Generating Highly Designable Proteins with Geometric Algebra Flow Matching

TL;DR

This paper presents a novel geometric algebra-based generative model for designing highly diverse and naturalistic protein backbones, improving the expressiveness and statistical fidelity of protein structure generation.

Contribution

Introduction of Clifford Frame Attention, an extension of IPA using geometric algebra, integrated into FrameFlow for enhanced protein backbone design.

Findings

Achieves high designability, diversity, and novelty in generated proteins.

Samples protein backbones that match natural secondary structure distributions.

Outperforms existing models in generating realistic protein structures.

Abstract

We introduce a generative model for protein backbone design utilizing geometric products and higher order message passing. In particular, we propose Clifford Frame Attention (CFA), an extension of the invariant point attention (IPA) architecture from AlphaFold2, in which the backbone residue frames and geometric features are represented in the projective geometric algebra. This enables to construct geometrically expressive messages between residues, including higher order terms, using the bilinear operations of the algebra. We evaluate our architecture by incorporating it into the framework of FrameFlow, a state-of-the-art flow matching model for protein backbone generation. The proposed model achieves high designability, diversity and novelty, while also sampling protein backbones that follow the statistical distribution of secondary structure elements found in naturally occurring proteins, a property so far only insufficiently achieved by many state-of-the-art generative models.