A simulation model of biofilms with autonomous cells: I. Analysis of a two-dimensional version

Physica A: Statistical Mechanics and its Applications

Volumn 362, Issue 2, 2006, Pages 382-402

  Tatek, Yergou B ^a   Slater, Gary W ^a  

^a UNIVERSITY OF OTTAWA   (Canada)

Author keywords

Bacteria; Biofilm; Monte Carlo simulation

Indexed keywords

ALGORITHMS; AUTONOMOUS AGENTS; BACTERIA; COMPUTER SIMULATION; MATHEMATICAL MODELS; MONTE CARLO METHODS; THERMODYNAMICS;

BIOFILM GROWTH; BOND FLUCTUATION ALGORITHM; MICROBIAL CELL;

BIOFILMS;

EID: 32544441898     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2005.08.011     Document Type: Article

References (40)

1. B.E. Rittmann, and P.L. McCarty Model of steady-state-biofilm kinetics Biotechnol. Bioeng. 22 1980 2343 2357
2. O. Wanner, and W. Gujer Multispecies biofilm model Biotechnol. Bioeng. 28 1986 314 328
3. B.E. Rittmann, and J.A. Manem Development and experimental evaluation of a steady-state, multispecies biofilm model Biotechnol. Bioeng. 39 1992 914 922
4. O. Wanner, and P. Reichert Mathematical modeling of mixed-culture biofilms Biotechnol. Bioeng. 49 1996 172 184
5. J. Dockery, and I. Klapper Finger formation in biofilm layers SIAM J. Appl. Math. 62 2002 853 869
6. H.J. Eberl, C. Picioreanu, J.J. Heijnen, and M.C.M. van Loosdrecht A three-dimensional numerical study on the correlation of spatial structure, hydrodynamics conditions, and mass transfer and conversion in biofilms Chem. Eng. Sci. 55 2000 6209 6222
7. 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
8. G.C. Barker, and M.J. Grimson A cellular automaton model of microbial growth Binary 5 1993 132 137
9. R.L. Colasanti Cellular automata model of microbial colonies Binary 4 1992 191 193
10. G.B. Ermentrout, and L. Edelstein-Keshet Cellular automata approaches to biological modeling J. Theor. Biol. 160 1993 97 133
11. S.W. Hermanowicz Model of two-dimensional biofilm morphology Water Sci. Technol. 37 1998 219 222
12. S.W. Hermanowicz Two-dimensional simulations of biofilm development: effects of external environmental conditions Water Sci. Technol. 39 1999 107 114
13. D.R. Noguera, G. Pizarro, D.A. Stahl, and B.E. Rittmann Simulations of multispecies biofilm development in three dimensions Water Sci. Technol. 39 1999 123 130
14. C. Picioreanu, M.C.M. van Loosdrecht, and J.J. Heijnen A new combined differential-discrete cellular automaton for biofilm modeling: application for growth in gel beads Biotechnol. Bioeng. 57 1998 718 731
15. 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 1 16
16. S.W. Hermanowicz Biofilm structure: an interplay of models and experiments S. Wuertz P.A. Wilderer P.L. Bishop Biofilms in Wastewater Treatment: An Interdisciplinary Approach 2002 International Water Association Publishing 1 18
17. J.U. Kreft, G. Booth, and J.W.T. Wimpenny Bacsim, a simulator for individual-based modelling of bacterial colony growth Microbiology 144 1998 3275 3287
18. J.-U. Kreft, C. Picioreanu, J.W.T. Wimpenny, and M.C.M. van Loosdrecht Individual-based modelling of biofilms Microbiology 147 2001 2897 2912
19. C. Picioreanu, J.-U. Kreft, and M.C.M. van Loosdrecht Particle-based multidimensional multispecies biofilm model Appl. Environ. Microbiol. 70 2004 3024 3040
20. I. Carmesin, and K. Kremer The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions Macromolecules 21 1988 2819 2823
21. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller Equation of state calculations by fast computing machines J. Chem. Phys. 21 1953 1087 1092
22. I. Teraoka Polymer Solutions 2001 Wiley-Interscience New York
23. S. Leibler, R.R.P. Singh, and M.E. Fisher Thermodynamic behaviour of two-dimensional vesicles Phys. Rev. Lett. 59 1987 1989 1992
24. A.C. Maggs, S. Leibler, M.E. Fisher, and C.J. Camacho Size of an inflated vesicle in two dimensions Phys. Rev. A 42 1990 691 695
25. C. Picioreanu, M.C.M. van Loostrecht, and J.J. Heijnen Modelling and predicting biofilm structure D.G. Allison P. Gilbert H.M. Lappin-Scott M. Wilson Community Structure and Co-operation in Biofilms 2000 Cambridge University Press Cambridge, UK 129 166
26. S.W. Hermanowicz A simple 2d biofilm model yields a variety of morphological features Math. Biosci. 169 2001 1 14
27. D.G. Davies, M.R. Parsek, B.H. Iglewski, J.W. Costerton, and E.P. Greenberg The involvement of cell-to-cell signals in the development of a bacterial biofilm Science 280 1998 295 298
28. R. Kolter, and R. Losik One for all and all for one Science 280 1998 226 227
29. C.J. Camacho, and M.E. Fisher Tunable fractal shapes in self-avoiding polygons and planar vesicles Phys. Rev. Lett. 65 1990 9 12
30. P.G. de Gennes Scaling Concept in Polymer Physics 1979 Cornell University Press Ithaca, NY
31. Y. Kantor Properties of tethered surfaces D. Nelson T. Piran S. Weinberg Statistical Mechanics of Membranes and Surfaces 1989 World Scientific Singapore 115 136
32. U. Seifert, and R. Lipowsky Adhesion of vesicles Phys. Rev. A 42 1990 4768 4771
33. H.-G. Döbereiner, B. Dubin-Thaler, G. Giannone, H.S. Xenias, and M.P. Sheetz Dynamic phase transitions in cell spreading Phys. Rev. Lett. 93 2004 108105-1
34. W. Helfrich Out-of-plane fluctuations of lipid bilayers Z. Naturforsch. 30c 1975 841 842
35. W. Helfrich, and R.-M. Servuss Undulations steric interaction and cohesion of fluid membranes Nuovo Cimento 3D 1984 137 151
36. F. Family, and T. Vicsek Dynamic of Fractal Surfaces 1991 World Scientific Singapore
37. T.A. Witten, and L.M. Sander Diffusion-limited aggregation, a kinetic critical phenomenon Phys. Rev. Lett. 47 1981 1400
38. M. Matsushita, and H. Fugikawa Diffusion-limited growth in bacterial colony formation Physica A 168 1990 498 506
39. M. Matsushita, J. Wakita, H. Itoh, K. Watanabe, T. Arai, T. Matsuyama, H. Sakaguchi, and M. Mimura Formation of colony patterns by a bacterial cell population Physica A 274 1999 190 199
40. J.C.M. Mombach, N. Lemke, B.E.J. Bodmann, and M.A.P. Idiart A mean-field theory of cellular growth Europhys. Lett. 59 2002 923 928