A fundamental motif in canonical nucleic acid structure is the base pair. Mutations that disrupt base pairs are typically destabilizing, but stability can often be restored by a second mutation that replaces the original base pair with an isosteric variant. Such concerted changes are a way to identify helical regions in secondary structures and to identify new functional motifs in sequenced genomes. In principle, such analysis can be extended to non-canonical nucleic acid structures, but this approach has not been utilized because the sequence requirements of such structures are not well understood. Here we investigate the sequence requirements of a G-quadruplex that can both bind GTP and promote peroxidase reactions. Characterization of all 256 variants of the central tetrad in this structure indicates that certain mutations can compensate for canonical G-G-G-G tetrads in the context of both GTP-binding and peroxidase activity. Furthermore, the sequence requirements of these two motifs are significantly different, indicating that tetrad sequence plays a role in determining the biochemical specificity of G-quadruplex activity. Our results provide insight into the sequence requirements of G-quadruplexes, and should facilitate the analysis of such motifs in sequenced genomes.