Interacting selectively and non-covalently with G-quadruplex DNA structures, in which groups of four guanines adopt a flat, cyclic Hoogsteen hydrogen-bonding arrangement known as a guanine tetrad. The stacking of guanine tetrads results in G-quadruplex DNA structures. G-quadruplex DNA can form under physiological conditions from some G-rich sequences, such as those found in telomeres, immunoglobulin switch regions, gene promoters, fragile X repeats, and the dimerization domain in the human immunodeficiency virus (HIV) genome.