Mapping the spaces of crystalline materials and proteins.

13^th January 2023, 14:00
Vitaly Kurlin
MIF

Abstract

Same or different? This question remained open for many real objects including periodic crystals and proteins. Since crystal structures are determined in a rigid form, there is little sense to distinguish them modulo rigid motion (a composition of translations and rotations). Considering the chirality or sign of orientation, it suffices to distinguish crystals modulo isometry, which is any transformation (for example, mirror reflection) maintaining inter-point distances. Geometric Data Science develops complete invariants that are DNA-style descriptors uniquely identifying classes of real objects modulo rigid motion, isometry, or other important equivalences. Such invariants practically distinguished all (660+ thousand) periodic crystals in the Cambridge Structural Database via 200+ billion pairwise comparisons. This experiment was completed over two days on a modest desktop, while traditional RMSD comparisons are estimated to require 34+ thousand years. The new invariants unexpectedly detected five pairs of duplicate structures that are geometrically identical, but one atomic identity was replaced with a different one (Cd with Mn in the pair HIFCAB vs JEPLIA). Since such a replacement seems physically impossible without perturbing geometry, five journals are investigating the integrity of the underlying publications. The more important conclusion is that all known and undiscovered crystals live in a common space of isometry classes of periodic point sets parameterized by complete invariants playing the role of geographic-style coordinates in this crystal universe whose first maps appeared in Acta Cryst A, v.79, p.1-13. A similar rigorous approach to proteins detected unexpected coincidences in the Protein Data Bank.