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Two new Cu(II) complexes with Picolinic acid and Tryptophan [Cu(II)(DPTR)(H2O)2](1:1) (1) and [Cu(II)(DPTR)(Phen)] (1:1:1) (2) were synthesized, characterized and studied their DNA binding, cleavage, docking and anti-cancer properties. The molecular modeling studies were carried out with energy minimized structures of metal complexes. CT-DNA binding studies revealed that the complexes bind through an intercalative mode and show good binding propensity. The docking study also confirms the intercalative mode of binding. The hydrolytic DNA cleavage activity of these complexes has been studied using gel electrophoresis. Complex 2 shows better efficiency than 1. Cell viability experiments indicated that the ligand, complexes show significant dose dependent cytotoxicity in selected cell lines. Graphical Abstract Two new Cu(II) complexes with Picolinic acid and Tryptophan, [Cu(II)(DPTR)(H2O)2](1:1) (1) and [Cu(II)(DPTR)(Phen)] (1:1:1) (2) were synthesized, characterized and studied their DNA binding, cleavage, docking and anti-cancer properties.