Formal Reduction for Rule-based Models

Molecular biological models usually suffer from a large combinatorial explosion. Indeed, proteins form complexes and modify each others, which leads to the formation of a huge number of distinct chemical species (i.e. non-isomorphic connected components of proteins). Thus we cannot generate explicitly the quantitative semantics of these models, and even less compute their properties.In this paper we propose a formal framework to automatically reduce the combinatorial complexity of the differential semantics of rule-based models. Our reduction is based on two abstractions, which are combined thanks to a generic product. The first abstraction tracks the flow of information between the different regions of chemical species, so as to detect and abstract away some useless correlations between the state of sites. The second abstraction detects pairs of sites having the same capabilities of interaction, and abstracts away any distinction between them. The initial semantics and the reduce one are formally related by Abstract Interpretation.