The lecture introduces the idea of describing molecular systems in terms of graph transformations or rules. By not making mechanistic details explicit, classical models in the 3 lecture can easily be used to mimic many cellular behaviors. However, mechanistic details can have significant consequences and cannot simply be tuned as rate constants. Moreover, combinatorics complexity due to post-translational modification and complex formation is ubiquitous.
In order to understand the mechanistic and Combinatorics aspects of molecular biology, a recent framework known as Kappa proposes to represent protein-protein interactions along the lines of symbolic chemistry, where molecules are graphs on top of typed atoms. Chemistry distinguishes between a rule (or diagram) and a reaction. In a reaction, the molecules are completely specified, whereas a rule makes explicit only those aspects of the molecules that are necessary for a reaction to occur. Consequently, a rule represents the transformation of a graph schema. If the pattern is contained in a molecular combination, the rule applies and generates a reaction. In Kappa, we speak of proteins as agents that have ports or sites carrying a state (e.g. phosphorylation), and on which agents interact as specified by rules. Rules are informed by biophysical and biochemical findings, but express them in an abstract transactional way. For a rule to induce dynamics, it must be equipped with one or two stochastic rate constants, depending on whether it applies in an intra- or intermolecular context.
These constants are probability rates that depend on the reaction volume and are important parameters for the Kappa simulator. The simulator implements a continuous-time Markov chain of rule applications that cause the content of a molecular mixture to evolve. In essence, the rule-based approach treats a model as a program written in a graphical language that defines a minimal notion of local mechanism. In addition to the simulator, the Kappa platform implements a static analyzer, causal analysis tools and a basic graphical user interface for all major operator systems.
