Genome Biology最新文献

{"title":"Author Correction: NERD-seq: a novel approach of Nanopore direct RNA sequencing that expands representation of non-coding RNAs","authors":"Luke Saville, Li Wu, Jemaneh Habtewold, Yubo Cheng, Babita Gollen, Liam Mitchell, Matthew Stuart-Edwards, Travis Haight, Majid Mohajerani, Athanasios Zovoilis","doi":"10.1186/s13059-024-03395-4","DOIUrl":"https://doi.org/10.1186/s13059-024-03395-4","url":null,"abstract":"<p>\u0000<b>Correction</b><b>: </b>\u0000<b>Genome Biol 25, 233 (2024)</b>\u0000</p><p>\u0000<b>https://doi.org/10.1186/s13059-024-03375-8</b>\u0000</p><br/><p>Following publication of the original article [1], the authors identified two typos in affiliation 3 and 4. The incorrect and correct affiliations are given below.</p><p>Incorrect: <sup>3</sup> Southern Alberta Genome Sciences Centre, Lethbridge, AB, T1K3M4, Canada</p><p>Correct: <sup>3</sup> Southern Alberta Genome Sciences Centre, University of Lethbridge, Lethbridge, AB, T1K3M4, Canada</p><p>Incorrect: <sup>4</sup> Canadian Centre for Behavioral Neuroscience, Lethbridge, AB, T1K3M4, Canada</p><p>Correct: <sup>4</sup> Canadian Centre for Behavioral Neuroscience, University of Lethbridge, Lethbridge, AB, T1K3M4, Canada</p><p>The original article [1] is corrected.</p><ol data-track-component=\"outbound reference\" data-track-context=\"references section\"><li data-counter=\"1.\"><p>Saville L, Wu L, Habtewold J, et al. NERD-seq: a novel approach of Nanopore direct RNA sequencing that expands representation of non-coding RNAs. Genome Biol. 2024;25:233. https://doi.org/10.1186/s13059-024-03375-8.</p><p>Article CAS PubMed PubMed Central Google Scholar </p></li></ol><p>Download references<svg aria-hidden=\"true\" focusable=\"false\" height=\"16\" role=\"img\" width=\"16\"><use xlink:href=\"#icon-eds-i-download-medium\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"></use></svg></p><h3>Authors and Affiliations</h3><ol><li><p>Department of Biochemistry and Medical Genetics, University of Manitoba, Winnipeg, MB, R3E3N4, Canada</p><p>Luke Saville, Li Wu, Jemaneh Habtewold, Liam Mitchell, Matthew Stuart-Edwards, Travis Haight & Athanasios Zovoilis</p></li><li><p>Paul Albrechtsen Research Institute, CCMB, Winnipeg, MB, R3E3N4, Canada</p><p>Luke Saville, Li Wu, Jemaneh Habtewold, Liam Mitchell, Matthew Stuart-Edwards, Travis Haight & Athanasios Zovoilis</p></li><li><p>Southern Alberta Genome Sciences Centre, University of Lethbridge, Lethbridge, AB, T1K3M4, Canada</p><p>Luke Saville, Yubo Cheng, Babita Gollen, Liam Mitchell, Matthew Stuart-Edwards, Travis Haight & Athanasios Zovoilis</p></li><li><p>Canadian Centre for Behavioral Neuroscience, University of Lethbridge, Lethbridge, AB, T1K3M4, Canada</p><p>Luke Saville, Yubo Cheng, Babita Gollen, Liam Mitchell, Matthew Stuart-Edwards, Travis Haight, Majid Mohajerani & Athanasios Zovoilis</p></li></ol><span>Authors</span><ol><li><span>Luke Saville</span>View author publications<p>You can also search for this author in <span>PubMed<span> </span>Google Scholar</span></p></li><li><span>Li Wu</span>View author publications<p>You can also search for this author in <span>PubMed<span> </span>Google Scholar</span></p></li><li><span>Jemaneh Habtewold</span>View author publications<p>You can also search for this author in <span>PubMed<span> </span>Google Scholar</span></p></li><li><span>Yubo Cheng</span>View author publications<p>You can also search for this author in <span>PubMed<span> </span>","PeriodicalId":12611,"journal":{"name":"Genome Biology","volume":"55 1","pages":""},"PeriodicalIF":12.3,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142325573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A realistic benchmark for differential abundance testing and confounder adjustment in human microbiome studies","authors":"Jakob Wirbel, Morgan Essex, Sofia Kirke Forslund, Georg Zeller","doi":"10.1186/s13059-024-03390-9","DOIUrl":"https://doi.org/10.1186/s13059-024-03390-9","url":null,"abstract":"In microbiome disease association studies, it is a fundamental task to test which microbes differ in their abundance between groups. Yet, consensus on suitable or optimal statistical methods for differential abundance testing is lacking, and it remains unexplored how these cope with confounding. Previous differential abundance benchmarks relying on simulated datasets did not quantitatively evaluate the similarity to real data, which undermines their recommendations. Our simulation framework implants calibrated signals into real taxonomic profiles, including signals mimicking confounders. Using several whole meta-genome and 16S rRNA gene amplicon datasets, we validate that our simulated data resembles real data from disease association studies much more than in previous benchmarks. With extensively parametrized simulations, we benchmark the performance of nineteen differential abundance methods and further evaluate the best ones on confounded simulations. Only classic statistical methods (linear models, the Wilcoxon test, t-test), limma, and fastANCOM properly control false discoveries at relatively high sensitivity. When additionally considering confounders, these issues are exacerbated, but we find that adjusted differential abundance testing can effectively mitigate them. In a large cardiometabolic disease dataset, we showcase that failure to account for covariates such as medication causes spurious association in real-world applications. Tight error control is critical for microbiome association studies. The unsatisfactory performance of many differential abundance methods and the persistent danger of unchecked confounding suggest these contribute to a lack of reproducibility among such studies. We have open-sourced our simulation and benchmarking software to foster a much-needed consolidation of statistical methodology for microbiome research.\u0000","PeriodicalId":12611,"journal":{"name":"Genome Biology","volume":"37 1","pages":""},"PeriodicalIF":12.3,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142317135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Recruitment of the m6A/m6Am demethylase FTO to target RNAs by the telomeric zinc finger protein ZBTB48","authors":"Syed Nabeel-Shah, Shuye Pu, Giovanni L. Burke, Nujhat Ahmed, Ulrich Braunschweig, Shaghayegh Farhangmehr, Hyunmin Lee, Mingkun Wu, Zuyao Ni, Hua Tang, Guoqing Zhong, Edyta Marcon, Zhaolei Zhang, Benjamin J. Blencowe, Jack F. Greenblatt","doi":"10.1186/s13059-024-03392-7","DOIUrl":"https://doi.org/10.1186/s13059-024-03392-7","url":null,"abstract":"N6-methyladenosine (m6A), the most abundant internal modification on eukaryotic mRNA, and N6, 2′-O-dimethyladenosine (m6Am), are epitranscriptomic marks that function in multiple aspects of posttranscriptional regulation. Fat mass and obesity-associated protein (FTO) can remove both m6A and m6Am; however, little is known about how FTO achieves its substrate selectivity. Here, we demonstrate that ZBTB48, a C2H2-zinc finger protein that functions in telomere maintenance, associates with FTO and binds both mRNA and the telomere-associated regulatory RNA TERRA to regulate the functional interactions of FTO with target transcripts. Specifically, depletion of ZBTB48 affects targeting of FTO to sites of m6A/m6Am modification, changes cellular m6A/m6Am levels and, consequently, alters decay rates of target RNAs. ZBTB48 ablation also accelerates growth of HCT-116 colorectal cancer cells and modulates FTO-dependent regulation of Metastasis-associated protein 1 (MTA1) transcripts by controlling the binding to MTA1 mRNA of the m6A reader IGF2BP2. Our findings thus uncover a previously unknown mechanism of posttranscriptional regulation in which ZBTB48 co-ordinates RNA-binding of the m6A/m6Am demethylase FTO to control expression of its target RNAs.","PeriodicalId":12611,"journal":{"name":"Genome Biology","volume":"98 1","pages":""},"PeriodicalIF":12.3,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142245225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A dynamic regulome of shoot-apical-meristem-related homeobox transcription factors modulates plant architecture in maize","authors":"Zi Luo, Leiming Wu, Xinxin Miao, Shuang Zhang, Ningning Wei, Shiya Zhao, Xiaoyang Shang, Hongyan Hu, Jiquan Xue, Tifu Zhang, Fang Yang, Shutu Xu, Lin Li","doi":"10.1186/s13059-024-03391-8","DOIUrl":"https://doi.org/10.1186/s13059-024-03391-8","url":null,"abstract":"The shoot apical meristem (SAM), from which all above-ground tissues of plants are derived, is critical to plant morphology and development. In maize (Zea mays), loss-of-function mutant studies have identified several SAM-related genes, most encoding homeobox transcription factors (TFs), located upstream of hierarchical networks of hundreds of genes. Here, we collect 46 transcriptome and 16 translatome datasets across 62 different tissues or stages from the maize inbred line B73. We construct a dynamic regulome for 27 members of three SAM-related homeobox subfamilies (KNOX, WOX, and ZF-HD) through machine-learning models for the detection of TF targets across different tissues and stages by combining tsCUT&Tag, ATAC-seq, and expression profiling. This dynamic regulome demonstrates the distinct binding specificity and co-factors for these homeobox subfamilies, indicative of functional divergence between and within them. Furthermore, we assemble a SAM dynamic regulome, illustrating potential functional mechanisms associated with plant architecture. Lastly, we generate a wox13a mutant that provides evidence that WOX13A directly regulates Gn1 expression to modulate plant height, validating the regulome of SAM-related homeobox genes. The SAM-related homeobox transcription-factor regulome presents an unprecedented opportunity to dissect the molecular mechanisms governing SAM maintenance and development, thereby advancing our understanding of maize growth and shoot architecture.","PeriodicalId":12611,"journal":{"name":"Genome Biology","volume":"10 1","pages":""},"PeriodicalIF":12.3,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142245279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ESCHR: a hyperparameter-randomized ensemble approach for robust clustering across diverse datasets","authors":"Sarah M. Goggin, Eli R. Zunder","doi":"10.1186/s13059-024-03386-5","DOIUrl":"https://doi.org/10.1186/s13059-024-03386-5","url":null,"abstract":"Clustering is widely used for single-cell analysis, but current methods are limited in accuracy, robustness, ease of use, and interpretability. To address these limitations, we developed an ensemble clustering method that outperforms other methods at hard clustering without the need for hyperparameter tuning. It also performs soft clustering to characterize continuum-like regions and quantify clustering uncertainty, demonstrated here by mapping the connectivity and intermediate transitions between MNIST handwritten digits and between hypothalamic tanycyte subpopulations. This hyperparameter-randomized ensemble approach improves the accuracy, robustness, ease of use, and interpretability of single-cell clustering, and may prove useful in other fields as well.","PeriodicalId":12611,"journal":{"name":"Genome Biology","volume":"19 1","pages":""},"PeriodicalIF":12.3,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142234448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Splam: a deep-learning-based splice site predictor that improves spliced alignments","authors":"Kuan-Hao Chao, Alan Mao, Steven L. Salzberg, Mihaela Pertea","doi":"10.1186/s13059-024-03379-4","DOIUrl":"https://doi.org/10.1186/s13059-024-03379-4","url":null,"abstract":"The process of splicing messenger RNA to remove introns plays a central role in creating genes and gene variants. We describe Splam, a novel method for predicting splice junctions in DNA using deep residual convolutional neural networks. Unlike previous models, Splam looks at a 400-base-pair window flanking each splice site, reflecting the biological splicing process that relies primarily on signals within this window. Splam also trains on donor and acceptor pairs together, mirroring how the splicing machinery recognizes both ends of each intron. Compared to SpliceAI, Splam is consistently more accurate, achieving 96% accuracy in predicting human splice junctions.","PeriodicalId":12611,"journal":{"name":"Genome Biology","volume":"61 1","pages":""},"PeriodicalIF":12.3,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142234461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Atlas of telomeric repeat diversity in Arabidopsis thaliana","authors":"Yueqi Tao, Wenfei Xian, Zhigui Bao, Fernando A. Rabanal, Andrea Movilli, Christa Lanz, Gautam Shirsekar, Detlef Weigel","doi":"10.1186/s13059-024-03388-3","DOIUrl":"https://doi.org/10.1186/s13059-024-03388-3","url":null,"abstract":"Telomeric repeat arrays at the ends of chromosomes are highly dynamic in composition, but their repetitive nature and technological limitations have made it difficult to assess their true variation in genome diversity surveys. We have comprehensively characterized the sequence variation immediately adjacent to the canonical telomeric repeat arrays at the very ends of chromosomes in 74 genetically diverse Arabidopsis thaliana accessions. We first describe several types of distinct telomeric repeat units and then identify evolutionary processes such as local homogenization and higher-order repeat formation that shape diversity of chromosome ends. By comparing largely isogenic samples, we also determine repeat number variation of the degenerate and variant telomeric repeat array at both the germline and somatic levels. Finally, our analysis of haplotype structure uncovers chromosome end-specific patterns in the distribution of variant telomeric repeats, and their linkage to the more proximal non-coding region. Our findings illustrate the spectrum of telomeric repeat variation at multiple levels in A. thaliana—in germline and soma, across all chromosome ends, and across genetic groups—thereby expanding our knowledge of the evolution of chromosome ends.","PeriodicalId":12611,"journal":{"name":"Genome Biology","volume":"4 1","pages":""},"PeriodicalIF":12.3,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142234447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dimension reduction, cell clustering, and cell–cell communication inference for single-cell transcriptomics with DcjComm","authors":"Qian Ding, Wenyi Yang, Guangfu Xue, Hongxin Liu, Yideng Cai, Jinhao Que, Xiyun Jin, Meng Luo, Fenglan Pang, Yuexin Yang, Yi Lin, Yusong Liu, Haoxiu Sun, Renjie Tan, Pingping Wang, Zhaochun Xu, Qinghua Jiang","doi":"10.1186/s13059-024-03385-6","DOIUrl":"https://doi.org/10.1186/s13059-024-03385-6","url":null,"abstract":"Advances in single-cell transcriptomics provide an unprecedented opportunity to explore complex biological processes. However, computational methods for analyzing single-cell transcriptomics still have room for improvement especially in dimension reduction, cell clustering, and cell–cell communication inference. Herein, we propose a versatile method, named DcjComm, for comprehensive analysis of single-cell transcriptomics. DcjComm detects functional modules to explore expression patterns and performs dimension reduction and clustering to discover cellular identities by the non-negative matrix factorization-based joint learning model. DcjComm then infers cell–cell communication by integrating ligand-receptor pairs, transcription factors, and target genes. DcjComm demonstrates superior performance compared to state-of-the-art methods.","PeriodicalId":12611,"journal":{"name":"Genome Biology","volume":"46 1","pages":""},"PeriodicalIF":12.3,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A comprehensive map of the aging blood methylome in humans","authors":"Kirsten Seale, Andrew Teschendorff, Alexander P. Reiner, Sarah Voisin, Nir Eynon","doi":"10.1186/s13059-024-03381-w","DOIUrl":"https://doi.org/10.1186/s13059-024-03381-w","url":null,"abstract":"During aging, the human methylome undergoes both differential and variable shifts, accompanied by increased entropy. The distinction between variably methylated positions (VMPs) and differentially methylated positions (DMPs), their contribution to epigenetic age, and the role of cell type heterogeneity remain unclear. We conduct a comprehensive analysis of > 32,000 human blood methylomes from 56 datasets (age range = 6–101 years). We find a significant proportion of the blood methylome that is differentially methylated with age (48% DMPs; FDR < 0.005) and variably methylated with age (37% VMPs; FDR < 0.005), with considerable overlap between the two groups (59% of DMPs are VMPs). Bivalent and Polycomb regions become increasingly methylated and divergent between individuals, while quiescent regions lose methylation more uniformly. Both chronological and biological clocks, but not pace-of-aging clocks, show a strong enrichment for CpGs undergoing both mean and variance changes during aging. The accumulation of DMPs shifting towards a methylation fraction of 50% drives the increase in entropy, smoothening the epigenetic landscape. However, approximately a quarter of DMPs exhibit anti-entropic effects, opposing this direction of change. While changes in cell type composition minimally affect DMPs, VMPs and entropy measurements are moderately sensitive to such alterations. This study represents the largest investigation to date of genome-wide DNA methylation changes and aging in a single tissue, providing valuable insights into primary molecular changes relevant to chronological and biological aging.\u0000","PeriodicalId":12611,"journal":{"name":"Genome Biology","volume":"18 1","pages":""},"PeriodicalIF":12.3,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142142592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Publisher Correction: scParser: sparse representation learning for scalable single-cell RNA sequencing data analysis","authors":"Kai Zhao, Hon-Cheong So, Zhixiang Lin","doi":"10.1186/s13059-024-03378-5","DOIUrl":"https://doi.org/10.1186/s13059-024-03378-5","url":null,"abstract":"&lt;p&gt;&lt;b&gt;Publisher Correction: Genome Biol 25, 223 (2024)&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt;https://doi.org/10.1186/s13059-024-03345-0&lt;/b&gt;&lt;/p&gt;&lt;br/&gt;&lt;p&gt;Following publication of the original article [1], the authors identified a typesetting error in Eq. 3, 4 and 10, as well as in Algorithm 1 equation. An erroneous “&lt;i&gt;ll&lt;/i&gt;” was typeset at the start of the equations.&lt;/p&gt;&lt;p&gt;The incorrect and corrected versions are published in this correction article.&lt;/p&gt;&lt;p&gt;Incorrect equation (3)&lt;/p&gt;&lt;span&gt;$$left{ begin{array}{ll} llmathcal{L}(d, p, v, s, g) = &amp; frac{1}{2} sumnolimits_{i,m} left( z_{i,m} - d_{j}^{mathsf{T}} v_{m} - p_{t}^{mathsf{T}} v_{m} - s_{i}^{mathsf{T}} g_{m} right)^{2} + &amp; frac{1}{2} lambda_{1} left( sumnolimits_{j} | d_{j} |^{2}_{2} + sumnolimits_{t} | d_{t} |^{2}_{2} + sumnolimits_{m} | v_{m} |^{2}_{2}right) + &amp; lambda_{2} left( frac{1}{2} (1-alpha) sumnolimits_{i} |s_{i}|_{2}^{2} + alpha sumnolimits_{i}|s_{i}|_{1} right), text{subject to} &amp; sumnolimits_{m} g_{mk}^{2} leq c, forall k = 1, ldots, K_{2}. end{array}right.$$&lt;/span&gt;(3)&lt;p&gt;Correct equation (3)&lt;/p&gt;&lt;span&gt;$$left{ begin{array}{ll}mathcal{L}(d, p, v, s, g) = &amp; frac{1}{2} sumnolimits_{i,m} left( z_{i,m} - d_{j}^{mathsf{T}} v_{m} - p_{t}^{mathsf{T}} v_{m} - s_{i}^{mathsf{T}} g_{m} right)^{2} + &amp; frac{1}{2} lambda_{1} left( sumnolimits_{j} | d_{j} |^{2}_{2} + sumnolimits_{t} | d_{t} |^{2}_{2} + sumnolimits_{m} | v_{m} |^{2}_{2}right) + &amp; lambda_{2} left( frac{1}{2} (1-alpha) sumnolimits_{i} |s_{i}|_{2}^{2} + alpha sumnolimits_{i}|s_{i}|_{1} right), text{subject to} &amp; sumnolimits_{m} g_{mk}^{2} leq c, forall k = 1, ldots, K_{2}. end{array}right.$$&lt;/span&gt;(3)&lt;p&gt;Incorrect equation (4)&lt;/p&gt;&lt;span&gt;$$left{ begin{array}{ll} ll mathcal{L}(D, P, V, S, G) = &amp; frac{1}{2} left| Z - left(X^{D} D + X^{P}Pright) V - SGright|_{text{F}}^{2}+ &amp; frac{1}{2} lambda_{1} left( |D|^{2}_{text{F}} + |P|^{2}_{text{F}} + |V|^{2}_{text{F}}right) + &amp; lambda_{2} left[ frac{1}{2} (1 - alpha) | S |^{2}_{text{F}} + alpha|S|_{1}right] text{subject to} &amp; left| G_{2} right|_{2}^{2} leq c, forall k = 1, ldots, K_{2}, end{array}right.$$&lt;/span&gt;(4)&lt;p&gt;Correct equation (4)&lt;/p&gt;&lt;span&gt;$$left{ begin{array}{ll}mathcal{L}(D, P, V, S, G) = &amp; frac{1}{2} left| Z - left(X^{D} D + X^{P}Pright) V - SGright|_{text{F}}^{2}+ &amp; frac{1}{2} lambda_{1} left( |D|^{2}_{text{F}} + |P|^{2}_{text{F}} + |V|^{2}_{text{F}}right) + &amp; lambda_{2} left[ frac{1}{2} (1 - alpha) | S |^{2}_{text{F}} + alpha|S|_{1}right] text{subject to} &amp; left| G_{2} right|_{2}^{2} leq c, forall k = 1, ldots, K_{2}, end{array}right.$$&lt;/span&gt;(4)&lt;p&gt;Incorrect equation (10)&lt;/p&gt;&lt;span&gt;$$left{ begin{array}{ll} llmathcal{L}(V, G) = &amp; frac{1}{2k} sumnolimits_{j=1}^{k} left| Z_{I_{j}} - left( X_{I_{j}}^{D} D_{I_{j}} + X_{I_{j}}^{P} P_{I_{j}} right) V - S_{I_{j}} Gright|^{2}_{F} + &amp; frac{1}{2} lambda_{1} left[ frac{1}{k} sumnolimits_{j=1}^{k} left(left| D_{I_{j}} right|^{2}_{text{F}} + left| P_{I_{j}} right|^{2}_{F}right) + |V|^{2}_{F}right] + &","PeriodicalId":12611,"journal":{"name":"Genome Biology","volume":"10 1","pages":""},"PeriodicalIF":12.3,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142130682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}