A polymer-solvent model of biofilm growth

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 467, Issue 2129, 2011, Pages 1449-1467

  Winstanley, H F ^a   Chapwanya, M ^b   Mcguinness, M J ^c   Fowler, A C ^d  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF PRETORIA   (South Africa)

^c VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

^d UNIVERSITY OF LIMERICK   (Ireland)

Author keywords

Biofilm; Flory Huggins theory; Mathematical model

Indexed keywords

BACTERIAL BIOFILM; BIOFILM GROWTH; EXTRA-CELLULAR POLYMERIC SUBSTANCES; FLORY-HUGGINS THEORY; NUMERICAL SOLUTION; ONE-DIMENSIONAL SOLUTIONS; POLYMER-SOLVENTS; TIME-DEPENDENT PROBLEM; TRAVELLING WAVE SOLUTION; TRAVELLING WAVES; VISCOELASTIC RHEOLOGY;

MATHEMATICAL MODELS; WAVE TRANSMISSION;

BIOFILMS;

EID: 79957522464     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2010.0327     Document Type: Article

References (41)

1. Alpkvist, E., Picioreanu, C., van Loosdrecht, M. C. M. & Heyden, A. 2006 Three-dimensional biofilm model with individual cells and continuum EPS matrix. Biotechnol. Bioeng. 94, 961-979. (doi:10.1002/bit.20917) (Pubitemid 44186903)
2. Bader, F. G. 1978 Analysis of double-substrate limited growth. Biotechnol. Bioeng. 20, 183-202. (doi:10.1002/bit.260200203) (Pubitemid 8293598)
3. Beeftink, H. H., van der Heijden, R. T. J. M. & Heijnen, J. J. 1990 Maintenance requirements: Energy supply from simultaneous endogenous respiration and substrate consumption. FEMS Microbiol. Lett. 73, 203-209. (doi:10.1016/0378-1097(90)90731-5) (Pubitemid 20106285)
4. Bryers, J. D. 2008 Medical biofilms. Biotechnol. Bioeng. 100, 1-18. (doi:10.1002/bit.21838) (Pubitemid 351579011)
5. Cahn, J. W. & Hilliard, J. E. 1958 Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28, 258-267. (doi:10.1063/1.1744102)
6. Chambless, J. D., Hunt, S. M. & Stewart, P. S. 2006 A three-dimensional computer model of four hypothetical mechanisms protecting biofilms from antimicrobials. Appl. Environ. Microbiol. 72, 2005-2013. (doi:10.1128/AEM.72.3.2005-2013.2006)
7. Chapelle, F. H. 2001 Ground-water microbiology and geochemistry, 2nd edn. New York, NY: Wiley.
8. Cogan, N. G. & Keener, J. P. 2004 The role of the biofilm matrix in structural development. Math. Med. Biol. 21, 147-166. (doi:10.1093/imammb/21.2. 147) (Pubitemid 38867857)
9. Cogan, N. G. & Keener, J. P. 2005 Channel formation in gels. SIAM J. Appl. Math. 65, 1839-1854. (doi:10.1137/040605515) (Pubitemid 41802080)
10. Costerton, J. W., Stewart, P. S. & Greenberg, E. P. 1999 Bacterial biofilms: A common cause of persistent infections. Science 284, 1318-1322. (doi:10.1126/science.284.5418.1318) (Pubitemid 29289651)
11. Dockery, J. & Klapper, I. 2001 Finger formation in biofilm layers. SIAM J. Appl. Math. 62, 853-869. (doi:10.1137/S0036139900371709) (Pubitemid 34750572)
12. Eberl, H. J., Parker, D. F. & Van Loosdrecht, M. C. M. 2001 A new deterministic spatio-temporal continuum model for biofilm development. J. Theor. Med. 3, 161-175. (doi:10.1080/10273660108833072) (Pubitemid 34498517)
13. Flemming, H. C. & Wingender, J. 2001 Relevance of microbial extracellular polymeric substances (EPSs). Part I. Structural and ecological aspects. Water Sci. Technol. 43, 1-8. (Pubitemid 32447429)
14. Flory, P. J. 1953 Principles of polymer chemistry. Cornell, NY: Cornell University Press.
15. Graessley, W. W. 2004 Polymeric liquids and networks: Structure and properties. New York, NY: Garland Science/Taylor and Francis.
16. Henze, M., Harremoes, P., Cour Jansen, J. & Arvin, E. 2002 Wastewater treatment: Biological and chemical processes, 3rd edn. Berlin, Germany: Springer.
17. Klapper, I. 2004 Effect of heterogeneous structure in mechanically unstressed biofilms on overall growth. Bull. Math. Biol. 66, 809-824. (doi:10.1016/j.bulm.2003.11.008) (Pubitemid 38800952)
18. Klapper, I. & Dockery, J. 2006 Role of cohesion in the material description of biofilms. Phys. Rev. E 74, 031902. (10.1103/PhysRevE.74.031902) (Pubitemid 44343491)
19. Klapper, I., Rupp, C. J., Cargo, R., Purvedorj, B. & Stoodley, P. 2002 Viscoelastic fluid description of bacterial biofilm material properties. Biotechnol. Bioeng. 80, 289-296. (doi:10.1002/bit.10376) (Pubitemid 35221627)
20. Körstgens, V., Flemming, H. C., Wingender, J. & Borchard, W. 2001 Influence of calcium ions on the mechanical properties of a model biofilm of mucoid Pseudomonas aeruginosa. Water Sci. Technol. 43, 49-57. (Pubitemid 32447435)
21. Kreft, J.-U., Picioreanu, C., Wimpenny, J. W. T. & van Loosdrecht, M. C. M. 2001 Individual-based modelling of biofilms. Microbiology 147, 2897-2912. (Pubitemid 33076979)
22. Monod, J. 1949 The growth of bacterial cultures. Annu. Rev. Microbiol. 3, 371-394. (doi:10.1146/annurev.mi.03.100149.002103)
23. Picioreanu, C., van Loosdrecht, M. C. M. & Heijnen, J. J. 1998 Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotechnol. Bioeng. 58, 101-116. (doi:10.1002/(SICI)1097-0290(19980405)58:13.0.CO;2-M) (Pubitemid 28103346)
24. Picioreanu, C., van Loosdrecht, M. C. M. & Heijnen, J. J. 1999 Discrete-differential modelling of biofilm structure. Water Sci. Technol. 39, 115-122. (doi:10.1016/S0273-1223(99)00158-4) (Pubitemid 29243593)
25. Picioreanu, C., van Loosdrecht, M. C. M. & Heijnen, J. J. 2000 A theoretical study on the effect of surface roughness on mass transport and transformation in biofilms. Biotechnol. Bioeng. 68, 355-369. (doi:10.1002/(SICI)1097-0290(20000520)68:43.0.CO;2-A) (Pubitemid 30238849)
26. Picioreanu, C., Kreft, J.-U. & van Loosdrecht, M. C. M. 2004 Particle-based multidimensional multispecies biofilm model. Appl. Environ. Microbiol. 70, 3024-3040. (doi:10.1128/AEM.70.5. 3024-3040.2004) (Pubitemid 38657821)
27. Rittmann, B. E. & McCarty, P. L. 1980 Model of steady-state-biofilm kinetics. Biotechnol. Bioeng. 22, 2343-2357. (doi:10.1002/bit.260221110) (Pubitemid 11215258)
28. Roose, T. & Fowler, A. C. 2008 Network development in biological gels: role in lymphatic vessel development. Bull. Math. Biol. 70, 1772-1789. (doi:10.1007/s11538-008-9324-3)
29. Shaw, T., Winston, M., Rupp, C. J., Klapper, I. & Stoodley, P. 2004 Commonality of elastic relaxation times in biofilms. Phys. Rev. Lett. 93, 098 102. (doi:10.1103/PhysRevLett.93.098102)
30. Stewart, P. S. 2003 Diffusion in biofilms. J. Bacteriol. 185, 1485-1491. (doi:10.1128/JB.185.5. 1485-1491.2003) (Pubitemid 36245948)
31. Stoodley, P., Cargo, R., Rupp, C. J., Wilson, S. & Klapper, I. 2002 Biofilm material properties as related to shear-Induced deformation and detachment phenomena. J. Ind. Microbiol. Biotechnol. 29, 361-367. (doi:10.1038/sj.jim.7000282) (Pubitemid 36071889)
32. Sutherland, I. W. 2001a Biofilm exopolysaccharides: A strong and sticky framework. Microbiology 147, 3-9. (Pubitemid 32094304)
33. Sutherland, I. W. 2001b The biofilm matrix-An immobilized but dynamic microbial environment. Trends Microbiol. 9, 222-227. (doi:10.1016/S0966-842X(01) 02012-1) (Pubitemid 32402231)
34. Tanaka, T. & Fillmore, D. J. 1979 Kinetics of swelling of gels. J. Chem. Phys. 70, 1214-1218. (doi:10.1063/1.437602)
35. Wanner, O. & Gujer, W. 1986 A multispecies biofilm model. Biotechnol. Bioeng. 28, 314-328. (doi:10.1002/bit.260280304)
36. Wanner, O., Eberl, H., Morgenroth, E., Noguera, D. R., Picioreanu, C., Rittmann, B. E. & van Loosdrecht, M. C. M. 2006 Mathematical modeling of biofilms. Report of the IWA Biofilm Modeling Task Group, Scientific and Technical Report no. 18. London, UK: IWA Publishing.
37. Wolgemuth, C. W., Mogilner, A. & Oster, G. 2004 The hydration dynamics of polyelectrolyte gels with applications to cell motility and drug delivery. Euro. Biophys. J. 33, 146-158. (doi:10.1007/s00249-003-0344-5) (Pubitemid 38987101)
38. Xavier, J. B., Picioreanu, C. & van Loosdrecht, M. C. M. 2004 Assessment of three-dimensional biofilm models through direct comparison with confocal microscopy imaging. Water Sci. Technol. 49, 177-185. (Pubitemid 39117193)
39. Xavier, J. B., Picioreanu, C. & van Loosdrecht, M. C. M. 2005 A general description of detachment for multidimensional modelling of biofilms. Biotechnol. Bioeng. 91, 651-669. (doi:10.1002/bit.20544) (Pubitemid 41283858)
40. Zhang, T., Cogan, N. G. & Wang, Q. 2008a Phase field models for biofilms. I. Theory and onedimensional simulations. SIAM J. Appl. Math. 69, 641-669. (doi:10.1137/070691966).
41. Zhang, T., Cogan, N. G. & Wang, Q. 2008b Phase field models for biofilms. II. 2-D numerical simulations of biofilm-flow interaction. Commun. Comput. Phys. 4, 72-101.