[Paper Review] EigenFold: Generative Protein Structure Prediction with Diffusion Models

Bowen Jing, Ezra Erives+4 more|PubMed|Apr 5, 2023

Protein Structure and DynamicsBiochemistry, Genetics and Molecular Biology39 citations

TL;DR

EigenFold introduces a diffusion-based generative framework that samples a distribution of protein structures for a given sequence by modeling the structure as a system of harmonic oscillators and using eigenmode cascading diffusion. It matches single-structure accuracy with competing methods and provides an uncertainty-aware ensemble of structures.

ABSTRACT

Protein structure prediction has reached revolutionary levels of accuracy on single structures, yet distributional modeling paradigms are needed to capture the conformational ensembles and flexibility that underlie biological function. Towards this goal, we develop EigenFold, a diffusion generative modeling framework for sampling a distribution of structures from a given protein sequence. We define a diffusion process that models the structure as a system of harmonic oscillators and which naturally induces a cascading-resolution generative process along the eigenmodes of the system. On recent CAMEO targets, EigenFold achieves a median TMScore of 0.84, while providing a more comprehensive picture of model uncertainty via the ensemble of sampled structures relative to existing methods. We then assess EigenFold's ability to model and predict conformational heterogeneity for fold-switching proteins and ligand-induced conformational change. Code is available at https://github.com/bjing2016/EigenFold.

Motivation & Objective

• Motivate the need for generative models to capture conformational ensembles and flexibility in proteins.
• Develop a harmonic diffusion process that respects protein graph structure and enables efficient sampling of structural ensembles.
• Leverage eigenmode (normal mode) projections to implement cascading-resolution generation with few inference steps.
• Integrate a score-based model that is SE(3)-equivariant and uses OmegaFold embeddings to guide structure generation.
• Evaluate single-structure accuracy and the model's ability to capture conformational diversity and uncertainty.

Proposed method

• Define forward diffusion with a harmonic potential on a protein structure graph to encode chemical constraints.
• Project diffusion into eigenmodes of the harmonic matrix to analyze mode-wise convergence and stiffness.
• Introduce a cascading-resolution sampling procedure that activates weaker modes first and progressively adds detail.
• Train an SE(3)-equivariant score model using graph neural networks with tensor-product layers.
• Rank samples using an approximate ELBO derived from the forward/reverse SDE for sample selection.

Experimental results

Research questions

• RQ1 Can a diffusion model on a harmonic energy landscape sample realistic protein structures from a fixed sequence?
• RQ2 Does sampling multiple structures reveal model uncertainty and correlate with ground-truth errors?
• RQ3 How well can EigenFold model conformational diversity and flexibility across fold-switching and ligand-induced changes?

Key findings

• EigenFold achieves a median TMScore of 0.84 on recent CAMEO targets in single-structure predictions.
• The ensemble of sampled structures provides insight into model uncertainty and correlates with ground-truth accuracy across multiple metrics.
• The approximate ELBO computed from forward/reverse trajectories correlates with absolute structural accuracy, enabling internal ranking of samples.
• EigenFold samples are comparable to RoseTTAFold for single-structure accuracy but lag AlphaFold2 and ESMFold on some metrics.
• The method enables sampling with 100–300 inference steps due to the eigenmode cascading approach.
• EigenFold can model conformational diversity with fold-switching and apo/holo datasets, showing moderate correlations between ensemble diversity and ground-truth conformational diversity.