Jérôme Feret 

INRIA

Title: Formal model reduction

Abstract: Modelers of molecular signaling networks must cope with the
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
differnt 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.