Three-dimensional biofilm model with individual cells and continuum EPS matrix

Abstract

An innovative type of biofilm model is derived by combining an individual description of microbial particles with a continuum representation of the biofilm matrix. This hybrid model retains the advantages of each approach, while providing a more realistic description of the temporal development of biofilm structure in two or three spatial dimensions. The general model derivation takes into account any possible number of soluble components. These are substrates and metabolic products, which diffuse and react in the biofilm within individual microbial cells. The cells grow, divide, and produce extracellular polymeric substances (EPS) in a multispecies model setting. The EPS matrix is described by a continuum representation as incompressible viscous fluid, which can expand and retract due to generation and consumption processes. The cells move due to a pushing mechanism between cells in colonies and by an advective mechanism supported by the EPS dynamics. Detachment of both cells and EPS follows a continuum approach, whereas cells attach in discrete events. Two case studies are presented for model illustration. Biofilm consolidation is explained by shrinking due to EPS and cell degradation processes. This mechanism describes formation of a denser layer of cells in the biofilm depth and occurrence of an irregularly shaped biofilm surface under nutrient limiting conditions. Micro-colony formation is investigated by growth of autotrophic microbial colonies in an EPS matrix produced by heterotrophic cells. Size and shape of colonies of ammonia and nitrite-oxidizing bacteria (NOB) are comparatively studied in a standard biofilm and in biofilms aerated from a membrane side.

Simulation of single-species bacterial-biofilm growth using the Glazier-Graner-Hogeweg model and the CompuCell3D modeling environment

“…Biofilm models generally divide into cellcentered models with discrete cells (cellular automata [8,39,69] or individual-based models [25,52,85]), and continuum models [3,26,28,84]. Hybrid models combine discrete cells with a continuum representation of the ECM and/or extracellular fluid [4] or with PDEs for reaction- 1 This model has previously received a number of names, of which the cellular Potts model (CPM) has been most popular. However, as we have discussed in detail in [33], the name Potts model evokes a set of incorrect or misleading expectations concerning the model, which have proved confusing.…”

“…In addition, most existing models have certain limitations that may impair their viability in describing complex real biofilms. Many cell-centered and hybrid models describe individual cells as points [66] or spheres [4]. However, cell shape can be essential in biological development, 4 and changes in cell shape reflect the elastic properties of cells.…”

Vibrio cholerae biofilm growth program and architecture revealed by single-cell live imaging

“…However, still lacking is a fundamental biophysical understanding of how bacteria, in time and space, build these 3D structures that attach to surfaces and resist mechanical and chemical perturbations. One common assumption is that bacteria produce polymeric matrices that expand the volume occupied by cells and carry them into the third dimension, as demonstrated by many computer simulations (9,10). Matrix proteins, extracellular DNA, lipids, and bacteriophages have also been shown to influence the formation of the overall biofilm structure (8).…”

Biomechanical Analysis of Infectious Biofilms

“…Early models for shear-based detachment imposed height-dependent rates rather than solve for the explicit hydrodynamic flow field [2], but still demonstrated that combining multiple detachment mechanisms can generate a variety of morphologies [17]. To consider the effects of flow, some continuum fluid-structure coupling models have been extended to include detachment as reduced interfacial growth [21,26] or a critical stress threshold [12,72], and suggest erosion smoothens while sloughing roughens the biofilm surface.…”