Deep generative models of protein structure uncover distant relationships across a continuous fold space

Our views of fold space implicitly rest upon many assumptions that impact how we analyze, interpret and understand protein structure, function and evolution. For instance, is there an optimal granularity in viewing protein structural similarities (e.g., architecture, topology or some other level)? Similarly, the discrete/continuous dichotomy of fold space is central, but remains unresolved. Discrete views of fold space bin similar folds into distinct, non-overlapping groups; unfortunately, such binning can miss remote relationships. While hierarchical systems like CATH are indispensable resources, less heuristic and more conceptually flexible approaches could enable more nuanced explorations of fold space. Building upon an Urfold model of protein structure, here we present a deep generative modeling framework, termed DeepUrfold, for analyzing protein relationships at scale. DeepUrfold's learned embeddings occupy high-dimensional latent spaces that can be distilled for a given protein in terms of an amalgamated representation uniting sequence, structure and biophysical properties. This approach is structure-guided, versus being purely structure-based, and DeepUrfold learns representations that, in a sense, define superfamilies. Deploying DeepUrfold with CATH reveals evolutionarily-remote relationships that evade existing methodologies, and suggests a mostly-continuous view of fold space-a view that extends beyond simple geometric similarity, towards the realm of integrated sequence ↔ structure ↔ function properties.