Atom Mapping of Chemical of Chemical Reactions via Constraint Programming

A chemical reaction is a process of transforming one set of molecules (educts) into another set (products). In the course of a reaction, chemical bonds which hold the atoms together are redistributed, so that each atom in a reaction educt appears in a specific position of a reaction product. Tracing atoms between educts and products refers to a non-trivial problem in computational chemistry and system biology, namely the “Atom Mapping Problem”. Our determination of atom mappings relies on the existence of an imaginary transition state (ITS), in which reacting bonds (formed, broken) are arranged in a cyclic topology. Cyclic mechanisms are very common in chemistry and almost all elementary homovalent and ambivalent reactions feature a cyclic ITS. The used approach aims at the identification of the cyclic ITS, that imposes additional restrictions on the bijection between educt and product atoms. Once the cyclic ITS is fixed, the overall mapping is easily derived. For this purpose we use Constraint Programming and we show that it is a very promising approach to solve the atom mapping task. The constraint-based model enables the enumeration of atom maps for different cyclic mechanisms and layouts. We present a generic atom mapping framework which based on an encoding that is able to describe different elementary ITS layouts. The generic framework unifies several formulations required to identify different ITS arrangements and it is flexible to incorporate new ones. Our framework also features a method for symmetry exclusion in order to eliminate equivalent mappings and to produce only distinct reaction mechanisms. The performance of the approach is evaluated for a collection of chemical reactions from the KEGG LIGAND database for various ITS cycle layouts. One mapping for most test reactions is located within milliseconds which makes the Constraint Programming approach very appealing in this field.