FAFE: Immune Complex Modeling with Geodesic Distance Loss on Noisy Group Frames

TL;DR

This paper introduces FAFE, a geodesic loss function that improves antibody-antigen complex modeling by addressing FAPE's gradient vanishing issue, leading to significantly better accuracy in protein structure prediction.

Contribution

The paper proposes a novel geodesic loss function, FAFE, which enhances the optimization of rotational and translational errors in protein complex modeling, overcoming limitations of existing loss functions.

Findings

Achieved 52.3% correct rate on the evaluation set, surpassing AF2.

Improved modeling accuracy on low-homology subsets by 100%.

Demonstrated the effectiveness of group-aware geodesic loss in protein structure prediction.

Abstract

Despite the striking success of general protein folding models such as AlphaFold2(AF2, Jumper et al. (2021)), the accurate computational modeling of antibody-antigen complexes remains a challenging task. In this paper, we first analyze AF2's primary loss function, known as the Frame Aligned Point Error (FAPE), and raise a previously overlooked issue that FAPE tends to face gradient vanishing problem on high-rotational-error targets. To address this fundamental limitation, we propose a novel geodesic loss called Frame Aligned Frame Error (FAFE, denoted as F2E to distinguish from FAPE), which enables the model to better optimize both the rotational and translational errors between two frames. We then prove that F2E can be reformulated as a group-aware geodesic loss, which translates the optimization of the residue-to-residue error to optimizing group-to-group geodesic frame distance. By fine-tuning AF2 with our proposed new loss function, we attain a correct rate of 52.3\% (DockQ $>$ 0.23) on an evaluation set and 43.8\% correct rate on a subset with low homology, with substantial improvement over AF2 by 182\% and 100\% respectively.