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Abstract <p>Proteins are fundamental to biological processes, mediating critical functions through precise molecular interactions. The rotational dynamics between ligand atoms and protein binding sites can significantly influence interaction efficacy by modifying spatial relationships. In our research, we present the PLAe (three-dimensional (3D) rotationally equivariant neural networks for predicting protein-ligand binding affinities) methodology. This novel model synergizes radial basis functions with e3nn networks to encapsulate the radial and angular dimensions of molecular features. Radial basis functions effectively measure interatomic distances, while e3nn—an advanced neural network utilizing spherical harmonics—maintains invariance under rotational and translational transformations. The Clebsch–Gordan coefficients are employed to integrate angular and atomic properties seamlessly. By merging radial basis and spherical harmonic elements with Clebsch–Gordan representations, our approach adeptly captures molecular rotational symmetries and interatomic interactions. The inclusion of an attention mechanism further refines the affinity predictions, ensuring a high level of precision. This integrative and sophisticated model sets a new benchmark to accurately predict protein-ligand binding affinities, leveraging intricate molecular details to enhance predictive performance.</p> Graphical Abstract <p>By combining radial basis and spherical harmonic features with CG representations,&#xa0;this representation should capture the rotational symmetry of molecules as well as the interactions and connections between atoms within molecules. </p>

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Relevance of 3D Rotationally Equivariant Neural Networks for Predicting Protein-Ligand Binding Affinities

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Gaili Li,
  • Yongna Yuan,
  • Ruisheng Zhang

摘要

Abstract

Proteins are fundamental to biological processes, mediating critical functions through precise molecular interactions. The rotational dynamics between ligand atoms and protein binding sites can significantly influence interaction efficacy by modifying spatial relationships. In our research, we present the PLAe (three-dimensional (3D) rotationally equivariant neural networks for predicting protein-ligand binding affinities) methodology. This novel model synergizes radial basis functions with e3nn networks to encapsulate the radial and angular dimensions of molecular features. Radial basis functions effectively measure interatomic distances, while e3nn—an advanced neural network utilizing spherical harmonics—maintains invariance under rotational and translational transformations. The Clebsch–Gordan coefficients are employed to integrate angular and atomic properties seamlessly. By merging radial basis and spherical harmonic elements with Clebsch–Gordan representations, our approach adeptly captures molecular rotational symmetries and interatomic interactions. The inclusion of an attention mechanism further refines the affinity predictions, ensuring a high level of precision. This integrative and sophisticated model sets a new benchmark to accurately predict protein-ligand binding affinities, leveraging intricate molecular details to enhance predictive performance.

Graphical Abstract

By combining radial basis and spherical harmonic features with CG representations, this representation should capture the rotational symmetry of molecules as well as the interactions and connections between atoms within molecules.