Graph Laplacian spectral descriptors for alignment-free molecular shape and electrostatic comparison

Shape-based virtual screening methods are widely used in drug discovery. Alignment-dependent approaches often provide high screening accuracy but are computationally expensive, whereas alignment-free methods are faster but generally less accurate. Here, we present GE-MolSG, a novel alignment-free molecular descriptor that combines shape and electrostatic information using spectral graph representations derived from the graph Laplacian. GE-MolSG outperforms the established alignment-free ElectroShape method and achieves performance comparable to ESP-Sim without requiring molecular alignment. To demonstrate the extensibility of the graph-based framework, we further explore a proof-of-concept patch-based extension termed GM-MolSG, which incorporates additional surface features. The graph-based formulation provides a flexible and extensible framework for incorporating surface-associated molecular properties into compact descriptors for rapid alignment-free similarity searching. Scientific contribution GE-MolSG introduces a novel alignment-free spectral graph approach for molecular comparison that combines shape and electrostatic information within compact spectral descriptors. The method outperforms the established alignment-free ElectroShape descriptor and achieves performance comparable to ESP-Sim without requiring molecular alignment, while providing a flexible basis for incorporating additional surface-associated molecular properties. As a proof-of-concept demonstration of this extensibility, we further explore a patch-based extension, GM-MolSG, incorporating local geometric and chemical surface descriptors.