Internal-Coordinate Density Modelling of Protein Structure: Covariance Matters

TL;DR

This paper introduces a novel method for modeling protein structure densities in internal coordinates using 3D constraints to accurately capture covariance, enabling scalable and flexible density models for various protein conformations.

Contribution

It presents a new covariance modeling strategy in internal coordinates with a variational autoencoder, improving protein density predictions in both unimodal and multimodal scenarios.

Findings

Effective covariance modeling in internal coordinates.

Scalable density models for full protein backbones.

Successful application to proteins with small and large conformational changes.

Abstract

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.