{"title":"Mutational signature refitting on sparse pan-cancer data.","authors":"Gal Gilad, Teresa M Przytycka, Roded Sharan","doi":"10.1186/s13015-026-00305-0","DOIUrl":"10.1186/s13015-026-00305-0","url":null,"abstract":"<p><strong>Background: </strong>Mutational processes shape cancer genomes, leaving characteristic marks that are termed signatures. The level of activity of each such process, or its signature exposure, provides important information on the disease, improving patient stratification and the prediction of drug response. Thus, there is growing interest in developing refitting methods that accurately decipher those exposures. Previous work in this domain was unsupervised in nature, employing algebraic decomposition and probabilistic inference methods.</p><p><strong>Results: </strong>We present SuRe, a supervised approach to signature refitting that demonstrates superiority over current methods. SuRe leverages a neural network model to capture correlations between signature exposures in real data. We show that SuRe outperforms previous methods on sparse mutation data from both tumor-type-specific and pan-cancer data sets, with an increasing performance advantage as the data become sparser.</p><p><strong>Conclusion: </strong>We further demonstrate the model's utility in clinical settings by predicting homologous recombination deficiency in breast cancer from sparse data. Furthermore, SuRe outperforms standard methods in the unsupervised stratification of over 13,000 patients from large-scale panel sequencing cohorts, highlighting its potential for analyzing targeted sequencing data.</p>","PeriodicalId":50823,"journal":{"name":"Algorithms for Molecular Biology","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13660035/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148474115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mahmudur Rahman Hera, Paul Medvedev, David Koslicki, Antonio Blanca
{"title":"Estimation of substitution and indel rates via k-mer statistics.","authors":"Mahmudur Rahman Hera, Paul Medvedev, David Koslicki, Antonio Blanca","doi":"10.1186/s13015-026-00299-9","DOIUrl":"10.1186/s13015-026-00299-9","url":null,"abstract":"<p><p>Methods utilizing <math><mi>k</mi></math> -mers are widely used in bioinformatics, yet our understanding of their statistical properties under realistic mutation models remains incomplete. Previously, substitution-only mutation models have been considered to derive precise expectations and variances for mutated <math><mi>k</mi></math> -mers and intervals of mutated and non-mutated sequences. In this work, we consider a mutation model that incorporates insertions and deletions in addition to single-nucleotide substitutions. Within this framework, we derive closed-form k-mer-based estimators for the three fundamental mutation parameters: substitution, deletion rate, and insertion rates. We provide theoretical guarantees in the form of concentration inequalities, ensuring accuracy of our estimators under reasonable model assumptions. Empirical evaluations on simulated evolution of genomic sequences confirm our theoretical findings, demonstrating that accounting for insertions and deletions signals allows for accurate estimation of mutation rates and improves upon the results obtained by considering a substitution-only model. An implementation of estimating the mutation parameters from a pair of fasta files is available here: https://github.com/KoslickiLab/estimate_rates_using_mutation_model.git . The results presented in this manuscript can be reproduced using the code available here: https://github.com/KoslickiLab/est_rates_experiments.git .</p>","PeriodicalId":50823,"journal":{"name":"Algorithms for Molecular Biology","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13632108/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148426107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A k-mer-based estimator of the substitution rate between repetitive sequences.","authors":"Haonan Wu, Antonio Blanca, Paul Medvedev","doi":"10.1186/s13015-026-00304-1","DOIUrl":"10.1186/s13015-026-00304-1","url":null,"abstract":"<p><strong>Background: </strong>K-mer-based analysis of genomic data is ubiquitous, but the presence of repetitive k-mers continues to pose problems for the accuracy of many methods. For example, the Mash tool (Ondov et al 2016) can accurately estimate the substitution rate between two low-repetitive sequences from their k-mer sketches; however, it is inaccurate on repetitive sequences such as the centromere of a human chromosome. Follow-up work by Blanca et al. (2021) has attempted to model how mutations affect k-mer sets based on strong assumptions that the sequence is non-repetitive and that mutations do not create spurious k-mer matches. However, the theoretical foundations for extending an estimator like Mash to work in the presence of repeat sequences have been lacking.</p><p><strong>Results: </strong>In this work, we relax the non-repetitive assumption and propose a novel estimator for the mutation rate. We derive theoretical bounds on our estimator's bias. Our experiments show that it remains accurate for repetitive genomic sequences, such as the alpha satellite higher order repeats in centromeres. We demonstrate our estimator's robustness across diverse datasets and various ranges of the substitution rate and k-mer size. Finally, we show how sketching can be used to avoid dealing with large k-mer sets while retaining accuracy. Our software is available at https://github.com/medvedevgroup/Repeat-Aware_Substitution_Rate_Estimator .</p>","PeriodicalId":50823,"journal":{"name":"Algorithms for Molecular Biology","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13602792/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148382853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Haplotype-aware long-read error correction.","authors":"Parvesh Barak, Daniel Gibney, Chirag Jain","doi":"10.1186/s13015-026-00302-3","DOIUrl":"10.1186/s13015-026-00302-3","url":null,"abstract":"<p><p>Error correction of long reads is an important initial step in genome assembly workflows. For organisms with ploidy greater than one, it is important to preserve haplotype-specific variation during read correction. This challenge has driven the development of several haplotype-aware correction methods. However, existing methods are based on either ad-hoc heuristics or deep learning approaches. In this paper, we introduce a rigorous formulation for this problem. Our approach builds on the minimum error correction framework used in reference-based haplotype phasing. We prove that the proposed formulation for error correction of reads in de novo context, i.e., without using a reference genome, is NP-hard. To make our exact algorithm scale to large datasets, we introduce practical heuristics. Experiments using PacBio HiFi sequencing datasets from human and plant genomes show that our approach achieves accuracy comparable to state-of-the-art methods. Implementation: https://github.com/at-cg/HALE .</p>","PeriodicalId":50823,"journal":{"name":"Algorithms for Molecular Biology","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13576334/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148354585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marcos E González Laffitte, Tieu-Long Phan, Peter F Stadler
{"title":"Extension of partial atom-to-atom maps: uniqueness and algorithms.","authors":"Marcos E González Laffitte, Tieu-Long Phan, Peter F Stadler","doi":"10.1186/s13015-026-00300-5","DOIUrl":"10.1186/s13015-026-00300-5","url":null,"abstract":"<p><p>Chemical reaction databases typically report the molecular structures of reactant and product compounds, as well as their stoichiometry, but lack information, in particular, on the correspondence of reactant and product atoms. These atom-to-atom maps (AAM), however, are crucial for applications including chemical synthesis planning in organic chemistry and the analysis of isotope labeling experiments in modern metabolomics. AAMs therefore need to be reconstructed computationally. This situation is aggravated, furthermore, by the fact that chemically correct AAMs are, fundamentally, determined by quantum-mechanical phenomena and thus cannot be reliably computed by solving graph-theoretical optimization problems defined by the reactant and product structures. A viable solution for this problem is to shift the focus into first identifying a partial AAM containing the reaction center, i.e., covering the atoms incident with all bonds that change during a reaction. This then leads to the problem of extending the partial map to the full reaction. The AAM of a reaction is faithfully represented by the Imaginary Transition State (ITS) graph, providing a convenient graph-theoretic framework to address the questions of when and how a partial AAM can be extended. We show that an unique extension exists whenever, and only if, these partial AAMs cover the reaction center. Moreover, uniqueness results are generalized to partial AAMs in situations where hydrogen atoms are not represented explicitly. In this case their extension can be computed by solving a constrained graph-isomorphism search between specific subgraphs of ITS graphs. We close by benchmarking different tools for this task.</p>","PeriodicalId":50823,"journal":{"name":"Algorithms for Molecular Biology","volume":"21 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13282873/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148284742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Lossless pangenome indexing using tag arrays.","authors":"Parsa Eskandar, Benedict Paten, Jouni Sirén","doi":"10.1186/s13015-026-00301-4","DOIUrl":"10.1186/s13015-026-00301-4","url":null,"abstract":"<p><p>Pangenome graphs represent the genomic variation by encoding multiple haplotypes within a unified graph structure. However, efficient and lossless indexing of such structures remains challenging due to the scale and complexity of pangenomic data. We present a practical and scalable indexing framework based on tag arrays, which annotate positions in the Burrows-Wheeler transform (BWT) with graph coordinates. Our method extends the FM-index with a run-length compressed tag structure that enables efficient retrieval of all unique graph locations where a query pattern appears. We introduce a novel construction algorithm that combines unique k-mers, graph-based extensions, and haplotype traversal to compute the tag array in a memory-efficient manner. To support large genomes, we process each chromosome independently and then merge the results into a unified index using properties of the multi-string BWT and r-index. Our evaluation on the HPRC graphs demonstrates that the tag array structure compresses effectively, scales well with added haplotypes, and preserves accurate mapping information across diverse regions of the genome. This indexing method enables lossless and haplotype-aware querying in complex pangenomes and offers a practical indexing layer to develop scalable aligners and downstream graph-based analysis tools. The index additionally supports efficient one-to-all coordinate translation, enabling any interval on a haplotype to be mapped to its corresponding intervals across all other haplotypes in the graph.</p>","PeriodicalId":50823,"journal":{"name":"Algorithms for Molecular Biology","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13520286/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148279738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dolphyin: a combinatorial algorithm for identifying 1-Dollo phylogenies in cancer.","authors":"Daniel W Feng, Mohammed El-Kebir","doi":"10.1186/s13015-026-00303-2","DOIUrl":"10.1186/s13015-026-00303-2","url":null,"abstract":"<p><strong>Background: </strong>Several recent cancer phylogeny inference methods have used the k-Dollo evolutionary model for single-nucleotide variants, which requires a phylogeny T on binary sequencing data matrix B such that each variant is gained once and lost at most k times. The 1-Dollo variant has been studied extensively but its hardness remains open.</p><p><strong>Results: </strong>We prove that the 1-DOLLO LINEAR PHYLOGENY (1DLP) problem, where we additionally require the resulting 1-Dollo phylogeny T to be linear, is equivalent to verifying whether matrix B has the Consecutive Ones Property, which can be determined in polynomial time. We also show that some practical extensions of 1DLP, such as the minimization of false negatives, are NP-hard. We then show how to recursively decompose any 1-Dollo phylogeny T, not necessarily linear, into several 1-Dollo linear phylogenies and extend this characterization to all matrices B that admit 1-Dollo phylogenies. We use this characterization to develop Dolphyin, a new exponential-time algorithm for inferring 1-Dollo phylogenies. Dolphyin is runtime-competitive with integer linear programming-based algorithm SPhyR (El-Kebir 2018) on simulated datasets and infers 1-Dollo phylogenies with false negative sequencing error rates at or below simulated ground truth rates. We apply Dolphyin to acute myeloid leukemia datasets and find that the majority of the cancers can be explained by 1-Dollo phylogenies with error rates in line with the used sequencing technology.</p><p><strong>Conclusion: </strong>Our work develops a novel, combinatorial algorithm for practical inference of 1-Dollo phylogenies.</p>","PeriodicalId":50823,"journal":{"name":"Algorithms for Molecular Biology","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13471185/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148206774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lukas Geis, Dennis Hecker, Martin Hoefer, Ulrich Meyer, Marcel H Schulz
{"title":"Probing transcription factor subsets in gene regulatory networks.","authors":"Lukas Geis, Dennis Hecker, Martin Hoefer, Ulrich Meyer, Marcel H Schulz","doi":"10.1186/s13015-026-00297-x","DOIUrl":"10.1186/s13015-026-00297-x","url":null,"abstract":"<p><p>Transcription factors (TFs) are essential players in the regulation of gene expression and thus have been the subject of interest in the context of diseases and the manipulation of specific cell functions or pathways. The complex interplay of TFs and genes can be modeled as a network, in which each edge represents a regulatory influence. A challenge in such networks is the identification of a set of TFs with the maximum regulatory influence, which is of particular importance in the context of perturbation studies. We model the task of finding a set of TFs to maximize the influence on a set of genes as a probing problem in a bipartite graph. We test different adaptive and non-adaptive algorithms on simulated graphs and discuss their properties and adaptivity gap. Then, we apply the algorithms on real-life data to find TFs regulating genes involved in T-cell mediated immunity and lymphoid leukemia. The approach has minimal data requirements and can be readily applied to all other types of bipartite networks.</p>","PeriodicalId":50823,"journal":{"name":"Algorithms for Molecular Biology","volume":"21 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13179610/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147950213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Comparing the ability of embedding methods on metabolic hypergraphs for capturing taxonomy-based features.","authors":"Mattia Cervellini, Blerina Sinaimeri, Catherine Matias, Alessio Martino","doi":"10.1186/s13015-026-00298-w","DOIUrl":"10.1186/s13015-026-00298-w","url":null,"abstract":"<p><strong>Background: </strong>Metabolic networks are complex systems that describe the biochemical reactions within an organism through pairwise interactions between chemical compounds. While this representation is widely used to study biological function, it fails to capture the full structure of metabolic reactions, many of which involve more than two compounds. Hypergraphs offer a more natural representation, where nodes represent metabolites and hyperedges represent reactions involving multiple participants. Clustering such metabolic hypergraphs can reveal systematic differences among evolutionarily distinct organisms, providing insight into ecological constraints and evolutionary pressures.</p><p><strong>Methods: </strong>In this study, we investigate how different graphs and hypergraphs embedding methods influence their unsupervised clustering, with the goal of capturing taxonomy-based classes. We apply 14 distinct embedding strategies to a large-scale dataset of 8467 metabolic hypergraphs. Each embedding was followed by hierarchical clustering using a fixed linkage method. To assess performance, we compared the resulting clusters against known taxonomic groupings.</p><p><strong>Results: </strong>Our findings show that the choice of hypergraph embedding has a significant effect on clustering outcomes. Among the tested methods, Bag of Hyperedges with Jaccard distance, Histogram Cosine Kernel, and a Hypergraph Auto-Encoder consistently performed best. We also advocate that the embedding method should be chosen based on the goal of the downstream task.</p>","PeriodicalId":50823,"journal":{"name":"Algorithms for Molecular Biology","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13270793/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147788014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Pattern matching with Elastic-Degenerate strings and Elastic-Founder graphs.","authors":"Rocco Ascone, Giulia Bernardini, Alessio Conte, Massimo Equi, Esteban Gabory, Roberto Grossi, Nadia Pisanti","doi":"10.1186/s13015-025-00289-3","DOIUrl":"10.1186/s13015-025-00289-3","url":null,"abstract":"<p><p>Elastic Degenerate (ED) strings and Elastic Founder (EF) graphs, here collectively named variable strings, are two representations of acyclic components of pangenomes which extend the well-known notion of indeterminate string. Recent studies have focused extensively on algorithmic tasks involving these structures and other forms of variable strings that they generalize. Among such tasks, the basic operation of matching a pattern into a text, a fundamental toolkit for pangenomic data analysis, deserves special attention. In this paper, (1) we establish a clear taxonomy across ED strings and EF graphs, categorizing types of variable strings from the simplest linear (solid) string to the most complex general cases; (2) we consider the problem MATCH(X,Y) of matching a solid or variable pattern of type X into a variable text of type Y, and investigate its time complexity when X and Y are chosen from types of variable strings in the taxonomy of (1). For all possible X and Y, we either provide a non-trivial, often sub-quadratic, upper bound for MATCH(X,Y), or we prove a quadratic conditional lower bound, taking as a reference the existing quadratic conditional lower bounds for MATCH(SOLID,ED) and MATCH(SOLID,EF). A preliminary version of this work appeared in [Ascone et al., WABI 2024].</p>","PeriodicalId":50823,"journal":{"name":"Algorithms for Molecular Biology","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13182080/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147788212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}