Modeling multispecies biofilms including new bacterial species invasion

Mathematical Biosciences

Volumn 259, Issue , 2015, Pages 20-26

  D'Acunto, B ^a   Frunzo, L ^a   Klapper, I ^b   Mattei, M R ^c  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b Temple University   (United States)

^c UNIVERSITY OF CASSINO AND SOUTHERN LAZIO   (Italy)

Author keywords

Bacterial species invasion; Free boundary problems; Multispecies biofilms; Nonlinear hyperbolic and parabolic partial differential equations; Numerical simulations

Indexed keywords

BIOFILMS; BIOLOGY; BOUNDARY CONDITIONS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; NONLINEAR EQUATIONS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

BACTERIAL SPECIES; ENVIRONMENTAL CONDITIONS; FREE-BOUNDARY PROBLEMS; METHOD OF CHARACTERISTICS; MULTI-SPECIES BIOFILMS; PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS; SPECIES CONCENTRATION; SUBSTRATE CONCENTRATIONS;

BACTERIA;

BACTERIUM; BIOFILM; BIOLOGICAL INVASION; BOUNDARY CONDITION; COLONIZATION; COMPUTER SIMULATION; NEW SPECIES; SPATIAL DISTRIBUTION;

ARTICLE; AUTOTROPH; BACTERIAL COLONIZATION; BACTERIAL GROWTH; BACTERIUM ADHERENCE; BIOFILM; DIFFUSION; HETEROTROPH; MATHEMATICAL MODEL; MICROBIAL BIOMASS; NEW SPECIES; SIMULATION; SPECIES DISTRIBUTION; SPECIES INVASION; BACTERIAL PHENOMENA AND FUNCTIONS; BIOLOGICAL MODEL; GROWTH, DEVELOPMENT AND AGING;

BACTERIA (MICROORGANISMS);

BACTERIAL PHYSIOLOGICAL PHENOMENA; BIOFILMS; MODELS, BIOLOGICAL;

EID: 84920600438     PISSN: 00255564     EISSN: 18793134     Source Type: Journal    
DOI: 10.1016/j.mbs.2014.10.009     Document Type: Article

References (20)

1. Wimpenny J., Manz W., Szewzyk U. Heterogeneity in biofilms. FEMS Microbiol. Rev. 2000, 24:661-671.
2. Sutherland I. The biofilm matrix - an immobilized but dynamic microbial environment. Trends Microbiol. 2001, 9:222-227.
3. Wilson S., Hamilton M., Hamilton G., Schumann M., Stoodley P. 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. 2004, 70:5847-5852.
4. Jackson C. Changes in community properties during microbial succession. OIKOS 2003, 101:444-448.
5. Martiny A., Jrgensen T., Albrechtsen H.J., Arvin E., Molin S. Long-term succession of structure and diversity of a biofilm formed in a model drinking water distribution system. Appl. Environ. Microbiol. 2003, 69:6899-6907.
6. Atkinson B., Davies I. The overall rate of substrate uptake (reaction) by microbial films. Trans. Inst. Chem. Engrs. 1974, 52:248-259.
7. Kissel J., McCarty P., Street R. Numerical simulations of mixed-culture biofilms. J. Environ. Eng. 1984, 110:393-411.
8. Wanner O., Gujer W. A multispecies biofilm model. Biotechnol. Bioeng. 1986, 28:314-328.
9. Wanner O., Reichert P. Mathematical modelling of mixed-culture biofilms. Biotechnol. Bioeng. 1996, 49:172-184.
10. D'Acunto B., Frunzo L. Qualitative analysis and simulations of a free boundary problem for multispecies biofilm models. Math. Comput. Model. 2011, 53:1596-1606.
11. Dockery J., Klapper I. Finger formation in biofilm layers. SIAM J. Appl. Math. 2002, 62:853-869.
12. Alpkvist E., Klapper I. A multidimensional multispecies continuum model for heterogeneous biofilm development. Bull. Math. Biol. 2007, 69:765-789.
13. Klapper I., Dockery J. Mathematical description of microbial biofilms. SIAM Rev. 2010, 52:221-265.
14. Klapper I., Szomolay B. An exclusion principle and the importance of mobility for a class of biofilm models. Bull. Math. Biol. 2011, 73:2213-2230.
15. B. D'Acunto, G. Esposito, L. Frunzo, M. Mattei, F. Pirozzi, Analysis and simulations of the initial phase in multispecies biofilm formation, CAIM doi: 10.1685/jornal.caim (2013).
16. D'Acunto B., Esposito G., Frunzo L., Pirozzi F. Dynamic modeling of sulfate reducing biofilms. Comput. Math. Appl. 2011, 62:2601-2608.
17. D'Acunto B., Frunzo L. Free boundary problem for an initial cell layer in multispecies biofilm formation. Appl. Math. Lett. 2012, 25:20-26.
18. Tchobanoglous G., Burton F.L., Stensel H.D. Wastewater Engineering: Treatment and Reuse 2003, McGraw-Hill, Canary Wharf, London.
19. Horn H., Hempel D. Growth and decay in an auto-/heterotrophic biofilm. Water Res. 1997, 31:2243-2252.
20. Wsche S., Horn H., Hempel D. Influence of growth conditions on biofilm development and mass transfer at the bulk/biofilm interface. Water Res. 2002, 36:4775-4784.