Maximum symmetrical split of molecular graphs. Application to organic synthesis design

Whereas the potential symmetry of a molecule may be a feature of importance in synthesis design, this one is often difficult to detect visually in the structural formula. In the present article, we describe an efficient algorithm for the perception of this molecular property. We have addressed this problem in terms of graph theory and defined it as the Maximum Symmetrical Split of a molecular graph. A solution is obtained by deleting in such a graph a minimum number of edges and vertices so that the resulting subgraph consists of exactly two isomorphic connected components that correspond to a pair of synthetically equivalent synthons. In view to reduce the search space of the problem, we have based our algorithm on CSP techniques. In this study, we have found that the maximum symmetrical split is an original kind of Constraint Satisfaction Problem. The algorithm has been implemented into the RESYN_Assistant system, and its performance has been tested on a set of varied molecules which were the targets of previously published synthetic studies. The results show that potential symmetry is perceived quickly and efficiently by the program. The graphical display of this perception information may help a chemist to design reflexive or highly convergent syntheses.