Abstract Interpretation of Cellular Signalling Networks

Cellular signalling pathways, where proteins can form complexes and undergo a large array of post translational modifications are highly combinatorial systems sending and receiving extra-cellular signals and triggering appropriate responses. Process-centric languages seem apt to their representation and simulation [1,2,3]. Rule-centric languages such as κ [4,5,6,7,8] and BNG [9,10] bring in additional ease of expression. We propose in this paper a method to enumerate a superset of the reachable complexes that a κ rule set can generate. This is done via the construction of a finite abstract interpretation. We find a simple criterion for this superset to be the exact set of reachable complexes, namely that the superset is closed under swap, an operation whereby pairs of edges of the same type can permute their ends. We also show that a simple syntactic restriction on rules is sufficient to ensure the generation of a swap-closed set of complexes. We conclude by showing that a substantial rule set (presented in Ref. [4]) modelling the EGF receptor pathway verifies that syntactic condition (up to suitable transformations), and therefore despite its apparent complexity has a rather simple set of reachables.