Representing catalytic mechanisms with rule composition

• Main Authors: Andersen, Jakob L, Fagerberg, Rolf, Flamm, Christoph, Fontana, Walter, Kolčák, Juri, Laurent, Christophe V. F. P, Merkle, Daniel, Nøjgaard, Nikolai
• Format: Journal Article
• Language: English
• Published: 12-01-2022
• Subjects: Computer Science - Discrete Mathematics; Physics - Chemical Physics; Quantitative Biology - Molecular Networks
• DOI: 10.48550/arxiv.2201.04515

Reaction mechanisms are often presented as sequences of elementary steps,
such as codified by arrow pushing. We propose an approach for representing such
mechanisms using graph transformation. In this framework, each elementary step
is a rule for modifying a molecular graph and a mechanism is a sequence of such
rules. To generate a compact representation of a multi-step reaction, we
compose the rules of individual steps into a composite rule, providing a
rigorous and fully automated approach to coarse-graining. While the composite
rule retains the graphical conditions necessary for the execution of a
mechanism, it also records information about transient changes not visible by
comparing educts and products. By projecting the rule onto a single "overlay
graph", we generalize Fujita's idea of an Imaginary Transition Structure from
elementary reactions to composite reactions. The utility of the overlay graph
construct is exemplified in the context of enzyme-catalyzed reactions. In a
first application, we exploit mechanistic information in the Mechanism and
Catalytic Site Atlas to construct overlay graphs of hydrolase reactions listed
in the database. These graphs point at a spectrum of catalytic entanglement of
enzyme and substrate, de-emphasizing the notion of a singular catalyst in favor
of a collection of catalytic sites that can be distributed across enzyme and
substrate. In a second application, we deploy composite rules to search the
Rhea database for reactions of known or unknown mechanism that are, in
principle, compatible with the mechanisms implied by the composite rules. We
believe this work adds to the utility of graph-transformation formalisms in
representing and reasoning about chemistry in an automated yet insightful
fashion.