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. We present a formal (and automated) abstract interpretation-based method for constructing a coarse-grained and self-consistent dynamical system aimed at molecular patterns that are distinguishable by the dynamics of the original system as posited by the rules. The method is formally sound and never requires the execution of the rule-based model. The coarse-grained variables do not depend on the values of the rate constants appearing in the rules, and typically form a system of greatly reduced dimension that can be amenable to numerical integration and further model reduction techniques.