On the impact of the distance between two genes on their interaction curve.

We analyze a basic building block of gene regulatory networks using a stochastic/geometric model in search of a mathematical backing for the discrete modeling frameworks. We consider a network consisting only of two interacting genes: a source gene and a target gene. The target gene is activated by the proteins encoded by the source gene. The interaction is therefore mediated by activator proteins that travel, like a signal, from the source to the target. We calculate the production curve of the target proteins in response to a constant-rate production of activator proteins. The latter has a sigmoidal shape (like a simple delay line) that is sharper and taller when the two genes are closer to each other. This provides further support for the use of discrete models in the analysis gene regulatory networks. Moreover, it suggests an evolutionary pressure towards making the interacting genes closer to each other to make their interactions more efficient and more reliable.

Evaluation of time profile reconstruction from complex two-color microarray designs.

BACKGROUND: As an alternative to the frequently used "reference design" for two-channel microarrays, other designs have been proposed. These designs have been shown to be more profitable from a theoretical point of view (more replicates of the conditions of interest for the same number of arrays). However, the interpretation of the measurements is less straightforward and a reconstruction method is needed to convert the observed ratios into the genuine profile of interest (e.g. a time profile). The potential advantages of using these alternative designs thus largely depend on the success of the profile reconstruction. Therefore, we compared to what extent different linear models agree with each other in reconstructing expression ratios and corresponding time profiles from a complex design. RESULTS: On average the correlation between the estimated ratios was high, and all methods agreed with each other in predicting the same profile, especially for genes of which the expression profile showed a large variance across the different time points. Assessing the similarity in profile shape, it appears that, the more similar the underlying principles of the methods (model and input data), the more similar their results. Methods with a dye effect seemed more robust against array failure. The influence of a different normalization was not drastic and independent of the method used. CONCLUSION: Including a dye effect such as in the methods lmbr_dye, anovaFix and anovaMix compensates for residual dye related inconsistencies in the data and renders the results more robust against array failure. Including random effects requires more parameters to be estimated and is only advised when a design is used with a sufficient number of replicates. Because of this, we believe lmbr_dye, anovaFix and anovaMix are most appropriate for practical use.

Epigenetic acquisition of inducibility of type III cytotoxicity in P. aeruginosa.

BACKGROUND: Pseudomonas aeruginosa, an opportunistic pathogen, is often encountered in chronic lung diseases such as cystic fibrosis or chronic obstructive pneumonia, as well as acute settings like mechanical ventilation acquired pneumonia or neutropenic patients. It is a major cause of mortality and morbidity in these diseases. In lungs, P. aeruginosa settles in a biofilm mode of growth with the secretion of exopolysaccharides in which it is encapsulated, enhancing its antibiotic resistance and contributing to the respiratory deficiency of patients. However, bacteria must first multiply to a high density and display a cytotoxic phenotype to avoid the host's defences. A virulence determinant implicated in this step of infection is the type III secretion system (TTSS), allowing toxin injection directly into host cells. At the beginning of the infection, most strains isolated from patients' lungs possess an inducible TTSS allowing toxins injection or secretion upon in vivo or in vitro activation signals. As the infection persists most of the bacteria permanently loose this capacity, although no mutations have been evidenced. We name "non inducible" this phenotype. As suggested by the presence of a positive feedback circuit in the regulatory network controlling TTSS expression, it may be due to an epigenetic switch allowing heritable phenotypic modifications without genotype's mutations. RESULTS: Using the generalised logical method, we designed a minimal model of the TTSS regulatory network that could support the epigenetic hypothesis, and studied its dynamics which helped to define a discriminating experimental scenario sufficient to validate the epigenetic hypothesis. A mathematical framework based on formal methods from computer science allowed a rigorous validation and certification of parameters of this model leading to epigenetic behaviour. Then, we demonstrated that a non inducible strain of P. aeruginosa can stably acquire the capacity to be induced by calcium depletion for the TTSS after a short pulse of a regulatory protein. Finally, the increased cytotoxicity of a strain after this epigenetic switch was demonstrated in vivo in an acute pulmonary infection model. CONCLUSION: These results may offer new perspectives for therapeutic strategies to prevent lethal infections by P. aeruginosa by reverting the epigenetic inducibility of type III cytotoxicity.

A hybrid model of cell cycle in mammals.

Time plays an essential role in many biological systems, especially in cell cycle. Many models of biological systems rely on differential equations, but parameter identification is an obstacle to use differential frameworks. In this paper, we present a new hybrid modeling framework that extends René Thomas' discrete modeling. The core idea is to associate with each qualitative state "celerities" allowing us to compute the time spent in each state. This hybrid framework is illustrated by building a 5-variable model of the mammalian cell cycle. Its parameters are determined by applying formal methods on the underlying discrete model and by constraining parameters using timing observations on the cell cycle. This first hybrid model presents the most important known behaviors of the cell cycle, including quiescent phase and endoreplication.

Regulatory networks.

The usefulness of mathematical models for the biological regulatory networks relies on the predictive capability of the models in order to suggest interesting hypotheses and suitable biological experiments. All mathematical frameworks dedicated to biological regulatory networks must manage a large number of abstract parameters, which are not directly measurable in the cell. The cornerstone to establish predictive models is the identification of the possible parameter values. Formal frameworks involve qualitative models with discrete values and computer-aided logic reasoning. They can provide the biologists with an automatic identification of the parameters via a formalization of some biological knowledge into temporal logic formulas. For pedagogical reasons, we focus on gene regulatory networks and develop a qualitative model of the detoxification of benzo[a]pyrene in human cells to illustrate the approach.

Boolean models of biosurfactants production in Pseudomonas fluorescens.

Cyclolipopeptides (CLPs) are biosurfactants produced by numerous Pseudomonas fluorescens strains. CLP production is known to be regulated at least by the GacA/GacS two-component pathway, but the full regulatory network is yet largely unknown. In the clinical strain MFN1032, CLP production is abolished by a mutation in the phospholipase C gene (plcC) and not restored by plcC complementation. Their production is also subject to phenotypic variation. We used a modelling approach with Boolean networks, which takes into account all these observations concerning CLP production without any assumption on the topology of the considered network. Intensive computation yielded numerous models that satisfy these properties. All models minimizing the number of components point to a bistability in CLP production, which requires the presence of a yet unknown key self-inducible regulator. Furthermore, all suggest that a set of yet unexplained phenotypic variants might also be due to this epigenetic switch. The simplest of these Boolean networks was used to propose a biological regulatory network for CLP production. This modelling approach has allowed a possible regulation to be unravelled and an unusual behaviour of CLP production in P. fluorescens to be explained.

Computing with bacterial constituents, cells and populations: from bioputing to bactoputing.

The relevance of biological materials and processes to computing-alias bioputing-has been explored for decades. These materials include DNA, RNA and proteins, while the processes include transcription, translation, signal transduction and regulation. Recently, the use of bacteria themselves as living computers has been explored but this use generally falls within the classical paradigm of computing. Computer scientists, however, have a variety of problems to which they seek solutions, while microbiologists are having new insights into the problems bacteria are solving and how they are solving them. Here, we envisage that bacteria might be used for new sorts of computing. These could be based on the capacity of bacteria to grow, move and adapt to a myriad different fickle environments both as individuals and as populations of bacteria plus bacteriophage. New principles might be based on the way that bacteria explore phenotype space via hyperstructure dynamics and the fundamental nature of the cell cycle. This computing might even extend to developing a high level language appropriate to using populations of bacteria and bacteriophage. Here, we offer a speculative tour of what we term bactoputing, namely the use of the natural behaviour of bacteria for calculating.

Analysing formal models of genetic regulatory networks with delays.

In this paper, we propose a refinement of the modelling of biological regulatory networks based on the discrete approach of Rene Thomas. We refine and automatise the use of delays of activation/inhibition in order to specify which variable is more quickly affected by a change of its regulators. The formalism of linear hybrid automata is well suited to allow such refinement. We then use HyTech for two purposes: to find automatically all paths from a specified initial state to another one; to synthesise constraints on the delay parameters in order to follow any specific path.

A stochastic automaton shows how enzyme assemblies may contribute to metabolic efficiency.

BACKGROUND: The advantages of grouping enzymes into metabolons and into higher order structures have long been debated. To quantify these advantages, we have developed a stochastic automaton that allows experiments to be performed in a virtual bacterium with both a membrane and a cytoplasm. We have investigated the general case of transport and metabolism as inspired by the phosphoenolpyruvate:sugar phosphotransferase system (PTS) for glucose importation and by glycolysis. RESULTS: We show that PTS and glycolytic metabolons can increase production of pyruvate eightfold at low concentrations of phosphoenolpyruvate. A fourfold increase in the numbers of enzyme EI led to a 40% increase in pyruvate production, similar to that observed in vivo in the presence of glucose. Although little improvement resulted from the assembly of metabolons into a hyperstructure, such assembly can generate gradients of metabolites and signaling molecules. CONCLUSION: in silico experiments may be performed successfully using stochastic automata such as HSIM (Hyperstructure Simulator) to help answer fundamental questions in metabolism about the properties of molecular assemblies and to devise strategies to modify such assemblies for biotechnological ends.

Validation of biological models with temporal logic and Timed Hybrid Petri Nets.

The Hybrid Functional Petri Nets (HFPN) formalism has shown its convenience for modelling biological systems. This class of models has been fruitfully applied in biology but the remarkable expressiveness of HFPN often leads to incomplete validations. In this paper, we propose a logical framework for Timed Hybrid Petri Nets (THPN), a sub-class of HFPN. We propose an extension of Event Clock Logic dedicated to THPN and a procedure to convert a THPN into a real-time automaton. A small biological model shows that our framework allows us to formally prove properties by a well suited model-checking procedure.

Application of formal methods to biological regulatory networks: extending Thomas' asynchronous logical approach with temporal logic.

Based on the discrete definition of biological regulatory networks developed by René Thomas, we provide a computer science formal approach to treat temporal properties of biological regulatory networks, expressed in computational tree logic. It is then possible to build all the models satisfying a set of given temporal properties. Our approach is illustrated with the mucus production in Pseudomonas aeruginosa. This application of formal methods from computer science to biological regulatory networks should open the way to many other fruitful applications.

Epigenesis and dynamic similarity in two regulatory networks in Pseudomonas aeruginosa.

Mucoidy and cytotoxicity arise from two independent modifications of the phenotype of the bacterium Pseudomonas aeruginosa that contribute to the mortality and morbidity of cystic fibrosis. We show that, even though the transcriptional regulatory networks controlling both processes are quite different from a molecular or mechanistic point of view, they may be identical from a dynamic point of view: epigenesis may in both cases be the cause of the acquisition of these new phenotypes. This was highlighted by the identity of formal graphs modelling these networks. A mathematical framework based on formal methods from computer science was defined and implemented with a software environment. It allows an easy and rigorous validation and certification of these models and of the experimental methods that can be proposed to falsify or validate the underlying hypothesis.

Hyperstructures, genome analysis and I-cells.

New concepts may prove necessary to profit from the avalanche of sequence data on the genome, transcriptome, proteome and interactome and to relate this information to cell physiology. Here, we focus on the concept of large activity-based structures, or hyperstructures, in which a variety of types of molecules are brought together to perform a function. We review the evidence for the existence of hyperstructures responsible for the initiation of DNA replication, the sequestration of newly replicated origins of replication, cell division and for metabolism. The processes responsible for hyperstructure formation include changes in enzyme affinities due to metabolite-induction, lipid-protein affinities, elevated local concentrations of proteins and their binding sites on DNA and RNA, and transertion. Experimental techniques exist that can be used to study hyperstructures and we review some of the ones less familiar to biologists. Finally, we speculate on how a variety of in silico approaches involving cellular automata and multi-agent systems could be combined to develop new concepts in the form of an Integrated cell (I-cell) which would undergo selection for growth and survival in a world of artificial microbiology.