An age-dependent model to analyse the evolutionary stability of bacterial quorum sensing.

Bacterial communication is enabled through the collective release and sensing of signalling molecules in a process called quorum sensing. Cooperative processes can easily be destabilized by the appearance of cheaters, who contribute little or nothing at all to the production of common goods. This especially applies for planktonic cultures. In this study, we analyse the dynamics of bacterial quorum sensing and its evolutionary stability under two levels of cooperation, namely signal and enzyme production. The model accounts for mutation rates and switches between planktonic and biofilm state of growth. We present a mathematical approach to model these dynamics using age-dependent colony models. We explore the conditions under which cooperation is stable and find that spatial structuring can lead to long-term scenarios such as coexistence or bistability, depending on the non-linear combination of different parameters like death rates and production costs.

Short term uptake and transport process for metformin in roots of Phragmites australis and Typha latifolia.

Metformin (MET) as an emerging contaminant has been detected in surface water and wastewater in numerous countries, due to insufficient retention in classical waste water treatment plants. In order to characterize the uptake of the compound during phytotreatment of waste water, a short term Pitman chamber experiment was carried out to assess the characteristics of MET uptake and transport by roots. Three different concentrations (0.5, 1.0 and 2.0 mmol L(-)(1)) were applied to cattail (Typha latifolia) and reed (Phragmites australis) roots which were used to investigate the uptake mechanism because they are frequently utilized in phytoremediation. In addition, quinidine was used as an inhibitor to assess the role of organic cation transporters (OCTs) in the uptake of MET by T. latifolia. The transport process of MET is different from carbamazepine (CBZ) and caffeine (CFN). In both T. latifolia and P. australis, the uptake processes were independent of initial concentrations. Quinidine, a known inhibitor of organic cation transporters, can significantly affect MET uptake by T. latifolia roots with inhibition ratios of 70-74%. Uptake into the root could be characterized by a linear model with R(2) values in the range of 0.881-0.999. Overall, the present study provides evidence that MET is taken up by plant roots and has the potential for subsequent translocation. OCTs could be one of the important pathways for MET uptake into the plant.

Model selection for microbial nutrient uptake using a cost-benefit approach.

We consider the uptake of various carbon sources by microorganisms based on four fundamental assumptions: (1) the uptake of nutrient follows a saturation characteristics (2) substrate processing has a benefit but comes at costs of maintaining the process chain (3) substrate uptake is controlled and (4) evolution optimized the control of substrate uptake. These assumptions result in relatively simple mathematical models. In case of two substrates, our main finding is the following: Depending on the overall topology of the metabolic pathway, three different behavioral patterns can be identified. (1) both substrates are consumed at a time, (2) one substrate is preferred and represses the uptake of the other (catabolite repression), or (3) a cell feeds exclusively on one or the other substrate, possibly leading to a population that splits in two sub-populations, each of them specialized on one substrate only. Batch-culture and retentostat data of toluene, benzoate, and acetate uptake by Geobacter metallireducens are used to demonstrate that the model structure is suited for a quantitative description of uptake dynamics.

Bet-hedging in stochastically switching environments.

We investigate the evolution of bet-hedging in a population that experiences a stochastically switching environment by means of adaptive dynamics. The aim is to extend known results to the situation at hand, and to deepen the understanding of the range of validity of these results. We find three different types of evolutionarily stable strategies (ESSs) depending on the frequency at which the environment changes: for a rapid change, a monomorphic phenotype adapted to the mean environment; for an intermediate range, a bimorphic bet-hedging phenotype; for slowly changing environments, a monomorphic phenotype adapted to the current environment. While the last result is only obtained by means of heuristic arguments and simulations, the first two results are based on the analysis of Lyapunov exponents for stochastically switching systems.

Stochastic modeling of Pseudomonas syringae growth in the phyllosphere.

Pseudomonas syringae is a gram-negative bacterium which lives on leaf surfaces. Its growth has been described using epifluorescence microscopy and image analysis; it was found to be growing in aggregates of a wide range of sizes. We develop a stochastic model to describe aggregate distribution and determine the mechanisms generating experimental observations. We found that a logistic birth-death model with migration (time-homogeneous Markov process) provides the best description of the observed data. We discuss how to analyze the joint distribution of the numbers of aggregates of different sizes at a given time and explore how to account for new aggregates being created, that is, the joint distribution of the family size statistics conditional on the total number of aggregates. We compute the first two moments. Through simulations we examine how the model's parameters affect the aggregate size distribution and successfully explain the quantitative experimental data available. Aggregation formation is thought to be the first step towards pathogenic behavior of this bacterium; understanding aggregate size distribution would prove useful to understand the switch from epiphytic to pathogenic behavior.