Modeling and prediction of molecular properties. Theory of grid-weighted holistic invariant molecular (G-WHIM) descriptors

Recently proposed three-dimensional molecular indices (WHIM descriptors) have been used to search for quantitative structure-activity and structure-property relationships for several classes of compounds. WHIM descriptors contain information about the whole molecular structure in terms of size, shape, symmetry and atom distribution. These indices are calculated from the Cartesian coordinates of the atoms weighted in different manners and represent a very general approach to describe molecules in a unitary conceptual framework. In this paper the WHIM descriptor approach is extended to treat interaction scalar fields. The new G-WHIM (grid-weighted holistic invariant molecular) descriptors are calculated from the coordinates of the grid points where the field has been evaluated, each being weighted by the field value. The fields considered in the proposed example are related to non-bonding, electrostatic, and H-bonding interaction energies, evaluated by classical potentials. Two different sets of descriptors are obtained, for negative and positive potential values separately. The information contained in the whole grid is synthesized in a few parameters to be used in structure-activity relationship studies, thus avoiding difficulties related to chemical information spread out over a great number of grid points and thereby overcoming the problem of the dependence of the results upon molecule alignment. The interpretability of the results is quite evident and is defined by the same mathematical properties of the algorithm used for their calculation. The models obtained confirm the great modeling power of the G-WHIM descriptors.