Pathway Realizability in Chemical Networks

The exploration of pathways and alternative pathways that have a specific function is of interest in numerous chemical contexts. A framework for specifying and searching for pathways has previously been developed, but a focus on which of the many pathway solutions are realizable, or can be made realizable, is missing. Realizable here means that there actually exists some sequencing of the reactions of the pathway that will execute the pathway. We present a method for analyzing the realizability of pathways based on the reachability question in Petri nets. For realizable pathways, our method also provides a certificate encoding an order of the reactions, which realizes the pathway. We present two extended notions of realizability of pathways, one of which is related to the concept of network catalysts. We exemplify our findings on the pentose phosphate pathway. Furthermore, we discuss the relevance of our concepts for elucidating the choices often implicitly made when depicting pathways. Lastly, we lay the foundation for the mathematical theory of realizability.