Protein tertiary structures capture the complex three-dimensional (3D) arrangements of the constituent atoms that define how proteins function. Different strategies have been applied in the form of representation learning to interpret these high-dimensional structure spaces. Factorization-based techniques, such as matrix and tensor factorization, have also been proven to be an effective set of approaches due to their utility in capturing latent organizations from complicated structural spaces and have already been applied in the context of tasks like tracking conformational changes across structure ensembles of biomolecules, identifying the biologically-active tertiary structure(s) from the given computed protein models, analyzing biomolecular dynamics simulations, etc. This paper exhibits a comprehensive review of factorization-driven methods employed to learn representations of tertiary structures for the protein structure prediction task. It covers how protein structures are encoded, represented, analyzed, and evaluated via different factorization-based frameworks. Furthermore, it outlines major open challenges and offers prospective research directions.
Since its introduction, the double cut and join (DCJ) operation has gained popularity in Computational Biology as a convenient abstraction that generalizes various genome rearrangement operations – mutation events that affect large genome segments. The central problem involving this operation is the DCJ distance problem, which seeks to minimize the number of DCJ operations required to transform one genome into another. In particular, recent studies incorporate intergenic region sizes to obtain more realistic rearrangement distance estimates. When the genomes differ in gene content, indel (insertion or deletion) events must also be considered. We present the first algorithm for the DCJ distance that incorporates intergenic information and supports indels, a 2-approximation applicable to single-copy, co-tailed genomes.
We present a dynamic functional connectivity (DFC)-based classification analysis of functional magnetic resonance imaging (fMRI) data from veterans with a type of post-traumatic stress disorder (PTSD) and from matched normal control (NC) veterans. Whole-brain resting-state fMRI (rsfMRI) data which were scanned from 23 PTSD (mean age 49) and 30 NC (mean age 50) veterans were used for analyses. A computational method using statistics of DFC and support-vector machine (SVM) classifier were used to correctly classify PTSD vs NC with up to 98
Representation learning is central to structural bioinformatics, enabling shared embeddings for protein fold recognition, structural similarity search, and function prediction. However, the organization and interpretability of latent representations learned from protein distance or contact maps remain poorly understood. We present a representation-focused comparative analysis of two of our previously developed geometric autoencoders, SuperFoldAE and its contractive variant ConSOLAE, trained on C_α distance maps. To characterize latent representations, we examine latent organization using visualizations, clustering alignment, perturbation sensitivity, resolution studies, and transfer tasks. While both models capture coarse fold structure, their latent spaces differ markedly in geometry and robustness. Representations learned with contractive regularization exhibit smoother, more compact, and more stable latent geometry, with stronger unsupervised alignment to fold structure (ARI = 0.87, NMI = 0.91). These geometric advantages are reflected in downstream behavior, including consistent Top-1 and Top-5 accuracy and support for unsupervised protein length prediction ( R^2 = 0.64 ). Overall, this study provides a concise comparative characterization of latent spaces learned by distance-map autoencoders, offering a geometric perspective that links latent geometry and stability to robust protein fold representations.
Spatial domain identification is a fundamental task in spatial transcriptomics, aiming to partition tissues into coherent regions that reflect both transcriptional similarity and spatial organization. Existing methods typically generate low-dimensional embeddings through predefined transformations or neural network encoders, and treat these representations as fixed inputs for downstream clustering. This limits the model’s ability to adapt to multiple spatial and expression-derived constraints. To address this limitation, we propose Graph-Regularized Embedding Refinement for Spatial Transcriptomics (GRER-ST), a refinement framework that enhances spatial domain identification by explicitly optimizing the latent embedding. GRER-ST first integrates spatial coordinates and gene expression profiles to construct an initial low-dimensional representation that captures local spatial context. A trainable latent embedding, initialized from this representation, is then refined under a unified objective that incorporates spatial smoothness, expression similarity, and neighborhood-based contrastive regularization. By refining the embedding rather than relying on a fixed representation, GRER-ST produces spatial domains that are both locally coherent and discriminative. Extensive experiments on multiple spatial transcriptomics datasets demonstrate that GRER-ST consistently outperforms baseline methods in spatial domain identification, yielding more spatially coherent domain structures. These findings suggest that embedding refinement is an effective and flexible strategy for integrating heterogeneous spatial and transcriptional information in spatial transcriptomics.
