Formal model reduction

Rule-based modeling provides a very compact representation for protein-protein interaction networks, which emphasizes the biochemical structure of chemical complexes. We track the flow of information throughout these biochemical structures so as to deduce a coarse-graining of the underlying ODE systems.

Combinatorial explosion of protein states generated by post-translational modifications and complex formation. Rule-based models provide a powerful alternative to approaches that require an explicit enumeration of all possible molecular species of a system. Such models consist of formal rules stipulating the (partial) contexts for specific protein-protein interactions to occur. These contexts specify molecular patterns that are usually less detailed than molecular species. Yet, the execution of rule-based dynamics requires stochastic simulation, which can be very costly. It thus appears desirable to convert a rule-based model into a reduced system of differential equations by exploiting the lower resolution at which rules specify interactions.

In this talk, we present a formal framework for constructing coarse-grained systems. We track the flow of information between different regions of chemical species, so as to detect and abstract away some useless correlations between the state of sites of molecular species.

The result of our abstraction is a set of molecular patterns, called fragments, and a system which describes exactly the concentration (or population) evolution of these fragments. The method never requires the execution of the concrete rule-based model and the soundness of the approach is described and proved by abstract interpretation.