Section: New Results

Analysis of gene regulatory networks by means of piecewise-linear (PL) models

Genetic Network Analyzer (GNA) is a tool for the qualitative modeling and simulation of the dynamics of gene regulatory networks by means of PL models, as described in Section  5.1 . GNA has been integrated with the other bioinformatics tools distributed by Genostar (http://www.genostar.com/ ). Version 8.4 of GNA was released by IBIS and Genostar this year. This version is an update of version 8.0, deposited at the Agence pour la Protection des Programmes (APP). Some bugs have been corrected in the new version and the program has been adapted to the latest versions of Java and the software platform of Genostar. A book chapter describing the current version of GNA has been published in a volume on the modeling of bacterial molecular networks [13] . The chapter is a tutorial illustrating the practical use of recent functionalities of GNA like the network editor and the formal verification module by means of an example network in E. coli.

The predictions obtained with the help of GNA are purely qualitative, describing the dynamics of the network by means of a state transition graph. While a qualitative analysis is appropriate for certain problems, the absence of precise quantitative predictions may not be desirable in others, such as the analysis of a limit cycle or the design of a controller for a synthetic network. The quantitative study of PL models of gene regulatory networks is hindered by the fact that the step functions describing the logic of regulatory interactions lead to discontinuities in the right-hand side of the PL models (Section  3.2 ). This has motivated extensions of the PL models based on differential inclusions and Filippov solutions. As of now, no numerical simulation tool for the simulation of these Filippov extensions is available. In collaboration with the BIPOP project-team, we have shown how tools developed for the simulation of nonsmooth mechanical, electrical and control systems can be adapted for this purpose. A paper describing these results is being prepared for submission.