Ophiuchus: Scalable Modeling of Protein Structures through Hierarchical Coarse-graining SO(3)-Equivariant Autoencoders

Three-dimensional native states of natural proteins display recurring and hierarchical patterns. Yet, traditional graph-based modeling of protein structures is often limited to operate within a single fine-grained resolution, and lacks hourglass neural architectures to learn those high-level building blocks. We narrow this gap by introducing Ophiuchus, an SO(3)-equivariant coarse-graining model that efficiently operates on all-atom protein structures. Our model departs from current approaches that employ graph modeling, instead focusing on local convolutional coarsening to model sequence-motif interactions with efficient time complexity in protein length. We measure the reconstruction capabilities of Ophiuchus across different compression rates, and compare it to existing models. We examine the learned latent space and demonstrate its utility through conformational interpolation. Our experiments demonstrate Ophiuchus to be a scalable basis for efficient protein modeling and generation. Proteins form the basis of all biological processes and understanding them is critical to biological discovery, medical research and drug development. Their three-dimensional structures often display modular organization across multiple scales, making them promising candidates for modeling in motif-based design spaces [Bystroff & Baker (1998); Mackenzie & Grigoryan (2017); Swanson et al. (2022)]. Harnessing these coarser, lower-frequency building blocks is of great relevance to the investigation of the mechanisms behind protein evolution, folding and dynamics [Mackenzie et al. (2016)], and may be instrumental in enabling more efficient computation on protein structural data through coarse and latent variable modeling [Kmiecik et al. (2016); Ramaswamy et al. (2021)]. Recent developments in deep learning architectures applied to protein sequences and structures demonstrate the remarkable capabilities of neural models in the domain of protein modeling and design [Jumper et al. (2021); Baek et al. (2021b); Ingraham et al. (2022); Watson et al. (2022)].