Table 1.
Summary of biofilm modelling work mentioned in this review.
| author (date) | model description | organism | purpose |
|---|---|---|---|
| O. Wanner, S. Gujer (1986) |
1D, continuum, deterministic | not specified | study of the competition between autotrophs and heterotrophs in a multispecies biofilm [45] |
| W. Nichols et al. (1989) | 1D, continuum, deterministic | Pseudomonas aeruginosa | study of antibiotic penetration of biofilms of mucoid and non-mucoid strains [47] |
| E. Ben-Jacob et al. (1994) | 2D, cellular automaton, stochastic | Bacillus subtilis | exploration of patterns of bacterial growth in various nutrient conditions [53] |
| O. Wanner, P. Reichert (1995) |
1D, continuum, deterministic | not specified | extension of previous work [45]; general approach to modelling mixed species biofilms, exploring spatial profiles of chemical compounds and microbial organisms [54] |
| P. S. Stewart et al. (1996) | 1D, continuum, deterministic | not specified | analysis of biocide action against biofilms [55] |
| C. Picioreanu et al. (2000) | 2D, continuum, deterministic | not specified | study of the effect of biofilm surface roughness on the mass transport within the biofilm [56] |
| M. G. Dodds et al. (2000) | 1D, continuum, deterministic | Pseudomonas aeruginosa | analysis of antimicrobial resistance mechanisms of biofilms [57] |
| J. Dockery, J. Keener (2001) |
1D, continuum, deterministic | Pseudomonas aeruginosa | general analysis of the quorum sensing mechanism in biofilms [37] |
| D. L. Chopp et al. (2002) | 1D, continuum, deterministic | Pseudomonas aeruginosa | prediction of acyl-HSL and oxygen concentration profiles within the biofilm and analysis of their effect on biofilm growth [58] |
| I. Chang et al. (2003) | 3D, cellular automaton, stochastic | not specified | effect of transport limitation on microbial growth and biofilm structure [59] |
| K. Anguige et al. (2004) | 1D, continuum | Pseudomonas aeruginosa | analysis of effects of quorum sensing inhibitors and antibiotics on the quorum sensing mechanism of biofilms [38] |
| C. Picioreanu et al. (2004) | 2D/3D, individual-based | not specified | analysis of the effect of multidimensional gradients on multispecies biofilm development [60] |
| J. Xavier et al. (2004) | 3D, individual-based | not specified | comparison of CLSM data to spatial structures of multispecies biofilms generated by the model [61] |
| J. Xavier et al. (2005) | 3D, individual-based | not specified | introduction of a general framework for IBM modelling [62] and evaluating the efficiency of biofilm treatment by detachment promoting agents [63] |
| K. Anguige et al. (2005) | 1D, continuum | Pseudomonas aeruginosa | quorum sensing inhibition [39]; extension of [38] |
| S. M. Hunt et al. (2005) | 3D, cellular automaton | not specified | analysis of antimicrobial action on biofilms, which focused on the scope of substrate limitation contribution on antimicrobial resistance [64] |
| J. D. Chanbless (2006) | 3D, hybrid differential-discrete cellular automaton, stochastic | not specified | exploration of four hypothetical mechanisms of antimicrobial resistance, i.e. poor antimicrobial penetration, stress response mechanism, physiological heterogeneity within the biofilm and persister cells [65] |
| A. K. Marcus et al. (2007) | 1D, conduction-based, deterministic | not specified | modelling the electrochemical processes in microbial fuel cells biofilms with focus on factors affecting electron flow [30] |
| J. Xavier, K. Foster (2007) |
2D, individual-based, deterministic | not specified | evolutionary outcomes of exopolymeric substances producers competing with non-producing individuals [46] |
| G. E. Kapellos (2007) | 2D, hybrid differential-discrete cellular automaton, deterministic | not specified | analysis of biofilm growth dynamics in porous media; first modelling work to account for fluid flow through the biofilm [66] |
| F. Romero-Campero, M. Pérez-Jiménez (2008) |
P-system | Vibrio fischeri | quorum sensing analysis using biochemical reaction networks [40] |
| J. Ward (2008) | 1D, continuum, deterministic | not specified | investigation of anti-quorum sensing treatment of biofilms [39] |
| N. Jayasinghe, R. Mahadevan (2010) |
1D, continuum model, combined with genome scale metabolism modelling | Geobacter sulfurreducens | analysis of the effect of maintenance energy requirements on maximum current production and thickness of biofilms in microbial fuel cells [10] |
| M. Frederick et al. (2011) | 2D, continuum, stochastic | not specified | analysis of how quorum sensing controlled EPS production affects biofilm formation [42] |
| Z. Wang et al. (2011) | 2D, cellular automaton, deterministic | Caldicellulosiruptfor obsidiansis, Clostridium thermocellum | study of cellulose degradation by biofilms in biofuel production [50,67] |
| L. Lardon et al. (2011) | 2D, individual-based | not specified | introduction of a biofilm modelling platform for non-programmers; iDynoMiCS [68] |
| D. Rodriguez et al. (2012) | 2D/3D, cellular automaton, stochastic | not specified | studying effects of surface roughness patterns on biofilm formation in the presence of flow [69] |
| M. Asally et al. (2012) | 2D, hybrid differential-discrete cellular automaton, deterministic | Bacillus subtilis | theoretical analysis of mechanical forces behind emergent pattern formation of biofilms [70] |
| F. Pérez-Reche (2012) | 3D, network, stochastic | not specified | analysis of network representation of soil samples with regards to potential microbial invasions [17] |
| R. Ferrier et al. (2013) | 2D, individual-based, stochastic | Listeria monocytogenes | estimating counts of food spoilage organisms on the surface of cheese [49] |
| A. Ehret, M. Böl (2013) |
3D, continuum, deterministic | Pseudomonas aeruginosa | study of mechanical role of EPS matrix on biofilms, representing the EPS matrix as a worm-like chain network [48] |
| S. Bottero et al. (2013) | 2D, cellular automaton, stochastic | not specified | examination of factors influencing the development of flow paths in a biofilm formed in porous media [71] |
| W. Harcombe (2014) | 2D, differential-discrete model, combined with genome scale metabolism modelling |
Escherichia coli Salmonella enterica Methylobacterium extorquens |
proposed a modelling framework for incorporating genomic scale information on the scale of microbial communities with the aim to predict the behaviour of multispecies consortia [72] |
| N. Jayasinghe et al. (2014) | 1D, continuum model, combined with genome scale metabolism modelling | Geobacter sulfurreducens | metabolic modelling of spatial heterogeneity of biofilms in microbial fuel cells [73] |
| J. Cole et al. (2015) | 3D, continuum model, combined with genome scale metabolism modelling | Escherichia coli | analysis of the effect of metabolic interactions within densely packed biofilm colonies, i.e. the relation between a cell's position within a colony and its metabolism [74] |
| B. Emerenini et al. (2015) | 2D/3D, continuum, deterministic | not specified | analysis of biofilm detachment regulated by quorum sensing mechanism [43] |
| R. Bennett et al. (2016) | hydrodynamic, deterministic | Pseudomonas aeruginosa et al. | analysis of individual cells flagellar spinning movements on the surface in early biofilm development [75] |
| P. Phalak et al. (2016) | 1D differential-discrete model combined with genome scale metabolism modelling |
Pseudomonas aeruginosa, Staphylococcus aureus |
role of metabolic factors on the spatial distribution of cells in a two species biofilm; the species were chosen for their common occurrence in chronic wound infections [76] |
| M. Azari et al. (2017) | activated sludge model | Candidatus brocadia et al. | wastewater treatment reactor study [27] |
| B. Né Dicte Martin et al. (2017) | 2D, cellular automaton, stochastic | Streptococcus gordonii, Porphyromonas gingivalis | assessment of mixed species interactions in oral biofilms [44] |
| I. Tack et al. (2017) | 2D, individual based, stochastic | Escherichia coli | analysis of the effect of various environmental factors on the biofilm morphology [77] |
| K. Coyte (2017) | 2D, hydrodynamic, game theory | Escherichia coli | analysis of the relative success of microbial strategies in porous media for various flow conditions [78] |
| S. Stump et al. (2018) | 2D, cellular automaton, stochastic | not specified | study of the competition between cooperators and cheaters within a microbial community [79] |