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Cayley Graphs of Semigroups Applied to Atom Tracking in Chemistry
Nikolai Nøjgaard1, Walter Fontana2, Marc Hellmuth3
1Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark.
Summary
We developed a formal method using Cayley graphs to track atoms in complex biochemical reactions. This approach aids in predicting product locations and analyzing metabolic pathways like the tricarboxylic acid cycle.
Area of Science:
- Biochemistry
- Computational Chemistry
- Systems Biology
Background:
- Atom tracking with isotope-labeled compounds is crucial for understanding reaction mechanisms.
- Limited formal methods exist for rigorous atom tracking in complex, stereospecific biochemical networks.
Purpose of the Study:
- To present a novel formal method for concurrent atom tracking through reaction sequences.
- To predict atom locations in product molecules and analyze biochemical systems.
Main Methods:
- Utilizing the right Cayley graph of a monoid for formal atom tracking.
- Applying the method to analyze the ANRORC mechanism and the tricarboxylic acid cycle.
Main Results:
- Demonstrated concurrent atom tracking through reaction sequences.
- Successfully predicted potential atom locations in product molecules.
- Analyzed carbon atom traces in the tricarboxylic acid cycle and inferred subsystems.
Conclusions:
- The Cayley graph approach provides a rigorous technique for atom tracking in complex biochemical systems.
- This method can systematically generate or refute hypotheses about reaction mechanisms.
- It enables the inference of naturally occurring subsystems within biochemical networks.
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