Leveraging the Wasserstein distance—a summation of sample-wise transport distances in data space—is advantageous in many applications for measuring support differences between two underlying density functions. However, when supports significantly overlap while densities exhibit substantial pointwise differences, it remains unclear whether and how this transport information can accurately identify these differences, particularly their analytic characterization in finite-sample settings. We address this issue by conducting an analysis of the information processing capabilities of the one-dimensional Wasserstein distance with finite samples. By utilizing the Poisson process and isolating the rate factor, we demonstrate the capability of capturing the pointwise density difference with Wasserstein distances and how this information harmonizes with support differences. The analyzed properties are confirmed using neural spike train decoding and amino acid contact frequency data. The results reveal that the one-dimensional Wasserstein distance highlights meaningful density differences related to both rate and support.

MOTIVATION: Post-translational modifications (PTMs) alter functional states and interaction specificity largely through the conformational changes they impose on protein structure. However, most existing resources remain sequence-centric and cannot reveal how chemical modifications reshape 3D structures. To address this gap, we propose a structural database that systematically extracts and contextualizes modification sites within experimentally determined protein structures, providing a foundation for future studies of protein structure, function, and regulatory mechanisms. RESULTS: We present StrucPTM, a database that extracts modified residues directly from the Protein Data Bank (PDB) structures using atom-level composition rules, substantially expanding coverage beyond annotation-dependent methods. Each validated PTM modification is mapped onto a UniProt entry. The database further characterizes residues using key structural descriptors-including secondary structure, relative solvent accessibility (RSA), and whether the PTM site lies at an interchain interface. All chains associated with the same UniProt ID are compared and grouped into homolog sets based on sequence identity. This emphasizes structural conservation among homologs, allowing PTM-induced conformational deviations to be distinguished from unrelated sequence divergence. AVAILABILITY AND IMPLEMENTATION: StrucPTM offers searchable access, interactive 3D visualization, and homolog-based structural comparison through its web interface: https://prix.hanyang.ac.kr/strucptm. The source code and datasets are permanently archived on Zenodo (DOI: 10.5281/zenodo.18939125) and are accessible via GitHub (https://github.com/HanyangBISLab/StrucPTM.git).

MOTIVATION: Protein sequence alignment is a crucial task in bioinformatics, yet aligning remote homologs with low sequence identity remains a longstanding challenge, particularly due to the difficulty of handling gaps. We introduce a new method that applies Optimal Transport (OT) theory to sequence alignment, providing a mathematically principled framework for modeling residue matches and gaps. RESULTS: OTalign formulates sequence alignment as an entropy-regularized unbalanced optimal transport (UOT) problem over embeddings derived from protein language models (PLMs). Unlike traditional methods, it introduces position-specific gap penalties that adapt to each sequence pair. On challenging remote-homolog benchmarks (SABmark, MALIDUP, MALISAM), OTalign consistently outperforms baselines (Needleman-Wunsch, HHalign) and recent PLM-based methods (PLMAlign, DeepBLAST), achieving F1 scores of 0.594 on SABmark Superfamily and 0.358 on SABmark Twilight. Furthermore, OTalign provides a quantitative and interpretable metric of how effectively PLM embeddings represent sequence similarity relationships. Finally, its differentiable nature enables end-to-end fine-tuning of PLMs, establishing a framework for learning embeddings explicitly optimized for alignment tasks. AVAILABILITY AND IMPLEMENTATION: This code is available at https://github.com/DeepFoldProtein/OTalign.

MOTIVATION: Protein structure prediction has been revolutionized and generalized with the advent of cutting-edge AI methods such as AlphaFold, but reliance on computationally intensive multiple sequence alignments (MSA) remains a major limitation. RESULTS: We introduce DeepFold-PLM, a novel framework that integrates advanced protein language models with vector embedding databases to enhance ultra-fast MSA construction, remote homology detection, and protein structure prediction. DeepFold-PLM utilizes high-dimensional embeddings and contrastive learning, significantly accelerate MSA generation, achieving 47 times faster than standard methods, while maintaining prediction accuracy comparable to AlphaFold. In addition, it enhances structure prediction by extending modeling capabilities to multimeric protein complexes, provides a scalable PyTorch-based implementation for efficient large-scale prediction. Our method also effectively increases sequence diversity (Neff = 8.65 versus 4.83 with JackHMMER) enriching coevolutionary information critical for accurate structure prediction. DeepFold-PLM thus represents a versatile and practical resource that enables high-throughput applications in computational structural biology. AVAILABILITY AND IMPLEMENTATION: Source codes and user-friendly Python API of all modules of DeepFold-PLM publicly available at https://github.com/DeepFoldProtein/DeepFold-PLM.

MOTIVATION: Predicting protein structures with high accuracy is a critical challenge for the broad community of life sciences and industry. Despite progress made by deep neural networks like AlphaFold2, there is a need for further improvements in the quality of detailed structures, such as side-chains, along with protein backbone structures. RESULTS: Building upon the successes of AlphaFold2, the modifications we made include changing the losses of side-chain torsion angles and frame aligned point error, adding loss functions for side chain confidence and secondary structure prediction, and replacing template feature generation with a new alignment method based on conditional random fields. We also performed re-optimization by conformational space annealing using a molecular mechanics energy function which integrates the potential energies obtained from distogram and side-chain prediction. In the CASP15 blind test for single protein and domain modeling (109 domains), DeepFold ranked fourth among 132 groups with improvements in the details of the structure in terms of backbone, side-chain, and Molprobity. In terms of protein backbone accuracy, DeepFold achieved a median GDT-TS score of 88.64 compared with 85.88 of AlphaFold2. For TBM-easy/hard targets, DeepFold ranked at the top based on Z-scores for GDT-TS. This shows its practical value to the structural biology community, which demands highly accurate structures. In addition, a thorough analysis of 55 domains from 39 targets with publicly available structures indicates that DeepFold shows superior side-chain accuracy and Molprobity scores among the top-performing groups. AVAILABILITY AND IMPLEMENTATION: DeepFold tools are open-source software available at https://github.com/newtonjoo/deepfold.

MOTIVATION: Domain boundary prediction is one of the most important problems in the study of protein structure and function. Many sequence-based domain boundary prediction methods are either template-based or machine learning (ML) based. ML-based methods often perform poorly due to their use of only local (i.e. short-range) features. These conventional features such as sequence profiles, secondary structures and solvent accessibilities are typically restricted to be within 20 residues of the domain boundary candidate. RESULTS: To address the performance of ML-based methods, we developed a new protein domain boundary prediction method (ConDo) that utilizes novel long-range features such as coevolutionary information in addition to the aforementioned local window features as inputs for ML. Toward this purpose, two types of coevolutionary information were extracted from multiple sequence alignment using direct coupling analysis: (i) partially aligned sequences, and (ii) correlated mutation information. Both the partially aligned sequence information and the modularity of residue-residue couplings possess long-range correlation information. AVAILABILITY AND IMPLEMENTATION: https://github.com/gicsaw/ConDo.git. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: In template-based modeling when using a single template, inter-atomic distances of an unknown protein structure are assumed to be distributed by Gaussian probability density functions, whose center peaks are located at the distances between corresponding atoms in the template structure. The width of the Gaussian distribution, the variability of a spatial restraint, is closely related to the reliability of the restraint information extracted from a template, and it should be accurately estimated for successful template-based protein structure modeling. RESULTS: To predict the variability of the spatial restraints in template-based modeling, we have devised a prediction model, Sigma-RF, by using the random forest (RF) algorithm. The benchmark results on 22 CASP9 targets show that the variability values from Sigma-RF are of higher correlations with the true distance deviation than those from Modeller. We assessed the effect of new sigma values by performing the single-domain homology modeling of 22 CASP9 targets and 24 CASP10 targets. For most of the targets tested, we could obtain more accurate 3D models from the identical alignments by using the Sigma-RF results than by using Modeller ones. CONCLUSIONS: We find that the average alignment quality of residues located between and at two aligned residues, quasi-local information, is the most contributing factor, by investigating the importance of input features used in the RF machine learning. This average alignment quality is shown to be more important than the previously identified quantity of a local information: the product of alignment qualities at two aligned residues.