, C. and E. P. Greenberg (1995). Self perception in bacteria: quorum sensing with acylated homoserine lactones. Curr. Opin. Microbiol. 118, 269–277.
Fuqua, C., M. R. Parsek and E. P. Greenberg (2001). Regulation of gene expression by cell-to-cell communication: acyl-homoserine lactone quorum sensing. Annu. Rev. Genet. 35, 439–468.
Gambello, M. J., S. Kaye and B. H. Iglewski (1993). LasR of Pseudomonas aeruginosa is a transcriptional activator of the alkaline protease gene (apr) and an enhancer of exotoxin A expression. Infect. Immun. 61, 1180–1184.
Koerber, A. J., J. R. King, J. P. Ward, P. Williams, J. M. Croft and R. E. Sockett (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.
Lide, D. R. (ed.) (1990). CRC Handbook of Chemistry and Physics, 71st edn, Boca Raton, FL.
Moré, M. I., L. D. Finger, J. L. Stryker, C. Fuqua, A. Eberhard and S. C. Winans (1996). Enzymatic synthesis of a quroum-sensing autoinducer through use of defined substrates. Science 272, 1655–1658.
Nilsson, P., A. Olofsson, M. Fagerlind, T. Faerström, S. Rice, S. Kjelleberg and P. Steinberg (2001). Kinetics of the AHL regulatory system in a model biofilm system: how many bacteria constitute a “quorum”? J. Mol. Biol. 309, 631–640.
Parsek, M. R. Jr., D. L. Val, B. L. Hanzelka, J. E. Cronan and E. P. Greenberg (1999). Acyl-homoserine lactone quorum-sensing signal generation. Proc. Natl Acad. Sci. 96, 4360–4365.
Pesci, E. C. and B. H. Iglewski (1997). The chain of command in Pseudomonas quorum sensing. Trends Microbiol. 5, 132–135.
Pesci, E. C., J. B. Milbank, J. P. Pearson, S. McKnight, A. S. Kende, E. P. Greenberg and B. H. Iglewski (1999). Quinolone signaling in the cell-to-cell communication system of Pseudomonas aeruginosa. Proc. Natl Acad. Sci. 96, 11229–11234.
Pesci, E. C., J. P. Pearson, P. C. Seed and B. H. Iglewski (1997). Regulation of las and rhl quorum sensing in Pseudomonas aeruginosa. J. Bacteriol. 179, 3127–3132.
Peterson, E. E. (1962). Chem. Eng. Sci. 17, 987.
Piper, K. R., S. B. von Bodman and S. K. Farrand (1993). Conjugation factor of Agrobacterium tumefaciens regulates Ti plasmid transfer by autoinduction. Nature 362, 448–450.
Prigent-Combaret, C., G. Prensier, T. T. L. Thi, O. Vidal, P. Lejeune and C. Dorel (2000). Developmental pathway for biofilm formation in curli-producting Escherichia coli strains: role of falgella, curli and colanic acid. Environ. Microbiol. 2, 450–464.
Rittmann, B. E. (2002) Personal communication.
Rittmann, B. E. and P. L. McCarty (1981). Substrate flux into biofilms of any thickness. J. Environ. Eng. 107, 831–849.
Rittmann, B. E. and P. McCarty (2001). Environmental Biotechnology, New York: McGraw-Hill.
Sáez, P. B. and B. E. Rittmann (1992). Accurate pseudoanalytical solution for steady-state biofilms. Biotechnol. Bioeng. 39, 790–793.
Sauer, K., A. K. Camper, G. D. Ehrlich, J. W. Costerton and D. G. Davies (2002). Pseudomonas aeruginosa displays multiple phenotypes during development as a biofilm. J. Bacteriol. 184, 1140–1154.
Schaefer, A. L., B. L. Hanzelka, M. R. Parsek and E. P. Greenberg (2000). Detection, purification and structural elucidation of acylhomoserine lactone inducer of Vibrio fischeri luminescence and other related molecules. Methods Enzymol. 305, 288–301.
Schaefer, A. L., D. L. Val, B. L. Hanzelka, J. E. Cronan, Jr. and E. P. Greenberg (1996). Generation of cell-to-cell signals in quorum sensing: acyl homoserine lactone synthase activity of a purified Vibrio fischeri luxI protein. Proc. Natl Acad. Sci. 93, 9505–9509.
Singh, P. K., A. L. Schaefer, M. R. Parsek, T. O. Moninger, M. J. Welsh and E. P. Greenberg (2000). Quorum-sensing signals indicate that cystic fibrosis lungs are infected with bacterial biofilms. Nature 407, 762–764.
Stewart, P. and J. W. Costerton (2001). Antibiotic resistance of bacteria in biofilms. Lancet 358, 135–138.
Suidan, M. T., B. E. Rittmann and U. K. Traegner (1987). Criteria establishing biofilm-kinetic types. Water Res. 21, 491–498.
Wanner, O. and W. Gujer (1986). A multispecies biofilm model. Biotechnol. Bioeng. 28, 314–328.
Ward, J. P., J. R. King, A. J. Koerber, P. Williams, J. M. Croft and R. E. Sockett (2001). Mathematical modelling of quorum sensing bacteria. IMA J. Math. Appl. Med. Biol. 18, 263–292.
Watnick, P. and R. Kolter (2000). Biofilm, city of microbes. J. Bacteriol. 182, 2675–2679.
Whiteley, M., M. G. Bangera, R. E. Bumgarner, M. R. Parsek, G. M. Teitzel, S. Lory and E. P. Greenberg (2001). Gene expression in Pseudomonas aeruginosa biofilms. Nature 413, 860–864.
Williamson, K. J. and P. L. McCarty (1976). Verification studies of the biofilm model for bacterial substrate utilization. J. Water Pol. Cont. Fed. 48, 281–289.
Xu, K. D., P. S. Stewart, F. Xia, C. T. Huang and G. A. McFeters (1998). Spatial physiological heterogeneity in Pseudomonas aeruginosa biofilm is determined by oxygen availability. Appl. Environ. Microbiol. 64, 4035–4039.
Yates, E. et al. (2002). N-acylhomoserine lactones undergo lactonolysis in a pH-, temperature-, and acyl chain length-dependent manner during growth of Yersinia pseudotuberculosis and Pseudomonas aeruginosa. Infect. Immun. 70, 5635–5646.
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Chopp, D.L., Kirisits, M.J., Moran, B. et al. The dependence of quorum sensing on the depth of a growing biofilm. Bull. Math. Biol. 65, 1053–1079 (2003). https://doi.org/10.1016/S0092-8240(03)00057-0
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DOI: https://doi.org/10.1016/S0092-8240(03)00057-0