Predicting Affinity Through Homology (PATH): Interpretable Binding Affinity Prediction with Persistent Homology

Abstract

AbstractAccurate binding affinity prediction is crucial to structure-based drug design. Recent work used computational topology to obtain an effective representation of protein-ligand interactions. Although persistent homology encodes geometric features, previous works on binding affinity prediction using persistent homology employed uninterpretable machine learning models and failed to explain the underlying geometric and topological features that drive accurate binding affinity prediction.In this work, we propose a novel, interpretable algorithm for protein-ligand binding affinity prediction. Our algorithm achieves interpretability through an effective embedding of distances across bipartite matchings of the protein and ligand atoms into real-valued functions by summing Gaussians centered at features constructed by persistent homology. We name these functionsinternuclear persistent contours (IPCs). Next, we introducepersistence fingerprints, a vector with 10 components that sketches the distances of different bipartite matching between protein and ligand atoms, refined from IPCs. Let the number of protein atoms in the protein-ligand complex ben, number of ligand atoms bem, andω≈ 2.4 be the matrix multiplication exponent. We show that for any 0 <ε< 1, after an 𝒪 (mnlog(mn)) preprocessing procedure, we can compute anε-accurate approximation to the persistence fingerprint in 𝒪 (mlog6ω(m/”)) time, independent of protein size. This is an improvement in time complexity by a factor of 𝒪 ((m+n)3) over any previous binding affinity prediction that uses persistent homology. We show that the representational power of persistence fingerprint generalizes to protein-ligand binding datasets beyond the training dataset. Then, we introducePATH, Predicting Affinity Through Homology, an interpretable, small ensemble of shallow regression trees for binding affinity prediction from persistence fingerprints. We show that despite using 1,400-fold fewer features, PATH has comparable performance to a previous state-of-the-art binding affinity prediction algorithm that uses persistent homology features. Moreover, PATH has the advantage of being interpretable. Finally, we visualize the features captured by persistence fingerprint for variant HIV-1 protease complexes and show that persistence fingerprint captures binding-relevant structural mutations. The source code for PATH is released open-source as part of the osprey protein design software package.