Understanding the emergence of the complex organization of biofilms from the interactions of its parts, individual cells and their environment, is the aim of the individual-based modelling (IbM) approach. This IbM is version 2 of BacSim, a model of colony growth, which was developed into a two-dimensional multi-substrate, multi-species model of nitrifying biofilms. It was compared with the established biomass-based model (BbM) of Picioreanu and others. Both models assume that biofilm growth is due to the processes of diffusion, reaction and growth (including biomass growth, division and spreading). In the IbM, each bacterium was a spherical cell in continuous space and had variable growth parameters. Spreading of biomass occurred by shoving of cells to minimize overlap between cells. In the BbM, biomass was distributed in a discrete grid and each species had uniform growth parameters. Spreading of biomass occurred by cellular automata rules. In the IbM, the effect of random variation of growth parameters of individual bacteria was negligible in contrast to the colony model, because the heterogeneity of substrate concentrations in the biofilm was more important. The growth of a single cell into a clone, and therefore also the growth of the less abundant species, depended on the randomly chosen site of attachment, owing to the heterogeneity of substrate concentrations in the biofilm. The IbM agreed with the BbM regarding the overall growth of the biofilm, due to the same diffusion-reaction processes. However, the biofilm shape was different due to the different biomass spreading mechanisms. The IbM biofilm was more confluent and rounded due to the steady, deterministic and directionally unconstrained spreading of the bacteria. Since the biofilm shape is influenced by the spreading mechanism, it is partially independent of growth, which is driven by diffusion-reaction. Chance in initial attachment events modifies the biofilm shape and the growth of single cells because of the high heterogeneity of substrate concentrations in the biofilm, which again results from the interaction of diffusion-reaction with spreading. This stresses the primary importance of spreading and chance in addition to diffusion-reaction in the emergence of the complexity of the biofilm community.


Article metrics loading...

Loading full text...

Full text loading...



  1. Ames, W. F. (1977).Numerical Methods for Partial Differential Equations 2nd edn. London:Thomas Nelson & Sons.
  2. Ben-Jacob, E., Schochet, O., Tenenbaum, A., Cohen, I., Czirok, A. & Vicsek, T. (1994). Generic modeling of cooperative growth-patterns in bacterial colonies. Nature 368, 46-49.[CrossRef] [Google Scholar]
  3. Bergey, D. H., Buchanan, R. E., Gibbons, N. E. & Cowan, S. T. (1974).Bergey’s Manual of Determinative Bacteriology 8th edn. Baltimore:Williams & Wilkins.
  4. Bryers, J. D. & Characklis, W. G. (1982). Processes governing primary biofilm formation. Biotechnol Bioeng 24, 2451-2476.[CrossRef] [Google Scholar]
  5. Costerton, J. W., Lewandowski, Z., Caldwell, D. E., Korber, D. R. & Lappin-Scott, H. M. (1995). Microbial biofilms. Annu Rev Microbiol 49, 711-745.[CrossRef] [Google Scholar]
  6. DeAngelis, D. L. & Gross, L. J. (1992).Individual-Based Models and Approaches in Ecology: Populations, Communities, and Ecosystems New York:Chapman and Hall.
  7. Donachie, W. D. & Robinson, A. C. (1987). Cell division: parameter values and the process. In Escherichia coli and Salmonella typhimurium: Cellular and Molecular Biology, pp. 1578–1593. Edited by F. C. Neidhardt and others. Washington, DC: American Society for Microbiology.
  8. Eberl, H. J., Picioreanu, C., Heijnen, J. J. & Loosdrecht, M. C. M. (2000). A three-dimensional numerical study on the correlation of spatial structure, hydrodynamic conditions, and mass transfer and conversion in biofilms. Chem Eng Sci 55, 6209-6222.[CrossRef] [Google Scholar]
  9. Eberl, H. J., Parker, D. F. & Loosdrecht, M. C. M. (2001). A new deterministic spatio-temporal continuum model for biofilm development. J Theor Med 3, 161–176.[CrossRef] [Google Scholar]
  10. Gibbs, J. T. & Bishop, P. L. (1995). A method for describing biofilm surface roughness using geostatistical techniques. Water Sci Technol 32(8), 91–98. [Google Scholar]
  11. Grimm, V. (1999). Ten years of individual-based modelling in ecology: what have we learned and what could we learn in the future? Ecol Model 115, 129-148.[CrossRef] [Google Scholar]
  12. Haralick, R. M., Shanmugam, K. & Dinstein, I. (1973). Textural features for image classification. IEEE Trans Syst Man Cybern SMC-3, 610-621. [Google Scholar]
  13. Hermanowicz, S. W. (1999). Two-dimensional simulations of biofilm development: Effects of external environmental conditions. Water Sci Technol 39(7), 107–114. [Google Scholar]
  14. Hermanowicz, S. W., Schindler, W. & Wilderer, U. (1995). Fractal structure of biofilms: new tools for investigation of morphology. Water Sci Technol 32(8), 99–105. [Google Scholar]
  15. Hermanowicz, S. W., Schindler, W. & Wilderer, U. (1996). Anisotropic morphology and fractal dimensions of biofilms. Water Res 30, 753-755.[CrossRef] [Google Scholar]
  16. Heydorn, A., Nielsen, A. T., Hentzer, M., Sternberg, C., Givskov, M., Ersbøll, B. K. & Molin, S. (2000). Quantification of biofilm structures by the novel computer program comstat. Microbiology 146, 2395-2407. [Google Scholar]
  17. Huston, M. A., DeAngelis, D. L. & Post, W. (1988). New computer models unify ecological theory. BioScience 38, 682-691.[CrossRef] [Google Scholar]
  18. Kreft, J.-U., Booth, G. & Wimpenny, J. W. T. (1998). BacSim, a simulator for individual-based modelling of bacterial colony growth. Microbiology 144, 3275-3287.[CrossRef] [Google Scholar]
  19. Kwok, W. K., Picioreanu, C., Ong, S. L., van Loosdrecht, M. C. M., Ng, W. J. & Heijnen, J. J. (1998). Influence of biomass production and detachment forces on biofilm structures in a biofilm airlift suspension reactor. Biotechnol Bioeng 58, 400-407.[CrossRef] [Google Scholar]
  20. Lewandowski, Z., Webb, D., Hamilton, M. & Harkin, G. (1999). Quantifying biofilm structure. Water Sci Technol 39(7), 71–76. [Google Scholar]
  21. Matsushita, M. (1997). Formation of colony patterns by a bacterial population. In Bacteria as Multicellular Organisms , pp. 366-393. Edited by J. A. Shapiro & M. Dworkin. New York:Oxford University Press.
  22. Murga, R., Stewart, P. S. & Daly, D. (1995). Quantitative analysis of biofilm thickness variability. Biotechnol Bioeng 45, 503-510.[CrossRef] [Google Scholar]
  23. Noguera, D. R., Okabe, S. & Picioreanu, C. (1999a). Biofilm modeling: Present status and future directions. Water Sci Technol 39(7), 273–278. [Google Scholar]
  24. Noguera, D. R., Pizarro, G., Stahl, D. A. & Rittmann, B. E. (1999b). Simulation of multispecies biofilm development in three dimensions. Water Sci Technol 39(7), 123–130. [Google Scholar]
  25. Peaceman, D. W. & Rachford, H. H.Jr (1955). The numerical solution of parabolic and elliptic differential equations. J Soc Indust Appl Math 3, 28-41.[CrossRef] [Google Scholar]
  26. Picioreanu, C., van Loosdrecht, M. C. M. & Heijnen, J. J. (1997). Modelling the effect of oxygen concentration on nitrite accumulation in a biofilm airlift suspension reactor. Water Sci Technol 36(7), 147–156. [Google Scholar]
  27. Picioreanu, C., van Loosdrecht, M. C. M. & Heijnen, J. J. (1998a). A new combined differential-discrete cellular automaton approach for biofilm modeling: application for growth in gel beads. Biotech Bioeng 57, 718-731.[CrossRef] [Google Scholar]
  28. Picioreanu, C., van Loosdrecht, M. C. M. & Heijnen, J. J. (1998b). Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotech Bioeng 58, 101-116.[CrossRef] [Google Scholar]
  29. Picioreanu, C., van Loosdrecht, M. C. M. & Heijnen, J. J. (1999). Discrete-differential modelling of biofilm structure. Water Sci Technol 39(7), 115–122. [Google Scholar]
  30. Russ, J. C. (1994).Fractal Surfaces. New York: Plenum Publishing Corporation.
  31. Shuler, M. L., Leung, S. K. & Dick, C. C. (1979). A mathematical model for the growth of a single bacterial cell. Ann NY Acad Sci 326, 35-55.[CrossRef] [Google Scholar]
  32. Stoodley, P., Boyle, J. D., De Beer, D. & Lappin-Scott, H. M. (1999). Evolving perspectives of biofilm structure. Biofouling 14, 75-90.[CrossRef] [Google Scholar]
  33. Tolker-Nielsen, T. & Molin, S. (2000). Spatial organization of microbial biofilm communities. Microbiol Ecol 40, 75-84. [Google Scholar]
  34. Tolker-Nielsen, T., Brinch, U. C., Ragas, P. C., Andersen, J. B., Jacobsen, C. S. & Molin, S. (2000). Development and dynamics of Pseudomonas sp. biofilms. J Bacteriol 182, 6482-6489.[CrossRef] [Google Scholar]
  35. Tukey, J. W. (1977).Exploratory Data Analysis. Reading, MA: Addison-Wesley.
  36. Weszka, J. S., Dyer, C. R. & Rosenfeld, A. (1976). A comparative study of texture measures for terrain classification. IEEE Trans Syst Man Cybern SMC-6, 269-285.[CrossRef] [Google Scholar]
  37. Wiesmann, U. (1994). Biological nitrogen removal from wastewater. Adv Biochem Eng Biotechnol 51, 113-154. [Google Scholar]
  38. Wimpenny, J. W. T. & Colasanti, R. (1997). A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models. FEMS Microbiol Ecol 22, 1-16.[CrossRef] [Google Scholar]
  39. Yang, X. M., Beyenal, H., Harkin, G. & Lewandowski, Z. (2000). Quantifying biofilm structure using image analysis. J Microbiol Methods 39, 109-119.[CrossRef] [Google Scholar]
  40. Zhang, T. C. & Bishop, P. L. (1994a). Density, porosity and pore structure of biofilms. Water Res 28, 2267-2277.[CrossRef] [Google Scholar]
  41. Zhang, T. C. & Bishop, P. L. (1994b). Evaluation of tortuosity factors and effective diffusivities in biofilms. Water Res 28, 2279-2287.[CrossRef] [Google Scholar]

Data & Media loading...

Most cited this month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error