Chemical Graph Transformation with Stereo-Information

Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their chemical activity may differ substantially. In this contribution we propose an extended chemical graph transformation system with attributes that encode information about local geometry. The modelling approach is based on the so-called ``ordered list method'', where an order is imposed on the set of incident edges of each vertex, and permutation groups determine equivalence classes of orderings that correspond to the same local spatial embedding. This method has previously been used in the context of graph transformation, but we here propose a framework that also allows for partially specified stereoinformation. While there are several stereochemical configurations to be considered, we focus here on the tetrahedral molecular shape, and suggest general principles for how to treat all other chemically relevant local geometries. We illustrate our framework using several chemical examples, including the enumeration of stereoisomers of carbohydrates and the stereospecific reaction for the aconitase enzyme in the citirc acid cycle.