Cell-signalling repression in bacterial quorum sensing.

In this paper we expand on two mathematical models for investigating the role of three distinct repression mechanisms within the so-called quorum sensing (QS) cell-signalling process of bacterial colonies growing (1) in liquid cultures and (2) in biofilms. The repression mechanisms studied are (i) reduction of cell signalling molecule (QSM) production by a constitutively produced agent degrading the messenger RNA of a crucial enzyme (QSE), (ii) lower QSM production rate due to a negative feedback process and (iii) loss of QSMs by binding directly to a constitutively produced agent; the first two mechanisms are known to be employed by the pathogenic bacterium Pseudomonas aeruginosa and the last is relevant to the plant pathogen Agrobacterium tumefaciens. The modelling approach assumes that the bacterial colony consists of two sub-populations, namely down- and up-regulated cells, that differ in the rates at which they produce QSMs, while QSM concentration governs the switching between sub-populations. Parameter estimates are obtained by curve-fitting experimental data (involving P. aeruginosa growth in liquid culture, obtained as part of this study) to solutions of model (1). Asymptotic analysis of the model (1) shows that mechanism (i) is necessary, but not sufficient, to predict the observed saturation of QSM levels in an exponentially growing colony; either mechanism (ii) or (iii) also needs to be incorporated to obtain saturation. Consequently, only a fraction of the population will become up-regulated. Furthermore, only mechanisms (i) and (iii) affect the main timescales for up-regulation. Repression was found to play a less significant role in a biofilms, but mechanisms (i)-(iii) were nevertheless found to reduce the ultimate up-regulated cell fraction and mechanisms (i) and (iii) to increase the timescale for substantial up-regulation and to decrease the wave speed of an expanding front of QS activity.

Modelling host tissue degradation by extracellular bacterial pathogens.

Extracellular bacterial pathogens such as Pseudomonas aeruginosa are able to penetrate into host tissues (given an initial breech in the outer barrier, e.g. a wound) through the action of exo-toxins and degradative exo-enzymes. A mathematical model of this process is presented which, in the absence of significant immune response, predicts the progression of the bacteria into the tissue as a travelling wave whose velocity can be determined explicitly in terms of the model parameters. Simple in vitro experiments in protein-based matrices are performed which yield results consistent with this behaviour. A complementary in vitro experimental system with distinct qualitative behaviour is also studied, giving further insight and confidence in the modelling approach.

Population differentiation of Potamogeton pectinatus in the Baltic Sea with reference to waterfowl dispersal.

Forty populations of Potamogeton pectinatus L. were sampled from around the Baltic Sea basin. Analysis of 62 ISSR 'loci' showed that the number of clones per population is very variable but shows a tendency to decrease with latitude. Analysis of molecular variance revealed that, overall, just over half the variability is stored within populations and just under half between them (phi(ST) 0.496). In pairwise comparisons, most populations are significantly differentiated. Genetic distance between populations, as measured by phi(ST), increases with geographical distance. Levels of population differentiation, however, are lower on the southeastern Swedish coast than elsewhere, a reduction correlated with the importance of this area as a staging post for the massive migrations of waterfowl from arctic Russia and western Siberia. Cumulative plots of phi(ST) against geographical distance along this coast suggest that, although it does not prevent significant population differentiation, bird traffic reduces it over distances of 150-200 km.

A mathematical model of partial-thickness burn-wound infection by Pseudomonas aeruginosa: quorum sensing and the build-up to invasion.

Pseudomonas aeruginosa remains a significant pathogen in burn-wound infection, its pathogenicity being associated with the production of a cocktail of virulence determinants which is regulated by a population-density-dependent mechanism termed quorum sensing. Quorum sensing is effected through the production and binding of signalling molecules. Here we present a mathematical model for the early stages of the infection process by P. aeruginosa in burn wounds which accounts for the quorum sensing system and for the diffusion of signalling molecules in the burn-wound environment. The results of the model and the effects of important parameters are discussed in detail. For example, the effect of the degradation rate of signalling molecules and its significance for anti-signalling therapies is discussed.

Mathematical modelling of quorum sensing in bacteria.

The regulation of density-dependent behaviour by means of quorum sensing is widespread in bacteria, the relevant phenomena including bioluminescence and population expansion by swarming, as well as virulence. The process of quorum sensing is regulated by the production and monitoring of certain molecules (referred to as QSMs); on reaching an apparent threshold concentration of QSMs (reflecting high bacterial density) the bacterial colony in concert 'switches on' the density-dependent trait. In this paper a mathematical model which describes bacterial population growth and quorum sensing in a well mixed system is proposed and studied. We view the population of bacteria as consisting of down-regulated and up-regulated sub-populations, with QSMs being produced at a much faster rate by the up-regulated cells. Using curve fitting techniques for parameter estimation, solutions of the resulting system of ordinary differential equations are shown to agree well with experimental data. Asymptotic analysis in a biologically relevant limit is used to investigate the timescales for up-regulation of an exponentially growing population of bacteria, revealing the existence of bifurcation between limited and near-total up-regulation. For a fixed population of cells steady-state analysis reveals that in general one physical steady-state solution exists and is linearly stable; we believe this solution to be a global attractor. A bifurcation between limited and near-total up-regulation is also discussed in the steady-state limit.

Genotypic diversity in field isolates of Babesia bovis from cattle with babesiosis after vaccination.

OBJECTIVE: To determine whether particular genotypes of Babesia bovis were common to field isolates obtained from cattle properties in Queensland where the B bovis vaccine had apparently failed. DESIGN: A comparative study of polymerase chain reaction genotypes in different populations of B bovis. PROCEDURE: Two polymerase chain reaction assays were applied to analyse DNA extracts of B bovis vaccine (K, T and Dixie strains) and 27 field isolates from 24 properties where disease outbreaks had occurred despite the use of the vaccine. To evaluate the stability of the genotypes identified, 11 of the field isolates were inoculated into experimental cattle that had either been previously vaccinated with T strain or not vaccinated. RESULTS: No particular genotype of B bovis was responsible for the problems observed in previously vaccinated herds. None of the isolates had genotypes identical to the vaccine strains used. No geographic trends among the genotypes were observed. Isolates that originated from the same property also had different genotypes. Blood passage of the 11 field isolates in either previously vaccinated or nonvaccinated cattle did not alter the original genotype. CONCLUSION: No particular genotypes identified by the Bv80 and BvVA1 polymerase chain reaction assays could be associated with vaccine failures.