Alignment of three-dimensional molecules using an image recognition algorithm

This paper describes a novel approach, based on image recognition in two dimensions, for the atom-based alignment of two rigid molecules in three dimensions. The atoms are characterised by their partial charges and their positions relative to the remaining atoms in the molecule. Based on this information, a cost of matching a pair of atoms, one from each molecule, is assigned to all possible pairs. A preliminary set of intermolecular atom equivalences that minimises the total atom matching cost is then determined using an algorithm for solving the linear assignment problem. Several geometric heuristics are described that aim to reduce the number of atom equivalences that are inconsistent with the 3D structures. Those that remain are used to calculate an alignment transformation that achieves an optimal superposition of atoms that have a similar local geometry and partial charge. This alignment is then refined by calculating a new set of equivalences consisting of atom pairs that are approximately overlaid, irrespective of partial charge. A range of examples is provided to demonstrate the efficiency and effectiveness of the method.