Rule composition in graph transformation models of chemical reactions

Graph transformation form a natural model for chemical reaction systems and provide a su cient level of detail to track individual atoms. Among alternative graph transformation formalisms the Double Pushout approach, which is firmly grounded in category theory, is particularly well-suited as a model of chemistry. We explore here the formal foundations of defining composition of transformation rules using ideas from concurrency theory. In addition of a generic construction we consider several special cases that each have an intuitive chemical interpretation. We illustrate the usefulness of these specialised operations by automatically calculating coarse-grained transformation rules for complete chemical pathways, that preserve the traces of atoms through the pathways. This type of computation has direct practical relevance for the analysis and design of isotope labelling experiments.