Early development and quorum sensing in bacterial biofilms

Abstract

We develop mathematical models to examine the formation, growth and quorum sensing activity of bacterial biofilms. The growth aspects of the model are based on the assumption of a continuum of bacterial cells whose growth generates movement, within the developing biofilm, described by a velocity field. A model proposed in Ward et al. (2001) to describe quorum sensing, a process by which bacteria monitor their own population density by the use of quorum sensing molecules (QSMs), is coupled with the growth model. The resulting system of nonlinear partial differential equations is solved numerically, revealing results which are qualitatively consistent with experimental ones. Analytical solutions derived by assuming uniform initial conditions demonstrate that, for large time, a biofilm grows algebraically with time; criteria for linear growth of the biofilm biomass, consistent with experimental data, are established. The analysis reveals, for a biologically realistic limit, the existence of a bifurcation between non-active and active quorum sensing in the biofilm. The model also predicts that travelling waves of quorum sensing behaviour can occur within a certain time frame; while the travelling wave analysis reveals a range of possible travelling wave speeds, numerical solutions suggest that the minimum wave speed, determined by linearisation, is realised for a wide class of initial conditions.

Association of Vibrio cholerae O1 El Tor and O139 Bengal with the Copepods Acartia tonsa and Eurytemora affinis

“…Similarly, results of earlier research revealed that vibrios, including V. cholerae, attached to and used the chitinaceous exoskeleton and eggs of aquatic invertebrates as nutrient substrates (6,19,20,35,38,42,51). Thus, the ability to attach to live copepods in "hot spots," in microcolonies or biofilms, may be crucial for efficient nutrient capture and may be an important factor in the persistence and/or ascendance of one genotype over another (50).…”

Mathematical Modelling of Bacterial Quorum Sensing: A Review

“…They also explored therapy implications by incorporating a putative drug that targets bacteria expressing a particular gene during virulence (given that their models predict that only a fraction of the population will be up-regulated if one of the suppression mechanisms is operating). Finally, they extended Ward et al (2003) to include QS repressions in biofilm development and studied how it affects travelling wave behaviour.…”

“…Pseudomonas aeruginosa Chopp et al (2002a, b), Ward et al (2003) Competence Streptococcus pneumoniae Karlsson et al (2007) C S P Exopolysaccharides - Frederick et al (2011) Motility (e.g. swimming, foraging) Tang et al (2007), van Gestel et al (2012) Virulence Pseudomonas aeruginosa Dockery and Keener (2001), Fagerlind et al (2003Fagerlind et al ( , 2005, Viretta and Fussenegger (2004), Netotea et al (2009) AHL, AHQ Koerber et al (2005), Jabbari et al (2010), Gustafsson et al (2004) AIP Escherichia coli Li et al (2006) AI-2, Indole Lee et al (2007) See Taga and Bassler (2003), Miller and Bassler (2001) and West et al (2012) for a more comprehensive list.…”

“…Moreover, they obtained a critical biofilm depth and the corresponding approximate time for the induction of QS. Ward et al (2003) combined the QS activity and biofilm formation by including growth along the surface, where cell growth generates movement within the colony. They presented a nonlinear PDE model as an extension of Ward et al (2001), with the addition of the release and diffusion of QS molecules.…”

Modeling Biofilms in Water Systems with New Variables: A Review

“…The ordinary differential equation-based spatiotemporal model discussed the correlations between the physical parameters and autoinducers in the biofilms matrix, where the biofilms were categorized into biotic part, consisting of living cells and abiotic materials, including EPS and dead cells. Then, Ward et al [62] considered the cell growth during the interaction between QS and biofilm formation. This model was based on a previous work, which described the QS system by three components: switch-off cells, switch-on cells and the switch, autoinducers, and assumed that higher concentrations of autoinducers increased the proportion of switch-on cells [63].…”