Towards a quantum treatment of DNA G-quadruplex: The FMO method elucidates interactions with alkali metal ions

G-quadruplex (Gq) is a non-canonical DNA secondary structure characterized by stacked layers formed by square coplanar guanine quartets, stabilized by the presence of several K+ ions placed between two neighbouring layers. In this study we investigate the Gq affinity for several alkali metals, namely Na+, K+ and Rb+ by using the fragment molecular orbital (FMO) method, which is a very promising quantum mechanics approach, whose application to metal bearing complexes is relatively new. We show that the Gq affinity for alkali metals, determined by the FMO3/6–311 G*//PCM[1] level of theory with the screened point charges approximation for all atoms to calculate the embedding electrostatic potential (ESP-SPTC), follows the trend K+>Na+>Rb+ in agreement with the existing literature data. Moreover, the partitioning of the formation energies for the metal complexes indicates that the metal ions size and their desolvation energy penalties are the key factors determining the Gq affinity. These results suggest that the appropriate model of the FMO approach is a valuable computational method to gain physical insights and for quantitative determination in biological metal complexes in the quantum mechanical framework.