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Chapter 13 : Modeling Biofilms
Authors:
Daniel R. Noguera1,
Gonzalo E. Pizarro2,
John M. Regan3
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Affiliations:
1: Department of Civil and Environmental Engineering, University of Wisconsin, Madison, Wisconsin 53706;
2: Department of Hydraulics and Environmental Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile;
3: Department of Civil and Environmental Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802
Content Type: Monograph
Publication Year:
2004
Category: Environmental Microbiology; Microbial Genetics and Molecular Biology
Book DOI:
10.1128/9781555817718
Chapter DOI:
10.1128/9781555817718.ch13
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Abstract:
Because all levels of biofilm models are useful depending on the application, this chapter describes and discusses biofilm modeling starting from the simple, homogeneous case to the more complex, structurally and functionally heterogeneous cases. Obviously, the complexity of the model is reduced when a single-species biofilm is modeled (i.e., a functionally homogeneous but structurally heterogeneous biofilm); thus, the discussions in the chapter focus on this simplified problem. In the cellular automata (CA) biofilm model, there are two superimposed lattices, one of them containing information on the location of food particles (substrate lattice) and the other one describing the location of microbial particles (microbial lattice). The simulation of biofilm activity is done by evaluating these stochastic processes over a series of time steps. A section describes the fundamental rules for these stochastic processes and their relation to the physical and biological parameters that represent the biofilm system. Biofilm erosion at the surface, another possible process controlling biofilm growth, can be implemented by selecting a maximum biofilm height, beyond which any microbial outgrowth will be removed from the biofilm. The evolution of biofilm modeling from the 1970s until now shows different approaches to the mathematical abstraction of the biofilm problem, but it is evident that the conceptual basis for all the models is similar and relies on mathematically coupling substrate diffusion with substrate utilization, microbial growth, and microbial decay or detachment.
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
Figures
Modeling Biofilms
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Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.fig13-1
FIGURE 1
Schematic representation of a homogeneous biofilm system.
10.1128/9781555817718/fig13-1_thmb.gif
10.1128/9781555817718/fig13-1.gif
FIGURE 1
Schematic representation of a homogeneous biofilm system.
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.fig13-2
FIGURE 2
Discretization of a 1D biofilm problem and corresponding explicit finite difference approximation of equations 2 to 4.
10.1128/9781555817718/fig13-2_thmb.gif
10.1128/9781555817718/fig13-2.gif
FIGURE 2
Discretization of a 1D biofilm problem and corresponding explicit finite difference approximation of equations 2 to 4.
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.fig13-3
FIGURE 3
The evaluation of growth and decay in a biofilm model produces an uneven distribution of the size of biofilm elements. A reevaluation of the boundaries between elements restores the equally sized element configuration.
10.1128/9781555817718/fig13-3_thmb.gif
10.1128/9781555817718/fig13-3.gif
FIGURE 3
The evaluation of growth and decay in a biofilm model produces an uneven distribution of the size of biofilm elements. A reevaluation of the boundaries between elements restores the equally sized element configuration.
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.fig13-4
FIGURE 4
Periodic boundaries in a 2D domain are illustrated by bending the planar domain to form a cylinder in which the left-most elements overlap with the right-most elements (i.e., elements in column 1 = elements in column n).
10.1128/9781555817718/fig13-4_thmb.gif
10.1128/9781555817718/fig13-4.gif
FIGURE 4
Periodic boundaries in a 2D domain are illustrated by bending the planar domain to form a cylinder in which the left-most elements overlap with the right-most elements (i.e., elements in column 1 = elements in column n).
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.fig13-5
FIGURE 5
Schematic representation of the mixing and transport steps in the CA diffusion rule. During mixing, all food particles change layers (shown in this figure is a 180° directional change). During the transport step, the particles are moved according to the layer in which they are located (e.g., north, east, south, or west, for the layers shown).
10.1128/9781555817718/fig13-5_thmb.gif
10.1128/9781555817718/fig13-5.gif
FIGURE 5
Schematic representation of the mixing and transport steps in the CA diffusion rule. During mixing, all food particles change layers (shown in this figure is a 180° directional change). During the transport step, the particles are moved according to the layer in which they are located (e.g., north, east, south, or west, for the layers shown).
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.fig13-6
FIGURE 6
Schematic representation of evaluation of connectivity and sloughing. Light squares represent microbial particles without an identified connection to the substratum. Dark squares represent connected microbial particles. Connectivity “flows” through microbial cells (steps 1 to 8) and unconnected cells are sloughed off (step 9).
10.1128/9781555817718/fig13-6_thmb.gif
10.1128/9781555817718/fig13-6.gif
FIGURE 6
Schematic representation of evaluation of connectivity and sloughing. Light squares represent microbial particles without an identified connection to the substratum. Dark squares represent connected microbial particles. Connectivity “flows” through microbial cells (steps 1 to 8) and unconnected cells are sloughed off (step 9).
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.fig13-7
FIGURE 7
Flowchart of algorithm used to simulate biofilm dynamics with the quantitative CA biofilm model.
10.1128/9781555817718/fig13-7_thmb.gif
10.1128/9781555817718/fig13-7.gif
FIGURE 7
Flowchart of algorithm used to simulate biofilm dynamics with the quantitative CA biofilm model.
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.fig13-8
FIGURE 8
Simulation of a functionally homogeneous and structurally heterogeneous biofilm using the CA model. The typical cycle includes growth, decay, and sloughing processes.
10.1128/9781555817718/fig13-8_thmb.gif
10.1128/9781555817718/fig13-8.gif
FIGURE 8
Simulation of a functionally homogeneous and structurally heterogeneous biofilm using the CA model. The typical cycle includes growth, decay, and sloughing processes.
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.fig13-9
FIGURE 9
Substrate flux (A) and biofilm thickness (B) during the simulation of a functionally homogeneous and structurally heterogeneous biofilm using the quantitative CA biofilm model.
10.1128/9781555817718/fig13-9_thmb.gif
10.1128/9781555817718/fig13-9.gif
FIGURE 9
Substrate flux (A) and biofilm thickness (B) during the simulation of a functionally homogeneous and structurally heterogeneous biofilm using the quantitative CA biofilm model.
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.fig13-10
FIGURE 10
Simulation of growth of a heterogeneous biofilm using the quantitative CA biofilm model. The biofilm has two microbial species, heterotrophs (dark areas) and nitrifiers (white areas).
10.1128/9781555817718/fig13-10_thmb.gif
10.1128/9781555817718/fig13-10.gif
FIGURE 10
Simulation of growth of a heterogeneous biofilm using the quantitative CA biofilm model. The biofilm has two microbial species, heterotrophs (dark areas) and nitrifiers (white areas).
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.fig13-11
FIGURE 11
Average concentration of microbial species (A) and chemical species (B) throughout the biofilm matrix at day 18 of the simulation.
10.1128/9781555817718/fig13-11_thmb.gif
10.1128/9781555817718/fig13-11.gif
FIGURE 11
Average concentration of microbial species (A) and chemical species (B) throughout the biofilm matrix at day 18 of the simulation.
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
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Tables
Modeling Biofilms
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Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.tab13-1
TABLE 1
Notation used in this chapter
TABLE 1
Notation used in this chapter
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.tab13-2
TABLE 2
Step-by-step instructions for using the pseudoanalytical model of Saéz and Rittmann a
TABLE 2
Step-by-step instructions for using the pseudoanalytical model of Saéz and Rittmann a
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.tab13-3
TABLE 3
Parameters used for the simulation of a functionally homogeneous, structurally heterogeneous biofilm presented in example 1
TABLE 3
Parameters used for the simulation of a functionally homogeneous, structurally heterogeneous biofilm presented in example 1
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.tab13-4
TABLE 4
Calculation of parameters for the quantitative CA biofilm model (example 1)
TABLE 4
Calculation of parameters for the quantitative CA biofilm model (example 1)
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.tab13-5
TABLE 5
Summary of parameters for microbial species in example 2, the functionally heterogeneous CA biofilm model
TABLE 5
Summary of parameters for microbial species in example 2, the functionally heterogeneous CA biofilm model
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13
/content/10.1128/9781555817718.chap13.tab13-6
TABLE 6
Summary of parameters for microbial species in example 2, the functionally heterogeneous CA biofilm model
TABLE 6
Summary of parameters for microbial species in example 2, the functionally heterogeneous CA biofilm model
Citation:
Noguera D, Pizarro G, Regan J.
2004.
Modeling Biofilms,
p 222-249.
In
Ghannoum M, O'Toole G (ed),
Microbial Biofilms.
ASM Press, Washington, DC.
doi: 10.1128/9781555817718.ch13