Quantitative structure-activity relationship for cyclic imide derivatives of protoporphyrinogen oxidase inhibitors: A study of quantum chemical descriptors from density functional theory

This study examined the applicability of various density functional theory (DFT)-based descriptors, such as energy gap (ΔE) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), weighted nucleophilic atomic frontier electron density (WNAFED, F _i ^N), mean molecular polarizability (α), and net atomic charge (Q _i), in quantitative structure-activity relationship (QSAR) studies on a class of important protoporphyrinogen oxidase (Protox) inhibitors including a series of cyclic imide derivatives with various heterocyclic rings and substituents. Our QSAR analysis using the quantum chemical descriptors calculated at the B3LYP/6-31G(d,p) level led to a useful explicit correlation relationship, i.e. pI ₅₀ = -5.7414 + 0.1424α - 0.0003α ² - 0.4546F _C. ^N + 0.2974Q _N. (n=26, R ²=0.87), showing that descriptors mean molecular polarizability, α, and WNAFED F _C. ^N of a critical carbon atom and net atomic charge (Q _i) in the molecules are most likely responsible for the in vitro biological activity of cyclic imides. It has been shown that the use of the DFT-based quantum chemical descriptors indeed led to a better QSAR equation than that obtained from the use of the corresponding descriptors calculated at a semiempirical PM3 level. The present work demonstrates that the DFT-based quantum chemical descriptors are potentially useful in the future QSAR studies for quantitatively predicting biological activity, and, therefore, the DFT-based QSAR approach could be expected to help facilitate the design of additional substituted cyclic imide derivatives of Protox inhibitors with the potentially higher biological activity.