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Section: New Results
Systems Biology
Analyzing SBGN-AF Networks Using Normal Logic Programs
A wide variety of signaling networks are available in the literature or in databases under the form of influence graphs. In order to understand the systems underlying these networks and to modify them for a medical purpose, it is necessary to understand their dynamics. Consequently, a variety of modelling techniques for these networks have been developped. In particular, it is possible to model their dynamical behavior with Boolean networks. The construction of these Boolean networks starting from influence graphs requires a parametrization of some Boolean functions. This task is most often realized by interpreting experimental results, that can be hard to obtain.
We introduced a method that allows to model any influence graph expressed in the Systems Biology Graphical Notation Activity Flow language (SBGN-AF) under the form of a Boolean network [32] , [29] . The parametrization does not rely on any experimental results but on general principles that govern the dynamics of signaling networks. Together with the translation of a SBGN-AF influence graph into predicates, these general principles expressed under the form of logic rules form a first-order normal logic program (NLP) equivalent to a Boolean network. We show that the trajectories as well as the steady-state of any SBGN-AF network can be obtained by computing the orbits and the supported models of its corresponding NLP, respectively.
Scalable methods for analysing dynamics of automata networks
In collaboration with T. Chatain, S. Haar, S. Schwoon, and L. Jezeguel (Inria MExICo ), we explored new techniques for computing the reachable attractors in automata networks using Petri net unfoldings [22] . Attractors of network dynamics represent the long-term behaviours of the modelled system. Their characterization is therefore crucial for understanding the response and differentiation capabilities of a dynamical system. In the scope of qualitative models of interaction networks, the computation of attractors reachable from a given state of the network faces combinatorial issues due to the state space explosion. Our new algorithm relies on Petri net unfoldings that can be used to compute a compact representation of the dynamics, in particular by exploiting the concurrency of the transitions in order to remove redundant sequences of transitions. We illustrate the applicability of the algorithm with Petri net models of cell signalling and regulation networks, Boolean and multi-valued. The proposed approach aims at being complementary to existing methods for deriving the attractors of Boolean models, while being generic since it actually applies to any safe Petri net.
In collaboration with M. Folschette, M. Magnin, O. Roux (IRCCyN , Nantes), and K. Inoue (Nii , Tokyo), we developed a framework for identifying classical Boolean or discrete networks models from Proces Hitting (PH) models [10] . The PH allows to model non-deterministic cooperations between interacting components, and we have shown that the dynamics of a single PH can embed (include) the dynamics of multiple discrete networks, where transitions functions are deterministic. Hence, if a behaviour is shown impossible at the PH model, it is necessary impossible in any included discrete models. Such kind of analysis is relevant in systems biology, where the cooperations between components are often under-determined and the enumeration of all compatible discrete models is intractable: our framework allows to reason on the dynamics of a single abstract model.
Finally, a chapter summarizing the recent advances on static analysis for dynamics of large biological networks has been published as part of the Logical Modeling of Biological Systems handbook [30] .