Jean-Paul Comet

Hybrid Modelling and Dynamical Analysis of Gene Regulatory Networks with Delays

René Thomas’ discrete modelling of gene regulatory networks (GRN) is a well-known approach to study the dynamics resulting from a set of interacting genes. It deals with some parameters which reflect the possible targets of trajectories. Those parameters are a priori unknown, but they may generally be deduced from a well-chosen set of biologically observed trajectories. Besides, it neglects the time delays for a gene to pass from one level of expression to another one. The purpose of this paper is to show that we can account for time delays of increasing or decreasing expression levels of genes in a GRN, while preserving powerful enough computer-aided reasoning capabilities. We designed a more accurate abstraction of GRN where delays are now supposed to be non-null unknown new parameters. We show that such models, together with hybrid model-checking algorithms, make it possible to obtain some results about the behaviour of a network of interacting genes, since dynamics depend on the respective values of the parameters. The characteristic of our approach is that, among possible execution trajectories in the model, we can automatically find out both viability cycles and absorption in capture basins. As a running example, we show that we are able to discriminate between various possible dynamics of mucus production in the bacterium Pseudomonas aeruginosa.

Semantics of Biological Regulatory Networks

The aim of the paper is to revisit the model of Biological Regulatory Networks (BRN) which was proposed by Rene Thomas to model the interactions between a set of genes. We give a formal semantics for BRN in terms of transition systems which formalizes the evolution rules given by Rene Thomas. Then we show how to use this model to find interesting properties of a BRN like the set of stable states, cycles etc using tools for analyzing transition systems.

Modeling and Analysis of Gene Regulatory Networks

This chapter describes basic principles for modeling genetic regulatory networks, using three different classes of formalisms: discrete, hybrid, and continuous differential systems. A short review of the mathematical tools for each formalism is presented. Based on several simple examples, which are worked out in detail, this chapter illustrates the study and analysis of the networks’ dynamics, their temporal evolution and asymptotic behaviors.

Modeling multi-valued genetic regulatory networks using high-level petri nets

Regulatory networks are at the core of all biological functions from bio-chemical pathways to gene regulation and cell communication processes. Because of the complexity of the interweaving retroactions, the overall behavior is difficult to grasp and the development of formal methods is needed in order to confront the supposed properties of the biological system to the model. We revisit here the tremendous work of R. Thomas and show that its binary and also its multi-valued approach can be expressed in a unified way with high-level Petri nets. A compact modeling of genetic networks is proposed in which the tokens represent genes expression levels and their dynamical behavior depends on a certain number of biological parameters. This allows us to take advantage of techniques and tools in the field of high-level Petri nets. A developed prototype allows a biologist to verify systematically the coherence of the system under various hypotheses. These hypotheses are translated into temporal logic formulae and the model-checking techniques are used to retain only the models whose behavior is coherent with the biological knowledge.

Formal Methods for Modeling Biological Regulatory Networks

This chapter presents how the formal methods can be used to analyse biological regulatory networks, which are at the core of all biological phenomena as, for example, cell differentiation or temperature control. The dynamics of such a system, i.e. its semantics, is often described by an ordinary differential equation system, but has also been abstracted into a discrete formalism due to R. Thomas. This second description is well adapted to stateof-the-art measurement techniques in biology, which often provide qualitative and coarse-grained descriptions of biological regulatory networks. This formalism permits us to design a formal framework for analysing the dynamics of biological systems. The verification tools, as model checking, can then be used not only to verify if the modelling is coherent with known biological properties, but also to help biologists in the modelling process. Actually, for a given biological regulatory network, a large class of semantics can be automatically built and model checking allows the selection of the semantics, which are coherent with the biological requirement, i.e. the temporal specification. This modelling process is illustrated with the well studied genetic regulatory network controlling immunity in bacteriophage lambda.

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.

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.

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.

Pairwise sequence alignment using a PROSITE pattern-derived similarity score

Existing methods for alignments are based on edition costs computed additionally position by position, according to a fixed substitution matrix: a substitution always has the same weight regardless of the position. Nevertheless the biologist favours a similarity according to his knowledge of the structure or the function of the sequences considered. In the particular case of proteins, we present a method consisting in integrating other information, such as patterns of the PROSITE databank, in the classical dynamic programming algorithm. The method consists in making an alignment by dynamic programming taking a decision not only letter by letter as in the Smith & Waterman algorithm but also by giving a reward when aligning patterns.

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 () and not restored by 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.