Scalable Anisotroplic Shape and Electrostatic Models for Biological Bromine Halogen Bonds

Halogens are important substituents of many drugs and secondary metabolites, but the structural and thermodynamic properties of their interactions are not properly treated by current molecular modeling and docking methods that assign simple isotropic point charges to atoms. Halogen bonds, for example, are becoming widely recognized as important for conferring specificity in protein-ligand complexes but, to this point, are most accurately described quantum mechanically. Thus, there is a need to develop methods to both accurately and efficiently model the energies and geometries of halogen interactions in bimolecular complexes. We present here a set of potential energy functions that, based on fundamental physical properties of halogens, properly model the anisotropic structure-energy relationships observed for halogen interactions from crystallographic and calorimetric data, and from ab initio calculations for bromine halogen bonds in a biological context. These energy functions indicate that electrostatics alone cannot account for the very short-range distances of bromine halogen bonds but require a flattening of the effective van der Waals radius that can be modeled through an angular dependence of the steric repulsion term of the standard Lennard-Jones type potential. This same function that describes the aspherical shape of the bromine is subsequently applied to model the charge distribution across the surface of the halogen, resulting in a force field that uniquely treats both the shape and electrostatic charge parameters of halogens anisotropically. Finally, the electrostatic potential was shown to have a distance dependence that is consistent with a charge-dipole rather than a simple Coulombic type interaction. The resulting force field for biological halogen bonds (ffBXB) is shown to accurately model the geometry-energy relationships of bromine interactions to both anionic and neutral oxygen acceptors and is shown to be tunable by simply scaling the electrostatic component to account for effects of varying electron-withdrawing substituents (as reflected in their Hammett constants) on the degree of polarization of the bromine. This approach has broad applications to modeling the structure energy relationships of halogen interactions, including the rational design of inhibitors against therapeutic targets.