Understanding and Quantifying Molecular Flexibility: Torsion Angular Bin Strings

Molecular flexibility is a commonly used, but not easily quantified term. It is at the core of understanding composition and size of a conformational ensemble and contributes to many molecular properties. For many computational workflows, it is necessary to reduce a conformational ensemble to meaningful representatives, however defining them and guaranteeing the ensemble's completeness is difficult. We introduce the concepts of torsion angular bin strings (TABS) as a discrete vector representation of a conformer's dihedral angles and the number of possible TABS (nTABS) as an estimation for the ensemble size of a molecule, respectively. Here, we show that nTABS corresponds to an upper limit for the size of the conformational space of small molecules and compare the classification of conformer ensembles by TABS with classifications by RMSD. Overcoming known drawbacks like the molecular size dependency and threshold picking of the RMSD measure, TABS is shown to meaningfully discretize the conformational space and hence allows e.g. for fast checks of the coverage of the conformational space. The current proof-of-concept implementation is based on the ETKDGv3 conformer generator as implemented in the RDKit and known torsion preferences extracted from small-molecule crystallographic data.