Using Graph Cliques to Compute combined 2D & 3D Molecule similarity.

Many molecular hunters prefer ligand based similarity searching methods as a virtual screening tool , to identify those structures that are most likely to bind to a drug target, typically a protein receptor or enzyme or search for similar structures by pharmacophoric properties , 3D shape , scaffolds or in context of graphs similar graphs.

In graph theory, a clique is a subset of vertices that form a complete subgraph, meaning that every pair of distinct vertices in the clique is adjacent (connected by an edge). A maximum clique (or max clique) is a clique of the largest possible size in a given graph. This means that it is not contained within any larger clique. A maximal clique is unique in its neighborhood but might not be the largest in the overall graph. If you want to understand graph concepts there is nice channel at youtube.

This post is inspired by the paper LiSica which was developed based on clique concepts to implement similarity search by 2D and 3D. The 3D search is implemented as an non alignment based search method which utilizes conformations. However, i wont be doing this here i will use a random seed to generate single conformations and compute similarity. These can be extended to include multiple conformations. However special data structures and compression algorithms would be needed to store precomputed spatial information in order to compute the similarity faster. Let first understand how the 2D search works,