Laurent Trilling

Applications of a formal approach to decipher discrete genetic networks.

BackgroundA growing demand for tools to assist the building and analysis of biological networks exists in systems biology. We argue that the use of a formal approach is relevant and applicable to address questions raised by biologists about such networks. The behaviour of these systems being complex, it is essential to exploit efficiently every bit of experimental information. In our approach, both the evolution rules and the partial knowledge about the structure and the behaviour of the network are formalized using a common constraint-based language.ResultsIn this article our formal and declarative approach is applied to three biological applications. The software environment that we developed allows to specifically address each application through a new class of biologically relevant queries. We show that we can describe easily and in a formal manner the partial knowledge about a genetic network. Moreover we show that this environment, based on a constraint algorithmic approach, offers a wide variety of functionalities, going beyond simple simulations, such as proof of consistency, model revision, prediction of properties, search for minimal models relatively to specified criteria.ConclusionsThe formal approach proposed here deeply changes the way to proceed in the exploration of genetic and biochemical networks, first by avoiding the usual trial-and-error procedure, and second by placing the emphasis on sets of solutions, rather than a single solution arbitrarily chosen among many others. Last, the constraint approach promotes an integration of model and experimental data in a single framework.

Automatic inference of regulatory and dynamical properties from incomplete gene interaction and expression data

Advanced mathematical methods and computational tools are required to properly understand the behavior of large and complex regulatory networks that control cellular processes. Since available data are predominantly qualitative or semi-quantitative, discrete (logical) modeling approaches are increasingly used to model these networks. Here, relying on the multilevel logical formalism developed by R. Thomas et al. [7,9,8], we propose a computational approach enabling (i) to check the existence of at least one consistent model, given partial data on the regulatory structure and dynamical properties, and (ii) to infer properties common to all consistent models. Such properties represent non trivial deductions and could be used by the biologist to design new experiments. Rather than focusing on a single plausible solution, i.e. a model fully defined, we consider the whole class of models consistent with the available data and some economy criteria, from which we deduce shared properties. We use constraint programming to represent this class of models as the set of all solutions of a set of constraints [3]. For the sake of efficiency, we have developed a framework, called SysBiOX, enabling (i) the integration of partial gene interaction and expression data into constraints and (ii) the resolution of these constraints in order to infer properties about the structure or the behaviors of the gene network. SysBiOX is implemented in ASP (Answer Set Programming) using Clingo [4].

Modélisation de réseaux biologiques discrets en programmation logique par contraintes

Computer tools are needed in systems biology to explore the behavioral properties of interaction networks in a context of incomplete and qualitative knowledge. We propose here an approach based on Logic Constraint Programming (CLP), which is combined with a discrete ion of the dynamics of interaction networks (namely the Thomas-Snoussi formalism, extended by H. de Jong, 2004) in order to assist the biologist in his work of qualitative data modeling and experiment design. Then we illustrate the flexibility of the approach with two biological applications.

Connections and Integration with SAT Solvers: A Survey and a Case Study in Computational Biology

Boolean constraints play a fundamental role in optimization and constraint satisfaction. The resolution of these constraints has been the subject of intense and successful work during the past decade, and SAT solvers have reached a spectacular maturity. This chapter gives a brief overview of the relevant literature on modern SAT solvers and on the recent efforts to better integrate Boolean reasoning with other constraint satisfaction techniques. As a case study that illustrates the use of SAT and CP, we consider an application in computational biology: the task to build gene regulatory networks (GRNs). We report on experiments made on this problem with a combined SAT/CP approach.

Formal Methods for Hopfield-Like Networks

Building a meaningful model of biological regulatory network is usually done by specifying the components (e.g. the genes) and their interactions, by guessing the values of parameters, by comparing the predicted behaviors to the observed ones, and by modifying in a trial-error process both architecture and parameters in order to reach an optimal fitness. We propose here a different approach to construct and analyze biological models avoiding the trial-error part, where structure and dynamics are represented as formal constraints. We apply the method to Hopfield-like networks, a formalism often used in both neural and regulatory networks modeling. The aim is to characterize automatically the set of all models consistent with all the available knowledge (about structure and behavior). The available knowledge is formalized into formal constraints. The latter are compiled into Boolean formula in conjunctive normal form and then submitted to a Boolean satisfiability solver. This approach allows to formulate a wide range of queries, expressed in a high level language, and possibly integrating formalized intuitions. In order to explore its potential, we use it to find cycles for 3-nodes networks and to determine the flower morphogenesis regulatory network of Arabidopsis thaliana. Applications of this technique are numerous and concern the building of models from data as well as the design of biological networks possessing specified behaviors.

A Logical Constraint-based Approach to Infer and Explore Diversity and Composition in Thresholded Boolean Automaton Networks.

Gene regulatory networks (GRN) are often modeled by Boolean networks to describe their structures and properties. Constraint logic programming (CPL) can be used to infer networks that satisfy constraints applied on their structure and their dynamics. Such approach yield complete satisfiable network sets that can be large. Having such complete sets allows to compare networks between each other and to understand how they can be constructed from other networks. In the present paper, we describe this inference approach applied to a particular class of thresholded Boolean automaton networks, a variation of Boolean neural networks, focusing on a necessary step to reduce the size of satisfiable sets to sets of non-redundant networks. For that purpose, we use a recent non-monotonic logic programming technology, namely Answer Set Programming (ASP). Our approach managed to yield complete network sets satisfying a given behavior, namely having a specific dynamics – a binary motif fixed in advance – on at least one node of networks of a given size. This allows us to illustrate how general rules could explain some relations of composition between these networks.

InterDB, a Prediction-Oriented Protein Interaction Database for C. elegans

Protein-protein interactions are critical to many biological processes, extending from the formation of cellular macromolecular structures and enzymatic complexes to the regulation of signal transduction pathways. With the availability of complete genome sequences, several groups have begun large-scale identification and characterization of such interactions, relying mostly on high-throughput two-hybrid systems. We collaborate with one such group, led by Marc Vidal, whose aim is the construction of a protein-protein interaction map for C. elegans. In this paper we first describe WISTdb, a database designed to store the interaction data generated in Marc Vidals laboratory. We then describe InterDB, a multi-organism prediction-oriented database of protein-protein interactions. We finally discuss our current approaches, based on inductive logic programming and on a data mining technique, for extracting predictive rules from the collected data.