PML is introduced, a novel computational framework that describes a binding interface as a family of multiscale manifolds, and results indicate that much of what determines binding strength is encoded in the shape of the interface itself, and that a single geometric description serves both classes without hand-tailored features.
Abstract
Predicting how tightly two biomolecules bind remains a major challenge, in part because different interaction classes present dissimilar interfaces, from compact metal-coordinated pockets to broad, featureless protein surfaces. We introduce persistent manifold learning (PML), a novel computational framework that describes a binding interface as a family of multiscale manifolds. Boundary-Induced Graph Laplacian, a discrete realization of de Rham–Hodge theory, then extracts topological invariants together with nonharmonic spectral information, capturing the geometry of an interface as well as its topology. These manifold embeddings are combined with protein and molecular language model representations and paired with gradient boosting decision trees. Our PML outperforms state-of-the-art methods on metalloprotein–ligand and protein–protein benchmarks. Relevance to Life Sciences. This work addresses a central problem in molecular biology and drug discovery: how to determine, from molecular structure alone, how tightly a molecule will bind to its target. Binding affinity governs therapeutic potency and selectivity, yet measuring it experimentally is slow and costly, making computational prediction essential for prioritizing candidates from large libraries. We apply our framework to two target classes ordinarily handled by separate methods: metalloenzymes, whose metal-coordinated active sites have long been exploited by drugs, and protein–protein interfaces, which regulate signaling and immune response yet resist conventional small molecules. Our results indicate that much of what determines binding strength is encoded in the shape of the interface itself, and that a single geometric description serves both classes without hand-tailored features. This suggests manifold-based representations may extend to other systems in which structure and sequence jointly determine function. Mathematical Content. The core of our approach involves de Rham–Hodge theory on compact Riemannian manifolds with boundary, a foundational tool in differential geometry rarely applied to molecular data. Binding interfaces are modeled as sublevel sets of Gaussian density fields, producing a filtration of manifolds whose topological transitions occur at the critical values of the level set function, as governed by Morse theory. The topology of each manifold is recovered from the kernels of Hodge Laplacians under normal and tangential boundary conditions, whose dimensions are Betti numbers by the Hodge and Friedrichs theorems, while their nonzero spectra reflect geometry. Discretization proceeds through discrete exterior calculus on Cartesian grids, yielding Boundary-Induced Graph Laplacians whose spectral analysis reduces to the singular values of the discrete differentials. Extending this across the filtration leads to persistent Hodge Laplacians on evolving manifolds, combining differential geometry, algebraic topology, and spectral theory into a multiscale representation of molecular shape.
Accurate identification of near-native ligand binding poses is a central challenge in structure-based drug design. From a physical point of view, the successful construction of a protein–ligand complex structure is dependent on whether protein and ligand can form enough atomically pairwise interactions that result in a global energy minimum. In this work, we report a machine learning scoring strategy for protein–ligand screening which explicitly considers the Native Contact Ratio (NCR), a topology inspired metric that quantifies the preservation of protein–ligand interfacial contacts as well as interaction energy. This physics-awared supervision strategy provides a simple but efficient gradient field that faithfully reflects the complicated protein energy landscape than conventional 3D coordinate-based objectives. Building on this principle, we present DeepNCR, an energy-informed Transformer framework that encodes approximate Coulombic and dispersive interaction potentials across the protein–ligand binding interface. Furthermore, we introduce a feature pruning step that compresses the interaction tensor from 1470 to 868 dimensions, further improving signal-to-noise ratio and directing model attention toward the interaction motifs critical for binding specificity. The model optimizes topological objectives and at inference drives pose refinement through a differentiable hybrid gradient field integrating predicted NCR and AutoDock Vina energetics. Extensive evaluation on the CASF-2016 benchmark and the 3D-DISCO cross-docking data set demonstrates consistently high performance: a Top-1 docking success rate of 94.7%, a 1% Enrichment Factor of 21.21 in virtual screening, and a Top-1 cross-docking success rate of 34.8%. Mechanistic analysis reveals that NCR-guided optimization enables decoy escaping from local energy minima and drives the recovery of disrupted native interactions, confirming that NCR captures the physical determinants of binding rather than mere geometric proximity.
Zhenqiang Zhang, Zhihao Wang, Yang Liu et al.· Journal of Chemical Informat...· 0 citations
An Algebraic Graph Neural Network model designed to encode molecular structures into a low-dimensional graph representation while preserving critical biochemical interactions is introduced, demonstrating superior performance in binding affinity prediction compared to state-of-the-art scoring functions.
Augustine Ouru, Xi Chen, Cameron Yeagle et al.· Computational and Mathematic...· 0 citations
Predicting protein–protein binding free energy (ΔG) from structure remains a central challenge in computational biophysics. Here, we present GULP (Graph-based Unified Learning for Protein binding), a graph neural network (GNN) that jointly learns from a residue-level graph representation of the binding interface and global physicochemical descriptors. We systematically investigate how training data distribution affects model performance by comparing a full training set with a balanced subset enriched for extreme-affinity complexes. GULP is computationally efficient and provides interpretable insights into residue-level and physicochemical contributions to binding. On external validation, GULP achieves a mean absolute error (MAE) of 2.31 kcal/mol and shows moderate agreement with experimental ΔG values (Pearson r = 0.54, Spearman ρ = 0.58).
The process of drug unbinding is of immense importance in the field of biophysics and therapeutics. The behavior of these systems is greatly influenced by their thermodynamic and kinetic properties. Therefore, it is crucial to accurately estimate the ligand binding free energies and rate of ligand dissociation, yet these processes are often governed by rare event transitions that lie beyond the reach of standard brute-force molecular dynamics simulations. While enhanced sampling simulations offer a solution, their efficacy is strictly contingent upon the selection of appropriate collective variables (CVs) which is non-trivial for complex systems like protein-ligand complexes. In this study, we present a method to derive optimized CV from transition state region (TS) via an interpretable machine learning (ML) model, Elastic Net. By employing some physically intuitive order parameters, the derived optimized CV from the TS-region greatly accelerate ligand binding-unbinding transitions and achieves rapid free energy surface (FES) convergence across diverse systems including buried and solvent exposed active sites such as Trpsin-benzamidine complex, host-guest systems and sodium epoxidase etc. Intriguingly significant contribution of the ligand hydration is found in the optimized CV which depicts crucial role of solvent in driving ligand binding-unbinding transitions. The estimated binding free energies for different protein-ligand complexes match quite well with experiments, while maintaining a low computational cost. The derived optimized CV is also used to calculate the ligand residence times across different systems and calculated residence times are within the experimental range for all systems, again with very little computational costs. Moreover, we show that the optimized CV constructed from TS region via an interpretable ML model is transferable across diverse systems, offering a robust and scalable framework for drug discovery and investigation of complex biomolecular recognition.
Protein-protein interactions (PPIs) govern a wide range of cellular functions. The ability to predict PPI interfaces from protein molecular surfaces is important for understanding protein function and enabling therapeutic discovery. While recent advances in structure-based learning, particularly molecular-surface geometric deep learning frameworks, have demonstrated that protein surfaces encode rich geometric and physicochemical information, such approaches often remain computationally intensive and data-hungry. Alternatively, topological data analysis (TDA) has emerged as a mathematically rigorous framework for extracting robust, multiscale shape information from complex data. In this work, we introduce a scalable TDA framework for extracting information on PPIs directly from localized protein surface patches. Our approach leverages multiscale topological descriptors, evaluated from patch-wise point cloud representations of protein mesh surfaces, combined with supervised machine learning models for interface prediction. On a full dataset of 3,362 proteins, the proposed approach substantially reduced computational cost relative to an established geometric deep learning method, MaSIF-site, decreasing preprocessing time from approximately 27 s/protein to 5-8 s/protein and total training time from approximately 6 h to 1-1.3 h. Importantly, this computational reduction is achieved while maintaining mean test area under the receiver operating characteristic curve (AUC) values of 0.76 and 0.77 for patch radii of 9 Å and 12 Å, respectively, thus approaching the MaSIF-site test AUC of 0.84. Our results suggest that topology offers a scalable and computationally efficient approach for high-throughput extraction of information from complex biomolecular interfaces.
Angan Mukherjee, ByungUk Park, Adam Malmstrom et al.· bioRxiv· 0 citations