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Chronic obstructive pulmonary disease (COPD) is a multifactorial disease of the respiratory system which develops as a result of a complex interaction of genetic and environmental factors closely related to lifestyle. We aimed to assess the combined effect of the PI3K/AKT/mTOR signaling pathway (PIK3R1, AKT1, MTOR, PTEN) and sirtuin (SIRT1, SIRT3, SIRT6) genes to COPD risk. SNPs of SIRT1 (rs3758391, rs3818292), SIRT3 (rs3782116, rs536715), SIRT6 (rs107251), AKT1 (rs2494732), PIK3R1 (rs10515070, rs831125, rs3730089), MTOR (rs2295080, rs2536), PTEN (rs701848, rs2735343) genes were genotyped by real-time polymerase chain reaction (PCR) among 1245 case and control samples. Logistic regression was used to detect the association of SNPs in different models. Linear regression analyses were performed to estimate the relationship between SNPs and lung function parameters and smoking pack-years. Significant associations with COPD were identified for SIRT1 (rs3818292) (P = 0.001, OR = 1.51 for AG), SIRT3 (rs3782116) (P = 0.0055, OR = 0.69) and SIRT3 (rs536715) (P = 0.00001, OR = 0.50) under the dominant model, SIRT6 (rs107251) (P = 0.00001, OR = 0.55 for СT), PIK3R1: (rs10515070 (P = 0.0023, OR = 1.47 for AT), rs831125 (P = 0.00001, OR = 2.28 for AG), rs3730089 (P = 0.0007, OR = 1.73 for GG)), PTEN: (rs701848 (P = 0.0015, OR = 1.35 under the log-additive model), and rs2735343 (P = 0.0001, OR = 1.64 for GC)). A significant genotype-dependent variation of lung function parameters was observed for SIRT1 (rs3818292), SIRT3 (rs3782116), PIK3R1 (rs3730089), and MTOR (rs2536). Gene-gene combinations that remained significantly associated with COPD were obtained; the highest risk of COPD was conferred by a combination of G allele of the PIK3R1 (rs831125) gene and GG of SIRT3 (rs536715) (OR = 3.45). The obtained results of polygenic analysis indicate the interaction of genes encoding sirtuins SIRT3, SIRT2, SIRT6 and PI3KR1, PTEN, MTOR and confirm the functional relationship between sirtuins and the PI3K/AKT/mTOR signaling pathway.