Elastic ellipsoidal functions defined by the observed hydration patterns around the DNA bases provide a new basis for measuring the recognition of ligands in the grooves of double-helical structures. Here a set of knowledge-based potentials suitable for quantitative description of such behavior is extracted from the observed positions of water molecules and amino acid atoms that form hydrogen bonds with the nitrogenous bases in high resolution crystal structures. Energies based on the displacement of hydrogen-bonding sites on drugs in DNA-crystal complexes relative to the preferred locations of water binding around the heterocyclic bases are low, pointing to the reliability of the potentials and the apparent displacement of water molecules by drug atoms in these structures. The validity of the energy functions has been further examined in a series of sequence substitution studies based on the structures of DNA bound to polyamides that have been designed to recognize the minor-groove edges of Watson-Crick basepairs. The higher energies of binding to incorrect sequences superimposed (without conformational adjustment or displacement of polyamide ligands) on observed high resolution structures confirm the hypothesis that the drug subunits associate with specific DNA bases. The knowledge-based functions also account satisfactorily for the measured free energies of DNA-polyamide association in solution and the observed sites of polyamide binding on nucleosomal DNA. The computations are generally consistent with mechanisms by which minor-groove binding ligands are thought to recognize DNA basepairs. The calculations suggest that the asymmetric distributions of hydrogen-bond-forming atoms on the minor-groove edge of the basepairs may underlie ligand discrimination of G·C from C·G pairs, in addition to the commonly believed role of steric hindrance. The analysis of polyamide-bound nucleosomal structures reveals other discrepancies in the expected chemical design, including unexpected contacts to DNA and modified basepair targets of some ligands. The ellipsoidal potentials thus appear promising as a mathematical tool for the study of drug- and protein-DNA interactions and for gaining new insights into DNA-binding mechanisms.