Papers › Generating Highly Designable Proteins with Geometric Algebra Flow Matching

Generating Highly Designable Proteins with Geometric Algebra Flow Matching

7 Nov 2024arXiv:2411.05238archive 2025-07-28

Simon Wagner, Leif Seute, Vsevolod Viliuga, Nicolas Wolf, Frauke Gräter, Jan Stühmer

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.

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