Protein Data Bank

Intrinsically disordered proteins (IDPs) differ from folded proteins in that they are dynamic, lack a stable three-dimensional conformation, and have low sequence similarity between similar proteins. The conformational heterogeneity of IDPs - while beneficial for their diverse functions - limits the use of traditional experimental tools to determine their conformation. The experimental difficulty, along with low sequence similarity, results in data scarcity, and makes it difficult to classify/detect IDPs that are similar or dissimilar, a task relevant to understand biology and evolution. We address this challenge using Multi-task ProtBERT (MT-ProtBERT), a multi-task extension of ProtBERT tailored for low-data regimes. MT-ProtBERT integrates Dynamic Window Masking, a Multi-Scale 1D Convolutional classifier (MS-Conv1D), and auxiliary objectives that jointly optimize masked language modeling and biochemistry-informed tasks. We evaluate this framework on two tasks under limited data: (i) phosphorylation site prediction (S/T/Y) in short sequences and small datasets, and (ii) protein compaction prediction on two small datasets (684 and 530 sequences), including sequences comparable in length to typical disordered regions. MT-ProtBERT consistently outperforms PARROT, an RNN-based IDP-specific model, across all tasks. These results demonstrate that combining self-supervised and biochemistry-informed tasks, and multi-scale learning enables robust modeling of unstructured proteins under data scarcity.

Protein-protein interaction (PPI) databases do not faithfully reflect biological realities. Instead, they are influenced by study and technical biases that distort certain protein and interaction attributes. Machine learning models can exploit these as learning shortcuts if the negative dataset is not constructed with care. So far, the shortcuts introduced during PPI dataset construction have only been examined in isolation. Here, we systematically characterize both reported and, to our knowledge, previously unreported biases in PPI datasets that lead machine learning models to learn shortcuts instead of biological signal. We analyze HIPPIE, IntAct, and STRING, dedicated PPI databases, as well as two datasets derived from 3D-structural information in the Protein Data Bank (PDB). We show that random data splitting introduces strong topological shortcuts. When train-test protein overlap is removed, the resulting datasets still retain usable shortcuts stemming from self-interactions, taxonomic identity, and functional relatedness, whose prevalence interestingly depends on the data source. We further show that sampling negatives from a set of high-confidence non-interactors, an intuitively appealing choice, can amplify the shortcut stemming from functional relatedness. To detect and mitigate these biases, we provide an open Nextflow pipeline that combines similarity-aware, data-loss-minimizing dataset splitting with bias-minimizing negative sampling, both formulated as integer linear programs. Its key concept of quantifying biases to minimize them through optimization-based negative sampling can, in principle, be extended to any machine learning problem where the pool of negative candidates is much larger than the positives and is thus of interest also beyond PPI prediction.

Bringing multiscale geometric analysis directly to irregular point clouds remains difficult: quantities such as local dimension, anisotropy, density variation, and geometric transitions are typically estimated through explicit neighborhood, manifold, or graph constructions, or left for neural networks to infer from coordinates. We introduce Heat Field Signatures (HFS), which lift a point cloud to a multiscale family of smooth ambient heat fields, providing a direct interface from discrete samples to geometric analysis. From this field, HFS computes closed-form global and local signatures directly from pairwise distances, capturing heat concentration, intrinsic dimension, anisotropy, and scale transitions. We further introduce the Heat Dimension Spectrum (HDS), a compact summary of multiscale geometric composition. HFS can be used as a closed-form descriptor, a lightweight learned representation, or a geometric feature channel for neural point-cloud models. Across synthetic and real-world benchmarks spanning subcellular, neuronal, tree, and protein data, HFS outperforms strong point-cloud and multiparameter-persistence baselines while substantially reducing end-to-end cost. On SCOP protein-fold classification, HFS improves over the strongest deep baseline by nearly $24$ percentage points using coordinates alone, while standalone HFS representations are exactly rotation-invariant by construction. More broadly, HFS turns a classical heat field into a practical interface for multiscale geometric analysis in modern point-cloud learning.

Protein structure modeling rests on a single computational primitive: the interaction between what a residue is (sequence content) and where it sits (three-dimensional geometry). What is the expressive limit of this layer class? We show that the complete bilinear operator over content-geometry outer products--the sufficient statistic of all second-order interactions--is the expressive ceiling, while the additive message passing of mainstream geometric GNNs is provably blind to content-geometry binding. We then introduce Hyper-Fold, a rank-K separable convolutional backbone approaching this ceiling at message-passing cost: each radius neighborhood is organized into a sequence hyperedge and a contact hyperedge, modulated by an edge-conditioned matrix-valued operator factorized into K learned basis operators with geometry-generated coefficients. Across enzyme function prediction, fold classification, and ligand binding site detection, Hyper-Fold and its hierarchical variant Hyper-Fold-Deep achieve the best results among protein-specific structure encoders; Hyper-Fold-Pocket, an anchored set-prediction head, surpasses UniSite-3D on UniSite-DS and two zero-shot benchmarks with no sequence language model features, 68x fewer parameters, and 4.8x lower latency--suggesting that a sufficiently expressive 3D backbone recovers information that fusion architectures previously borrowed from evolution-scale pretraining.

Foundation models for protein structure prediction remain unreliable on certain targets. External oracles can flag and correct these failures, but biological oracles are expensive, making oracle budget a critical constraint. Existing guidance methods, such as FK-steering, DPO, and Best K-of-N sampling, differ in how they spend this budget, yet no systematic comparison exists to guide method selection. To bridge this gap, we benchmark these methods alongside the recently proposed Optimisation Over Outputs (O3), which applies off-the-shelf optimisers within a generative model's latent subspace. We extend the usage of O3 to protein structure prediction models. Overall, our work provides the first practical reference for oracle budget-aware guidance. Our evaluation on two protein targets, calmodulin (1CLL) and E. coli aspartate transcarbamoylase (9EEH), reveals that no single method consistently dominates across all budgets and oracles. Specifically, O3 proves most effective at low oracle budgets, while FK-steering and DPO demonstrate improved performance as the budget increases. We distil these findings into actionable recommendations for practitioners operating under real-world oracle-budget constraints.

AlphaFold3-class structure predictors pair a representational trunk, which processes sequence and context, with a diffusion module, which generates atomic coordinates. How biological information changes as it crosses this architectural boundary remains poorly understood. We analyze per-residue activations from the Pairformer trunk and diffusion module of Boltz-1 using linear probes, sparse autoencoders (SAEs), and causal interventions. From the trunk, both geometry (secondary structure, disorder) and sequence chemistry (amino-acid identity, signal peptides, disulfide-bond annotations) are linearly decodable. In the diffusion module, the two diverge. Secondary structure transfers essentially unchanged, whereas sequence chemistry is strongly attenuated. We then test whether decodable directions can steer the model, intervening on the final trunk single representation that conditions the diffusion module. Helix and coil directions change predicted structure dose-dependently against matched-norm random controls, but a beta-strand direction that is highly predictive (F1 =0.82) produces no measurable increase in strand content: linear decodability does not imply causal influence at the site we tested. The same probes also score markedly lower against sparse SwissProt annotations than against dense DSSP labels, because unannotated residues that the model gets right are charged as false positives; such scores are therefore lower bounds. Finally, supervised probes outscore single SAE features wherever a label already exists. We release the trained trunk and diffusion SAEs, Boltz-1 per-residue activations, and the analysis code.

Multiple Sequence Alignments (MSAs) provide protein language models with explicit evolutionary context, but their large depth makes subsampling unavoidable under limited token budgets. Existing strategies, including random selection, identity-based filtering, and diversity-driven sampling, are effective heuristics, yet provide limited control over the evolutionary signals retained in the subset. In this work, we recast MSA subsampling as an explicit optimization problem, where key evolutionary measures, including query identity and diversity, are treated as controllable objectives. Building on this view, we introduce AP-REASONER, an Affinity-Propagation-based factor-graph approach. With evolution-aware unary factors, exemplar-consistency factors, and two control knobs, AP-REASONER performs factor-graph reasoning through message passing to infer a fixed-budget MSA subset. Experiments on long-range contact prediction and conformational ensemble prediction show that AP-REASONER outperforms baseline subsamplers on structure-sensitive downstream tasks and enables controllable recovery of alternative protein conformations. These results highlight the value of modeling MSA subsampling as a controllable optimization problem, where factor-graph reasoning offers an effective alternative to heuristic selection.

Protein language models learn transferable sequence representations. However, because they primarily model contextual dependencies along amino-acid sequences, their training objectives do not explicitly constrain the model to learn three-dimensional residue contacts formed after folding . Here, we introduce LC-SEPLM (Long-range Contact-supervised ESM Protein Language Model), which adapts ESM2 with LoRA and long-range residue-pair contact supervision while retaining sequence-only downstream inference. Pair-specific queries use cross-attention over the complete sequence to extract global sequence context associated with long-range spatial contacts. To expose the model to diverse structural information, we trained LC-SEPLM on 500,000 AlphaFold Swiss-Prot proteins. In downstream evaluation, LC-SEPLM improved all eight protein-level tasks relative to ESM2. The largest gain occurred in remote-homology recognition, where macro-F1 increased from 0.6122 to 0.6769 (+0.0647, or 6.47 percentage points). On the official ESM-S EC benchmark, LC-SEPLM also outperformed ESM-S with a maximum absolute gain of 0.1771. These results support residue-pair contact supervision as a bounded route for introducing structural information into protein sequence representations while preserving sequence-only inference.

AlphaFold2's 93 million parameters, shaped by the evolutionary record of protein structure encoded in the Protein Data Bank and in sequence alignments, are conventionally treated only as machinery for converting sequence to structure. We propose they are also a scientific object that can be analyzed directly: a learned encoding of protein conformational organization that can be probed and characterized. By smoothing the Evoformer's weight tensors with a Gaussian convolution and scaling the result, we show that the trained model produces physically structured conformational landscapes. Under perturbation, ubiquitin's native contacts break in the order established by decades of folding experiments. For KaiB, five independently trained models agree that the alternative fold is not recovered under perturbation. For alpha-synuclein, five models produce five different but coherent landscapes, mapping where the training signal has determined the representation and where it has not. Matched-power noise controls confirm that random corruption of equal magnitude produces debris, not conformations. The model learned to predict static structures; the conformational organization visible under perturbation was not an explicit training target, suggesting it emerged as a byproduct of that objective. AlphaFold2's weights appear to encode structural constraints, shaped by evolutionary and structural training data, that extend beyond what unperturbed inference reveals. We call the approach of reading them neural spectroscopy, and Scaled Gaussian Convolution one such protocol.

Machine learning interatomic potentials (MLPs) have revolutionized atomistic modeling, offering the potential to replace traditional methods like Density Functional Theory (DFT). However, inference time of MLPs is orders of magnitude slower than that of classical force fields, hindering real-world applications for biomolecular systems that require timescales of microseconds and beyond. Implicit solvent MLPs can address this issue, but are faced with data challenges associated with coarse-grained modeling. Consequently, previous approaches relied on empirical force field data, thereby inherently limiting the MLP's accuracy. Here, we introduce the Transferable Water Implicit Network (TWIN), an implicit water MLP parametrized entirely by an Equivariant Graph Neural Network and trained solely on ab initio and experimental labels. We demonstrate TWIN's transferability across drug-like molecules, peptides, and proteins, achieving excellent results on ab initio and experimental crystallographic and NMR benchmarks, consistently outperforming previous machine-learning-based implicit solvent or coarse-grained models. Furthermore, TWIN closely matches DFT-based explicit solvent MLPs while providing a two-order-of-magnitude faster timestep evaluation, paving the way for efficient ab initio-level modeling of biomolecular systems in aqueous environments.

Foundation models for structural biology have achieved remarkable performance in predicting biomolecular structure and show promise for the design of proteins and small molecules. Yet understanding which internal features drive their outputs remains challenging. Standard sparse autoencoders (SAEs), effective on transformer-style sequence embeddings, do not transfer cleanly to pairformer-like architectures: naively operating on pairwise representations yields a quadratic blow-up of features and obscures concepts distributed jointly across sequence and pair representations. We introduce PairSAE, which summarizes pairwise tensors via an N-mode SVD into token-wise interaction roles, then uses a sparse autoencoder to learn a shared set of token-level features that decode into both sequence and pair representations. Evaluated on Boltz-2 activations for PLINDER protein-ligand complexes, PairSAE yields interpretable features that align with UniProt annotations and predict Boltz-2 affinity values. These results indicate that PairSAE links the latent space of foundation models for structural biology to interpretable structural concepts, clarifying what the model "knows" while avoiding pairformer-induced pitfalls that limit conventional SAEs.

Data augmentation (DA) has been proven to be an effective means for improving protein representation learning (PRL) by generating additional training samples. Although mainstream perturbation- and sampling-based augmentation methods can produce data containing sufficient variations, they carry the risk of disrupting the protein structure and function. Some crafted protein homology modeling tools can generate conformations, but reduce structural diversity. The above dilemmas lead us to a question: Can we restore the disrupted structure caused by DA operations, providing data with both the original structure and diverse variations? In this work, we first analyze and empirically reveal the structure defect and performance degradation issues of existing DA methods. Based on the findings, we propose a simple yet effective DA method, Manifold Restore Mixing (MRM), for protein representation learning. Specifically, inspired by manifold mixup, we mix the hidden representations of original and augmented protein data to generate new samples that restore structural information lost in DA while introducing diverse variations. Furthermore, we develop a sample difficulty scheduler that adjusts the beta distribution in mixup to provide models with progressively challenging mixed samples during training, which improves the final performance. Comprehensive experiments on various PRL backbones and downstream tasks demonstrate the effectiveness and generalization of our method. The complete code and weights will be released upon acceptance. We provide a implementation at https://github.com/KingGugu/MRM.

Correct identification of fish species is highly significant for food security, economic development, and climate resilience in Bangladesh. Protein sequences directly reflect functional and evolutionary constraints which are important for species authentication and biodiversity monitoring. Yet there exists no benchmark for native Bangladeshi fish species identification from protein sequence. In this study, we addressed this gap by introducing the first curated dataset for nine native Bangladeshi fish species of 2845 high quality protein sequences. We also established the first protein sequence classification baseline for this domain through a systematic benchmarking of seven architectural paradigms. Moreover, we propose a realistic deployable novel hybrid architecture of MotifCNN and Transformer with Terminal-Aware Positional-Encoding (MotifCNN-Transformer+TA-PE). Our novel architecture achieves 79.80% accuracy with macro-F1 of 0.80. The highest 83.04% accuracy is achieved by finetuned protein language model ProtBERT that has 420M parameters and requires dual 16GB GPUs for inference. According to McNemar's test, ProtBERT's 3.24% accuracy gain over our MotifCNN-Transformer+TA-PE is statistically insignificant (p = 0.1120). Our novel architecture beats it among six of the nine classes in per class identification. Also our MotifCNN-Transformer+TA-PE is approximately 5x faster, 42x smaller, and supports 16x larger batch size than ProtBERT and has GPU free inference, making it more practical for deployment in resources constrained areas such as rural Bangladesh. Beyond this, our foundational work shows effects of phylogenetic relationships on sequence similarity and establishes pathways for fisheries management, food authentication and biodiversity conservation in South Asia's protein dependent economy.

Graph-based representations are widely used in protein modeling, yet many existing approaches rely primarily on sequence adjacency or geometric proximity, which only partially reflect the principles governing protein folding. Proteins instead adopt complex three-dimensional conformations organized around secondary structure elements, such as $α$-helices and $β$-sheets, which encode recurring local motifs and stabilizing hydrogen-bond interactions. In this work, we introduce a secondary-structure-aware graph neural network for protein representation learning. Residue-level node representations are augmented with secondary structure assignments, and graph edges are constructed from hydrogen-bond interactions filtered by their energetic strength. This design enables the model to capture both local structural context and long-range couplings that are central to protein stability and function. We evaluate the proposed approach on commonly used protein benchmarks and observe consistent improvements over existing graph-based methods. In addition, the resulting graph representations offer enhanced biological interpretability, as the learned connectivity aligns with established structural motifs. These findings suggest that incorporating secondary structure and energy-filtered hydrogen-bond topology provides an effective inductive bias for protein representation learning. The code is released at https://github.com/mohamedmohamed2021/SSProNet

Despite its importance to applications in protein design, predicting protein properties like binding affinity and thermostability from sparse experimental data remains a significant challenge. Accordingly, we introduce a class of sequence kernels that exploit evolutionary substitution matrices as well as local linearity and demonstrate that the resulting Gaussian processes provide data-efficient models of protein property landscapes, frequently outperforming alternatives that rely on foundation model embeddings. Furthermore--by learning what are in effect structure-aware substitution matrices--we show that our kernels can readily incorporate structural information from foundation models. We demonstrate that these structure-conditioned kernels are well suited to multi-task learning across multiple protein property landscapes and can decisively outperform local supervised learning methods.

Multimodal $ΔΔG$ predictors integrating protein language models with inverse-folding representations achieve strong in-distribution accuracy on the Megascale dataset but exhibit limited robustness on out-of-distribution (OOD) proteins, persistent forward-reverse bias on paired-mutation benchmarks, and under-representation of rare stabilizing mutations. Existing approaches address these limitations primarily through additional architectural components, leaving optimization-level intervention comparatively underexplored. We introduce a constraint-aware optimization framework combining Balanced Mean Squared Error, a Siamese anti-symmetric regularizer, and a novel OOD-margin consistency loss on the per-position feature representation, requiring no architectural changes to the SPURS backbone. Across eleven benchmarks and three random seeds, the framework improves Spearman correlation on S669 from 0.486 to 0.540 ($σ=0.002$ across seeds), matching the published SPURS baseline (0.50) without architectural modification, and on S461 from 0.653 to 0.711, with consistent smaller gains on five additional OOD datasets. A controlled diagnostic on Ssym reveals that anti-symmetric training does not eliminate systematic forward-reverse bias, indicating that gains arise through implicit regularization rather than exact thermodynamic constraint enforcement.

Generative emulators of protein dynamics produce plausible trajectories at a fraction of the cost of molecular dynamics, but they inherit their training distribution and tend to revisit known states rather than reach rare ones under long-horizon extrapolation. Inspired by classical enhanced sampling, we introduce an implicit, history-dependent bias in the generative space of a pretrained emulator. Specifically, a history-aware score estimator augments the frozen emulator with a distance-weighted bias that steers reverse-time sampling away from previously generated structures, regularized by an environment-support term. To preserve structural validity at long horizons, a score-based refinement step re-projects drifted samples onto the data manifold using the frozen emulator. Our experiments demonstrate that the method (i) raises diversity by $35\%$ on DynamicPDB-80; (ii) on $12$ zero-shot Fast-Folding proteins, the learned bias alone reaches the unbiased emulator's coverage up to ${\sim}15\times$ faster, and pairing it with refinement reaches the coverage up to ${\sim}37\times$ faster while covering ${\sim}3\times$ as many low-energy states. Code will be released soon.

Despite the growing availability of cryo-electron microscopy (cryo-EM) density maps, effectively leveraging them for protein representation remains challenging. First, current methods lack a general-purpose protein pretraining framework tailored for cryo-EM density maps, designed for protein-related property prediction. Second, existing approaches typically partition density maps into local box regions and model them independently, overlooking interactions across boxes which are essential for capturing global structural context in cryo-EM density map. To address these challenges, we propose CryoProt, a protein pretraining framework designed for cryo-EM density maps. CryoProt introduces a Map Encoder based on multi-head latent attention (MLA), where box-level representations interact through a shared latent space, enabling explicit modeling of cross-box dependencies within the density map. Furthermore, we adopt a multi-task pretraining strategy to learn generalizable representations that can be effectively transferred to diverse downstream tasks, such as protein flexibility prediction, where cryo-EM density maps are not required and can be inferred implicitly by the pretrained model. Experimental results demonstrate that CryoProt consistently outperforms existing state-of-the-art methods across multiple benchmarks, achieving up to 12% improvement over the best-performing baselines, highlighting the importance of modeling cross-box interactions in cryo-EM data. The source code is publicly available at https://anonymous.4open.science/r/CryoProt.

Protein-language systems are often evaluated by whether they generate plausible biological text, but a structural question has a sharper semantics: it denotes a measurement in a 3D coordinate system. We introduce ProtStructQA, an executable benchmark for protein structural question answering in which each natural-language question is generated from a hidden typed domain-specific language (DSL) program and the answer is obtained by executing that program on an AlphaFold-predicted structure. ProtStructQA releases 382.2K questions covering confidence, distances, predicted aligned error (PAE), solvent exposure, secondary structure, topology and contacts, and held-out compositions: a 330K active benchmark over 10K proteins from four species, plus a 52.2K hard-negative robustness pool. Without fine-tuning, we evaluate Qwen3 models from 0.6B to 8B under direct prompting, chain-of-thought, grammar-constrained executable voting, executable voting with chain-of-thought, and multi-turn ReAct-style tool use, and replicate the headline finding on Gemma-3-1B and Gemma-3-12B. We find a capability-dependent denotation threshold between Qwen3-1.7B and Qwen3-4B: below it, tool-mediated ReAct dominates because models often fail to produce executable denotations; above it, chain-of-thought flips from mostly harmful to strongly beneficial and becomes the strongest strategy on most splits. Parse-failure and family-level analyses show that the threshold is a transition from unparseable language to executable structural denotation, while grammar and execution remain selectively valuable for PAE and secondary-structure queries. ProtStructQA reframes scientific QA as compilation from language to measurement and provides a diagnostic testbed for when language models can map words to executable 3D structural measurements.

We present AMix-2, a protein-text foundation model that establishes protein as a native modality in large language models (LLMs), unifying protein understanding and sequence design within a single foundation model. AMix-2 is built upon two key ideas: (1) a unified protein-text formulation that embeds natural language and protein sequence in a shared token space, enabling one model to perform biological reasoning and conditional design instead of separate downstream task-specialized models; and (2) a block-wise diffusion language modeling backbone that combines causal generation across blocks with bidirectional context and iterative refinement within blocks. This scheme better matches the intrinsic nature of proteins than a strict left-to-right factorization. To evaluate protein foundation models under realistic generalization settings, we further introduce ProteinArena, a comprehensive benchmark with time-aware and homology-aware protocols across various understanding and design tasks, and with baselines covering classical bioinformatics tools, protein-specialized models and LLMs. On ProteinArena, AMix-2 outperforms frontier LLMs and demonstrates competitive performance to task-specific protein models. Controlled experiments further show that the diffusion-based paradigm generally surpasses its autoregressive counterpart, highlighting the advantage of flexible generation order for protein sequences. We release both AMix-2 and ProteinArena to facilitate open research in protein foundation models.

Protein structure classification (PSC) uses supervised learning to predict a protein's CATH/SCOP(e) class from the protein's sequence or 3D structural feature(s). We already modeled 3D structures as (static) protein structure networks (PSNs), demonstrating the competitiveness of PSN-based features to sequence or direct (i.e. non-network) 3D structural features in the PSC task. More recently, we demonstrated the power of features extracted from dynamic PSNs over features extracted from static PSNs (and thus by transitivity over sequence and direct 3D structural features) in the same task. That dynamic PSN approach used traditional machine learning (ML), combining manual (pre-engineered) features with an off-the-shelf classifier. Here, we evaluate whether automatic deep learning (DL) from the dynamic PSNs yields improvements. Our evaluation on 72 datasets spanning ~44,000 CATH- or SCOPe-labeled dynamic PSNs reveals that in terms of PSC accuracy, traditional ML and DL are (close to) tied for a large majority of the datasets, while DL is on average 10+ times slower. We are the first to evaluate traditional ML vs. DL in the dynamic PSN-based PSC task.

Recent advances in generative modeling show that pretrained representations can improve generation as conditioning features or alignment targets. Motivated by this, we study protein representations for predicting structures beyond conventional function annotation. We propose TriProRep, a structure-aware pretraining method that jointly models three aligned residue-level views: amino-acid identity, backbone geometry, and local full-atom geometry, discretely encoded via VQ-VAE tokenizers. By pretraining to recover original tokens from generator-corrupted views, TriProRep learns to distinguish plausible but incorrect cross-view augmentations from the original protein. We further introduce RepSP, a benchmark for evaluating protein representations in structure-predictive settings. RepSP tests three uses of representations: homodimer co-folding from apo-chain representations, residue-level prediction of homodimer-derived interaction properties, and representation-aligned monomer structure prediction. Across these tasks, TriProRep improves over sequence-only and prior structure-aware representation models, while maintaining competitive performance on conventional benchmarks.

Classifying protein topology is essential for deciphering biological function, but progress is held back by the lack of large-scale benchmarks that avoid duplicates and by models that do not scale well. We introduce TEDBench, a large-scale, non-redundant benchmark for protein fold classification constructed from the Encyclopedia of Domains (TED) and Foldseek-clustered AlphaFold structures. We show that on TEDBench, current protein representation learning methods either require very large models or fail to deliver strong performance. To address this challenge, we propose Masked Invariant Autoencoders (MiAE), a self-supervised framework for protein structure representation learning. MiAE uses an extremely high masking ratio of up to 90% with an $\mathrm{SE(3)}$-invariant encoder and a lightweight decoder that reconstructs backbone coordinates from the latent representation and mask tokens. MiAE scales well and outperforms supervised counterparts and state-of-the-art baselines on TEDBench, establishing a strong recipe for protein fold classification. To test transfer beyond AlphaFold structures, we further benchmark on a curated dataset from experimental structures of CATH v4.4. TEDBench is available at https://github.com/BorgwardtLab/TEDBench.

Masked language modeling (MLM) is the standard objective for training protein language models, typically implemented by randomly masking individual residues at a fixed rate (e.g., 15%). This practice implicitly assumes that all sequence positions contribute equally to representation learning. In downstream fitness prediction tasks, however, protein sequences are governed by three-dimensional structural dependencies and long-range residue contacts that induce strong nonlocal couplings between residues. We introduce Bucket Masking, a structure-aware masking strategy that selects groups of residues based on their proximity in three-dimensional space, preferentially masking structurally coupled regions during training. By conditioning the masking distribution on residue contacts, Bucket Masking shifts the learning objective toward modeling long-range interactions that are critical for protein function. Across four downstream protein fitness prediction tasks, Bucket Masking enables up to a 14% improvement over standard random masking, excelling at predicting higher-order mutational interactions. Through controlled ablations, we show that these improvements arise from mask placement rather than span size, establishing masking as a positional inductive bias.

Generative models trained on public databases of protein structures, most of which have been determined by X-ray crystallography, now provide powerful priors for structure prediction. However, they are not readily conditioned on the measurements from a new crystallographic experiment, limiting their use for X-ray structure determination. In crystallography, the measured structure-factor amplitudes do not by themselves determine an electron density map or atomic structure because the associated phases are unobserved and must be inferred. Structure determination therefore remains an inverse problem in which candidate models must be both structurally plausible and consistent with measured diffraction data, often requiring substantial manual refinement by human experts. Emerging methods aim to incorporate experimental information more directly into predictive and refinement workflows. We present CrystalBoltz, a generative framework that casts crystallographic refinement as Bayesian inference over atomic structures and operates directly on structure-factor amplitudes. CrystalBoltz moves from unguided generation with a pre-trained prior over protein structures to experiment-guided posterior sampling, followed by atomic coordinate and B-factor refinement. Across multiple protein crystallography datasets, CrystalBoltz attains lower coordinate RMSD and lower R-factors than the strongest baselines considered, while reducing runtime by a factor of 33 relative to existing experimentally guided refinement.

Protein structure tokenizers (PSTs) are workhorses in protein language modeling, function prediction, and evolutionary analysis. However, existing PSTs only capture local geometry of static structures, and miss the correlated motions and alternative conformational states revealed by protein ensembles. Here we introduce Ensembits, the first tokenizer of protein conformational ensembles. Ensembits address challenges inherent to tokenizing dynamics: deriving informative geometric descriptors across conformations, permutation-invariance encoding of variable-size ensembles, and conquering sparsity in dynamics data. Trained with a Residual VQ-VAE using a frame distillation objective on a large molecular dynamics corpus, Ensembits outperforms all related methods on RMSF prediction, and is the strongest standalone structural tokenizer on an token-conditioned ANOVA test on per-residue motion amplitude. Ensembits further matches or exceeds static tokenizers on EC, GO, binding site/affinity prediction, and zero-shot mutation-effect prediction despite using far less pretraining data. Notably, the distillation objective enables Ensembits to predict dynamics token from one single predicted structure, which alleviates dynamics data sparsity. As the field moves from static structure prediction toward ensemble generation, Ensembits offer the discrete vocabulary needed to bring dynamics into protein language modeling and design.

Proteins encode diverse functions within complex three-dimensional structures, yet most deep learning representations remain highly entangled, obscuring the biophysical signals that underlie function. Here we introduce ProtDiS, a knowledge-guided framework that decomposes pretrained protein micro-environment embeddings into biologically grounded and task-relevant dimensions. Inspired by the information bottleneck principle, ProtDiS learns representations that balance informativeness and compression, yielding structural features that are more specific, independent, and information-efficient, and achieving consistent improvements across twelve downstream tasks, with the largest gains under structure-based splits. Protein- and residue-level analyses further show that ProtDiS differentiates proteins with similar folds but divergent functions and captures fine-grained biophysical signals critical. These findings suggest that knowledge-guided decomposition provides a general and interpretable approach for structuring latent spaces in protein structural modeling. The source code and implementation details are publicly available at https://github.com/AI-HPC-Research-Team/ProtDiS.

Accurately modeling and designing protein complex structures is a central problem in computational structural biology, with broad implications for understanding cellular function and developing therapeutics. This thesis investigates two fundamental aspects of this problem using deep learning: domain-specific architectures that capture the hierarchical nature of protein structures, and search algorithms that efficiently navigate the vast sequence spaces of protein complexes to identify interacting homologs for improving complex structure prediction and to design protein sequences.

Multimodal models that jointly reason over protein sequences, structures, and function annotations within a unified representation hold immense potential for integrating multimodal data and generating new proteins with designed functional properties. To utilize transformer architectures, such models require a tokenizer that converts protein structure from continuous atomic coordinates into discrete representations suitable for scalable multimodal training. The quality of such models are fundamentally upper bounded by the fidelity and expressiveness of the underlying tokenized structure. However, existing tokenizers prioritize reconstruction over generative abilities. To address these gaps, we introduce Yeti, a simple and compact protein structure tokenizer based on lookup free quantization and trained end to end with a flow matching objective for multimodal learning. Compared to existing models, Yeti generally achieves the best codebook utilization and token diversity, and second best reconstruction accuracy (with 10x fewer parameters than ESM3) on diverse datasets. To validate Yeti's generative capability, we trained a compact multimodal model jointly over its structure tokens and amino acid sequence entirely from scratch, with no pretrained initialization. The resulting multimodal model generates plausible structures under unconditional cogeneration of protein sequence and structures, achieving comparable results to 10x larger models. Together, these results demonstrate that Yeti is a compact and expressive protein structure tokenizer suitable for training multimodal models that cogenerates highly plausible sequences and structures.

Predicting microbial operon co-membership requires integrating two complementary biological signals: protein-scale molecular identity and genome-context organization. While recent biological foundation models provide powerful representations of each view independently, naive concatenation of these modalities ignores a key biological property -- protein identity and genomic context may agree when adjacent genes form a coherent functional module, or conflict when sequence similarity is misleading but genomic layout indicates independent regulation. We present MicroFuse, a protein-to-genome expert fusion framework that integrates structure-aware protein representations from ProstT5 with genome-context representations from Bacformer through a four-expert Mixture-of-Experts module (protein, genome-context, agreement, and conflict experts) with a learned soft router. Training combines binary cross-entropy with symmetric cross-modal InfoNCE alignment and disagreement-weighted supervised contrastive shaping. We further construct OG-Operon100K, a 100,000-pair scaffold-level benchmark from the OMG metagenomic corpus with biologically grounded positive and negative criteria. On OG-Operon100K, MicroFuse achieves the strongest AUROC, AUPRC, mAP, and mAR among ProstT5-only, Bacformer-only, and Concat MLP baselines. Ablations identify cross-modal contrastive alignment as the dominant component, and a hard sequence-conflict subset reveals MicroFuse's largest gains precisely in biologically ambiguous cases where protein identity alone is misleading.

Protein language models (pLMs) produce per-residue representations that capture evolutionary and structural information, yet their mean-pooled sequence embeddings are not explicitly trained to reflect functional, evolutionary or structural similarity between proteins. We present Protein Sentence Transformers (ProtSent), a contrastive fine-tuning framework for adapting PLMs into general-purpose embedding models. ProtSent trains with MultipleNegativesRankingLoss across five protein-pair datasets: Pfam families, structurally derived hard negatives, AlphaFold DB structural pairs, and StringDB protein--protein interactions, and Deep Mutational Scanning data. We evaluate on 23~downstream tasks using frozen embeddings with a k-nearest-neighbor probe to measure embedding neighborhood quality. On ESM-2 150M, ProtSent improves 15 of 23 tasks, with gains of +105% on remote homology detection, +17% on variant effect prediction, and +19.9% Recall@1 on SCOPe-40 structural retrieval. The 35M variant improves 16 of 23 tasks with +40.5% on remote homology and +15.5% Recall@1 on SCOPe-40. Contrastive fine-tuning restructures the embedding space to better capture protein function and structure, without any task-specific supervision. We release the models, public data, and training recipe and code.

The integration of deep learning approaches in biomedical research has been transformative, enabling breakthroughs in various applications. Despite these strides, its application in protein inference is impeded by the scarcity of extensively labeled datasets, a challenge compounded by the high costs and complexities of accurate protein annotation. In this study, we introduce GraphPI, a novel framework that treats protein inference as a node classification problem. We treat proteins as interconnected nodes within a protein-peptide-PSM graph, utilizing a Graph Neural Network-based architecture to elucidate their interrelations. To address label scarcity, we train the model on a set of unlabeled public protein datasets with pseudo-labels derived from an existing protein inference algorithm, enhanced by self-training to iteratively refine labels based on confidence scores. Contrary to prevalent methodologies necessitating dataset-specific training, our research illustrates that GraphPI, due to the well normalized nature of Percolator features, exhibits universal applicability without dataset-specific fine-tuning, a feature that not only mitigates the risk of overfitting but also enhances computational efficiency. Our empirical experiments reveal notable performance on various test datasets and deliver significantly reduced computation times compared to common protein inference algorithms.

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

The inverse Potts problem for estimating evolutionary single-site fields and pairwise couplings in homologous protein sequences from their single-site and pairwise amino acid frequencies observed in their multiple sequence alignment would be still one of useful methods in the studies of protein structure and evolution. Since the reproducibility of fields and couplings are the most important, the Boltzmann machine method is employed here, although it is computationally intensive. In order to reduce computational time required for the Boltzmann machine, parallel, persistent Markov chain Monte Carlo method is employed to estimate the single-site and pairwise marginal distributions in each learning step. Also, stochastic gradient descent methods are used to reduce computational time for each learning. Another problem is how to adjust the values of hyperparameters; there are two regularization parameters for evolutionary fields and couplings. The precision of contact residue pair prediction is often used to adjust the hyperparameters. However, it is not sensitive to these regularization parameters. Here, they are adjusted for the fields and couplings to satisfy a specific condition that is appropriate for protein conformations. This method has been applied to eight protein families.

Proteins carry out biological functions through the coordinated action of groups of residues organized into structural arrangements. These arrangements, which we refer to as protein units, exist at an intermediate scale, being larger than individual residues yet smaller than entire proteins. A deeper understanding of protein function can be achieved by identifying these units and their associations with function. However, existing approaches either focus on residue-level signals, rely on curated annotations, or segment protein structures without incorporating functional information, thereby limiting interpretable analysis of structure-function relationships. We introduce PUFFIN, a data-driven framework for discovering protein units by jointly learning structural partitioning and functional supervision. PUFFIN represents proteins as residue-level structure graphs and applies a graph neural network with a structure-aware pooling mechanism that partitions each protein into multi-residue units, with functional supervision that shapes the partition. We show that the learned units are structurally coherent, exhibit organized associations with molecular function, and show meaningful correspondence with curated InterPro annotations. Together, these results demonstrate that PUFFIN provides an interpretable framework for analyzing structure-function relationships using learned protein units and their statistical function associations. We made our source code available at https://github.com/boun-tabi-lifelu/puffin.

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.

A growing number of neural architectures have been proposed to enforce geometric constraints, including projection-based networks, exponential-map updates, constrained output layers, and manifold neural ODEs. We provide a unified framework for these geometry-preserving architectures by organizing them according to where and how constraints are enforced, either throughout the intermediate layers or only at the final output. This perspective reveals several gaps in the existing theory. To address these gaps, we prove high-level approximation theorems for projected neural ODEs, intermediate augmented architectures, and final augmented architectures on prox-regular constraint sets, including smooth manifolds with boundary. Numerical experiments on synthetic dynamics over S^2, the disk, SO(3), together with real-world protein backbone data on SE(3), demonstrate exact feasibility for analytic updates and show that the final augmentation have simpler architecture and outperform in most tasks considered. When the constraint set is unknown, we learn projections via small-time heat-kernel limits, showing diffusion/flow-matching can be used as data-based projections. Moreover, we also the demonstrate the usefulness of the architectures that enforce non-convex constraints for path planning on manifolds with boundary.

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.