The development of methods that can predict the metal-mediated biological activity based only on the 3D structure of metal-unbound proteins has become a goal of major importance. This work is dedicated to the amino terminal Cu(II)- and Ni(II)-binding (ATCUN) motifs that participate in the DNA cleavage and have antitumor activity. We have calculated herein, for the first time, the 3D electrostatic spectral moments for 415 different proteins, including 133 potential ATCUN antitumor proteins. Using these parameters as input for Linear Discriminant Analysis, we have found a model that discriminates between ATCUN-DNA cleavage proteins and nonactive proteins with 91.32% Accuracy (379 out of 415 of proteins including both training and external validation series). Finally, the model has predicted for the first time the DNA cleavage function of proteins from the pathogen parasites. We have predicted possible ATCUN-like proteins with a probability higher than 99% in nine parasite families such as Trypanosoma, Plasmodium, Leishmania, or Toxoplasma. The distribution by biological function of the ATCUN proteins predicted has been the following: oxidoreductases 70.5%, signaling proteins 62.5%, lyases 58.2%, membrane proteins 45.5%, ligases 44.4%, hydrolases 41.3%, transferases 39.2%, cell adhesion proteins 34.5%, metal binders 33.5%, translation proteins 25.0%, transporters 16.7%, structural proteins 9.1%, and isomerases 8.2%. The model is implemented at http://miaja.tic.udc.es/Bio-AIMS/ATCUNPred.php.