Ring kinematics-informed conformation space exploration

Conformational searches and ML-driven geometry predictions (e.g., AlphaFold) work in the space of molecule's degrees of freedom. When dealing with cycles, cyclicity constraints impose complex interdependence between them, so that arbitrary changes of cyclic dihedral angles lead to heavy distortions of some bond lengths and valence angles of the ring. This renders navigation through conformational space of cyclic molecules to be very challenging. Inverse kinematics is a theory that provides a mathematically strict solution to this problem. It allows one to identify degrees of freedom for any polycyclic molecule, that is, its dihedral angles that can be set independently from each other. Then for any values of degrees of freedom, inverse kinematics can reconstruct the remaining dihedrals so that all rings are closed with given bond lengths and valence angles. This approach offers a handy and efficient way for constructing and navigating conformational space of any molecule using either naïve Monte-Carlo sampling or sophisticated machine learning models. Inverse kinematics can considerably narrow the conformational space of a polycyclic molecule to include only cyclicity-preserving regions. Thus, it can be viewed as a physical constraint on the model, making the latter obey the laws of kinematics, which govern the rings conformations. We believe that inverse kinematics will be universally used in the ever-growing field of geometry prediction of complex interlinked molecules.

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