Local Traces: An Over-Approximation of the Behaviour of the Proteins in Rule-Based Models
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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, 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.
KeywordsTransition System Simplicial Complex Local Transition Agent Type Concurrent System
This work has been motivated by models written by Héctor Medina, and by Nathalie Théret and Jean Cocquet. We deeply thank them, as well as Pierre Boutillier, Ioana Cristescu, Vincent Danos, Walter Fontana, Russ Harmer, Jean Krivine, Jonathan Laurent, and Jean Yang, for fruitful discussions.
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