SE(3)-equivariant convolutional neural networks for biomolecular interactions
Creators: name: Bhadra-Lobo, Siddharth
Publisher: name: No Publisher Supplied
Year: 2025

description: Protein-protein and protein-small molecule interactions are critical for biological function. A comprehensive solution to the biomolecular interactions problem could greatly enhance our understanding and development of biomolecules. Protein structural data plays an important role in creating models for these interactions, as it provides rich information for improving model generalizability and interpretation. This dissertation investigates deep learning approaches for biomolecular interactions through the use of SE(3)-equivariant convolutional neural networks (SE(3)-CNNs). These networks apply mathematical constraints to existing deep learning architectures to learn physically relevant, geometric features. SE(3)-CNNs provide a robust framework for addressing complex molecular biophysical challenges, leveraging representation learning to identify crucial interaction features and extend these insights to new, unseen data. In the first stage, we developed Dock2D to rapidly prototype solutions to the biomolecular interaction problem using deep learning. We create a synthetic 2D dataset containing receptor and ligand shape pairs, and prototype deep learning solutions based around two tasks, interaction pose (IP) prediction and interaction fact (IF). The first task is to solve docking two shapes together, the second is to determine if two shapes interact or not. We create the datasets with an underlying energy function parameterized by spatial transformations applied to a ligand shape relative to a receptor shape, where a lower energy is associated with stronger interaction. We implement fast Fourier transforms (FFT) for translational sampling and several rotational sampling methods to solve the two interaction problems, using fully-convolutional, SE(2)-equivariant convolutional neural networks (SE(2)-CNNs). These SE(2)-CNNs generate useful and generalizable interaction geometric features that reduce the need for rotational sampling and demonstrate that the IP and IF tasks are related through cross-evaluation. In the second stage, we apply the solutions to the IP and IF tasks to real data in 3D, we collect antibody-antigen complex structural data and their associated binding affinity values ($Delta G$), and expanded with homology model data augmentation. We implement SE(3)-CNNs similar in structure to Dock2D and construct a SO(3) angular grid adjacency network to extend the Dock2D solutions involving uniform rotational sampling orientation of the ligand with respect to the receptor. This model, SE3Dock, effectively solves the re-docking problem, defined as putting the known antibody-antigen complexes back together. Since we already know that the IP and IF tasks are related, we were able to joint-train a regression model for binding affinity prediction, however only achieved enough accuracy to rank binding affinity for unseen antibody-antigen complexes. The follow-up model, SE3Bind, is a reformulation that removes the need for spatial sampling, for both the IP and IF tasks based on the a new dataset generation procedure, that presents the receptor-ligand pairs centered and already in their docked complex. While this model requires further development and testing, it successfully solves the IP task. To extend the advantages of using the SE(3)-CNNs onto protein-small molecule interactions, we developed SE3Lig. This model does not use FFT-based correlation or energies, and instead predicts probabilities for 18 different atom channels by in-painting the atomic density of cofactors, water, and ions---onto 0.5~AA resolution grids. The in-painted probability densities can be numerically compared between predicted atomic channels or taken as composites to infer what molecule or molecular fragment binds, and how relatively likely within specific regions on a protein. The SE(3)-CNN allows for data efficient training, without data augmentation or rotational sampling for this task, resulting in rapid model training and evaluation. Since AI generated protein structures typically do not predict small molecule positions, our model is well suited for rapid screening of the plethora of AI predicted protein structures, for small molecule interaction.