Efficient Heuristics for Maximum Common Substructure Search

Abstract

Maximum common substructure search is a computationally hard optimization problem with diverse applications in the field of cheminformatics, including similarity search, lead optimization, molecule alignment, and clustering. Most of these applications have strict constraints on running time, so heuristic methods are often preferred. However, the development of an algorithm that is both fast enough and accurate enough for most practical purposes is still a challenge. Moreover, in some applications, the quality of a common substructure depends not only on its size but also on various topological features of the one-to-one atom correspondence it defines. Two state-of-the-art heuristic algorithms for finding maximum common substructures have been implemented at ChemAxon Ltd., and effective heuristics have been developed to improve both their efficiency and the relevance of the atom mappings they provide. The implementations have been thoroughly evaluated and compared with existing solutions (KCOMBU and Indigo). The heuristics have been found to greatly improve the performance and applicability of the algorithms. The purpose of this paper is to introduce the applied methods and present the experimental results.

When Does Chemical Elaboration Induce a Ligand To Change Its Binding Mode?

“…By examination of a number of chemical structures with high substructure scores, we determined that B was almost inevitably a substructure of A if the score was above 0.9. To test this cutoff value, we later evaluated each pair using the MCS (Maximum Common Substructure) tool implemented in ChemAxon 48 . The MCS is defined as the largest subgraph shared by graphs representing the chemical structures of the large and small ligands; similarity between the graph of the smaller ligand and the shared subgraph implies that the smaller ligand is indeed a substructure of the larger ligand.…”

“…This computational solvent mapping server carries out global docking using 16 distinct small molecule probes, then reports consensus clusters at which many overlapping probe molecules are found. In parallel, we used the MCS (maximum common substructure) tool implemented in ChemAxon 48 to identify the portion of the larger ligand’s chemical structure that is common to both the larger and smaller ligands in our pair.…”

“…We next used the MCS tool implemented in ChemAxon 48 to identify the pairs of corresponding atoms that comprise the maximum common structure (MCS) between the chemical structures of the two ligands. Using a custom script developed in the MMTSB toolset 56 , we superposed the three-dimensional structure of the larger ligand onto the smaller ligand, by RMSD alignment of the shared substructure.…”

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

“…Both approaches are described for undirected, unlabelled graphs; their extension to richer graphs is discussed in section 2.3. Other approaches have been tried, mixed integer programming [37] and heuristics [17]; SAT encodings seem to struggle even for subgraph isomorphism [31].…”

Enumerating common molecular substructures

“…In this setting, common molecular substructures correspond to common connected induced subgraphs, which gives rise to the computational problem of finding a maximum common connected induced subgraph (MCCIS) of two input molecular graphs. Many heuristics (Rahman et al, 2009;Englert and Kovács, 2015) and exact approaches (McCreesh et al, 2016;Droschinsky et al, 2017) have been proposed for MCCIS. A frequent variant of MCCIS is to enumerate all maximal common connected induced subgraphs, which we refer to as MCCIS-E. Koch (2001) proposed an exact algorithm for MCCIS-E.…”