An Alignment-Free, Property-Dependent, Spectral Descriptor of Molecular Surfaces
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Authors
Tehrani, Alireza
Date
2025-05-05
Type
thesis
Language
eng
Keyword
Chemistry , Quantum chemistry , Cheminformatics
Alternative Title
Abstract
Constructing numerical descriptors that capture a molecule’s structure, electronic, and physicochemical properties is a fundamental challenge of molecular representation for cheminformatics and chemical machine learning. Existing molecular descriptors either require molecular alignment which is computationally expensive or fail to combine molecular shape and property into a unified descriptor. This thesis addresses these limitations by utilizing the spectral geometry of the Laplace-Beltrami operator to develop a novel alignment-free spectrum-like descriptor, called the property-spectrum. This descriptor compactly encodes surface properties, satisfies molecular invariances, and can theoretically reconstruct the exact molecular shape as more surface properties are incorporated.
We develop an efficient computational protocol to accurately compute the property-spectrum across diverse chemical systems and surface properties. Applied to the electrostatic potential mapped on molecular surfaces, the electrostatic-spectrum exhibits continuity with conformational changes and bond stretching. It also differentiates functional groups and accurately clusters thermophilic and mesophilic proteins. To compute the property-spectrum for large databases and (bio-)molecular systems, we develop two free and open-source software packages: BFit, which performs fast and accurate electron density fitting using the Kullback-Leibler divergence measure, and cuGBasis, which accelerates the computation of electron density-based descriptors by leveraging GPUs with a memory-optimized molecular basis-set encoding.
The property-spectrum captures rich chemical information and enables broad applications, including predictive modeling without relying on complex deep-learning architectures. We demonstrate that the property-spectra descriptor achieves high accuracy in ligand-based virtual screening and predicting molecular hydration-free energies. Additionally, we use the property-spectrum to quantitatively assess the transferability and distinguishability of atoms-in-molecule surfaces based on shape and electron density. Finally, we present a rigorous mathematical derivation to extend the property-spectrum to encode volumetric electron densities through conformal transformations of the underlying Riemannian metric. We conclude by establishing a geometric analogue of the holographic electron density theorem and enhancing the property-spectrum to develop more powerful local descriptors (e.g., for active sites) that retain global information about a (bio-)molecule.