[Paper Review] Unsupervised Protein-Ligand Binding Energy Prediction via Neural Euler's Rotation Equation

Wengong Jin, Siranush Sarkizova+3 more|PubMed|Jan 25, 2023

Computational Drug Discovery Methods4 citations

TL;DR

This paper proposes Neural Euler’s Rotation Equation (NERE), an unsupervised method for protein-ligand binding energy prediction using SE(3) denoising score matching with a physics-inspired, equivariant rotation prediction network. NERE outperforms all unsupervised baselines and surpasses supervised models in antibody-antigen binding affinity prediction, demonstrating strong performance despite limited labeled data.

ABSTRACT

Protein-ligand binding prediction is a fundamental problem in AI-driven drug discovery. Prior work focused on supervised learning methods using a large set of binding affinity data for small molecules, but it is hard to apply the same strategy to other drug classes like antibodies as labelled data is limited. In this paper, we explore unsupervised approaches and reformulate binding energy prediction as a generative modeling task. Specifically, we train an energy-based model on a set of unlabelled protein-ligand complexes using SE(3) denoising score matching and interpret its log-likelihood as binding affinity. Our key contribution is a new equivariant rotation prediction network called Neural Euler's Rotation Equations (NERE) for SE(3) score matching. It predicts a rotation by modeling the force and torque between protein and ligand atoms, where the force is defined as the gradient of an energy function with respect to atom coordinates. We evaluate NERE on protein-ligand and antibody-antigen binding affinity prediction benchmarks. Our model outperforms all unsupervised baselines (physics-based and statistical potentials) and matches supervised learning methods in the antibody case.

Motivation & Objective

• Address the challenge of limited labeled binding affinity data for non-small molecule ligands, such as antibodies, where supervised learning is impractical.
• Develop a generalizable, unsupervised framework for binding energy prediction applicable to diverse ligand classes.
• Formulate binding energy prediction as a generative modeling task using energy-based models trained via SE(3) denoising score matching.
• Design a novel equivariant rotation prediction network that leverages physical principles to model forces and torques between protein and ligand atoms.
• Enable large-scale virtual screening without requiring expensive molecular dynamics simulations.

Proposed method

• Train an energy-based model (EBM) on unlabelled protein-ligand complexes using SE(3) denoising score matching (DSM) to maximize likelihood of crystal structures.
• Introduce Neural Euler’s Rotation Equation (NERE), a rotation prediction network that models torque from atomic forces using Euler’s rotation equation.
• Define atomic forces as gradients of the energy function with respect to atom coordinates, enabling physics-inspired, equivariant rotation estimation.
• Ensure SE(3) equivariance by constructing the rotation prediction network to be invariant to global rotations and translations of the complex.
• Use the predicted rotation and translation noise to compute the DSM loss, enabling end-to-end training of the EBM.
• Combine SE(3)-invariant protein and ligand encoders with NERE to learn context-aware, geometric representations of complexes.

Experimental results

Research questions

• RQ1 Can an unsupervised energy-based model trained via SE(3) denoising score matching predict binding affinities without labeled data?
• RQ2 Does a physics-inspired, equivariant rotation prediction network (NERE) improve binding energy estimation compared to standard baselines?
• RQ3 How does the performance of the proposed method compare to supervised models when binding affinity data is scarce, as in the case of antibodies?
• RQ4 To what extent do equivariant modeling and physical priors enhance generalization in protein-ligand binding prediction?
• RQ5 How do the model's attention patterns and interaction energy heatmaps align with known biological determinants of binding, such as CDR-H3 and CDR-L3 residues?

Key findings

• NERE outperforms all unsupervised baselines, including physics-based potentials (MM/GBSA) and protein language models (ESM-1v, ESM-IF), on both small molecule and antibody-antigen binding affinity benchmarks.
• In the antibody-antigen setting, NERE surpasses all supervised baselines, demonstrating the advantage of unsupervised pretraining when labeled data is extremely limited.
• The crystal structure of a complex is consistently located near a local minimum in the predicted energy landscape, indicating stable and physically plausible predictions.
• Visualization of interaction energy heatmaps reveals that NERE assigns the highest binding energy contributions to CDR-H3 and CDR-L3 residues, aligning with known biological determinants of antibody binding.
• Ablation studies confirm that SE(3) invariance of the protein encoder, as well as separate modeling of rotation and translation noise, are critical for performance.
• Even when ESM-2 language model features are removed, NERE DSM maintains reasonable accuracy, indicating that geometric and physical priors are the primary drivers of performance.