In this work, we conducted a QSAR study on 18 molecules using descriptors from the Density Functional Theory (DFT) in order to predict the inhibitory activity of hydroxamic acids on histone deacetylase 7. This study is performed using the principal component analysis (PCA) method, the Ascendant Hierarchical Classification (AHC), the linear multiple regression method (LMR) and the nonlinear multiple regression (NLMR). DFT calculations were performed to obtain information on the structure and information on the properties on a series of hydroxamic acids compounds studied. Multivariate statistical analysis yielded two quantitative models (model MLR and model MNLR) with the quantum descriptors: electronic affinity (AE), vibration frequency of the OH bond (ν(OH)) and that of the NH bond (ν(NH)). The LMR model gives statistically significant results and shows a good predictability R2 = 0.9659, S = 0.488, F = 85 and p-value < 0.0001. Electronic affinity is the priority descriptor in predicting the activity of HDAC7 inhibitors in this study. The results obtained suggest that the descriptors derived from the DFT could be useful to predict the activity of histone deacetylase 7 inhibitors. These models were evaluated according to the criteria of Tropsha et al.
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