Rule-based modeling highlights the Combinatorics aspects of signaling. But in what sense might these aspects be important for cellular processes ? It's not clear, for example, whether the exact combination of phosphorylated residues on a protein is critical for information processing or propagation, or whether it's just the overall amount of phosphorylation that matters on the basis of the change in the protein's overall electrostatic charge. The level of abstraction at which the Kappa language was conceived is not ideal for expressing the combinatorial state within a (protein) agent ; on the other hand, it is exceptionally well suited to expressing the combinatorics of binding interactions in a complex of protein agents. It is well known that the protein-protein interactions underlying cell signalling are moderated by a variety of scaffolding proteins that bring together enzymes and their substrates.
Recent modeling efforts suggest that scaffold assembly may be a process where Combinatorics elements can have a substantial impact that can be adequately represented in Kappa. The Combinatorics aspect comes into play when scaffold proteins can come together. A connected set of reunited proteins can form a network or surface bringing together many instances of an enzyme with many instances of a substrate, thus greatly increasing their local interaction frequency and hence catalytic rate.
In the particular case where the scaffold consists of linear polymers, the catalytic rate in equilibrium can be calculated exactly as a function of affinity and abundance of scaffold monomers for the continuous case (concentrations) and the discrete case (particle numbers). All grouped interactions are subject to an effect (" the prozone effect "), in which low scaffold concentrations favor interactions between ligands, while high concentrations oppose them by isolating ligands on different scaffold molecules. The advantage of a polymeric system is that the catalytic rate can be easily regulated and that Combinatorics strongly attenuates the prozone effect. By bringing proteins of distinct origins into interaction, scaffold aggregates could prove essential for combining information from different signaling pathways.
