Mayer-Homology Learning Prediction of Protein-Ligand Binding Affinities

Area of Science:

• Computational chemistry
• Topological data analysis
• Machine learning

Background:

• Artificial intelligence (AI) is transforming drug design, requiring effective molecular features for machine learning (ML) models.
• Advanced mathematical techniques, particularly topology, are vital for extracting meaningful molecular descriptors.
• Persistent homology theory offers insights into molecular structures by analyzing topological invariants.

Purpose of the Study:

• To introduce Persistent Mayer Homology (PMH) theory for richer topological information across multiple scales.
• To develop a novel multiscale topological vectorization method for molecular representation using PMH.
• To enhance descriptive and predictive analyses in molecular data for AI-driven drug discovery.

Main Methods:

• Extension of standard homology theory using Mayer homology with generalized differentials satisfying d^N = 0 (N >= 2).
• Development and application of Persistent Mayer Homology (PMH) theory.
• Creation of a multiscale topological vectorization for molecular representation.
• Benchmarking on protein-ligand datasets (PDBbind-v2007, PDBbind-v2013, PDBbind-v2016).

Main Results:

• PMH theory provides richer topological information compared to standard methods.
• The novel multiscale topological vectorization effectively represents molecular data.
• Mayer homology models demonstrated superior performance in predicting protein-ligand binding affinities on benchmark datasets.

Conclusions:

• PMH offers a powerful framework for molecular representation in AI-assisted drug design.
• The developed vectorization method enhances ML model accuracy for predicting binding affinities.
• This work provides valuable tools for advancing computational drug discovery and pharmaceutical research.