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Mathematical Biosciences and Engineering (MBE)
 

Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects
Pages: 625 - 653, Issue 3, June 2017

doi:10.3934/mbe.2017036      Abstract        References        Full text (810.0K)           Related Articles

Blessing O. Emerenini - Biomedical Physics, Dept. Physics, Ryerson University, 350 Victoria Street Toronto, ON, M5B 2K3, Canada (email)
Stefanie Sonner - Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstr. 36, 8010 Graz, Austria (email)
Hermann J. Eberl - Biophysics Interdepartmental Program and Department, of Mathematics and Statistics, University of Guelph, Guelph ON, N1G 2W1, Canada (email)

1 F. Abbas, R. Sudarsan and H. J. Eberl, Longtime behaviour of one-dimensional biofilm moels with shear dependent detachment rates, Math. Biosc. Eng., 9 (2012), 215-239.       
2 H. Amman, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, Function Spaces, Differential Operators and Nonlinear Analysis, Teubner-Texte Math., 133 (1993), 9-126.       
3 D. Aronson, M. G. Crandall and L. A. Peletier, Stabilization of solutions of a degenerate nonlinear diffusion problem, Nonlinear Anal., 6 (1982), 1001-1022.       
4 N. Barraud, D. J. Hassett, S. H. Hwang, S. A. Rice, S. Kjelleberg and J. S, Webb, Involvement of nitric oxide in biofilm dispersal of Pseudomonas Aeruginosa, J. Bacteriol, 188 (2006), 7344-7353.
5 G. Boyadjiev and N. Kutev, Comparison principle for quasilinear elliptic and parabolic systems, Comptes rendus de l'Académie bulgare des Sciences, 55 (2002), 9-12.       
6 A. Boyd and A. M. Chakrabarty, Role of alginate lyase in cell detachment of Pseudomonas Aeruginosa, Appl. Environ. Microbiol., 60 (1994), 2355-2359.
7 V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, American Mathematical Society, Providence, RI, 2002.       
8 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), 1027-1036.
9 D. A. D'Argenio, M. W. Calfee, P. B. Rainey and E. C. Pesci, Autolysis and autoaggregation in Pseudomonas Aeruginosa colony morphology mutants, J. Bacteriol.,184 (2002), 6481-6489.
10 L. Demaret, H. J. Eberl, M. A. Efendiev and R. Lasser, Analysis and simulation of a meso-scale model of diffusive resistance of bacterial biofilms to penetration of antibiotics, Adv. Math. Sci. Appl., 18 (2008), 269-304.       
11 R. M. Donlan, Biofilms and device-associated infections, Emerging Infec. Dis., 7 (2001).
12 R. Duddu, D. L. Chopp and B. Moran, A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment, Biotechnol. Bioeng., 103 (2009), 92-104
13 H. J. Eberl, D. F. Parker and M. C. M. van Loosdrecht, A new deterministic spatio-temporal continuum model for biofilm development, J. Theor. Med., 3 (2001), 161-175.
14 H. J. Eberl and L. Demaret, A finite difference scheme for a degenerated diffusion equation arising in microbial ecology, Electron. J. Differential Equations, 15 (2007), 77-96.       
15 H. J. Eberl and R. Sudarsan, Exposure of biofilms to slow flow fields: The convective contribution to growth and disinfections, J. Theor. Biol., 253 (2008), 788-807.       
16 M. A. Efendiev, H. J. Eberl and S. V. Zelik, Existence and longtime behaviour of solutions of a nonlinear reaction-diffusion system arising in the modeling of biofilms, Nonlin. Diff. Sys. Rel. Topics, RIMS Kyoto, 1258 (2002), 49-71.       
17 M. A. Efendiev, H. J. Eberl and S. V. Zelik, Existence and longtime behavior of a biofilm model, Comm. Pur. Appl. Math., 8 (2009), 509-531.       
18 B. O. Emerenini, B. A. Hense, C. Kuttler and H. J. Eberl, A mathematical model of quorum sensing induced biofilm detachment, PLoS ONE, 10 (2015).
19 A. Fekete, C. Kuttler, M. Rothballer, B. A. Hense, D. Fischer, K. Buddrus-Schiemann, M. Lucio, J. Müller, P. Schmitt-Kopplin and A. Hartmann, Dynamic regulation of N-acyl-homoserine lactone production and degradation in Pseudomonas putida IsoF., FEMS Microbiology Ecology, 72 (2010), 22-34.
20 M. R. Frederick, C. Kuttler, B. A. Hense and H. J. Eberl, A mathematical model of quorum sensing regulated EPS production in biofilms, Theor. Biol. Med. Mod., 8 (2011),
21 M. R. Frederick, C. Kuttler, B. A. Hense, J. Müller and H. J. Eberl, A mathematical model of quorum sensing in patchy biofilm communities with slow background flow, Can. Appl. Math. Quarterly, 18 (2011), 267-298.
22 S. M. Hunt, M. A. Hamilton, J. T. Sears, G. Harkin and J. Reno, A computer investigation of chemically mediated detachment in bacterial biofilms, J. Microbiol., 149 (2003), 1155-1163.
23 S. M. Hunt, E. M. Werner, B. Huang, M. A. Hamilton and P. S. Stewart, Hypothesis for the role of nutrient starvation in biofilm detachment, J. Appl. Environ. Microb., 70 (2004), 7418-7425.
24 H. Khassehkhan, M. A. Efendiev and H. J. Eberl, A degenerate diffusion-reaction model of an amensalistic biofilm control system: existence and simulation of solutions, Disc. Cont. Dyn. Sys. Series B, 12 (2009), 371-388.       
25 O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasi-linear Equations of parabolic Type, American Mathematical Society, Providence RI, 1968.       
26 J. B. Langebrake, G. E. Dilanji, S. J. Hagen and P. de Leenheer, Traveling waves in response to a diffusing quorum sensing signal in spatially-extended bacterial colonies, J. Theor. Biol., 363 (2014), 53-61.       
27 P. D. Marsh, Dental plaque as a biofilm and a microbial community implications for health and disease, BMC Oral Health, 6 (2006), S14.
28 N. Muhammad and H. J. Eberl, OpenMP parallelization of a Mickens time-integration scheme for a mixed-culture biofilm model and its performance on multi-core and multi-processor computers, LNCS, 5976 (2010), 180-195.
29 G. A. O'Toole and P. S. Stewart, Biofilms strike back, Nature Biotechnology, 23 (2005), 1378-1379.
30 M. R. Parsek and P. K. Singh, Bacterial biofilms: An emerging link to disease pathogenesis, Annu. Rev. Microbiol., 57 (2003), 677-701.
31 C. Picioreanu, M. C. M. van Loosdrecht and J. J. Heijnen, Two-dimensional model of biofilm detachment caused by internal stress from liquid flow, Biotechnol. Bioeng., 72 (2001), 205-218.
32 A. Radu, J. Vrouwenvelder, M. C. M. van Loosdrecht and C. Picioreanu, Effect of flow velocity, substrate concentration and hydraulic cleaning on biofouling of reverse osmosis feed channels, Chem. Eng. J., 188 (2012), 30-39.
33 M. Renardy and R. C. Rogers, An Introduction to Partial Differential Equations, $2^{nd}$ edition, Springer Verlag, New York, 2004.       
34 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), 3477-3485.
35 Y. Saad, Iterative Methods for Sparse Linear Systems, $2^{nd}$ edition, SIAM, Philadelphia, 2003.       
36 S. Sirca and M. Morvat, Computational Methods for Physicists, Springer, Heidelberg, 2012.       
37 C. Solano, M. Echeverz and LasaI, Biofilm dispersion and quorum sensing, Curr. Opin. Microbiol., 18 (2014), 96-104.
38 S. Sonner, M. A. Efendiev and H. J. Eberl, On the well-posedness of a mathematical model of quorum-sensing in patchy biofilm communities, Math. Methods Appl. Sci., 34 (2011), 1667-1684.       
39 S. Sonner, M. A. Efendiev and H. J. Eberl, On the well-posedness of mathematical models for multicomponent biofilms, Math. Methods Appl. Sci., 38 (2015), 3753-3775.       
40 P. S. Stewart, A model of biofilm detachment, Biotechnol. Bioeng., 41 (1993), 111-117.
41 M. G. Trulear and W. G. Characklis, Dynamics of biofilm processes, J. Water Pollut. Control Fed., 54 (1982), 1288-1301.
42 B. L. Vaughan Jr, B. G. Smith and D. L. Chopp, The Influence of Fluid Flow on Modeling Quorum Sensing in Bacterial Biofilms, Bull. Math. Biol., 72 (2010), 1143-1165.
43 O. Wanner and P. Reichert, Mathematical modelling of mixed-culture biofilm, Biotech. Bioeng., 49 (1996), 172-184.
44 O. Wanner, H. J. Eberl, E. Morgenroth, D. R. Noguera, C. Picioreanu, B. E. Rittmann and M. C. M. van Loosdrecht, Mathematical Modelling of Biofilms, IWA Publishing, London, 2006.
45 J. S. Webb, Differentiation and dispersal in biofilms, Book chapter in The Biofilm Mode of Life: Mechanisms and Adaptations, Horizon Biosci., Oxford (2007), 167-178.
46 J. B. Xavier, C. Piciroeanu and M. C. M. van Loosdrecht, A general description of detachment for multidimensional modelling of biofilms, Biotechnol. Bioeng., 91 (2005), 651-669.
47 J. B. Xavier, C. Picioreanu, S. A. Rani, M. C. M. van Loosdrecht and P. S. Stewart, Biofilm-control strategies based on enzymic disruption of the extracellular polymeric substance matrix a modelling study, Microbiol., 151 (2005), 3817-3832.

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