Section: New Results
Methods: Analysis, simulation, and identification of bacterial regulatory networks
Our efforts focused on several on-going projects around the development of methods and tools for the analysis of bacterial regulatory networks: (i) the development of the tool GNA into an integrated modeling and simulation environment, including network definition and formal verification modules, and (ii) the structural and parametric identification of the networks.
Integrated modeling, simulation, analysis, and verification in GNA
Within the framework of two European projects, COBIOS and EC-MOAN (Section 8.2 ), IBIS has continued to extend the Genetic Network Analyzer (GNA) modeling and simulation tool. GNA uses PL models to qualitatively model the dynamics of genetic regulatory networks (Section 5.1 ).
In the EC-MOAN project, we have continued to make formal verification technology available to the users of GNA, in collaboration with Radu Mateescu of the VASY project-team. We have notably finished the extension of GNA with a formal verification module that allows the user to specify dynamic properties of genetic regulatory networks by means of so-called patterns, high-level query templates that capture recurring questions of biological interest. The patterns can be automatically translated to temporal logic, for instance the CTRL (Computation Tree Regular Logic) that Pedro Monteiro developed in the framework of his PhD thesis. The formal verification module allows the user of GNA to have access to formal verification tools through a service-oriented architecture. This architecture, which has been completely implemented by Estelle Dumas, Pedro Monteiro, and Michel Page, integrates modeling and simulation clients like GNA to model-checker servers, via an intermediate request manager. In particular, the client can perform formal verification requests through the web, which the request manager dispatches to an appropriate model-checker server. When the model-checker server has answered the request, the results are sent back to the client for display and further analysis in the graphical user interface of the tool. The service-oriented architecture is modular and general, and has the advantage of reusing existing formal verification technology as much as possible. In collaboration with Gregor Goessler (POP-ART) and Grégory Batt (CONTRAINTES), we have developed efficient, implicit encodings of the state transition graphs representing the qualitative network dynamics, so as to optimize the interactions between GNA and the model-checker servers. These implicit encoding are currently being exploited for the development of methods for the verification of incompletely specified PL models of genetic regulatory networks.
Version 7 of GNA which includes the connection with model-checking tools through the service-oriented architecture, has been deposited at the Agence pour la Protection des Programmes (APP) and released in the summer of 2009. A paper for BMC Bioinformatics on GNA 7, which illustrated its use for the qualitative analysis of the E. coli carbon starvation network (Section 6.1 ), was accepted this year [5] . In parallel, a paper on the use of the temporal logic CTRL for the formal verification of genetic regulatory logic is under revision for a special journal issue associated with the conference Computational Methods in Systems Biology, which was held in Rostock in 2008. We also finished a chapter on version 7 of GNA that will be published in a forthcoming book volume on the modeling of bacterial molecular networks [13] .
In the COBIOS project, IBIS and Genostar jointly developed a conceptual model to represent bacterial regulatory networks. The model has been implemented into a library called IogmaNetwork , using the underlying entity-relationship data and knowledge model of Genostar's Iogma platform. This work has notably involved Bruno Besson, Hidde de Jong, Michel Page, François Rechenmann, and engineers of Genostar. In the period covered by this report, IBIS contributed to the test, debugging, and extension of this library, among other things assuring the compatibility with the Systems Biology Graphical Notation (SBGN) standard. A stable version of the library has been completed. Most of the work in COBIOS, however, has concerned the integration of the IogmaNetwork library as a network editor into GNA. The aim is to support the entire modeling process from the structural definition or design of networks to their simulation and analysis within a single environment. Moreover, the integration of the IogmaNetwork library allows the user of GNA to access other modules in the Iogma environment, such as PathwayExplorer. The integration has involved a complete reorganization of the architecture of GNA and the development of a new graphical user interface. This allows the modeler to flexibly move back and forth between the definition of a network, the reduction of this network to a form compatible with the piecewise-linear models supported by GNA, and the semi-automatic translation of the network structure into a model. A version of GNA including the network editor will be available by the end of the COBIOS project in 2010.
Identification of bacterial regulatory networks
The work on PL models and GNA has been inspired by the fact that in most cases only steady-state, discrete-type experimental data is available, providing a qualitative description of the system dynamics. Modern experimental techniques are increasingly providing high-quality, time-course observations of the network dynamics and are thus paving the way for the use of quantitative models (Section 3.1 ). A major problem is the identification of such quantitative models from the data, either estimating parameter values or inferring the structure of the network. In addition to using standard heuristic techniques for system identification, several novel methods for the identification of bacterial regulatory networks are under development within IBIS.
A first effort in this direction has been carried out in the context of the ANR project MetaGenoReg (Section 8.1 ), led by Daniel Kahn (BAMBOO). Matteo Brilli (BAMBOO) has developed an approximate model of central metabolism of E. coli , using so-called linlog functions to approximately describe the rates of the enzymatic reactions. We use metabolome and transcriptome data sets from MetaGenoReg partners and the literature to estimate the parameters of the linlog models, a task greatly simplified by the mathematical form of the latter. One of the problems encountered is the occurrence of missing data, due to experimental problems or instrumental failures. We try to address the problem of missing data using approaches from the statistical literature based on EM algorithms. The objective is to ultimately integrate the resulting model of metabolism, assumed to be at quasi-steady state, into a kinetic model describing the regulation of gene expression. The model reduction and parameter estimation challenges encountered in this context form the subject of the PhD thesis of Sara Berthoumieux.
While this approach is mostly concerned with parametric identification, a second effort addresses the combined structural and parametric identification of bacterial regulatory networks from times-series data, continuing ideas originally developed in the HYGEIA project. Eugenio Cinquemani, who joined IBIS in November 2009, has continued a collaboration with Giancarlo Ferrari-Trecate (University of Pavia, Italy) and Riccardo Porreca (ETH Zürich, Switzerland). We consider the problem of learning ODE models where regulatory interactions are captured by sums and products of sigmoidal nonlinearities. To this end, statistical regression and hypothesis testing tools for the identification of best fitting models of appropriate complexity are used. One major challenge is the intractable number of alternative model structures that should be compared on the basis of the data. We are developing methods for the a priori selection of the most relevant model structures based on the use of biological knowledge and on a data preprocessing step inspired by model verification. An article on this work is currently under submission.
