Pathway Realisability in Chemical Networks

TL;DR

This paper introduces a Petri net-based method to determine the realisability of chemical pathways, providing certificates for realizability and exploring extended notions related to network catalysts, with applications to the pentose phosphate pathway.

Contribution

It presents a novel approach to assess pathway realisability in chemical networks using Petri nets, including certificates and extended concepts, advancing the theoretical framework.

Findings

Method for analyzing pathway realisability using Petri nets

Certificates encoding reaction sequences for realizable pathways

Application to the pentose phosphate pathway

Abstract

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 realisable, or can be made realisable, is missing. Realisable here means that there actually exists some sequencing of the reactions of the pathway that will execute the pathway. We present a method for analysing the realisability of pathways based on the reachability question in Petri nets. For realisable pathways, our method also provides a certificate encoding an order of the reactions which realises the pathway. We present two extended notions of realisability 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 realisability.