QSAR Analysis of Substituted Cinnamic Acid Derivatives with Antibacterial Activity

Background: Antimicrobial resistance continues to demand efficient discovery strategies. Phenylpropanoid scaffolds, such as cinnamic acid derivatives, exhibit a broad spectrum of antimicrobial potential.

Aim: to construct and validate a QSAR model for substituted cinnamic acid derivatives and to identify molecular descriptors associated with their antibacterial activity.

Methods: Chemical structures and antibacterial activities for 32 literature-derived cinnamic-acid derivatives were compiled; activity was expressed as log(1/MIC). The dataset comprised 22 learning and 10 test compounds. Three-dimensional structures were optimized in HyperChem using MM+ molecular mechanics followed by semi-empirical optimization. A total of 4,885 molecular descriptors were calculated using Dragon 7. Prior to modeling, descriptor data were standardized and low-variance variables were removed. Non-linear QSAR models were constructed in Statistica 13 using Multivariate Adaptive Regression Splines (MARSplines), which represent predictor effects by piecewise basis functions separated by data-dependent knots. Model construction involved generation of basis functions followed by pruning of less informative terms. Models with different interaction orders and numbers of basis functions were compared using R², leave-one-out Q², and mean absolute error (MAE); residual normality was assessed using the Shapiro–Wilk test.

Results: The selected additive MARSplines model (interaction order 1; 12 basis functions) yielded R² = 0.9720, Q²(LOO) = 0.9995, and MAE = 0.0662. The model included 12 descriptors representing complementary structural properties: Geary autocorrelations GATS2e and GATS5e weighted by Sanderson electronegativity; GATS6s and GATS8s weighted by intrinsic state; Moran autocorrelation MATS3i weighted by ionization potential; 3D-MoRSE descriptors Mor26s and Mor32u; radial distribution functions RDF110m, RDF130e, and RDF130v weighted by atomic mass, electronegativity, and van der Waals volume, respectively; the valence-state descriptor SssCH; and Eig14_AEA. The MARS equation revealed descriptor-specific threshold effects, with predictor contributions changing after the corresponding knot values were exceeded.

Conclusions: The MARSplines QSAR model identified non-linear associations between antibacterial activity and molecular features describing topological autocorrelation, intrinsic state, ionization potential, three-dimensional molecular information, and radial distributions of atomic properties. These results provide an interpretable description of structural features associated with antibacterial activity within the investigated series of cinnamic-acid derivatives.