SPINET: Sheaf Protein Inverse Folding Network

Protein inverse folding aims to recover amino acid sequences for a given 3D protein structure, underpinning broad applications such as enzyme engineering and drug discovery.Current methods often follow a serial pipeline, in which a structure encoder predicts a coarse sequence, which is then refined by protein language models (PLMs). However, because PLMs only perform post-hoc sequence edits, the refinement is bounded by the quality of upstream predictions.Thanks to recent multimodal protein language models (MPLMs), we could directly encode structure to generate sequences with pretrained structural knowledge, but we observe that they are not effective for inverse folding. Therefore, we introduce a symmetric dual-path architecture that both leverages PLMs for pretrained sequence evolution knowledge and MPLMs for pretrained structural knowledge to iteratively guide protein sequence generation.Through extensive experiments across standard protein inverse folding benchmarks, our method achieves state-of-the-art performance, surpassing prior approaches, and ablation studies validate the rationale of our symmetric design, revealing a promising direction for the community.

Proteins move and deform to ensure their biological functions. Despite significant progress in protein structure prediction, approximating conformational ensembles at physiological conditions remains a fundamental open problem. This paper presents a novel perspective on the problem by directly targeting continuous compact representations of protein motions inferred from sparse experimental observations. We develop a task-specific loss function enforcing data symmetries, including scaling and permutation operations. Our method PETIMOT (Protein sEquence and sTructure-based Inference of MOTions) leverages transfer learning from pre-trained protein language models through an SE(3)-equivariant graph neural network. When trained and evaluated on the Protein Data Bank, PETIMOT shows superior performance in time and accuracy, capturing protein dynamics, particularly large/slow conformational changes, compared to state-of-the-art diffusion and flow-matching approaches, as well as traditional physics-based models. Our code and protocols are available at https://github.com/PhyloSofS-Team/PETIMOT.

How do protein structure prediction models fold proteins? We investigate this question through causal interventions on the folding trunks of ESMFold, OpenFold, and Boltz-1. Across all three models, we find a shared two-stage computational structure. In the first stage, early blocks initialize pairwise biochemical signals: features like charge propagate from sequence into pairwise representations through architecture-specific pathways. In the second stage, late blocks develop pairwise spatial features: distance and contact information accumulate in the pairwise representation. We verify these mechanisms causally by showing that steering charge and distance features induces predictable structural changes. Furthermore, these representations are functionally interchangeable: pairwise states can be linearly aligned and substituted across models. Together, these results suggest that folding trunks with different architectures, inputs, and training procedures converge on a shared representational organization for mapping sequence chemistry into spatial geometry.