Cayley Graphs of Semigroups Applied to Atom Tracking in Chemistry

TL;DR

This paper introduces a formal method using Cayley graphs of monoids to track atoms in complex chemical reactions, aiding in hypothesis generation and subsystem inference in biochemical networks.

Contribution

It presents a novel application of Cayley graphs to atom tracking in chemical reactions, enabling systematic analysis and inference of biochemical subsystems.

Findings

Analyzed carbon traces in the TCA cycle.

Inferred subsystems from Cayley graph projections.

Demonstrated the method's potential for reaction mechanism analysis.

Abstract

While atom tracking with isotope-labeled compounds is an essential and sophisticated wet-lab tool in order to, e.g., illuminate reaction mechanisms, there exists only a limited amount of formal methods to approach the problem. Specifically when large (bio-)chemical networks are considered where reactions are stereo-specific, rigorous techniques are inevitable. We present an approach using the right Cayley graph of a monoid in order to track atoms concurrently through sequences of reactions and predict their potential location in product molecules. This can not only be used to systematically build hypothesis or reject reaction mechanisms (we will use the ANRORC mechanism "Addition of the Nucleophile, Ring Opening, and Ring Closure" as an example), but also to infer naturally occurring subsystems of (bio-)chemical systems. Our results include the analysis of the carbon traces within the TCA cycle and infer subsystems based on projections of the right Cayley graph onto a set of relevant atoms.