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Individual-based modelling of biofilms

Cardiff School of Biosciences, Cardiff University, PO Box 915, Cardiff CF10 3TL, UK¹
Kluyver Institute of Biotechnology, Delft University of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands²

Author for correspondence: Jan-Ulrich Kreft. Tel: +44 29 2087 5278. Fax: +44 29 2087 4305. e-mail: kreft{at}cardiff.ac.uk

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 Escherichia coli 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 E. coli 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.

Keywords: biofilm structure, nitrification, spatial heterogeneity, chance, complexity

Abbreviations: 2D, 3D, two-, three-dimensional; IbM, individual-based model/modelling; BbM, biomass-based model/modelling; CV, coefficient of variation

^a Present address: Abteilung Theoretische Biologie, Botanisches Institut, Universität Bonn, Kirschallee 1, D-53115 Bonn, Germany.

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