IEEE Transactions on Computational Biology and Bioinformatics

Background and objectiveGene regulatory networks are formed by complex regulatory relationships between transcription factors and their target genes. A systematic understanding of these regulatory relationships is crucial for deciphering the molecular mechanisms that underlie cell state transitions under physiological and pathological conditions. Single-cell expression data can reveal cell-type-specific transcriptional regulation, and computational methods have recently been developed to infer gene regulatory networks from single-cell transcriptomics and prior regulatory knowledge. However, existing methods could not explore the common and specific information in expression correlations and prior regulatory knowledge, which can adversely affect prediction performance. MethodsWe propose a novel method for inferring gene regulatory networks from single-cell RNA sequencing data. The proposed method consists of dual-channel graph neural networks and a weight-shared common graph neural network, enabling effective fusion of prior regulatory knowledge with gene co-expression patterns. Furthermore, we formulate a new computational framework built upon the proposed algorithm, which integrates differential gene expression profiles and regulatory changes to identify key regulators that distinguish different cell states. ResultsExperimental results demonstrate that our method significantly improves the accuracy of regulatory inference across multiple datasets, outperforming other state-of-the-art approaches. Our method also exhibits robustness to noise and missing data. Analysis of two single-cell expression datasets suggests that the proposed framework could help identify key regulators involved in tumor metastasis and drug resistance. ConclusionThese results indicate that the proposed method could advance the understanding of the biological mechanisms underlying diseases by reconstructing single-cell gene regulatory networks and identifying key regulators across different cell states.

Large-scale clinical and biomedical datasets increasingly contain both diverse subgroup attributes (e.g., demographic or clinical subgroups) and multiple prediction targets. Although various machine learning approaches can address subgroup differences or multi-target prediction, they often consider these aspects independently rather than jointly. To more effectively capture the shared and subgroup-specific information in such complex datasets, we propose the Integrative Transfer Network (ITN), a deep neural network designed to leverage data across subgroups and multiple related outcomes simultaneously. In extensive experiments, including time-to-event and classification tasks where demographic subgroups and multiple disease end-points are prevalent, ITN demonstrates consistent improvements in subgroup-specific prediction by borrowing strength from other subgroups and outcomes. We envision ITN as a unified frame-work for learning from heterogeneous datasets where subgroup-specific insights are critical.

Drug-target interaction prediction and binding affinity prediction are two key tasks in drug discovery and drug repurposing. Although deep learning methods have made significant progress, existing models typically rely on global representations of drugs and proteins, making it difficult to adequately model fine-grained interactions between their local units. Fixed multimodal fusion strategies also struggle to dynamically adjust the contributions of different modalities for different drug-target combinations. To address these issues, we propose DQHTFI, a fine-grained interaction prediction framework for drug-target interaction classification and binding affinity regression. DQHTFI employs BRICS fragments and Pfam functional domains as the basic interaction units and jointly learns semantic and structural representations. We design a dynamic-query hypergraph Transformer framework in which hyperedges are constructed among the multimodal features of fragment-domain pairs. Dynamic queries are generated from the cross-conditioned features of fragment-domain pairs to adaptively adjust the contribution of each modality, thereby modeling higher-order interactions between local units. Our proposed model achieves competitive results on multiple benchmark datasets.

BackgroundPhylogenetic tree reconstruction from single cell data based on copy-number alterations (CNAs) is an important problem in cancer genomics. Methods have been developed to address this problem by computing pairwise distances between copy-number profiles and employing a tree reconstruction algorithm. Despite the tight interplay between distance estimation and tree reconstruction, these two steps are often treated as separate problems, with the choice of the reconstruction algorithm receiving little attention. Most methods rely on classical Neighbor Joining (NJ), an algorithm designed for unrooted phylogenies that does not account for the fixed diploid root inherent to copy-number evolution. ResultsWe identify the Deepest Least Common Ancestor NJ (DLCA-NJ), not previously applied in this context, as the appropriate algorithm for phylogenies from copy-number data. By leveraging the known diploid root, it consistently outperforms standard NJ on simulated benchmarks across all evaluated metrics, with the most pronounced improvement in root placement accuracy. Building on these findings, we introduce Sparse Rooted Neighbor Joining (SRNJ), a scalable adaptation of DLCA-NJ. SRNJ significantly reduces running time while trading off only a minor loss in accuracy. We provide theoretical and empirical evidence of robustness to mutation rate using both synthetic and real biological datasets. ConclusionsRooted NJ variants offer a principled way to exploit the known diploid root when reconstructing phylogenies from copy-number data, and SRNJ extends this advantage to datasets whose size places the full distance matrix out of reach. The gains are clearest where distances are reliable, as on simulated data, while on real data accuracy appears to be constrained by distance estimation rather than by the reconstruction algorithm, leaving room for improvement as callers advance.

Automated, accurate, and fast developmental-stage classification of C. elegans from microscopy-based morphological images is essential for aging research, drug screening, and disease modeling. However, it remains challenging due to morphological similarities between stages and the limited annotated data. In this work, we propose HyperDev, a hyperbolic few-shot learning framework that addresses these limitations by directly encoding developmental hierarchies in the embedding space, unlike conventional Euclidean approaches that treat stages as independent classes. HyperDev uses Poincare ball geometry, combined with a biologically informed developmental prior, to naturally represent stage relationships. We introduce our self-curated C. elegans dataset spanning seven developmental stages (Egg, L1-L4, Adult, Dauer) with extreme class imbalance (6-8 samples per minority class). HyperDev achieves competitive classification accuracy (76.9-88.3%) while providing intrinsic explainability across nine 7-way few-shot evaluation settings. The learned embeddings exhibited strong biological alignment (Pearson r = 0.669, p < 0.001), while significantly outperforming ProtoNet (r = 0.187), MatchingNet (r = 0.235), and RelationNet (r = 0.464). These results establish hyperbolic geometry as a principled approach to explainable few-shot learning in biological imaging, where understanding learned representations is as critical as predictive performance. Clinical RelevanceBy enabling explainable, data-efficient developmental staging from scarce samples, HyperDev supports improved phenotype quantification for aging research, disease modeling, and drug screening.

Large-scale prediction and assessment of clinical patient responses (i.e., RECIST class) to drug combinations remains challenging due to scarce patient-derived data. The existing prediction methods mainly rely on cancer cell line models. However, substantial biological heterogeneity between cancer cell lines and cancer patients within same tissues, as well as the heterogeneity between one tissue and another, often limit the generalizability of these methods in clinical patients. To overcome these limitations, here we present CaMeRe, a Causally-inspired Meta-representation learning framework designed to predict patient-specific clinical Response to drug combinations. In situations where stable causal factors and domain-specific response-modulating factors are unobservable, explicit discrete domain labels are unavailable, and data is scarce, CaMeRe designed a domain-invariant causal representation learning (DICRL) model guided by the invariant information bottleneck theory and causal intervention invariance principle, and also built a meta-learning framework with bi-level domain generalization to optimize DICRL model for achieving multi-domain generalization within and across tissues. By integrating the causal representation learning and meta learning framework, CaMeRe not only exhibited robust multi-domain generalization performance across multiple clinical drug combination response datasets and PDXs drug combination response datasets and generalization scenarios, but also had better interpretability. We applied CaMeRe to predict drug-combination response scores for 3,423 patients across 542,080 drug combinations. The predicted scores were significantly associated with biomarkers of known drug combinations and enabled the prioritization of candidate drug combinations across 11 cancer types, with stronger support from literature and clinical trial evidences than random baselines. We believe that CaMeRe can be a useful tool for predicting large-scale clinical individual drug combination responses and it has broad clinical applications.

Clinical trials are critical milestones in the drug development pipeline, yet their high failure rates and substantial costs underscore the need for robust predictive models. This study introduces a Heterogeneous Gated Graph Transformer (HGGT) model tailored to predict clinical trial success. Unlike existing methods that typically model trial-related entities in isolation or with homogeneous graphs, HGGT explicitly models the rich heterogeneous relationships among trials, diseases, drugs, genes, targets, abstracts, and eligibility criteria through a gated graph transformer architecture, which dynamically learns and weights multi-type relational interactions to capture complex biological and clinical dependencies. By integrating heterogeneous graph representation with transformer-based context modeling, HGGT effectively captures non-linear, multi-scale interactions across biomedical entities, leading to improved predictive performance for trial success. Experimental results demonstrate that the HGGT model achieves strong performance, with the highest PR-AUC, F1 score, and ROC-AUC across three phases. These findings highlight the potential of graph-based deep learning approaches in optimizing clinical trial design and resource allocation, ultimately accelerating the translation of novel therapies into clinical practice.

1Drug--drug interactions between biotech and small-molecule drugs play a critical role in medication safety and therapeutic efficacy. However, most existing computational DDI prediction methods focus primarily on interactions between small-molecule drugs, leaving biotech-small-molecule interactions comparatively underexplored. In this study, we propose B-SMART-Former, an explainable deep learning framework for predicting interaction types between biotech and small-molecule drugs. The proposed framework integrates ChemBERTa embeddings and Morgan molecular fingerprints for small molecules with ProtBERT embeddings for biotech drugs, eliminating the need for similarity-based features while leveraging complementary molecular representations. These multimodal features are processed by a hybrid architecture that combines Transformer-based self-attention, residual convolutional learning, and a multi-layer perceptron classifier to capture both global contextual dependencies and local discriminative patterns. The model is formulated as a multi-class classification task and evaluated using stratified 10-fold cross-validation. To improve model transparency, Integrated Gradients is employed as a post-hoc explainability method to identify the molecular features that contribute most strongly to each prediction. Experimental results demonstrate that B-SMART-Former achieves a micro-averaged AUROC of 0.9978 and an AUPR of 0.9682 while relying solely on intrinsic molecular representations, remaining competitive with similarity-based approaches. The proposed framework offers an effective and explainable solution for biotech-small-molecule DDI prediction and provides a practical foundation for future computational drug interaction studies.

Spatial transcriptomics enables the study of gene expression within its native tissue context, providing critical insights into cellular organization and microenvironment-driven biological processes. A key challenge in this field is spatial domain identification, which aims to partition tissue into coherent regions by jointly leveraging gene expression and spatial information. Existing approaches are predominantly based on Graph Neural Networks (GNNs), and approach based on Transformers particularly, Bidirectional Encoder Reppresentation Transformer (BERT) model for modelling both local and long-range dependencies remains largely unexplored. In this work, we propose BERT for Spatial Transcriptomics (BertST), a transformer-based framework that reformulates spatial transcriptomics as a graph-to-text representation learning problem. Building upon the BERTwalk paradigm, we construct a task-specific multi-graph representation integrating spatial adjacency, pruned gene-expression similarity, and a fully connected gene-expression graph. This design enables the modelling of both local spatial structure and global molecular relationships. Random walks over these graphs are treated as sequences, allowing a BERT model to learn contextualised node embeddings. To further enhance representation quality, we introduce a hierarchical multi-graph propagation strategy, where embedding refinement is performed sequentially: first on the fully connected graph to capture global structure, followed by the pruned graph to refine molecular relationships, and finally on the spatial graph to enforce local smoothness. This ordering ensures that global information is effectively distributed and progressively constrained by biologically meaningful neighbourhoods. We also improve computational efficiency by leveraging \textit{PecanPy}, a fast and scalable implementation of node2vec, enabling efficient random walk generation on dense graphs. Experimental results on multiple 10x Visium datasets, including DLPFC and Human Breast Cancer, demonstrate that BertST consistently outperforms or matches GNN-based methods such as ConST, CCST, and SpaceFlow in terms of Adjusted Rand Index (ARI) and Adjusted Mutual Information (AMI). Overall, BertST highlights the potential of transformer-based architectures for spatial omics analysis by effectively capturing both local and long-range spatial-molecular dependencies, offering a promising alternative to traditional graph-based methods.

Predicting drug-target interactions (DTI) for entirely unseen drugs or proteins--the cold-start problem--remains a critical challenge in computational drug discovery. While sequence-based methods naturally support zero-shot generalization, they often ignore relational topology, and existing graph-based approaches either rely on global diffusion that blurs the boundary between inductive and transductive evaluation or require a few known interaction samples at test time (few-shot). We present EBD-DTI, a framework that enables zero-shot inference in graph-based DTI models without requiring any known interactions for unseen entities. The key innovation is episodic cold-start training : at each epoch, a random subset of training entities is masked and treated as pseudo-cold, forcing the model to learn cold-start inference with explicit gradient supervision. A bridge-conditioned local subgraph, together with multi-hop diffusion, provides cold entities with relational context from their nearest observed neighbors. Experiments on three benchmarks (BioSNAP, BindingDB, and DrugBank) demonstrate that EBD-DTI achieves competitive or superior performance compared to state-of-the-art methods under strict zero-shot evaluation, with episodic training improving AUC by up to 12%.

Protein function prediction traditionally relies on structured gene ontology (GO) labels or multi-label classifiers. However, these labels or classifiers cannot flexibly describe molecular function, biological process, cellular component, and free-text functional narratives in a single output. In comparison, generation-based approaches offer an intuitive paradigm for flexible free-text protein annotation, with large language models (LLMs) as a representative method for protein-text modeling. Recent efforts on utilizing LLMs for protein semantic understanding and annotation generation have adopted sequence-only encoding or sequence-text contrastive alignment paradigms, yet without explicit consideration of three-dimensional structural information. To address these limitations in current protein function prediction methods, we present ProtBLIP2-SST, a two-stage framework built on the BLIP2 model architecture that bridges protein sequence, structure, and text for open-ended protein functional caption generation. Specifically, we first integrate sequence and structure information through SaProt, a protein language model (PLM) with a structure-aware vocabulary that fuses residue tokens with Foldseek-derived 3Di structural tokens. To empower the LLM to understand protein semantics, we employ a Q-Former (a querying transformer in BLIP2) with learnable query tokens as the cross-modal projector to align protein features from the frozen SaProt encoder and text features from a frozen BiomedBERT via protein-text contrasting, protein-text matching, and protein captioning objectives. After alignment, the protein features are linearly projected and prepended to the prompt embeddings of the LLM for protein captioning fine-tuning with LoRA. Trained on 441k protein-text pairs from Swiss-Prot with corresponding structures from the AlphaFold Database, our ProtBLIP2-SST outperforms sequence-only and sequence-text alignment baselines on protein captioning metrics, with ablation studies demonstrating the effectiveness of integrating structure with sequence information for improved protein understanding. Through a unified two-stage alignment-and-generation pipeline, ProtBLIP2-SST integrates protein sequence and structural information, overcomes the rigidity of traditional GO-centric classification, generating open-ended captions that jointly describe molecular function, subcellular location, and homology context in one single output.

Deep learning methods, such as AlphaFold and RosettaFold, achieve high accuracy in protein structure prediction. However, predicting the structure of large protein complexes remains challenging due to their large size and intricate multi-chain interactions. Docking-based methods can handle large proteins, but are limited by the huge combinatorial binding space of multichains. Assembly-based approaches offer an alternative, but their accuracy critically relies on the precision of predicted subcomponents. Addressing the challenges, we propose HDOCK-Multimer (HDM), a structure prediction framework of large protein complexes by integrating ab initio docking and combinatorial assembly. HDM can efficiently reduce reliance on subcom-ponent accuracy through docking process, while leveraging the pairwise interactions of subcom-ponents through assembly strategy. HDM is extensively validated on three benchmarks of 35 large heteromeric complexes, 172 large protein complexes, and 7 CASP15 targets, and compared with state-of-the-art methods including MoLPC, CombFold, AlphaFold-Multimer (AFM), and AlphaFold3 (AF3). It is shown that HDOCK-Multimer substantially outperforms the other methods. In addition, HDM also shows ability to predict the stoichiometry and model the complex without stoichiometry input. It is anticipated that HDM will serve as a powerful tool for studying large protein complexes or molecular machines. The HDM package is freely available at https://github.com/huang-laboratory/HDOCK-Multimer/.

Identifying prognostic biomarkers from high-dimensional transcriptomic data poses a triple challenge: achieving sparsity, preserving biological network topology, and integrating complementary nonlinear signals. Existing methods typically ignore network structure, miss nonlinear interactions, or lack a principled mechanism to fuse heterogeneous model outputs. We introduce GR-SAFS (Graph-Regularized Stacking with Adaptive Feature Selection), a framework with three modules: a Graph-Lasso engine embedding gene co-expression network Laplacian priors, run in parallel with a Random Forest engine; an empirical cumulative distribution function (eCDF) alignment layer that places sparse and dense importances on a common percentile scale; and a diversity-penalized quadratic programming router whose strict convexity yields a unique global optimum. On the TCGA-LUAD cohort, GR-SAFS identifies a 20-gene signature with a training concordance index of 0.700. Across two independent crossplatform microarray cohorts, GR-SAFS is the only method whose frozen signature retains statistically significant risk stratification in every cohort, where stronger-C-index baselines lose significance on at least one external cohort. Functional enrichment anchors the signature to a coherent Wnt/{beta};-catenin axis. An open-source implementation is released for full reproducibility.

Hybridization is an important evolutionary process, commonly modeled by the network multispecies coalescent. Reconstructing evolutionary histories under this model is notoriously costly, even for level-1 networks where hybridization events are isolated from each other. The widely used methods that combine speed with statistical guarantees rely on quartet concordance factors computed for all subsets of four species, resulting in an o(n4k) bottleneck that severely limits scalability to large numbers of species (n) and genes (k). Among quartet-based methods, NANUQ+ is notable because it decomposes the problem into two steps: first reconstructing a tree of blobs, which compresses each non-treelike part of the network, called a blob, into a single vertex, and second reconstructing the internal structure of each level-1 blob, specifically its circular order and hybrid vertex. Here, we investigate whether level-1 blob reconstruction is difficult once the tree of blobs is known. We present a fast and statistically consistent algorithm, called NetCS, based on two simple primitives: majority voting and merge sort, circumventing the bottleneck of computing all quartet concordance factors. In simulations, NetCS achieved comparable accuracy to NANUQ+ and was dramatically faster, enabling analyses of 200 taxa and 1000 genes in only a few minutes. Both methods attained near-perfect accuracy when given the true tree of blobs; however, their performance degraded in end-to-end pipelines due to errors in tree of blobs reconstruction. Strikingly, even methods that reconstruct level-1 networks directly struggled to accurately predict hybrid ancestry. Our results suggest that reconstructing level-1 blobs is unexpectedly easy once the tree of blobs is known, and that a major challenge for phylogenetic network inference lies in accurate tree of blobs reconstruction.

Antimicrobial resistance (AMR) creates an urgent need for efficient strategies to identify effective antibacterial combinations. Combination therapy, including antimicrobial peptides (AMPs) paired with conventional antibiotics, is a promising approach, but exhaustive experimental screening across drug pairs and bacterial targets is impractical. This study introduces a hybrid GCN-based hypergraph neural network (HGNN) for predicting antimicrobial-agent combination outcomes against bacterial targets. Each antimicrobial-agent-antimicrobial-agent-bacterium triplet is represented as a ternary hyperedge, enabling the model to learn context-dependent interaction patterns. The framework integrates SMILES-derived molecular graph embeddings for antimicrobial agents, including conventional antibiotics and AMPs, with taxonomy-derived bacterial representations. The prediction task was formulated as a three-class classification problem: synergy, antagonism, and non-interaction. The non-interaction class included experimentally verified indifferent records and synthetic presumed non-interaction triplets generated by negative sampling. Model development used drug-pair-grouped splitting, five-fold grouped cross-validation within the training/validation partition, and final evaluation on a held-out test set. On the held-out three-class test set, the selected GCN-based HGNN achieved an accuracy of 0.83, weighted F1-score of 0.84, macro F1-score of 0.80, and ROC-AUC of 0.95. Per-class evaluation showed accuracies of 0.80 for synergy, 0.92 for antagonism, and 0.85 for non-interaction. Pair-type analysis showed strong performance across AMP-AMP, AMP-conventional antibiotic, and conventional antibiotic-conventional antibiotic combinations. These findings suggest that hypergraph-based representation learning can support computational prioritization of antimicrobial combinations for experimental follow-up. Further studies will be needed to improve model interpretability and to perform prospective validation of predicted synergistic combinations.

Accurately predicting the effects of mutations on protein-RNA binding is crucial for elucidating disease mechanisms. Yet, exhaustively exploring the space of all possible variants is prohibitively expensive, motivating computational methods that can quantify mutation-induced changes in binding affinity (aka {Delta}{Delta}G) accurately and efficiently. We present iSCALE, an interpretable and generalizable deep learning method that adopts an implicit Spatial Coupling-Aware Ligand Encoding strategy to predict mutation-induced binding affinity changes. By injecting this implicit multiscale encoding scheme into a bidirectional state space modeling architecture, iSCALE learns a generalizable multiscale coupling pattern that achieves superior performances on not only the protein-RNA binding {Delta}{Delta}G, but also the protein stability {Delta}{Delta}G and protein-protein binding {Delta}{Delta}G predictions. Detailed analyses demonstrate that the model attention scores align well with structural characteristics. In addition, iSCALE shows good discriminative ability when predicting close samples such as complexes of same mutation but with different ligands or the same complex but with different mutation sites. In summary, iSCALE serves as an effective in silico tool for large-scale protein-RNA binding {Delta}{Delta}G prediction, which pushes the border of understanding in mutation-induced pathological outcomes.

Current studies in human genomics typically rely on the standard genome reference GRCh38 which is known to be biased toward populations of European ancestry and therefore has limitations when applied to other populations. Although various graph-based pangenome references were constructed for several populations to deal with this bias, their usage in practice is currently still limited compared to linear genome references. Here we present a framework for constructing a population-specific genome reference using GRCh38 as backbone with alternate-contig awareness to enhance genomic data analysis in the target population. We demonstrated the advantages of our framework using both public and in-house Vietnamese whole-genome sequencing (WGS) datasets. Genomic variants derived from high-coverage WGS data of the 1000 Vietnamese Genomes Project (VN1K) were imported into our framework to build a Vietnamese-specific Genome Reference (VGR). VGR was then compared to GRCh38 in read alignment and variant calling using high-coverage WGS data of 99 Vietnamese individuals (KHV) from the 1000 Genomes Project (1kGP). Using Omni array genotyping data from 99 KHV samples as an independent benchmark, we found that VGR improved variant-calling precision and reduced false-positive calls compared to GRCh38. Our framework could be easily used for other populations as long as they have a variant database similar to VN1K. Our code is publicly available at github.com/VinGenome/VGR

Genes can be described through multiple heterogeneous biological views, including genomic sequence, transcript sequence, protein sequence, textual knowledge, and single-cell expression context, yet existing gene embeddings remain largely modality-specific and difficult to compare or reuse when many views are unavailable. We study a narrower but practically important question: whether pretrained embeddings from these distinct sources can be organized into a shared gene representation interface that remains usable under severe missing-modality conditions. To investigate this question, we introduce RepGene, a lightweight single-branch framework that combines modality adapters, a shared encoder, presence-aware fusion, and self-supervised cross-view objectives to map five biological views into one latent space. Our goal is not to claim a new multimodal learning principle or to establish superiority over all simpler fusion strategies, but to provide an initial technical instantiation for testing whether such a shared interface is feasible in a fixed-feature setting. Under a two-stage protocol in which RepGene is trained self-supervised on frozen upstream embeddings and evaluated by downstream linear probing, we find preliminary evidence that the learned representation is broadly competitive in the full-modality setting and remains informative when only partial modality subsets are observed at inference time. The strongest signal in our study is robustness under missing views: average performance changes are often limited when one modality is removed, and even single-view inference remains non-trivial in the evaluated benchmark regime. These results do not resolve unified biological representation learning, and they should be interpreted in light of incomplete simple-fusion baselines, limited architectural ablation, benchmark dependence, and possible upstream feature exposure. We therefore position RepGene as a feasibility study and a starting point for stronger comparisons, broader benchmarks, and leakage-aware validation.

MotivationIn this paper, we demonstrate that it is feasible to train a deep generative model for dimensionality reduction with millions of features using few samples, which makes this type of generative model a more versatile alternative to standard methods for dimensionality reduction. Specifically, we hypothesize that for a decoder-only model, the number of training samples required is almost independent of the feature dimensionality in most network architectures. ResultsThrough an extensive set of experiments on synthetic non-linear data, we validate this hypothesis. We also train the model on a downsampled version of the 1000 Genomes Project (1KGP) dataset to further assess its behavior under controlled reductions in sample size. Furthermore, we train a deep generative decoder (DGD) on a curated dataset from the International Cancer Genome Consortium (ICGC), which contains 4.4 million features. It is trained on approximately 4,000 samples and tested on 1,000 samples. The resulting latent representation exhibits clear clustering, and when methods are reduced to the same number of dimensions, it outperforms PCA and VAE for tumor type classification. Additionally, the DGD is computationally efficient and can be trained on a 16GB GPU. Availability and implementationCode is available at https://github.com/cpancott/ReceptiveDGD. Contactcorrado.pancotti@helmholtz-munich.de; akrogh@di.ku.dk Supplementary informationSupplementary data are available with this preprint.

Relative Lempel-Ziv (RLZ) is an effective compression method for large, repetitive collections; however, the fundamental primitives required to elevate it from a passive archival format to a tractable representation for compressed construction have yet to be fully established. In this paper, we introduce an algorithmic framework for structurally comparing and lexicographically sorting sequences of RLZ factors. We characterize when direct factor comparisons are necessary and when they can be bypassed using RLZ specific shortcuts. We further introduce a method for extending truncated factors into right-maximal matches, enabling the recovery of matching statistics from the RLZ parse. Experimentally, RLZ sorting achieved speedups of up to 3.93x over character-based sorting. Together, these results advance the use of the RLZ format as a foundation for compressed construction.