The electronic structure of periodic quadruple helix guanine wires, which mimic G4-DNA molecules, was studied as a function of the stacking distance between consecutive planes, by means of first principles density functional theory calculations. We show that, whereas for the native DNA interplane separation of 3.4 A the HOMO- and LUMO-derived bands are poorly dispersive, the bandwidths can be significantly increased when compressive strain is applied along the helical axis. Our findings indicate that efficient band conduction for both holes and electrons can be supported by such wires for stacking distances below 2.6 A, which imply a huge axial deformation with respect to double and quadruple helices in solutions and in crystals.