# Computing double-pushout graph transformation rules and atom-to-atom maps from KEGG RCLASS data

## TL;DR

This paper introduces a tool called laveau that converts KEGG RCLASS data into atom-to-atom maps and DPO rules, enabling better modeling of metabolic reactions.

## Contribution

The novel contribution is a method to compute DPO rules and atom-to-atom maps from KEGG RCLASS data, which were previously difficult to use for such purposes.

## Key findings

- The laveau tool successfully generated 1232 DPO rules and 1594 atom-to-atom maps from 3195 RCLASSes.
- The method combines RDM pattern graphs into subgraphs of reactants and products, preserving atom correspondences.
- The results provide a crucial resource for atom-level modeling of enzyme-catalyzed reactions in metabolic networks.

## Abstract

Atom-to-atom maps play an important role in many applications. However, they are often difficult to obtain. The KEGG reaction database does not provide atom-to-atom maps for its reactions and instead offers a description of local changes for pairs of reactant and product molecules in terms of so-called RCLASSes. Developed for classification purposes, RCLASS data are difficult to use for purposes such as the construction of atom-to-atom maps or reaction rules. DPO graph transformation rules, on the other hand, work as a convenient and efficient representation, particularly for these applications. The RCLASS data can be understood as collections of local graph patterns in the reactants and products of a reaction, together with partial correspondences of atoms. The problem of converting RCLASS data into DPO rules, therefore, is a special case of the graph reconstruction problem, which consists of inferring a graph from a collection of subgraphs.

We developed laveau, a tool that computes explicit DPO rules from KEGG reactions and RCLASS data. The algorithm proceeds stepwise, starting with a translation of individual RDM codes, specifically developed by the KEGG database, into equivalent RDM pattern graphs. Multiple RDM pattern graphs for the same RCLASS are then combined based on their embeddings into the reactant and product molecules, observing certain consistency conditions. In the final step, these combined pairwise patterns are merged into a pair of subgraphs of reactants and products, respectively. If RCLASSes connecting all pairs of reactant and product molecules are available, the complete reaction center(s) is/are contained in the union of these subgraphs. The atom-to-atom map inherited from the RDM codes then defines a DPO transformation rule. Application of these rules to the reactants then yields complete atom-to-atom maps (AAMs). Starting from 3195 RCLASSes, laveau generates a total of 1232 DPO rules and 1594 AAMs.

The laveau software makes it possible to extract local atom-to-atom maps from the RCLASSes of the KEGG database, covering a large set of enzyme-catalyzed reactions. The results are made available in the form of DPO rules for use in atom-level models of metabolic networks, filling a crucial gap in the available data.