Quantitative Structure−Activity Relationship for Cyclic Imide Derivatives of Protoporphyrinogen Oxidase Inhibitors: A Study of Quantum Chemical Descriptors from Density Functional Theory

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Abstract
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, ), mean molecular polarizability (α), and net atomic charge (Qi), 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. pI50 = −5.7414 + 0.1424α − 0.0003α2 − 0.4546 + 0.2974QN•• (n=26, R2=0.87), showing that descriptors mean molecular polarizability, α, and WNAFED of a critical carbon atom and net atomic charge (Qi) 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.