Section: New Results

Static analysis of rule-based models

Thanks to rule-based modeling languages, we can assemble large sets of mechanistic protein-protein interactions within integrated models. Our goal would be to understand how the behavior 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. To this extend, static analysis can be used to derive various abstractions of the semantics, each of them offering new perspectives on the models.

Trace approximation

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

In [13], we propose an abstract interpretation of the behavior of each protein, in isolation. Given a model written in Kappa, this abstraction computes for each kind of proteins a transition system that describes which conformations this protein may take and how a protein may 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 behavior of each protein of the model.

Detection of polymer formation

Participants : Pierre Boutillier, Aurélie Faure de Pebeyre, Jérôme Feret [correspondant] .

Rule-based languages, such as Kappa and BNGL, allow for the description of very combinatorial models of interactions between proteins. A huge (when not infinite) number of different kinds of bio-molecular compounds may arise due to proteins with multiple binding and phosphorylation sites. Knowing beforehand whether a model may involve an infinite number of different kinds of bio-molecular compounds is crucial for the modeler. On the first hand, having an infinite number of kinds of bio-molecular compounds is sometimes a hint for modeling flaws: forgetting to specify the conflicts among binding rules is a common mistake. On the second hand, it impacts the choice of the semantics for the models (among stochastic, differential, hybrid).

In [22], we introduce a data-structure to abstract the potential unbounded polymers that may be formed in a rule-based model. This data-structure is a graph, the nodes and the edges of which are labeled with patterns. By construction, every potentially unbounded polymer is associated to at least one cycle in that graph. This data-structure has two main advantages. Firstly, as opposed to site-graphs, one can reason about cycles without enumerating them (by the means of Tarjan's algorithm for detecting strongly connected components). Secondly, this data-structures may be combined easily with information coming from additional reachability analysis: the edges that are labeled with an overlap that is proved unreachable in the model may be safely discarded.

The static analyzer KaSa

Participants : Pierre Boutillier, Ferdinanda Camporesi, Jean Coquet, Jérôme Feret [correspondant] , Kim Quyên Lý, Nathalie Théret, Pierre Vignet.

KaSa is a static analyzer for Kappa models. Its goal is two-fold. Firstly, KaSa assists the modeler by warning about potential issues in the model. Secondly, KaSa may provide useful properties to check that what is implemented is what the modeler has in mind and to provide a quick overview of the model for the people who have not written it. The cornerstone of KaSa is a fix-point engine which detects some patterns that may never occur whatever the evolution of the system may be. From this, many useful information may be collected KaSa warns about rules that may never be applied, about potential irreversible transformations of proteins (that may not be reverted even thanks to an arbitrary number of computation steps) and about the potential formation of unbounded molecular compounds. Lastly, KaSa detects potential influences (activation/inhibition relation) between rules.

In [21], we illustrate the main features of KaSa on a model of the extracellular activation of the transforming growth factor, TGF-b.