Canonized then Minimized RMSD for Three-Dimensional Structures

Existing molecular canonization algorithms typically operate on one-dimensional (1D) string representations or two-dimensional (2D) connectivity graphs of a molecule and are not able to differentiate equivalent atoms based on three-dimensional (3D) structures. The stereochemical tags on each atom are in fact determined according to established Cahn-Ingold-Prelog (CIP) rules for comparing grades, which can help to further differentiate atoms with similar environment. Therefore, a stereochemical-rule-based canonization algorithm that is capable of assigning canonical indices using 3D structural information is of great value. On top of the Schneider-Sayle-Landrum (SSL) partition-based canonization algorithm, we propose an enhanced canonization algorithm to expand its applicability. The initial index assignment rules are redesigned, so that the obtained canonical indices are compatible with most of the common CIP Sequence Rules, which greatly eases the stereochemical assignment. Furthermore, a branching tiebreaking step is added to secure an accurate evaluation of the structural difference through the minimized root-mean-square deviation (RMSD) between structures, with an option to include hydrogen atoms or not. Our algorithm is implemented with Python and can efficiently obtain minimized RMSD taking into account the symmetry of molecular systems, contributing to the fields of drug design, molecular docking, and data analysis of molecular dynamics (MD) simulation.