Section: New Results

Rule-based modeling

Reachability analysis via orthogonal sets of patterns

Participants : Kim Quyên Ly, Jérôme Feret [correspondant] .

Rule-based modeling languages, as Kappa, allow for the description of very detailed mechanistic models. Yet, as the rules become more and more numerous, there is a need for formal methods to enhance the level of confidence in the models that are described with these languages. We develop abstract interpretation tools to capture invariants about the biochemical structure of bio-molecular species that may occur in a given model. In previous works, we have focused on the relationships between the states of the sites that belong to a same instance of a protein. This comes down to detect for a specific set of patterns, which ones may be reachable during the execution of the model. This paper [6], we generalize this approach to a broader family of abstract domains, that we call orthogonal sets of patterns. More precisely, an orthogonal set of patterns is obtained by refining recursively the information about some patterns containing a given protein, so as to partition of the set of occurrences of this protein in any mixture.

Local traces: an over-approximation of the behaviour of the proteins in rule-based models

Participants : Kim Quyên Ly, Jérôme Feret [correspondant] .

Thanks to rule-based modelling languages, we can assemble large sets of mechanistic protein-protein interactions within integrated models. Our goal would be to understand how the behaviour of these systems emerges from these low-level interactions. Yet this is a quite long term challenge and it is desirable to offer intermediary levels of abstraction, so as to get a better understanding of the models and to increase our confidence within our mechanistic assumptions. In this paper [5], we propose an abstract interpretation of the behaviour of each protein, in isolation. Given a model written in Kappa, this abstraction computes for each kind of protein a transition system that describes which conformations this protein can take and how a protein can pass from one conformation to another one. Then, we use simplicial complexes to abstract away the interleaving order of the transformations between conformations that commute. As a result, we get a compact summary of the potential behaviour of each protein of the model.