Combining Graph Transformations and Semigroups for Isotopic Labeling Design

Representing Catalytic Mechanisms with Rule Composition

An "imaginary transition structure" overlays the molecular graphs of the educt and product sides of an elementary chemical reaction in a single graph to highlight the changes in bond structure. We generalize this idea to reactions with complex mechanisms in a formally rigorous approach based on composing arrow-pushing steps represented as graph-transformation rules to construct an overall composite rule and a derived transition structure. This transition structure retains information about transient bond changes that are invisible at the overall level and can be constructed automatically from an existing database of detailed enzymatic mechanisms. We use the construction to (i) illuminate the distribution of catalytic action across enzymes and substrates and (ii) to search in a large database for reactions of known or unknown mechanisms that are compatible with the mechanism captured by the constructed composite rule.

Cayley Graphs of Semigroups Applied to Atom Tracking in Chemistry

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.