From Staphylococcus aureus gene regulation to its pattern formation.

The focus of this paper is to develop a new partial differential equation model for the pattern formation of the human pathogen Staphylococcus aureus, starting from a newly developed model of selected gene regulation mechanisms. In our model, we do not only account for the bacteria densities and nutrient concentrations, but also for the quorum sensing and biofilm components, since they enable bacteria to coordinate their behavior and provide the environment in which the colony grows. To this end, we model the relevant gene regulation systems using ordinary differential equations and therefrom derive our evolution equations for quorum sensing and biofilm environment by time-scale arguments. Furthermore, we compare and validate our model and the corresponding simulation results with biological real data observations of Staphylococcus aureus mutant colony growth in the laboratory. We show that we are able to adequately display the qualitative biological features of pattern formation in selected mutants, using the parameter changes indicated by the gene regulation mechanisms.

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.

State-dependent neutral delay equations from population dynamics.

A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE--shift system) is a limiting case of a system of two standard delay equations.

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.

A delay model for quorum sensing of Pseudomonas putida.

The bacterial strain Pseudomonas putida IsoF, isolated from a tomato rhizosphere, possesses a quorum sensing regulation system, which allows the bacteria to recognise aspects of their environment or to communicate with each other by the so-called autoinducer molecules. In an experimental study, the time series of the autoinducer production did not show the expected behaviour, as it was observed for other bacterial species by indirect measurements. The modelling approach introduced here allows an explanation of the behaviour, supporting the hypothesis of the existence of a further (not yet detected) enzyme, which degrades the autoinducer into an inactive form. Especially the properties of the considered delay differential system allow for the description of the time series. For example the appearance of a first small maximum in the initial phase can be explained by a delay differential equation.

Oscillations of Hes7 caused by negative autoregulation and ubiquitination.

Loss of Hes7 function leads to irregular somite formation demonstrating that Hes7 is a crucial component of the segmentation clock during somitogenesis. Experiments revealed that not only the repressor functionality but also the half-life of the protein is crucial for oscillatory expression of Hes7 and regular somite formation. Numerical integration of a delay equation system supported this finding. However, in a recent paper it was shown that the number of binding sites is also decisive for damped or undamped oscillations. It was shown that for more than one binding site the Hill coefficient increases. This leads to a completely different behavior. The oscillations are undamped and thus the mathematical model can no longer explain the results observed in the experiments. In this paper we propose a more sophisticated model for the Hes7 oscillator. Since Hes7 is degraded by the ubiquitin-proteasome pathway we include Michaelis-Menten kinetics for the ubiquitination of Hes7. We identify the Michaelis-Menten constant as an additional model parameter for oscillatory behavior. By increasing the Michaelis-Menten constant we found damped oscillations even if the Hill coefficient is increased.

PAProC: a prediction algorithm for proteasomal cleavages available on the WWW.

The first version of PAProC (Prediction Algorithm for Proteasomal Cleavages) is now available to the general public. PAProC is a prediction tool for cleavages by human and yeast proteasomes, based on experimental cleavage data. It will be particularly useful for immunologists working on antigen processing and the prediction of major histocompatibility complex class I molecule (MHC I) ligands and cytotoxic T-lymphocyte (CTL) epitopes. Likewise, in cases in which proteasomal protein degradation has been indicated in disease, PAProC can be used to assess the general cleavability of disease-linked proteins. On its web site (http://www.paproc.de), background information and hyperlinks are provided for the user (e.g., to SYFPEITHI, the database for the prediction of MHC I ligands).

An algorithm for the prediction of proteasomal cleavages.

Proteasomes, major proteolytic sites in eukaryotic cells, play an important part in major histocompatibility class I (MHC I) ligand generation and thus in the regulation of specific immune responses. Their cleavage specificity is of outstanding interest for this process. In order to generalize previously determined cleavage motifs of 20 S proteasomes, we developed network-based model proteasomes trained by an evolutionary algorithm with experimental cleavage data of yeast and human 20 S proteasomes. A window of ten flanking amino acid residues proved sufficient for the model proteasomes to reproduce the experimental results with 98-100 % accuracy. Actual experimental data were reproduced significantly better than randomly selected cleavage sites, suggesting that our model proteasomes were able to extract rules inherent to proteasomal cleavage data. The affinity parameters of the model, which decide for or against cleavage, correspond with the cleavage motifs determined experimentally. The predictive power of the model was verified for unknown (to the program) test conditions: the prediction of cleavage numbers in proteins and the generation of MHC I ligands from short peptides. In summary, our model proteasomes reproduce and predict proteasomal cleavages with high degree of accuracy. They present a promising approach for predicting proteasomal cleavage products in future attempts and, in combination with existing algorithms for MHC I ligand prediction, will be tested to improve cytotoxic T lymphocyte epitope prediction.