The optimized structures of Cu-mediated metal-DNA parts formed from pyridine(pyridine-2,6-dicarboxylato) copper(II) (Dipic-Cu-Py), pyridine(pyridine-2,6-dicarboxamido)copper(II) (Dipam-Cu-Py), bis(8-hydroxyquinolinato)copper(II) (HQ-Cu-HQ), and N,N '-ethylenebis(salicylideneiminato)copper(II) (Sal-Cu-Sal) complexes were determined by B3LYP functional with 6-311++G(d,p)-LANL2DZ (Cu) basis sets. The geometric parameters of the mentioned molecules were found and their HOMO, LUMO and NBO analyses were performed. According to energy gaps of the investigated complexes, HQ-Cu-HQ parts were found as the best conductor complex. However, the effect of sugar and phosphate groups on the energy gaps of HQ-Cu-HQ base pairs could not be determined. For that reason, NEGF-DFT calculations for some Cu-mediated M-DNA parts were carried out. NEGF results showed that the electrical conductivities of HQ-Cu-HQ base pairs were quite high, and the sugar and phosphate groups significantly reduced their conductivities. The HQ-Cu-HQ base pairs without the sugar and phosphate groups were estimated as good candidates for nanowires.