Linearized embedding: A new metric matrix algorithm for calculating molecular conformations subject to geometric constraints

Abstract

There are many methods in the literature for calculating conformations of a molecule subject to geometric constraints, such as those derived from two-dimensional NMR experiments. One of the most general ones is the EMBED algorithm, based on distance geometry, where all constraints except chirality are converted into upper and lower bounds on interatomic distances. Here we propose a variation on this where the molecule is assumed to have fixed bond lengths, vicinal bond angles and chiral centers; and these holonomic constraints are enforced separately from the experimental constraints by being built into the mathematical structure of the problem. The advantages of this approach are: (1) for molecules having large rigid groups of atoms, there are substantially fewer variables in the problem than all the atomic coordinates; (2) rigid groups achieve in the end more accurate local geometry (e.g., planar aromatic rings are truly planar, chiral centers always have their correct absolute chirality); (3) it is easier to detect inconsistencies between the holonomic and the experimental constraints; and (4) when generating a random sampling of conformers consistent with all constraints, the probability of achieving satisfactory structures tends to be greater.