Persistent Directed Flag Laplacian (PDFL)-Based Machine Learning for Protein–Ligand Binding Affinity Prediction

Directionality in molecular and biomolecular networks plays an important role in the accurate representation of the complex, dynamic, and asymmetrical nature of interactions present in protein-ligand binding, signal transduction, and biological pathways. Most traditional techniques of topological data analysis (TDA), such as persistent homology (PH) and persistent Laplacian (PL), overlook this aspect in their standard form. To address this, we present the persistent directed flag Laplacian (PDFL), which incorporates directed flag complexes to account for edges with directionality originated from polarization, gene regulation, heterogeneous interactions, etc. This study marks the first application of PDFL, providing an in-depth analysis of spectral graph theory combined with machine learning. In addition to its superior accuracy and reliability, the PDFL model offers simplicity by requiring only raw inputs without complex data processing. We validated our multikernel PDFL model for its scoring power against other state-of-the-art methods on three popular benchmarks, namely PDBbind v2007, v2013, and v2016. The computational results indicate that the proposed PDFL model outperforms competitors in protein-ligand binding affinity predictions, suggesting that PDFL is a promising tool for protein engineering, drug discovery, and general applications in science and engineering.