PIS: A Physics-Informed System for Accurate State Partitioning of $Aβ_{42}$ Protein Trajectories

Diffusion models have been widely explored in protein backbone generation due to their powerful generation capabilities.However, in today's AI-driven biological research, predicting the structure of unknown multi-chain protein aggregates (called "complexes" in biology) remains an unsolved challenge.This is because existing static or dynamic protein datasets focus solely on static snapshots or single-entity trajectories, neglecting the dynamic process of multiple monomers forming complexes.To alleviate this dilemma, we present DynaPPI, a dynamic protein dataset comprising molecular dynamics (MD) trajectories of protein complex formation from dissociated chains to the bound state, as a pivotal resource to bridge the gap between static structural biology and the inherently temporal nature of dynamic molecular interactions.Benefiting from this dataset, diffusion models can explicitly learn the dynamic binding trajectories of known complexes and accurately predict the structures of unknown complexes based on their diverse generative properties, thereby further catalyzing AI-driven structural biology and protein interactomics.

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.

Proteins are inherently multiscale physical systems whose functional properties emerge from coordinated structural organization across multiple spatial resolutions, ranging from atomic interactions to global fold topology. However, existing protein representation learning methods typically operate at a single structural level or treat different sources of structural information as parallel modalities, without explicitly modeling their hierarchical relationships. We introduce PRIME (Protein Representation via Physics-Informed Multiscale Equivariant Hierarchies), a unified framework that models proteins as a nested family of five physically grounded structural graphs spanning surface, atomic, residue, secondary-structure, and protein levels. Adjacent levels are connected through deterministic, physics-informed assignment operators, enabling bidirectional information exchange via bottom-up aggregation and top-down contextual refinement. Experiments on standard protein representation learning benchmarks demonstrate strong and competitive performance across diverse tasks, with particularly notable gains on the Fold Classification benchmark, where PRIME outperforms the strongest geometric GNN baseline by margins of 13.80 and 18.30 points on the harder Superfamily and Fold splits, and achieves a state-of-the-art accuracy of 84.10% on Reaction Class prediction, surpassing all baseline methods, including ESM. Ablation studies confirm that each structural level contributes complementary and non-redundant information, and adaptive cross-attention analysis reveals that PRIME autonomously identifies the most task-relevant structural resolutions at prediction time. Our source code is publicly available at https://github.com/HySonLab/PRIME