Local Traces: An Over-Approximation of the Behavior of the Proteins in Rule-Based Models

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 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. 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.