Stacked Generalization with Applicability Domain Outperforms Simple QSAR on in Vitro Toxicological Data.

The development of in silico tools able to predict bioactivity and toxicity of chemical substances is a powerful solution envisioned to assess toxicity as early as possible. To enable the development of such tools, the ToxCast program has generated and made publicly available in vitro bioactivity data for thousands of compounds. The goal of the present study is to characterize and explore the data from ToxCast in terms of Machine Learning capability. For this, a large scale analysis on the entire database has been performed to build models to predict bioactivities measured in in vitro assays. Simple classical QSAR algorithms (ANN, SVM, LDA, random forest, and Bayesian) were first applied on the data, and the results of these algorithms suggested that they do not seem to be well-suited for data sets with a high proportion of inactive compounds. The study then showed for the first time that the use of an ensemble method named "Stacked generalization" could improve the model performance on this type of data. Indeed, for 61% of 483 models, the Stacked method led to models with higher performance. Moreover, the combination of this ensemble method with an applicability domain filter allows one to assess the reliability of the predictions for further compound prioritization. In particular we showed that for 50% of the models, the ROC score is better if we do not consider the compounds that are not within the applicability domain.

G-Networks to Predict the Outcome of Sensing of Toxicity.

G-Networks and their simplified version known as the Random Neural Network have often been used to classify data. In this paper, we present a use of the Random Neural Network to the early detection of potential of toxicity chemical compounds through the prediction of their bioactivity from the compounds' physico-chemical structure, and propose that it be automated using machine learning (ML) techniques. Specifically the Random Neural Network is shown to be an effective analytical tool to this effect, and the approach is illustrated and compared with several ML techniques.

On circuit functionality in Boolean networks.

It has been proved, for several classes of continuous and discrete dynamical systems, that the presence of a positive (resp. negative) circuit in the interaction graph of a system is a necessary condition for the presence of multiple stable states (resp. a cyclic attractor). A positive (resp. negative) circuit is said to be functional when it "generates" several stable states (resp. a cyclic attractor). However, there are no definite mathematical frameworks translating the underlying meaning of "generates." Focusing on Boolean networks, we recall and propose some definitions concerning the notion of functionality along with associated mathematical results.

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.

Stable periodicity and negative circuits in differential systems.

We provide a counter-example to a conjecture of René Thomas on the relationship between negative feedback circuits and stable periodicity in ordinary differential equation systems (Kaufman et al. in J Theor Biol 248:675-685, 2007). We also prove a weak version of this conjecture by using a theorem of Snoussi.

Symbolic modeling of genetic regulatory networks.

Understanding the functioning of genetic regulatory networks supposes a modeling of biological processes in order to simulate behaviors and to reason on the model. Unfortunately, the modeling task is confronted to incomplete knowledge about the system. To deal with this problem we propose a methodology that uses the qualitative approach developed by Thomas. A symbolic transition system can represent the set of all possible models in a concise and symbolic way. We introduce a new method based on model-checking techniques and symbolic execution to extract constraints on parameters leading to dynamics coherent with known behaviors. Our method allows us to efficiently respond to two kinds of questions: is there any model coherent with a certain hypothetic behavior? Are there behaviors common to all selected models? The first question is illustrated with the example of the mucus production in Pseudomonas aeruginosa while the second one is illustrated with the example of immunity control in bacteriophage lambda.

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.

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.

Topology-based abstraction of complex biological systems: application to the Golgi apparatus.

Many complex cellular processes involve major changes in topology and geometry. We have developed a method using topology-based geometric modelling in which the edge labels of an n-dimensional generalized map (a subclass of graphs) represent the relations between neighbouring biological compartments. We illustrate our method using two topological models of the Golgi apparatus. These models can be animated using transformation rules, which depend on geometric and/or biochemical data and which modify both these data and the topology. Both models constitute plausible topological representations of the Golgi apparatus, but only the model based on a recent hypothesis about the Golgi apparatus is fully compatible with data from electron microscopy. Finally, we outline how our method may help biologists to choose between different hypotheses.

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.

Analysing gene regulatory networks by both constraint programming and model-checking.

In this article, we propose a formal method to analyse gene regulatory networks (GRN). The dynamics of such systems is often described by an ordinary differential equation system, but has also been abstracted into a discrete transition system. This modeling depends on parameters for which different values are possible. Each instantiation of these parameters defines a possible dynamics and verification tools can be used to select the tuples of values which lead to dynamics consistent with known behaviours. GRN are so complex that their discrete modeling gives a number of possible dynamics exponential in function of the GRN's size (number of genes and interactions). In this paper, we propose to use constraint programming and CTL formal language to determine the set of all dynamics consistent with the known behavioral properties without enumerating all of them. This approach allows us therefore to minimize the computation time necessary for the research of these parameters.

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.