Generating Highly Designable Proteins with Geometric Algebra Flow Matching
This work addresses the problem of generating realistic and diverse protein structures for computational biology, representing an incremental improvement over existing methods.
The paper tackles protein backbone design by introducing a generative model that integrates geometric algebra and higher-order message passing into a flow matching framework, achieving high designability, diversity, and novelty while accurately matching natural protein secondary structure distributions.
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.