G-RMSD: Root Mean Square Deviation Based Method for Three-dimensional Molecular Similarity Determination

Abstract

<div>We present the Generalized Root Mean Square Deviation (G-RMSD) method. G-RMSD is an optimization method to calculate the minimal RMSD value of two atomic structures by optimal superimposition. The method is not restricted to systems with an equal number of atoms or a unique atom matching and can handle any type of chemical structure, including transition states and non-valence bond structures. It requires only Cartesian coordinates for the structures, but can also include further information, i.e. atom and bond types. Applications of G-RMSD to the classification of alpha-D-glucose conformers and 3D partial structure search using a dataset containing equilibrium (EQ), dissociation channel (DC), and transition state (TS) structures are demonstrated. We find that G-RMSD allows for a successful classification and mapping for a wide variety of molecular structures.</div><div><br></div>

Visualization of reaction route map and dynamical trajectory in reduced dimension

“…First, we consider how to evaluate the similarity between two structures of a given molecular system. Although several useful molecular similarities have been proposed in biochemistry and chemoinformatics, such as the Tanimoto coefficient 22 and the generalized root mean square deviation (G-RMSD), 23 In order to obtain the optimal distance between the structures, it is necessary to remove the displacements caused by the translational and rotational degrees of freedom of the two structures. The former can be removed exactly by setting each center of mass to the origin of the coordinate system, and the latter can be removed by determining the optimal orientation of the x-y-z axes to minimize d ij using the Kabsch algorithm.…”

“…The recently proposed G-RMSD is based on a bipartite matching algorithm, which can provide structure similarity between two structures with different molecular sizes without any inherent atomic mapping. 23…”