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Overexpression of telomerase is one of the hallmarks of human cancer. Telomerase is important for maintaining the integrity of the ends of chromosomes, which are called telomeres. A growing number of human disease syndromes are associated with organ failure caused by mutations in telomerase (hTERT or hTR). Mutations in telomerase lead to telomere shortening by decreasing the stability of the telomerase complex, reducing its accumulation, or directly affecting its enzymatic activity. In this work, potential human telomerase mutations were identified by a systematic computational approach. Moreover, molecular docking methods were used to predict the effects of these mutations on the affinity of certain ligands (C_9i, C_9k, 16A, and NSC749234). The C_9k inhibitor had the best binding affinity for wild-type (WT) telomerase. Moreover, C_9i and C_9k had improved interactions with human telomerase in most of the mutant models. The R631 and Y717 residues of WT telomerase formed interactions with all studied ligands and these interactions were also commonly found in most of the mutant models. Residues forming stable interactions with ligands in molecular dynamics (MD) were traced, and the MD simulations showed that the C_9k ligand formed different conformations with WT telomerase than the C_9i ligand.