Colorectal and prostate cancers are two of the most common types and cause of a high rate of deaths worldwide. Therefore, any strategy to stop or at least slacken the development and progression of malignant cells is an important therapeutic choice. The aim of the present work is the identification of novel cancer chemotherapy agents. Nowadays, many different drug discovery approaches are available, but this paper focuses on Molecular Topology, which has already demonstrated its extraordinary efficacy in this field, particularly in the identification of new hit and lead compounds against cancer. This methodology uses the graph theoretical formalism to numerically characterize molecular structures through the so called topological indices. Once obtained a specific framework, it allows the construction of complex mathematical models that can be used to predict physical, chemical or biological properties of compounds. In addition, Molecular Topology is highly efficient in selecting and designing new hit and lead drugs. According to the aforementioned, Molecular Topology has been applied here for the construction of specific Akt/mTOR and β-catenin inhibition mathematical models in order to identify and select novel antitumor agents.

Based on the results obtained by the selected mathematical models, six novel potential inhibitors of the Akt/mTOR and β-catenin pathways were identified. These compounds were then tested in vitro to confirm their biological activity.

Five of the selected compounds, CAS n° 256378-54-8 (Inhibitor n°1), 663203-38-1 (Inhibitor n°2), 247079-73-8 (Inhibitor n°3), 689769-86-6 (Inhibitor n°4) and 431925-096 (Inhibitor n°6) gave positive responses and resulted to be active for Akt/mTOR and/or β-catenin inhibition. This study confirms once again the Molecular Topology’s reliability and efficacy to find out novel drugs in the field of cancer.