Internal-Coordinate Density Modelling of Protein Structure: Covariance Matters
This addresses the problem of reliably predicting protein structural distributions for computational biology, representing an incremental advance in protein machine learning.
The paper tackles the challenge of predicting distributions of structural states in proteins by developing a new strategy for modelling protein densities in internal coordinates, using 3D constraints to induce covariance structure, and demonstrates its scalability to full protein backbones in unimodal and multimodal settings.
After the recent ground-breaking advances in protein structure prediction, one of the remaining challenges in protein machine learning is to reliably predict distributions of structural states. Parametric models of fluctuations are difficult to fit due to complex covariance structures between degrees of freedom in the protein chain, often causing models to either violate local or global structural constraints. In this paper, we present a new strategy for modelling protein densities in internal coordinates, which uses constraints in 3D space to induce covariance structure between the internal degrees of freedom. We illustrate the potential of the procedure by constructing a variational autoencoder with full covariance output induced by the constraints implied by the conditional mean in 3D, and demonstrate that our approach makes it possible to scale density models of internal coordinates to full protein backbones in two settings: 1) a unimodal setting for proteins exhibiting small fluctuations and limited amounts of available data, and 2) a multimodal setting for larger conformational changes in a high data regime.