Mathematical description of microbial biofilms

SIAM Review

Volumn 52, Issue 2, 2010, Pages 221-265

  Klapper, Isaac ^a   Dockeryt, Jack ^a  

^a MONTANA STATE UNIVERSITY   (United States)

Author keywords

Antimicrobial tolerance; Biofilms; Biomechanics; Quorum sensing

Indexed keywords

ANTIMICROBIAL TOLERANCE; MATHEMATICAL DESCRIPTIONS; MICROBIAL BIOFILM; MICROBIAL COMMUNITIES; QUORUM-SENSING; TOLERANCE MECHANISMS;

BIOFILMS; BIOMECHANICS; MICROORGANISMS;

BIOFILTERS;

EID: 77954339797     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/080739720     Document Type: Review

References (262)

1. D.G. ALLISON, The biofilm matrix, Biofouling, 19 (2003), pp. 139-150.
2. E. ALPKVIST, N. OVERGAARD, S. GUSTAFSSON, AND A. HEYDEN, A new mathematical model for chemotactic bacterial colony growth, Wat. Sci. Tech., 49 (2004), pp. 187-192.
3. E. ALPKVIST, C. PICIOREANU, M.C.M. VAN LOOSDRECHT, AND A. HEYDEN, Three-dimensional biofilm model with individual cells and continuum EPS matrix, Biotech. Bioeng., 94 (2006), pp. 961-979.
4. E. ALPKVIST AND I. KLAPPER, Description of mechanical response including detachment using a novel particle method of biofilm/flow interaction, Wat. Sci. Tech., 55 (2007), pp. 265-273.
5. E. ALPKVIST AND I. KLAPPER, A multidimensional multispecies continuum model for heterogenous biofilm, Bull. Math. Biol., 69 (2007), pp. 765-789.
6. J.B. ANDERSON, C. STERNBERG, L.K. POULSEN, M. GIVSKOV, AND S. MOLIN, New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria, Appl. Environ. Microbiol., 64 (1998), pp. 2240-2246.
7. K. ANGUIGE, J.R. KING, J.P. WARD, AND P. WILLIAMS, Mathematical modelling of therapies targeted at bacterial quorum sensing, Math. Biosci., 192 (2004), pp. 39-83.
8. K. ANGUIGE, J.R. KING, AND J.P. WARD, Modelling antibiotic- and anti-quorum sensing treatment of a spatially-structured Pseudomonas aeruginosa population, J. Math. Biol., 51 (2005), pp. 557-594.
9. K. ANGUIGE, J.R. KING, AND J.P. WARD, A multi-phase mathematical model of quorum sensing in a maturing Pseudomonas aeruginosa biofilm, Math. Biosci., 203 (2006), pp. 240-276.
10. D. ANGELI, J.E. FERRELL, J. R., AND E.D. SONTAG, Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems, Proc. Natl. Acad. Sci. USA, 101 (2004), pp. 1822-1827.
11. B. ATKINSON AND I.J. DAVIES, The overall rate of substrate uptake (reaction) by microbial films, Trans. Inst. Chem. Engrs., 52 (1974), pp. 248-259.
12. B.P. AYATI AND I. KLAPPER, A multiscale model of biofilm as a senescence-structured fluid, Multiscale Model. Sim., 6, (2007) pp. 347-365.
13. N. BAGGE, M. SCHUSTER, M. HENTZER, O. CIOFU, M. GIVSKOV, E.P. GREENBERG, AND N. HøIBY, Pseudomonas aeruginosa biofilms exposed to imipenem exhibit changes in global gene expression and beta-lactamase and alginate production, Antimicrob. Agents Chemother., 48 (2004), pp. 1175-1187.
14. N.Q. BALABAN, J. MERRIN, R. CHAIT, L. KOWALIK, AND S. LEIBLER, Bacterial persistence as a phenotypic switch, Science, 305 (2004), pp. 1622-1625.
15. M.L. BARCLAY, E.J. BEGG, AND S.T. CHAMBERS, Adaptive resistance following single doses of gentamicin in a dynamic in vitro model, Antimicrob. Agents Chemother., 36 (1992), pp. 1951-1957.
16. M.L. BARCLAY, E.J. BEGG, S.T. CHAMBERS, AND B.A. PEDDIE, The effect of aminoglycosideinduced adaptive resistance on the antibacterial activity of other antibiotics against Pseudomonas aeruginosa in vitro, J. Antimicrob. Chemother., 38 (1996), pp. 853-858.
17. M.L. BARCLAY AND E.J. BEGG, Aminoglycoside adaptive resistance: Importance for effective dosing regimens, Drugs, 61 (2001), pp. 713-721.
18. I. B. BEECH AND J. SUNNER, Biocorrosion: Towards understanding interactions between biofilms and metals, Current Opinion Biotech., 15 (2004), pp. 181-186.
19. R.D. BERG, The indigenous gastrointestinal microflora, Trends Microbiol., 4 (1996), pp. 430435.
20. J. W. BlGGER, Treatment of staphylococcal infections with penicillin by intermittent sterilization, Lancet, 2 (1944), pp. 497-500.
21. P.L. BISHOP, Biofilm structure and kinetics, Wat. Sci. Tech., 36 (1997), pp. 287-294.
22. B.R. BOLES AND A.R. HOR.SWILL, Agr-mediated dispersal of Staphylococcus aureus biofilms, PLoS Pathogens, 4 (4) (2008), article el000052.
23. M. BÖL, R.B. MÖHLE, M. HAESNER, T.R. NEU, H. HORN, AND R. KRULL, 3D finite element model of biofilm detachment using real biofilm structures from CLSM data, Biotech. Bioeng., 103 (2009), pp. 177-186.
24. A. BROOUN, S. LIU, AND K. LEWIS, A dose-response study of antibiotic resistance in Pseudomonas aeruginosa biofilms, Antimicrob. Agents Chemother., 44 (2000), pp. 640-646.
25. M.R. W. BROWN, P.J. COLLIER, AND P. GILBERT, Influence of growth-rate on the susceptibility to antimicrobial agents: Modification of the cell envelope and batch and continuous culture, Antimicrob. Agents Chemother., 34 (1990), pp. 1623-1628.
26. J.D. BRYERS, Medical biofilms, Biotech. Bioeng., 100 (2007), pp. 1-18.
27. S. BUSBY AND V. DE LORENZO, Cell regulation: Putting together pieces of the big puzzle, Current Opinion Microbiol., 4 (2001), pp. 117-118.
28. P.M. CHAIKIN AND T.C. LUBENSKY, Principles of Condensed Matter Physics, Cambridge University Press, Cambridge, UK, 2000.
29. M. CHALFIE, Y. TU, G. EUSKIRCHEN, W.W. WARD, AND D.C. PRASHER, Green fluorescent protein as a marker for gene expression, Science, 263 (1994), pp. 802-805.
30. J.D. CHAMBLESS, S.M. HUNT, AND P.S. STEWART, A three-dimensional computer model of four hypothetical mechanisms protecting biofilms from antimicrobials, Appl. Environ. Microbiol., 72 (2006), pp. 2005-2013.
31. J.D. CHAMBLESS AND P.S. STEWART, A three-dimensional computer model analysis of three hypothetical biofilm detachment mechanisms, Biotech. Bioeng., 97 (2007), pp. 1573-1584.
32. W.G. CHARACKLIS, Fouling biofilm development: A process analysis, Biotech. Bioeng., 23 (1981), pp. 1923-1960.
33. M.A.S. CHAUDHRY AND S.A. BEG, A review on the mathematical modeling of biofilm processes: Advances in fundamentals of biofilm modeling, Chem. Eng. Technol., 9 (1998), pp. 701-710.
34. X. CHEN AND P.S. STEWART, Role of electrostatic interactions in cohesion of bacterial biofilms, Appl. Microbiol. Biotechnol., 59 (2002), pp. 718-720.
35. D.L. CHOPP, M.J. KIRISITS, M.R. PARSEK, AND B. MORAN, A mathematical model of quorum sensing in a growing P. aeruginosa biofilm, J. Indust. Microbiol. Biotechnol., 29 (2002), pp. 339-346.
36. D.L. CHOPP, M.J. KIRISITS, M.R. PARSEK, AND B. MORAN, The dependence of quorum sensing on the depth of a growing biofilm, Bull. Math. Biol., 65 (2003), pp. 1053-1079.
37. N.G. COGAN AND J.P. KEENER, The role of the biofilm matrix in structural development, Math. Med. Biol., 21 (2004), pp. 147-166.
38. N.G. COGAN, R. CORTEZ, AND L. FAUCI, Modeling physiological resistance in bacterial biofilms, Bull. Math. Biol., 21 (2005), pp. 831-853.
39. N.G. COGAN AND J.P. KEENER, Channel formation in gels, SIAM J. Appl. Math., 65 (2005), pp. 1839-1854.
40. N.G. COGAN, Effects of persister formation on bacterial response to dosing, J. Theor. Biol., 238 (2006), pp. 694-703.
41. F.M. COHAN AND E.B. PERRY, A systematics for discovering the fundamental units of bacterial diversity, Current Biol., 17 (2007), pp. R373-R386.
42. Y. COHEN, Bioremediation of oil by marine microbial mats, Int. Microbiol., 5 (2002), pp. 189-193.
43. J.W. COSTERTON, P.S. STEWART, AND E.P. GREENBERG, Bacterial biofilms: A common cause of persistent infections, Science, 284 (1999), pp. 1318-1322.
44. J.W. COSTERTON, K.J. CHENG, G.G. GEESEY, T.I. LADD, J.C. NICKEL, M. DASGUPTA, AND T.J. MARRIE, Bacterial biofilms in nature and disease, Annu. Rev. Microbiol., 41 (1987), pp. 435-464.
45. J.E. COSTERTON, Z. LEWANDOWSKI, D.DEBEER, D. CALDWELL, D. KORBER, AND G. JAMES, Biofilms, the customized microniche, J. Bacteriol., 176 (1994), pp. 2137-2142.
46. J.W. COSTERTON, The Biofilm Primer, Springer, Berlin, 2007.
47. J.W. COSTERTON, Z. LEWANDOWSKI, D.E. CALDWELL, D.R. KORBER, AND H.M. LAPPINSCOTT, Microbial biofilms, Annu. Rev. Microbiol., 49 (1995), pp. 711-745.
48. R.O. DAROUICHE, A. DHIR, A.J. MILLER, G.G. LANDON, I.I RAAD, AND D.M MUSHER, Vancomycin penetration into biofilm covering infected prostheses and effect on bacteria, J. Infectious Diseases, 170 (1994), pp. 720-723.
49. M.E. DAVEY AND G.A. O'TOOLE, Microbial biofilms: From ecology to molecular genetics, Microbiol. Mol. Biol. Rev., 64 (2000), pp. 847-867.
50. M.E. DAVEY, N.C. CAIAZZA, AND G.A. O'TOOLE, Rhamnolipid surfactant production affects biofilm architecture in Pseudomonas aeruginosa PAO1, J. Bacteriol., 185 (2003), pp. 1027-1036.
51. D.G. DAVIES, J.P. PEARSON, B.H. IGLEWSKI, J.W. COSTERTON, E.P. GREENBERG, AND M.R. PARSEK, The involvement of cell-to-cell signals in the development of bacterial biofilm, Science, 280 (1998), pp. 295-298.
52. D. DE BEER, R. SRINIVASAN, AND P.S. STEWART, Direct measurement of chlorine penetration into biofilms during disinfection, Appl. Environ. Microbiol., 60 (1994), pp. 4339-4344.
53. D. DE BEER, P. STOODLEY, AND Z. LEWANDOWSKI, Effects of biofilm structure on oxygen distribution and mass transport phenomenon, Biotech. Bioeng., 43 (1994), pp. 1131-1138.
54. P. DE LEENHEER AND N. COGAN, Failure of antibiotic treatment in microbial populations, J. Math. Biol., 59 (2009), pp. 563-579.
55. J.G. DILLON, S. MILLER, M. HULLAR, N. PINEL, AND D.A. STAHL, Spatial and temporal variability in a stratified hypersaline microbial mat community, FEMS Microbiol. Ecol., 68 (2009), pp. 46-58.
56. R. DILLON AND L. FAUCI, A microscale model of bacterial and biofilm dynamics in porous media, Biotech. Bioeng., 68 (2000), pp. 536-547.
57. R. DILLON, L. FAUCI, A. FOGELSON, AND D. GAVER, Modeling biofilm processes using the immersed boundary method, J. Comput. Phys., 129 (1996), pp. 57-73.
58. J.D. DOCKERY AND J.P. KEENER, A mathematical model for quorum sensing in Pseudomonas aeruginosa, Bull. Math. Bio., 63 (2001), pp. 95-116.
59. J.D. DOCKERY AND I. KLAPPER, Finger formation in biofilm layers, SIAM J. Appl. Math., 62 (2001), pp. 853-869.
60. M. DOI AND S.F. EDWARDS, The Theory of Polymer Dynamics, Oxford Science Publications, Clarendon Press, Oxford, UK, 1988.
61. M. DOI AND A. ONUKI, Dynamic coupling between stress and composition in polymer-solutions and blends, J. Phys. II, 2 (1992), pp. 1631-1656
62. R. DUDDU, S. BORDAS, D.L. CHOPP, AND B. MORAN, A combined extended finite element and level set method for biofilm growth, Internat. J. Numer. Methods Engrg., 74 (2007), pp. 848-870.
63. H.J. DUPIN, P.K. KITANIDIS, AND P.L. MCCARTY, Pore-scale modeling of biological clogging due to aggregate expansion: A material mechanics approach, Water Resour. Res., 37 (2001), pp. 2965-2979.
64. A. EBERHARD, Inhibition and activation of bacterial luciferase synthesis, J. Bacteriol., 109 (1972), pp. 1101-1105.
65. A. EBERHARD, A.L. BURLINGAME, C. EBERHARD, G.L. KENYON, K.H. NEALSON, AND N.J. OPPENHEIMER, Structural identification of autoinducer of Photobacterium fischeri luciferase, Biochemistry, 20 (1981), pp. 2444-2449.
66. H.J. EBERL, D.F. PARKER, AND M.C. M. VAN LOOSDRECHT, A new deterministic spatiotemporal continuum model for biofilm development, J. Theor. Med., 3 (2001), pp. 161-175.
67. H.J. EBERL AND R. SUDARSAN, Exposure of biofilms to slow flow fields: The convective contribution to growth and disinfection, J. Theor. Biol., 253 (2008), pp. 788-807.
68. M. EHRENBERG AND A. SVERREDAL, A model for copy number control of the plasmid R1, J. Mol. Biol., 246 (1995), pp. 472-485.
69. J.G ELKINS, D.J. HASSETT, P.S. STEWART, H.P. SCHWEIZER, AND T.R. MCDERMOTT, Protective role of catalase in Pseudomonas aeruginosa biofilm resistance to hydrogen peroxide, Appl. Environ. Microbiol., 65 (1999), pp. 4594-4600.
70. J. ENGEBRECHT, K. NEALSON, AND M. SILVERMAN, Bacterial bioluminescence: Isolation and genetic analysis of functions from Vibrio fischeri, Cell., 32 (1983), pp. 773-781.
71. D.J. EVANS, D.G. ALLISON, M.R.W. BROWN, AND P. GILBERT, Susceptibility of Pseudomonas aeruginosa and Escherichia coli biofilms towards ciprofloxacin: Effect of specific growth rate, J. Antimicrob. Chemother., 27 (1991), pp. 177-184.
72. M.G. FAGERLIND, Mathematical Modelling of Bacterial Quorum Sensing and Biofilm Formation, thesis, The University of New South Wales, Sydney, Australia.
73. M.G. FAGERLIND, S.A. RICE, P. NILSSON, M. HARLÉN, S. JAMES, T. CHARLTON, AND S. KJELLEBERG, The role of regulators in the expression of quorum-sensing signals in Pseudomonas aeruginosa, J. Mol. Microbiol. Biotechnol., 6 (2003), pp. 88-100.
74. M.G. FAGERLIND, P. NILSSON, M. HARLEN, S. KARLSSON, S.A. RICE, AND S. KJELLEBERG, Modeling the effect of acylated homoserine lactone antagonists in Pseudomonas aeruginosa, Biosystems, 80 (2005), pp. 201-213.
75. J.D. FERRY, Viscoelastic Properties of Polymers, John Wiley & Sons, New York, 1980.
76. H.-C. FLEMMING, Biofilms and environmental protection, Wat. Sci. Technol., 27 (1993), pp. 110.
77. H.-C. FLEMMING, J. WINGENDER, C. MAYER, V. KORSTGENS, AND W. BORCHARD, Cohesiveness in biofilm matrix polymers, in Community Structure and Cooperation in Biofilms, D. Allison, P. Gilbert, H.M. Lappin-Scott, and M. Wilson, eds., SGM Sympos. Ser. 59, Cambridge University Press, Cambridge, UK, 2000, pp. 87-105.
78. H.-C. FLEMMING AND J. WINGENDER, Relevance of microbial extracellular polymeric substances (EPSs)-Part I: Structural and ecological aspects, Wat. Sci. Technol., 43 (2001), pp. 1-8.
79. H.-C. FLEMMING, T.R. NEU, AND D. WOZNIAK, The EPS matrix: The "house of biofilm cells," J. Bacteriol., 189 (2007), pp. 7945-7947.
80. C. FUQUA, S. C. WINANS, AND E. P. GREENBERG, Census and consensus in bacterial ecosystems: The luxR-luxI family of quorum-sensing transcriptional regulators, Annu. Rev. Microbiol., 50 (1996), pp. 727-751.
81. C. A. Fux, S. WILSON, AND P. STOODLEY, Detachment characteristics and oxacillin resistance of Staphylococcus aureus biofilm emboli in an in vitro catheter infection model, J. Bacteriol., 186 (2004), pp. 4486-1491.
82. C. A. Fux, J.W. COSTERTON, P.S. STEWART, AND P. STOODLEY, Survival strategies of infectious biofilms, Trends in Microbiol., 13 (2005), pp. 34-40.
83. V. GADANI, P. VILLON, J. MANEM, AND B. RITTMAN, A new method to solve a non-steady-state multispecies biofilm model, Bull. Math. Biol., 55 (1993), pp. 1039-1061.
84. P. GILBERT, D.G. ALLISON, AND A.J. MCBAIN, Biofilms in vitro and in vivo: Do singular mechanisms imply cross-resistance1?, J. Appl. Microbiol., 92 (2002), pp. 98S-110S.
85. B. GIWERCMAN, E.T. JENSEN, N. HOIBY, A. KHARAZMI, AND J.W. COSTERTON, Induction of β-lactamase production in Pseudomonas aeruginosa biofilms, Antimicrob. Agents Chemother., 35 (1991), pp. 1008-1010.
86. A. GJALTEMA, P.A.M. ARTS, M.C. M. VAN LOOSDRECHT, J.G. KUENEN, AND J.J. HEIJNEN, Heterogeneity of biofilms in rotating annular reactors: Occurrence, structure, and consequences, Biotech. Bioeng., 44 (1994), pp. 194-204.
87. C. A. GORDON, N.A. HODGES, AND C. MARRIOT, Antibiotic interaction and diffusion through alginate and exopolussacharide of cystic fibrosis-derived Pseudomonas aeruginosa, J. Antimicrob. Chemother., 22 (1988), pp. 667-674.
88. A.B. GORYACHEV, D.J. TOH, AND T. LEE, Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants, Biosystems, 83 (2006), pp. 178-187.
89. A.B. GORYACHEV, D.-J. TOH, K.B. WEE, T. LEE, H.-B. ZHANG, AND L.-H. ZHANG, Transition to quorum sensing in an agrobacterium population: A stochastic model, PLoS Comput. Biol., 1 (2005), article e37.
90. S.J. GOULD, Planet of the bacteria, Washington Post Horizon, 119 (1996), p. 344.
91. E.P. GREENBERG, Quorum sensing in Gram-negative bacteria, ASM News, 63 (1997), pp. 371377.
92. H.P. GREENSPAN, On the s elf-inhibited growth of cell cultures, Growth, 38 (1974), pp. 81-95.
93. H.P. GREENSPAN, On the growth and stability of cell cultures and solid tumors, J. Theor. Biol., 56 (1975), pp. 229-242.
94. K.J. GROBE, J. ZAHLLER., AND P.S. STEWART, Role of dose concentration in biocide efficacy against Pseudomonas aeruginosa biofilms, J. Ind. Microbiol. Biotechnol., 29 (2002), pp. 1015.
95. W. GUJER AND O. WANNER, Modeling mixed population biofilms, in Biofilms, John Wiley & Sons, New York, 1990.
96. L. HALL-STOODLEY, J.W. COSTERTON, AND P. STOODLEY, Bacterial biofilms: From the natural environment to infectious diseases, Nature Rev. Microbiol., 2 (2004), pp. 95-108.
97. G.W. HANLON, Bacteriophages: An appraisal of their role in the treatment of bacterial infections, Internat. J. Antimicrobial Agents, 30 (2007), pp. 118-128.
98. E.L. HASELTINE AND F.H. ARNOLD, Implications of rewiring bacterial quorum sensing, Appl. Environ. Microbiol., 74 (2008), pp. 437-445.
99. D.J. HASSETT, J.F. MA, J.G. ELKINS, T.R. MCDERMOTT, U.A. OCHSNER, S.E. WEST, C. T. HUANG, J. FREDERICKS, S. BURNETT, P.S. STEWART, G. MCFETERS, L. PASSADOR, AND B.H. IGLEWSKI, Quorum sensing in Pseudomonas aeruginosa controls expression of catalase and superoxide dismutase genes and mediates biofilm susceptibility to hydrogen peroxide, Mol. Microbiol., 34 (1999), pp. 1082-1093.
100. B.A. HENSE, C KUTTLER, J. MÜLLER, M. ROTHBALLER, A. HARTMANN, AND J.-U. KREFT, Does efficiency sensing unify diffusion and quorum sensing?, Nat. Rev. Micro., 5 (2007), pp. 1740-1526.
101. M. HENTZER, H. WU, J.B. ANDERSEN, K. RIEDEL, T.B. RASMUSSEN, N. BAGGE, N. KUMAR, M.A. SCHEMBRI, Z. SONG, P. KRISTOFFERSEN, M. MANEFIELD, J.W. COSTERTON, S. MOLIN, L. EBERL, P. STEINBERG, S. KJELLEBERG, N. HOIBY, AND M. GIVSKOV, Attenuation of Pseudomonas aeruginosa virulence by quorum sensing inhibitors, EMBO J., 22 (2003), pp. 3803-3815.
102. S.W. HERMANOWICZ, A model of two-dimensional biofilm morphology, Wat. Sci. Tech., 37 (1998), pp. 219-222.
103. S.W. HERMANOWICZ, A simple 2D biofilm model yields a variety of morphological features, Math. Biosci., 169 (2001), pp. 1-14.
104. H. HORN, H. REIFF, AND E. MORGENROTH, Simulation of growth and detachment in biofilm systems under defined hydrodynamic conditions, Biotech. Bioeng., 81 (2002), pp. 607-617.
105. A.R. HORSWILL, P. STOODLEY, P.S. STEWART, AND M.R. PARSEK, The impact of the chemical, biological, and physical environment on quorum sensing in structured microbial communities, Analyt. Bioanalyt. Chem., 387 (2007), pp. 371-380.
106. A. HOUARIA, J. PICARDA, H. HABAROUB, L. GALASC, H. VAUDRYC, V. HEIMD, AND P. DI MARTINOA, Rheology of biofilms formed at the surface of NF membranes in a drinking water production unit, Biofouling, 24 (2008), pp. 235-240.
107. S.A. Huws, A.J. MCBAIN, AND P. GILBERT, Protozoan grazing and its impact upon population dynamics in biofilm communities, J. Appl. Microbiol., 98 (2005), pp. 238-244.
108. S. JAMES, P. NILSSON, S. KJELLEBERG, AND T. FAGERSTROM, Luminescence control in the marine bacterium Vibrio fischeri: An analysis of the dynamics of lux regulation, J. Mol. Biol., 296 (2000), pp. 1127-1137.
109. A. JAYARAMAN AND T.K. WOOD, Bacterial quorum sensing: Signals, circuits, and implications for biofilms and disease, Annu. Rev. Biomed., 10 (2008), pp. 8.1-8.23.
110. K.K. JEFFERSON, What drives bacteria to produce biofilms?, FEMS Microbiol. Lett., 236 (2004), pp. 163-173.
111. L.L. JAHNKE, W. EDER, R. HUBER, J.M. HOPE, K.U. HINRICHS, J.M. HAYES, D.J. DES MARAIS, S.L. CADY, AND R.E. SUMMONS, Signature lipids and stable carbon isotope analyses of octopus spring hyperthermophilic communities compared with those of Aquificales representatives, Appl. Environ. Microbiol., 67 (2001), pp. 5179-5189.
112. P.O. JENSEN, T. BJARNSHOLT, T.B. RASMUSSEN, H. CALUM, C MOSER, T. PRESSLER, M. GIVSKOV, AND N. HOIBY, Rapid necrotic killing of PMNs is caused by quorum sensing controlled production of rhamnolipid by Pseudomonas aeruginosa, Microbiology, 3 (2006), pp. 225-231.
113. B.B. JøRGENSEN AND D.J. DES MARAIS, Optical properties of benthic photosynthetic communities: studies of cyanobacterial mats, Limnol. Oceanogr., 33 (1988), pp. 99-113.
114. B.B. JøRGENSEN AND D.J. DES MARAIS, The diffusive boundary layer of sediments: oxygen microgradients over a microbial mat, Limnol. Oceanogr., 35 (1990), pp. 1343-1355.
115. E.S. KEMPER AND F.E. HANSON, Aspects of light production by Photobacterium fischeri, J. Bacteriol., 95 (1968), pp. 975-979.
116. I. KEREN, N. KALDALU, A. SPOERING, Y. WANG, AND K. LEWIS, Persister cells and tolerance to antimicrobials, FEMS Microbiol. Lett., 230 (2004), pp. 13-18.
117. H. KHASSEHKHAN AND H.J. EBERL, Interface tracking for a non-linear, degenerated diffusionreaction equation describing formation of bacterial biofilms, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 13 (2006), pp. 131-144 (suppl).
118. A. KHOURY, K. LAM, B.D. ELLIS, AND J.W. COSTERTON, Practical measures to control devicerelated bacterial infections, Int. J. Artif. Organs, 38 (1991), pp. M174-M178.
119. S.L. KINNIMENT AND J.W.T. WIMPENNY, Measurements of the distribution of adenylate concentrations and adenylate energy charge across Pseudomonas aeruginosa biofilms, Appl. Environ. Microbiol., 58 (1992), pp. 1629-1635.
120. M.J. KIRISITS, J.J. MARGOLIS, B.L. PUREVDORJ-GAGE, B. VAUGHAN, D.L. CHOPP, P. STOODLEY, AND M.R. PARSEK, Influence of the hydrodynamic environment on quorum sensing in Pseudomonas aeruginosa biofilms, J. Bacteriology, 189 (2007), pp. 8357-8360.
121. J.C KISSEL, P.L. MCCARTY, AND R.L. STREET, Numerical simulation of mixed-culture biofilm, J. Environ. Eng., 110 (1984), pp. 393-411.
122. S. KJELLEBERG AND S. MOLIN, 7S there a role for quorum sensing signals in bacterial biofilms?, Current Opinion Microbiol., 5 (2002), pp. 254-258.
123. I. KLAPPER, C. J. RUPP, R. CARGO, B. PUREVDORJ, AND P. STOODLEY, A viscoelastic fluid description of bacterial biofilm material properties, Biotech. Bioeng., 80 (2002), pp. 289-296.
124. I. KLAPPER AND J. DOCKERY, Role of cohesion in material description of biofilms, Phys. Rev. E, 74 (2006), article 031902.
125. I. KLAPPER, P. GILBERT, B.P. AYATI, J. DOCKERY, AND P.S. STEWART, Senescence can explain microbial persistence, Microbiology, 153 (2007), pp. 3623-3630.
126. B.J. KLAYMAN, I. KLAPPER, P.S. STEWART, AND A.K. CAMPER, Measurements of accumulation and displacement at the single cell cluster level in Pseudomonas aeruginosa biofilms, Environ. Microbiol., 10 (2008), pp. 2344-2354.
127. A.J. KOERBER, J.R. KING, J.P. WARD, P. WILLIAMS, J.M. CROFT, AND R.E. SOCKETT, A mathematical model of partial-thickness bum-wound infection by Pseudomonas aeruginosa: Quorum sensing and the build-up to invasion, Bull. Math. Biol., 64 (2002), pp. 239259.
128. A.J. KOERBER, J.R. KING, AND P. WILLIAMS, Deterministic and stochastic modelling of endosome escape by Staphylococcus aureus: "Quorum" sensing by a single bacterium, J. Math. Biol., 50 (2005), pp. 440-488.
129. A. KONOPKA, Microbial ecology: Searching for principles, Microbe, 1 (2006), pp. 175-179.
130. V. KORSTGENS, H.C FLEMMING, J. WINGENDER, AND W. BORCHARD, Uniaxial compression measurement device for investigation of the mechanical stability of biofilms, J. Microbiol. Methods, 46 (2001), pp. 9-17.
131. V. KORSTGENS, H.C FLEMMING, J. WINGENDER, AND W. BORCHARD, Influence of calcium ions on the mechanical properties of a model biofilm of mucoid Pseudomonas aeruginosa, Wat. Sci. Technol., 43 (2001), pp. 49-57.
132. J.U. KREFT, G. BOOTH, AND J.W.T. WIMPENNY, BacSim, a simulator for individual-based modelling of bacterial colony growth, Microbiology, 144 (1998), pp. 3275-3287.
133. J.U. KREFT, C. PICIOREANU, J.W.T. WIMPENNY, AND M.CM. VAN LOOSDRECHT, Individualbased modelling of biofilms, Microbiology, 147 (2001), pp. 2897-2912.
134. J.U. KREFT AND J.W.T. WIMPENNY, Effect of EPS on biofilm structure and function as revealed by an individual-based model of biofilm growth, Wat. Sci. Tech., 43 (2001), pp. 135-141.
135. E. KUSSELL, R. KISHONY, N.Q. BALABAN, AND S. LEIBLER, Bacterial persistence: A model of survival in changing environments, Genetics, 169 (2005), pp. 1807-1814.
136. R.G. LARSON, Constitutive Equations for Polymer Melts and Solutions, ButterworthHeinemann Ser. Chem. Engrg., Butterworth, Boston, 1988.
137. C. S. LASPIDOU AND B.E. RITTMANN, Modeling the development of biofilm density including active bacteria, inert biomass, and extracellular polymeric substances, Wat. Res., 38 (2004), pp. 3349-3361.
138. J.R. LAWRENCE, B. SCHARF, G. PACKROFF, AND T.R. NEU, Microscale evaluation of the effects of grazing by invertebrates with contrasting feeding modes on river architecture and composition, Microb. Ecol., 44 (2002), pp. 199-207.
139. A.K. LEE AND D.K. NEWMAN, Microbial iron respiration: Impacts on corrosion processes, Appl. Microbiol. Biotechnol., 62 (2003), pp. 134-139.
140. K. LEWIS, Riddle of bioflm resistance, Antimicrob. Agents. Chemo., 45 (2001), pp. 999-1007.
141. R.E. LEY, R. KNIGHT, AND J.I. GORDON, The human microbiome: Eliminating the biomedical/environmental dichotomy in microbial ecology, Environ. Microbiol., 9 (2007), pp. 3-4.
142. J. LI, L. WANG, Y. HASHIMOTO, C. Y. TSAO, T.K. WOOD, J.J. VALDES, E. ZAFIRIOU, AND W.E. BENTLEY, A stochastic model of Escherichia coli A1-2 quorum signal circuit reveals alternative synthesis pathways, Mol. Syst. Biol., 2 (2006), article 67.
143. B. MANZ, F. VOLKA, D. GOLL, AND H. HORN, Investigation of biofilm structure, flow patterns and detachment with magnetic resonance imaging, Wat. Sci. Tech., 52 (2005), pp. 1-6.
144. P.D. MARSH, Dental plaque: Biological significance of a biofilm and community life-style, J. Clin. Periodentol., 32 (2005), pp. 7-15.
145. S.T. MILNER, Hydrodynamics of semidilute polymer-solutions, Phys. Rev. Lett., 66 (1991), pp. 1477-1480.
146. R.B. MOHLE, T. LANGEMANN, M. HAESNER, W. AUGUSTIN, S. SCHOLL, T.R. NEU, D.C. HEMPEL, AND H. HORN, Structure and shear strength of microbial biofilms as determined with confocal laser scanning microscopy and fluid dynamic gauging using a novel rotating disc biofilm reactor, Biotech. Bioeng., 98 (2007), pp. 747-755.
147. D. MONROE, Looking for chinks in the armor of bacterial biofilms, PLoS Biol., 5 (2007), article e307.
148. E. MORGENROTH, H.J. EBERL, M.C. M. VAN LOOSDRECHT, D.R. NOGUERA, G.E. PIZARRO, C. PICIOREANU, B.E. RITTMANN, A.O. SCHWARZ, AND O. WANNER, Comparing biofilm models for a single species biofilm system, Wat. Sci. Tech., 49 (2004), pp. 145-154.
149. J. MULLER, C KUTTLER, B.A. HENSE, M. ROTHBALLER, A. HARTMANN, Cell-cell communication by quorum sensing and dimension-reduction, J. Math. Biol., 53 (2006), pp. 672-702.
150. K.H. NEALSON, T. PLATT, J. WOODLAND HASTINGS, Cellular control of the synthesis and activity of the bacterial luminescent system, J. Bacteriology, 104 (1970), pp. 313-322.
151. V.T. NGUYEN, E. MORGENROTH, AND H.J. EBERL, A mesoscale model for hydrodynamics in biofilms that takes flow effects into account, Wat. Sci. Tech., 52 (2005), pp. 167-172.
152. W.W. NICHOLS, S.M. DORRINGTON, M.P.E. SLACK, AND H.L. WALMSLEY, Inhibition of tobramycin diffusion by binding to alginate, Antimicrob. Agents Chemother., 32 (1988), pp. 518-523.
153. W.W. NICHOLS, M.J. EVANS, M.P.E. SLACK, AND H.L. WALMSLEY, The penetration of antibiotics into aggregates of mucoid and non-mucoid Pseudomonas aeruginosa, J. Gen. Microbiol., 135 (1989), pp. 1291-1303.
154. D.R. NOGUERA, G. PIZARRO, D.A. STAHL, AND B.E. RITTMAN, Simulation of multispecies biofilm development in three dimensions, Wat. Sci. Tech., 39 (1999), pp. 123-130.
155. U.A. OCHSNER, A.K. KOCH, A. FIECHTER, AND J. REISER, Isolation and characterization of a regulatory gene affecting rhamnolipid biosurfactant synthesis in Pseudomonas aeruginosa, J. Bacteriol., 176 (1994), pp. 2044-2054.
156. A. OHASHI AND H. HARADA, Adhesion strength of biofilm developed in an attached growth reactor, Wat. Sci. Tech., 29 (1994), pp. 281-288.
157. A. OHASHI AND H. HARADA, A novel concept for evaluation of biofilm adhesion strength by applying tensile force and shear force, Wat. Sci. Tech., 34 (1996), pp. 201-211.
158. A. OHASHI, T. KOYAMA, K. SYUTSUBO, AND H. HARADA, A novel method for evaluation of biofilm tensile strength resisting erosion, Wat. Sci. Tech., 39 (1999), pp. 261-268.
159. G. O'TOOLE, H.B. KAPLAN, AND R. KOLTER, Biofilm formation as microbial development, Annu. Rev. Microbiol., 54 (2000), pp. 49-79.
160. S.J. PAMP AND T. TOLKER.-NIELSEN, Multiple roles of biosurfactants in structural biofilm development by Pseudomonas aeruginosa, J. Bacteriol., 189 (2007), pp. 2531-2539.
161. M.R. PARSEK AND E.P. GREENBERG, Acyl-homoserine lactone quorum sensing in Gramnegative bacteria: A signaling mechanism involved in associations with higher organisms, Proc. Natl. Acad. Sci. USA, 97 (1997), pp. 8789-8793.
162. M.R. PARSEK AND E.P. GREENBERG, Sociomicrobiology: The connections between quorum sensing and biofilms, Trends in Microbiol., 13 (2005), pp. 27-33.
163. L. PASSADOR, K.D. TUCKER, K.R. GUERTIN, M.P. JOURNET, A.S. KENDE, AND B.H. IGLEWSKI, Functional analysis of the Pseudomonas aeruginosa autoinducer PAI, J. Bacteriol., 178 (1996), pp. 5995-6000.
164. J.P. PEARSON, E.C. PESCI, AND B.H. IGLEWSKI, Roles of Pseudomonas aeruginosa las and rhl quorum-sensing systems in control of elastase and rhamnolipid biosynthesis genes, J. Bacteriol., 179 (1997), pp. 5756-5767.
165. J.P. PEARSON, C. VAN DELDEN, AND B.H. IGLEWSKI, Active efflux and diffusion are involved in transport of Pseudomonas aeruginosa cell-to-cell signals, J. Bacteriol., 181 (1999), pp. 1203-1210.
166. E.G. PESCI, J.P. PEARSON, P.C. SEED, AND B.H. IGLEWSKI, Regulation of las and rhl quorum sensing in Pseudomonas aeruginosa, J. Bacteriol., 179 (1997), pp. 3127-3132.
167. E.C. PESCI AND B.H. IGLEWSKI, Signalling in Pseudomonas aeruginosa, in Microbial Signalling and Communication, Cambridge University Press, Cambridge, UK, 1999, pp. 105-115.
168. C. PICIOREANU, J.J. HEIJNEN, AND M.C. VAN LOOSDRECHT, A new combined differentialdiscrete cellular automaton approach for biofilm modeling: Application for growth in gel beads, Biotech. Bioeng., 57 (1998), pp. 718-731.
169. C. PICIOREANU, M.C. VAN LOOSDRECHT, AND J. J. HEIJNEN, Effect of diffusive and convective substrate transport on biofilm structure formation: A two-dimensional modeling study, Biotech. Bioeng., 69 (2000), pp. 504-515.
170. C. PICIOREANU, M.C. VAN LOOSDRECHT, AND J. J. HEIJNEN, Two-dimensional model of biofilm detachment caused by internal stress from liquid flow, Biotech. Bioeng., 72 (1998), pp. 205-218.
171. C. PICIOREANU, Multidimensional Modeling of Biofilm Structure, Ph.D. thesis, Department of Biotechnology, TU Delft, The Netherlands, 1999.
172. G. PIZARRO, D. GRIFFEATH, AND D.R. NOGUERA, Quantitative cellular automaton model for biofilms, J. Environment. Engrg., 127 (2001), pp. 782-789.
173. G.E. PIZARRO, C. GARCIA, R. MORENO, AND M.E. SEPULVEDA, Two-dimensional cellular automaton model for mixed-culture biofilm, Wat. Sci. Tech., 49 (2004), pp. 193-198.
174. N.J. POPLAWSKI, A. SHIRINIFARD, M. SWAT, AND J.A. GLAZIER, Simulation of single-species bacterial-biofilm growth using the Glazier-Graner-Hogeweg model and the Compucell 3D modeling environment, Math. Biosci. Eng., 8, (2008) pp. 356-388.
175. E.H. POPPELE AND R.M. HOZALSKI, Micro-cantilever method for measuring the tensile strength of biofilms and microbial floes, J. Microbiol. Meth., 55 (2007), pp. 607-615.
176. B. PUREVDORJ, J.W. COSTERTON, AND P. STOODLEY, Influence of hydrodynamics and cell signaling on the structure and behavior of Pseudomonas aeruginosa biofilms, Appl. Environ. Microbiol., 68 (2002), pp. 4457-4464.
177. B. PUREVDORJ-GAGE, J.W. COSTERTON, AND P. STOODLEY, Phenotypic differentiation and seeding dispersal in non-mucoid and mucoid Pseudomonas aeruginosa biofilms, Microbiology, "l51 (2005), pp. 1569-1576.
178. National Institutes of Health, Immunology of Biofilms (R01), grants.nih.gov/grants/guide/pa-files/PA-07-288.html (2007).
179. S.A. RANI, B. PITTS, H. BEYENAL, R.A. VELUCHAMY, Z. LEWANDOWSKI, W.M. DAVISON, K. BUCKINGHAM-MEYER, AND P.S. STEWART, Spatial patterns of DNA replication, protein synthesis, and oxygen concentration within bacterial biofilms reveal diverse physiological states, J. Bacteriol., 189 (2007), pp. 4223-4233.
180. R.J. REDFIELD, IS quorum sensing a side effect of diffusion sensing?, Trends in Microbiol., 10 (2002), pp. 365-370.
181. P. REICHERT, Aquasim: A tool for simulation and data analysis of aquatic systems, Water Sci. Tech., 30 (1994), pp. 21-30.
182. N.P. REVSBECH AND D.M. WARD, Microelectrode studies of interstitial water chemistry and photosynthetic activity in a hot spring microbial mat, Appl. Environ. Microbiol., 48 (1984), pp. 270-275.
183. A.L. REYSENBACH, M. EHRINGER, AND K. HERSHBERGER, Microbial diversity at 83 degrees C in Calcite Springs, Yellowstone National Park: Another environment where the Aquificales and Korarchaeota coexist, Extremophiles, 4 (2000), pp. 61-67.
184. A. RHOADS, H. BEYENAL, AND Z. LEWANDOSKI, Microbial fuel cell using anaerobic respiration as an anodic reaction and biomineralized manganese as a cathodic reactant, Environ. Sci. Technol., 39 (2005), pp. 4666-4671.
185. S.A. RICE, K.S. KOH, S.Y. QUECK, M. LABBATE, K.W. LAM, AND S. KJELLEBERG, Biofilm formation and sloughing in Serratia marcescens are controlled by quorum sensing and nutrient cues, J. Bacteriol., 187 (2005), pp. 3477-3485.
186. B.E. RITTMANN, The effect of shear stress on biofilm loss rate, Biotech. Bioeng., 24 (1982), pp. 501-506.
187. M.E. ROBERTS AND P.S. STEWART, Modelling protection from antimicrobial agents in biofilms through the formation of persister cells, Microbiology, 151 (2005), pp. 75-80.
188. S.S. ROGERS, C. VAN DER WALLE, AND T.A. WAIGH, Microrheology of bacterial biofilms in vitro: Staphylococcus aureus and Pseudomonas aeruginosa, Langmuir, 24 (2208), pp. 13549-13555.
189. F.J. ROMERO-CAMPERO AND M.J. PEREZ-JIMENEZ, A model of the quorum sensing system in vibrio fischeri using P systems, Artificial Life, 14 (2008), pp. 95-109.
190. F.C. SAILER, B.M. MEBER.G, AND K.D. YOUNG, β-lactam induction of colanic acid gene expression in Escherichia coli, FEMS Microbiol. Lett., 226 (2003), pp. 245-249.
191. S.S. SANDERSON AND P.S. STEWART, Evidence of bacterial adaptation to monochloramine in Pseudomonas aeruginosa biofilms and evaluation of biocide action model, Biotech. Bioeng., 56 (1997), pp. 201-209.
192. K.M. SANDOZ, S.M. MITZIMBERG, AND M. SCHUSTER, Social cheating in Pseudomonas aeruginosa quorum sensin, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 15876-15881.
193. S.R. SCHOOLING, U.K. CHARAF, D.G. ALLISON, AND P. GILBERT, A role for rhamnolipid in biofilm dispersion, Biofilms, 1 (2004), pp. 91-99.
194. M. SCHUSTER, C.P. LOSTROH, T. OGI, AND E.P. GREENBERG, Identification, timing, and signal specificity of Pseudomonas aeruginosa quorum-controlled genes: A transcriptome analysis, J. Bacteriol., 185 (2003), pp. 2066-2079.
195. P.C. SEED, L. PASSADOR, AND B.H. IGLEWSKI, Activation of the Pseudomonas aeruginosa lasl gene by LasR and the Pseudomonas autoinducer PAI: An autoinduction regulatory hierarchy, J. Bacteriol., 177 (1995), pp. 654-659.
196. F. SEPANDJ, H. CERI, A GIBB, R. READ, AND M. OLSON, Minimum inhibitory concentration (MIC) versus minimum biofilm eliminating concentration (MBEC) in evaluation of antibiotic sensitivity of Gram-negative bacilli causing peritonitis, Peritoneal Dialysis Internat., 24 (2004), pp. 65-67.
197. T. SHAW, M. WINSTON, C. RUPP, I. KLAPPER, AND P. STOODLEY, Commonality of elastic relaxation times in biofilms, Phys. Rev. Lett., 93 (2004), article 098102.
198. J.D. SHROUT, D.L. CHOPP, C.L. JUST, M. HENTZER, M. GIVSKOV, AND M.R. PARSEK, The impact of quorum sensing and swarming motility on Pseudomonas aeruginosa biofilm formation is nutritionally conditional, Mol. Microbiol., 62 (2006), pp. 1264-1277.
199. H.L. SMITH AND P. WALTMAN, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, Cambridge, UK, 1995.
200. E.J. STEWART, R. MADDEN, G. PAUL, AND F. TADDEI, Aging and death in an organism that reproduces by morphologically symmetric division, PLoS Biol., 3 (2005), article e45.
201. P.S. STEWART, A model of biofilm detachment, Biotech. Bioeng., 41 (1993), pp. 111-117.
202. P.S. STEWART AND J. RAQUEPAS, Implications of reaction-diffusion theory for the disinfection of microbial biofilms by reactive antimicrobial agents, Chem. Engrg. Sci., 50 (1995), pp. 3099-3104.
203. P.S. STEWART, R. MURGA, R. SRINIVASAN, AND D. DEBEER, Biofilm structural heterogeneity visualized by 3 microscopic methods, Wat. Res., 29 (1995), pp. 2006-2009.
204. P.S. STEWART, Theoretical aspects of antibiotic diffusion into microbial biofilms, Antimicrob. Agents Chemother., 40 (1996), pp. 2517-2522.
205. P.S. STEWART, Mechanisms of antibiotic resistance in bacterial biofilms, Internat. J. Med. Microbiol., 292 (2002), pp. 107-113.
206. P.S. STEWART, Diffusion in biofilms, J. Bacteriol., 185 (2003), pp. 1485-1491.
207. P.S. STEWART AND M.J. FRANKLIN, Physiological heterogeneity in biofilms, Nat. Rev. Microbiol., 6 (2008), pp. 199-210.
208. P. STOODLEY, F. JORGENSEN, P. WILLIAMS, AND H.M. LAPPIN-SCOTT, The role of hydrodynamics and ahl signaling molecules as determinants of structure of Pseudomonas aeruginosa biofilms, in Biofilms: The Good, the Bad, and the Ugly, R. Bayston et al., eds.. BioLine Press, Cardiff, UK, 1999, pp. 323-330.
209. P. STOODLEY, Z. LEWANDOWSKI, J.D. BOYLE, AND H.M. LAPPIN-SCOTT, Structural deformation of bacterial biofilms caused by short term fluctuations in flow velocity: An in-situ demonstration of biofilm viscoelasticity, Biotech. Bioeng., 65 (1999), pp. 83-92.
210. P. STOODLEY, K. SAUER, D.G. DAVIES, AND J.W. COSTERTON, Biofilms as complex differentiated communities, Annu. Rev. Microbiol., 56 (2002), pp. 187-209.
211. R. SUDARSAN, K. MILFERSTEDT, E. MORGENROTH, AND H.J. EBERL, Quantification of detachment forces on rigid biofilm colonies in a roto torque reactor using computational fluid dynamics tools, Wat. Sci. Tech., 52 (2005), pp. 149-154.
212. P. SUCI, M.W. MITTELMAN, F.P. YU, AND G.G. GEESEY, Investigation of ciprofloxacin penetration into Pseudomonas aeruginosa biofilms, Antimicrob. Agents Chemother., 38 (1994), pp. 2125-2133.
213. N. SUFYA, D.G. ALLISON, AND P. GILBERT, Clonal variation in maximum specific growth rate and susceptibility towards antimicrobials, J. Appl. Microbiol., 95 (2003), pp. 1261-1267.
214. I.W. SUTHERLAND, The biofilm matrix-an immobilized but dynamic microbial environment, Trends in Microbiol., 9 (2001), pp. 222-227.
215. B. SZOMOLAY, I. KLAPPER, J. DOCKERY, AND P.S. STEWART, Adaptive responses to antimicrobial agents in biofilms, Environ. Microbiol., 8 (2005), pp. 1186-1191.
216. B. SZOMOLAY, Analysis of a moving boundary value problem arising in biofilm modelling, Math. Methods Appl. Sci., 31 (2008), pp. 1835-1859.
217. H. TANAKA, Viscoelastic model of phase separation, Phys. Rev. E, 56 (1997), pp. 4451-4462.
218. G. TCHOBANOGLOUS, F.L. BURTON, AND H.D STENSEL, Wastewater Engineering: Treatment and Reuse, McGraw-Hill, New York, 2002.
219. B.W. TOWLER, A. CUNNINGHAM, P. STOODLEY, AND L. MCKITTRICK, A model of fluid-biofilm interaction using a Burger material law, Biotech. Bioeng. 96 (2007), pp. 259-271.
220. B.W. TOWLER, C.J. RUPP, A. CUNNINGHAM, AND P. STOODLEY, Viscoelastic properties of a mixed culture biofilm from rheometer creep analysis, Biofouling, 19 (2003), pp. 279-285.
221. C. VAN DELDEN AND B. H. IGLEWSKI, Cell-to-cell signaling and Pseudomonas aeruginosa infections, Emerging Infectious Diseases, 4 (1998), pp. 551-560.
222. A.U. VIRETTA AND M. FUSSENEGGER, Modeling the quorum sensing regulatory network of humanpathogenic Pseudomonas aeruginosa, Biotechnol. Progr., 20 (2004), pp. 670-678.
223. P.E. VAUDAUX, G. ZULIAN, E. HUGGLER, AND F. A. WALDVOGEL, Attachment of Staphylococcus aureus to polymethylmethacrylate increases its resistance to phagocytosis in foreign body infection, Infection and Immunity, 50 (1985), pp. 472-477.
224. H.A. VIDELA AND L.K. HERRERA, Microbiologically influenced corrosion: Looking forward to the future, Int. Microbiol., 8 (2005), pp. 169-180.
225. V.E. WAGNER, D. BUSHNELL, L. PASSADOR, A.I. BROOKS, AND B.H. IGLEWSKI, Microarray analysis of Pseudomonas aeruginosa quorum-sensing regulons: Effects of growth phase and environment, J. Bacteriol., 185 (2003), pp. 2080-2095.
226. M.C. WALTERS, F. ROE, A. BUGNICOURT, M.J. FRANKLIN, AND P.S. STEWART, Contributions of antibiotic penetration, oxygen limitation, and low metabolic activity to tolerance of Pseudomonas aeruginosa biofilms to ciprofloxacin and tobramycin, Antimicrob. Agents Chemother., 47 (2003), pp. 317-323.
227. Q. WANG AND T. ZHANG, Kinetic Theories for Biofilms, Discrete Contin. Dyn. Syst. Ser. B, submitted.
228. O. WANNER AND W. GUJER, Competition in biofilms, Wat. Sci. Tech., 17 (1984), pp. 27-44.
229. O. WANNER AND W. GUJER, A multispecies biofilm model, Biotech. Bioeng., 28 (1986), pp. 314-328.
230. O. WANNER AND P. RIECHERT, Mathematical modeling of mixed-culture biofilm, Biotech. Bioeng., 49 (1996), pp. 172-184.
231. O. WANNER, H. EBERL, E. MORGENROTH, D. NOGUERA, C. PICIOREANU, B. RITTMANN, AND M. VAN LOOSDRECHT, Mathematical Modeling of Biofilms, Report 18, IWA Task Group on Biofilm Modeling, Scientific and Technical IWA Publishing, London, 2006.
232. J.P. WARD, J.R. KING, A.J. KOERBER, J.M. CROFT, R.E. SOCKETT, AND P. WILLIAMS, Early development and quorum sensing in bacterial biofilms, J. Math. Biol., 47 (2003), pp. 23-55.
233. J.P. WARD, J.R. KING, A.J. KOERBER, P. WILLIAMS, J.M. CROFT, AND R.E. SOCKETT, Mathematical modelling of quorum sensing in bacteria, IMA J. Math. Appl. Med. Biol., 18 (2001), pp. 263-292.
234. J.P. WARD, J.R. KING, A.J. KOERBER, J.M. CROFT, R.E. SOCKETT, AND P. WILLIAMS, Cell signalling repression in bacterial quorum sensing, Math. Med. Biol., 21 (2004), pp. 169-204.
235. D.M. WARD, A microbiological perspective on microbial species, Microbe, 1 (2006), pp. 269-278.
236. J. WARD, Mathematical modelling of quorum sensing control in biofilms, in The Control of Biofilm Infections by Signal Manipulation, N. Balaban, ed., Springer, Berlin, 2008, pp. 79-108.
237. K.A. WARREN-RHODES, K.L. RHODES, S.B. POINTING, S.A. EWING, D.C. LACAP, B. GOMEZSILVA, R. AMUNDSON, E.I. FRIEDMANN, AND C.P. MCKAY, Hypolithic cyanobacteria, dry limit of photosynthesis, and microbial ecology in the hyperarid Atacama desert, Microbial Ecol., 52 (2006), pp. 389-398.
238. C.M. WATERS AND B.L. BASSLER, Quorum sensing: Cell-to-cell communication in bacteria, Annu. Rev. Cell Dev. Biol., 21 (2005), pp. 319-346.
239. G.F. WEBB, Theory of Nonlinear Age-Dependent Population Dynamics, Marcel Dekker, New York, 1989.
240. G.F. WEBB, E.M.C. D'AGATA, P. MACAL, AND S. RUAN, A model of antibiotic-resistant bacterial epidemics in hospitals, Proc. Natl. Acad. Sci. USA, 102 (2005), pp. 13343-13348.
241. R.P. WENZEL, Health care-associated infections: Major issues in the early years of the 21st century, Clin. Infect. Dis., 45 (2007), pp. S85-S88 (Suppl. 1).
242. E. WENTLAND, P.S. STEWART, C.-T. HUANG, AND G.A. MCFETERS, Spatial variations in growth rate within Klebsiella pneumoniae colonies and biofilm, Biotech. Prog., 12 (1996), pp. 316-321.
243. E. WERNER, F. ROE, A. BUGNICOURT, M.J. FRANKLIN, A. HEYDORN, S. MOLIN, B. PITTS, AND P.S. STEWART, Stratified growth in Pseudomonas aeruginosa biofilms, Appl. Environ. Microbiol., 70 (2004), pp. 6188-6196.
244. W.B. WHITMAN, D.C. COLEMAN, AND W.J. WIEBE, Prokaryotes: The unseen majority, Proc. Natl. Acad. Sci. USA, 95 (1998), pp. 6578-6583.
245. M. WHITELY, M.G. BANGERA, R.E. BUMGARNER, M.R. PARSEK, G.M. TEITZEL, S. LORY, AND E.P. GREENBERG, Gene expression in Pseudomonas aeruginosa biofilms, Nature, 413 (2001), pp. 860-864.
246. P. WILLIAMS, Quorum sensing, communication and cross-kingdom signalling in the bacterial world, Microbiology, 153 (2007), pp. 3923-3938.
247. P. WILLIAMS, K. WINZER, W. CHAN, AND M. CAMARA, Look who's talking: Communication and quorum sensing in the bacterial world, Philos. Trans. R. Soc. Lond. Ser. B Biol. Sci., 362 (2007), pp. 1119-1134.
248. S. WILSON, M.A. HAMILTON, G.G. HAMILTON, M.R. SCHUMANN, AND P. STOODLEY, Statistical quantification of detachment rates and size distributions of cell clumps from wild-type (PA01) and cell signalling mutant (JP1) Pseudomonas aeruginosa biofilms, Appl. Environ. Microbiol., 70 (2004), pp. 5847-5852.
249. J.W.T. WIMPENNY AND S.L. KINNIMENT, Biochemical reactions and the establishment of gradients within biofilms, in Microbial Biofilms, H.M. Lappin-Scott and J.W. Costerton, eds., Cambridge University Press, Cambridge, UK, 1995.
250. J.W.T. WIMPENNY AND R. COLASANTI, A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models, FEMS Microbiol. Ecol., 22 (1997), pp. 1-16.
251. M.K. WINSON, M. CAMARA, A. LATIFI, M. FOGLINO, S.R. CHHABRA, M. DAYKIN, M. BALLY, V. CHAPON, G.P.C. SALMOND, B.W. BYCROFT, A. LAZDUNSKI, G.S.A.B. STEWART, AND P. WILLIAMS, Multiple N-acyl-l-homoserine lactone signal molecules regulate production of virulence determinants and secondary metabolites in Pseudomonas aeruginosa, Proc. Natl. Acad. Sci. USA, 92 (1995), pp. 9427-9431.
252. K. WINZER, K.H. HARDIE, AND P. WILLIAMS, Bacterial cell-to-cell communication: Sorry can't talk now - gone to lunch!, Current Opinion Microbiol., 5 (2002), pp. 216-222.
253. B.D. WOOD AND S. WHITAKER, Diffusion and reaction in biofilms, Chem. Engrg. Sci., 53 (1998), pp. 397-425.
254. B.D. WOOD AND S. WHITAKER, Cellular growth in biofilms, Biotech. Bioeng., 64 (1999), pp. 656-670.
255. J.B. XAVIER, C. PICIOREANU, AND M.CM. VAN LOOSDRECHT, A general description of detachment for multidimensional modelling of biofilms, Biotech. Bioeng., 91 (2005), pp. 651-669.
256. J.B. XAVIER AND K.R. FOSTER, Cooperation and conflict in microbial biofilms, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 876-881.
257. K.D. XU, P.S. STEWART, F. XIA, C.-T. HUANG, AND G.A. MCFETERS, Spatial physiological heterogeneity in Pseudomonas aeruginosa biofilm is determined by oxygen availability, Appl. Environ. Microbiol., 64 (1998), pp. 4035-4039.
258. J.M. YARWOOD, D.J. BARTELS, E.M. VOLPER, AND E.P. GREENBERG, Quorum sensing in Staphylococcus aureus biofilms, J. Bacteriol, 186 (2004), pp. 1838-1850.
259. T.C. ZHANG AND P.L. BISHOP, Experimental determination of the dissolved oxygen boundary layer and mass transfer resistance near the fluid-biofilm interface, Wat. Sci. Tech., 30 (1994), pp. 47-58.
260. T.C. ZHANG, Y.C. FU, AND P.L. BISHOP, Competition in biofilms, Wat. Sci. Tech., 29 (1994), pp. 263-270.
261. T. ZHANG, N.C. COGAN, AND Q. WANG, Phase field models for biofilms. I. Theory and one-dimensional simulations, SIAM J. Appl. Math., 69 (2008), pp. 641-669.
262. T. ZHANG, N. COGAN, AND Q. WANG, Phase-field models for biofilms II. 2-D numerical simulations of biofilm-flow interactions, Comm. Comput. Phys., 4 (2008), pp. 72-101.