Mayer-Homology Learning Prediction of Protein-Ligand Binding Affinities

Artificial intelligence-assisted drug design is revolutionizing the pharmaceutical industry. Effective molecular features are crucial for accurate machine learning predictions, and advanced mathematics plays a key role in designing these features. Persistent homology theory, which equips topological invariants with persistence, provides valuable insights into molecular structures. The standard homology theory is based on a differential rule for the boundary operator that satisfies <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn></mml:math> . Our recent work has extended this rule by employing Mayer homology with generalized differentials that satisfy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow><mml:mi>N</mml:mi></mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn></mml:math> for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn></mml:math> , leading to the development of persistent Mayer homology (PMH) theory and richer topological information across various scales. In this study, we utilize PMH to create a novel multiscale topological vectorization for molecular representation, offering valuable tools for descriptive and predictive analyses in molecular data and machine learning prediction. Specifically, benchmark tests on established protein-ligand datasets, including PDBbind-v2007, PDBbind-v2013, and PDBbind-v2016, demonstrate the superior performance of our Mayer homology models in predicting protein-ligand binding affinities.