Cayley Graphs of Semigroups Applied to Atom Tracking in Chemistry

Nikolai Nøjgaard, Walter Fontana, Marc Hellmuth, Daniel Merkle*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


While atom tracking with isotope-labeled compounds is an essential and sophisticated wet-lab tool to, for example, 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 stereospecific, rigorous techniques are inevitable. We present an approach using the right Cayley graph of a monoid 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 tricarboxylic acid cycle and infer subsystems based on projections of the right Cayley graph onto a set of relevant atoms.

Original languageEnglish
JournalJournal of Computational Biology
Issue number7
Pages (from-to)701-715
Publication statusPublished - Jul 2021

Bibliographical note

Publisher Copyright:
© Copyright 2021, Mary Ann Liebert, Inc., publishers 2021.


  • algorithmic cheminformatics
  • chemical reaction networks
  • computational biology
  • double pushout
  • graph transformations


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