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Research Square 2021年

作者： Wang, Guan Kitaoka, Traci Crawford, Ali Mao, Qian Hesketh, Andrew Guppy, Fergus M. Ash, Garrett I. Liu, Jason Gerstein, Mark B. Pitsiladis, Yannis P. Sport and Exercise Science and Sports Medicine Research and Enterprise Group University of Brighton Brighton United Kingdom Centre for Regenerative Medicine and Devices University of Brighton Brighton United Kingdom Illumina San DiegoCA United States BGI Shenzhen China School of Pharmacy and Biomolecular Sciences University of Brighton Brighton United Kingdom Centre for Stress and Age-related Disease University of Brighton Brighton United Kingdom Veterans Affairs Connecticut Healthcare System West HavenCT United States Center for Medical Informatics Yale University New HavenCT United States Program in Computational Biology & Bioinformatics Yale University New HavenCT United States Department of Molecular Biophysics & Biochemistry Yale University New HavenCT United States Department of Computer Science Yale University New HavenCT United States Department of Statistics and Data Science Yale University New HavenCT United States

RNA-seq has matured and become an important tool for studying RNA biology. Here we compared two RNA-seq (Illumina sequencing by synthesis and MGI DNBSEQTM) and two microarray platforms (Illumina Expression BeadChip and GeneChipTM Human Transcriptome Array 2.0) in healthy individuals administered recombinant human erythropoietin for transcriptome-wide quantification of differential gene expression. The results show that total RNA sequencing combined with DNB-seq produced a multitude of genes of biological relevance and significance in response to recombinant human erythropoietin, in contrast to other platforms. Through data triangulation linking genes to functions, genes representing the processes of erythropoiesis as well as non-erythropoietic functions of erythropoietin were unveiled. This study provides a knowledge base of genes characterising the responses to recombinant human erythropoietin through cross-platform comparison and validation. © 2021, CC BY.

关键词： RNA

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Direct mapping of Peptide-to-Spectra-Matches to genome information facilitates qualifying proteomics information

Research Square

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Research Square 2021年

作者： Anders, John Petruschke, Hannes Jehmlich, Nico Haange, Sven-Bastiaan von Bergen, Martin Stadler, Peter F. Bioinformatics Group Department of Computer Science Interdisciplinary Center for Bioinformatics Universität Leipzig Härtelstraße 16–18 LeipzigD-04107 Germany Institute of Biochemistry Faculty of Life Sciences University of Leipzig Talstraße 33 LeipzigD-04103 Germany Department of Molecular Systems Biology Helmholtz Centre for Environmental Research - UFZ Permoserstrasse 15 LeipzigD-04318 Germany Halle-Jena-Leipzig Competence Center for Scalable Data Services and Solutions Dresden-Leipzig Leipzig Research Center for Civilization Diseases University Leipzig LeipzigD-04107 Germany Max Planck Institute for Mathematics in the Sciences Inselstraße 22 LeipzigD-04103 Germany Department of Theoretical Chemistry University of Vienna Währinger Straße 17 ViennaA-1090 Austria Faculdad de Ciencias Universidad Nacional de Colombia Sede Bogotá Ciudad Universitaria D.C. BogotáCOL-111321 Colombia Santa Fe Institute 1399 Hyde Park Rd. Santa FeNM87501 United States

Background: Small Proteins have received increasing attention in recent years. They have in particular been implicated as signals contributing to the coordination of bacterial communities. In genome annotations they are often missing or hidden among large numbers of hypothetical proteins because genome annotation pipelines often exclude short open reading frames or over-predict hypothetical proteins based on simple models. The validation of novel proteins, and in particular of small proteins (sProteins), therefore requires additional evidence. Proteogenomics is considered the gold standard for this purpose. It extends beyond established annotations and includes all possible open reading frames (ORFs) as potential sources of peptides, thus allowing the discovery of novel, unannotated proteins. Typically this results in large numbers of putative novel small proteins fraught with large fractions of false-positive predictions. Results: We observe that number and quality of the Peptide-to-Spectra-Matches (PSMs) that map to a candidate ORF can be highly informative for the purpose of distinguishing proteins from spurious ORF annotations. We report here on a workflow that aggregates PSM quality information and local context into simple descriptors and reliably separates likely proteins from the large pool of false-positive, i.e., most likely untranslated ORFs. We investigated the artificial gut microbiome model SIHUMIx, comprising eight different species, for which we validate 5114 proteins that previously have been annotated only as hypothetical ORFs. In addition, we identified 37 non-annotated protein candidates for which we found evidence in proteomic and transcriptomic level. Half (19) of these candidates have close functional homologs in other species. Another 12 candidates have homologs designated as hypothetical proteins in other species. The remaining six candidates are short ( © 2021, CC BY.

关键词： Peptides

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Subgrouping of Burkitt lymphoma variants by DNA methylation is driven by an EBV-associated epigenotype

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Hematological Oncology 2023年第S2期41卷

作者： S. Glaser C. Del Val R. Wagener H. Kretzmer W. Klapper M. Hummel O. Ammerpohl P. Lichter B. Burkhardt L. Trümper S. Mbulaiteye Institute of Human Genetics Ulm University and Ulm University Medical Center Ulm Germany Department of Computer Science and Artifical Intelligence Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI) Universtiy of Granada Granada Spain Transciptome Bioinformatics Group LIFE Research Center for Civilization Diseases University of Leipzig Leipzig Germany Department of Pathology University of Kiel/University Hospital Schleswig-Holstein Kiel Germany Institute of Pathology Charité – University Medicine Berlin Berlin Germany Division of Molecular Genetics German Cancer Research Center Heidelberg Germany Department of Pediatric Hematology and Oncology University Hospital Münster Münster Germany Hematology and Oncology University of Göttingen Göttingen Germany Division of Cancer Epidemiology and Genetics National Cancer Institute National Institutes of Health Bethesda MC USA

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Strategic priorities for transformative progress in advancing biology with proteomics and artificial intelligence

arXiv

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arXiv 2025年

作者： Sun, Yingying Jun, A. Liu, Zhiwei Sun, Rui Qian, Liujia Payne, Samuel H. Bittremieux, Wout Ralser, Markus Li, Chen Chen, Yi Dong, Zhen Perez-Riverol, Yasset Khan, Asif Sander, Chris Aebersold, Ruedi Vizcaíno, Juan Antonio Krieger, Jonathan R. Yao, Jianhua Wen, Han Zhang, Linfeng Zhu, Yunping Xuan, Yue Sun, Benjamin Boyang Qiao, Liang Hermjakob, Henning Tang, Haixu Gao, Huanhuan Deng, Yamin Zhong, Qing Chang, Cheng Bandeira, Nuno Li, Ming Weinan, E. Sun, Siqi Yang, Yuedong Omenn, Gilbert S. Zhang, Yue Xu, Ping Fu, Yan Liu, Xiaowen Overall, Christopher M. Wang, Yu Deutsch, Eric W. Chen, Luonan Cox, Jürgen Demichev, Vadim He, Fuchu Huang, Jiaxing Jin, Huilin Liu, Chao Li, Nan Luan, Zhongzhi Song, Jiangning Yu, Kaicheng Wan, Wanggen Wang, Tai Zhang, Kang Zhang, Le Bell, Peter A. Mann, Matthias Zhang, Bing Guo, Tiannan Affiliated Hangzhou First People’s Hospital State Key Laboratory of Medical Proteomics School of Medicine Westlake University Zhejiang Province Hangzhou China Westlake Center for Intelligent Proteomics Westlake Laboratory of Life Sciences and Biomedicine Zhejiang Province Hangzhou China Biology Department Brigham Young University ProvoUT84602 United States Department of Computer Science University of Antwerp Antwerp2020 Belgium Department of Biochemistry CharitéUniversitätsmedizin Berlin Berlin Germany Biomedicine Discovery Institute Department of Biochemistry and Molecular Biology Monash University MelbourneVICVIC 3800 Australia Wellcome Genome Campus Hinxton CambridgeCB10 1SD United Kingdom Harvard Medical School Ludwig Center at Harvard United States Harvard Medical School Broad Institute Ludwig Center at Harvard Dana-Farber Cancer Institute United States Department of Biology Institute of Molecular Systems Biology ETH Zürich Zürich Switzerland Bruker Ltd. MiltonONL9T 6P4 Canada AI for Life Sciences Lab Tencent Shenzhen518057 China State Key Laboratory of Medical Proteomics AI for Science Institute Beijing100080 China Beijing Institute of Lifeomics Beijing102206 China Thermo Fisher Scientific GmbH Hanna-Kunath Str. 11 Bremen28199 Germany Informatics and Predictive Sciences Research Bristol Myers Squibb United States Department of Chemistry Fudan University Songhu Road 2005 Shanghai200438 China Department of Computer Science Luddy School of Informatics Computing and Engineering Indiana University IN47408 United States ProCan® Children’s Medical Research Institute Faculty of Medicine and Health The University of Sydney WestmeadNSW Australia La Jolla CA United States Central China Institute of Artificial Intelligence University of Waterloo Canada AI for Science Institute Center for Machine Learning Research School of Mathematical Sciences Peking University China Research Institute of Intelligent Complex Systems Fudan U

Artificial intelligence (AI) is transforming scientific research, including proteomics. Advances in mass spectrometry (MS)-based proteomics data quality, diversity, and scale, combined with groundbreaking AI techniques, are unlocking new challenges and opportunities in biological discovery. Here, we highlight key areas where AI is driving innovation, from data analysis to new biological insights. These include developing an AI-friendly ecosystem for proteomics data generation, sharing, and analysis;improving peptide and protein identification and quantification;characterizing protein-protein interactions and protein complexes;advancing spatial and perturbation proteomics;integrating multi-omics data;and ultimately enabling AI-empowered virtual cells. © 2025, CC BY.

关键词： Biotic

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Defining autocatalysis in chemical reaction networks

arXiv

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arXiv 2021年

作者： Andersen, Jakob Lykke Flamm, Christoph Merkle, Daniel Stadler, Peter F. Department of Mathematics and Computer Science University of Southern Denmark Campusvej 55 Odense MDK-5230 Denmark Institute for Theoretical Chemistry University of Vienna Währingerstraße 17 WienA-1090 Austria Bioinformatics Group Department of Computer Science University of Leipzig Härtelstraße 16-18 LeipzigD-04107 Germany Interdisciplinary Center for Bioinformatics University of Leipzig Härtelstraße 16-18 LeipzigD-04107 Germany Halle-Jena-Leipzig University of Leipzig Härtelstraße 16-18 LeipzigD-04107 Germany Competence Center for Scalable Data Services and Solutions Dresden-Leipzig University of Leipzig Härtelstraße 16-18 LeipzigD-04107 Germany Leipzig Research Center for Civilization Diseases University of Leipzig Härtelstraße 16-18 LeipzigD-04107 Germany Centre for Biotechnology and Biomedicine University of Leipzig Härtelstraße 16-18 LeipzigD-04107 Germany Max Planck Institute for Mathematics in the Sciences Inselstraße 22 LeipzigD-04103 Germany Facultad de Ciencias Universidad Nacional de Colombia Sede Bogotá Colombia Santa Fe Institute 1399 Hyde Park Rd. Santa FeNM87501 United States

Autocatalysis is a deceptively simple concept, referring to the situation that a chemical species X catalyzes its own formation. From the perspective of chemical kinetics, autocatalysts show a regime of superlinear growth. Given a chemical reaction network, however, it is not at all straightforward to identify species that are autocatalytic in the sense that there is a sub-network that takes X as input and produces more than one copy of X as output. The difficulty arises from the need to distinguish autocatalysis e.g. from the superposition of a cycle that consumes and produces equal amounts of X and a pathway that produces X. To deal with this issue, a number of competing notions, such as exclusive autocatalysis and autocatalytic cycles, have been introduced. A closer inspection of concepts and their usage by different authors shows, however, that subtle differences in the definitions often makes conceptually matching ideas difficult to bring together formally. In this contribution we make some of the available approaches comparable by translating them into a common formal framework that uses integer hyperflows as a basis to study autocatalysis in large chemical reaction networks. As an application we investigate the prevalence of autocatalysis in metabolic networks. Copyright © 2021, The Authors. All rights reserved.

关键词： Growth kinetics

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Automatic Intelligent System Using Medical of Things for Multiple Sclerosis Detection

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Computational intelligence and neuroscience 2023年第1期2023卷 4776770页

作者： Sujatha Krishnamoorthy Yaxi Zhang Seifedine Kadry Muhammad Attique Khan Majed Alhaisoni Nasser Mustafa Weifeng Yu Abdullah Alqahtani Zhejiang Bioinformatics International Science and Technology Cooperation Center Wenzhou-Kean University Wenzhou Zhejiang Province China. Wenzhou Municipal Key Lab of Applied Biomedical and Biopharmaceutical Informatics Wenzhou-Kean University Wenzhou Zhejiang Province China. Department of Neurology Wenzhou Central Hospital Medical Group Wenzhou 325000 China. Department of Applied Data Science Noroff University College Kristiansand Norway. Artificial Intelligence Research Center (AIRC) Ajman University Ajman 346 UAE. Department of Electrical and Computer Engineering Lebanese American University Byblos Lebanon. Department of Computer Science HITEC University Taxila Pakistan. Computer Sciences Department College of Computer and Information Sciences Princess Nourah Bint Abdulrahman University Riyadh 11671 Saudi Arabia. Wenzhou-Kean University School of Science and Technology Wenzhou Zhejiang Province China. College of Computer Engineering and Sciences Prince Sattam Bin Abdulaziz University Al-Kharj Saudi Arabia.

Malfunctions in the immune system cause multiple sclerosis (MS), which initiates mild to severe nerve damage. MS will disturb the signal communication between the brain and other body parts, and early diagnosis will help reduce the harshness of MS in humankind. Magnetic resonance imaging (MRI) supported MS detection is a standard clinical procedure in which the bio-image recorded with a chosen modality is considered to assess the severity of the disease. The proposed research aims to implement a convolutional neural network (CNN) supported scheme to detect MS lesions in the chosen brain MRI slices. The stages of this framework include (i) image collection and resizing, (ii) deep feature mining, (iii) hand-crafted feature mining, (iii) feature optimization with firefly algorithm, and (iv) serial feature integration and classification. In this work, five-fold cross-validation is executed, and the final result is considered for the assessment. The brain MRI slices with/without the skull section are examined separately, presenting the attained results. The experimental outcome of this study confirms that the VGG16 with random forest (RF) classifier offered a classification accuracy of >98% MRI with skull, and VGG16 with K-nearest neighbor (KNN) provided an accuracy of >98% without the skull.

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Indirect identification of horizontal gene transfer

arXiv

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arXiv 2020年

作者： Schaller, David Lafond, Manuel Stadler, Peter F. Wieseke, Nicolas Hellmuth, Marc Max Planck Institute for Mathematics in the Sciences Inselstraße 22 LeipzigD-04103 Germany Bioinformatics Group Department of Computer Science Interdisciplinary Center for Bioinformatics Universität Leipzig Härtelstraße 16–18 LeipzigD-04107 Germany Department of Computer Science Université de Sherbrooke 2500 boul. de l’Université SherbrookeQCJ1K 2R1 Canada Halle-Jena-Leipzig Competence Center for Scalable Data Services and Solutions Dresden-Leipzig Leipzig Research Center for Civilization Diseases Centre for Biotechnology and Biomedicine at Leipzig University Universität Leipzig Institute for Theoretical Chemistry University of Vienna Währingerstrasse 17 WienA-1090 Austria Facultad de Ciencias Universidad National de Colombia Sede Bogotá Colombia Santa Fe Insitute 1399 Hyde Park Rd. Santa FeNM87501 United States Swarm Intelligence and Complex Systems Group Department of Computer Science Leipzig University Augustusplatz 10 LeipzigD-04109 Germany Department of Mathematics Faculty of Science Stockholm University StockholmSE - 106 91 Sweden

Several implicit methods to infer Horizontal Gene Transfer (HGT) focus on pairs of genes that have diverged only after the divergence of the two species in which the genes reside. This situation defines the edge set of a graph, the later-divergence-time (LDT) graph, whose vertices correspond to genes colored by their species. We investigate these graphs in the setting of relaxed scenarios, i.e., evolutionary scenarios that encompass all commonly used variants of duplication-transfer-loss scenarios in the literature. We characterize LDT graphs as a subclass of properly vertex-colored cographs, and provide a polynomial-time recognition algorithm as well as an algorithm to construct a relaxed scenario that explains a given LDT. An edge in an LDT graph implies that the two corresponding genes are separated by at least one HGT event. The converse is not true, however. We show that the complete xenology relation is described by an rs-Fitch graph, i.e., a complete multipartite graph satisfying constraints on the vertex coloring. This class of vertex-colored graphs is also recognizable in polynomial time. We finally address the question "how much information about all HGT events is contained in LDT graphs" with the help of simulations of evolutionary scenarios with a wide range of duplication, loss, and HGT events. In particular, we show that a simple greedy graph editing scheme can be used to efficiently detect HGT events that are implicitly contained in LDT graphs. © 2020, CC BY.

关键词： Phylogenetic

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Complete edge-colored permutation graphs

arXiv

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arXiv 2020年

作者： Hartmann, Tom Bannach, Max Middendorf, Martin Stadler, Peter F. Wieseke, Nicolas Hellmuth, Marc Bioinformatics Group Department of Computer Science & Interdisciplinary Center for Bioinformatics Universität Leipzig Härtelstraße 16–18 LeipzigD-04107 Germany Institute for Theoretical Computer Science Universität zu Lübeck Ratzeburger Allee 160 LübeckD-23562 Germany Swarm Intelligence and Complex Systems Group Faculty of Mathematics and Computer Science University of Leipzig Augustusplatz 10 LeipzigD-04109 Germany Halle-Jena-Leipzig Competence Center for Scalable Data Services and Solutions Dresden-Leipzig Leipzig Research Center for Civilization Diseases Centre for Biotechnology and Biomedicine at Leipzig University Universität Leipzig Max Planck Institute for Mathematics in the Sciences Inselstraße 22 LeipzigD-04103 Germany Institute for Theoretical Chemistry University of Vienna Währingerstrasse 17 WienA-1090 Austria Facultad de Ciencias Universidad National de Colombia Sede Bogotá Colombia Santa Fe Insitute 1399 Hyde Park Rd. Santa FeNM87501 United States School of Computing University of Leeds EC Stoner Building LeedsLS2 9JT United Kingdom

We introduce the concept of complete edge-colored permutation graphs as complete graphs that are the edge-disjoint union of "classical" permutation graphs. We show that a graph G = (V, E) is a complete edge-colored permutation graph if and only if each monochromatic subgraph of G is a "classical" permutation graph and G does not contain a triangle with 3 different colors. Using the modular decomposition as a framework we demonstrate that complete edge-colored permutation graphs are characterized in terms of their strong prime modules, which induce also complete edge-colored permutation graphs. This leads to an O(|V |2)-time recognition algorithm. We show, moreover, that complete edge-colored permutation graphs form a superclass of so-called symbolic ultrametrics and that the coloring of such graphs is always a Gallai coloring. Copyright © 2020, The Authors. All rights reserved.

关键词： Graphic methods

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Leveraging implicit knowledge in neural networks for functional dissection and engineering of proteins (vol 1, pg 225, 2019)

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NATURE MACHINE INTELLIGENCE 2019年第6期1卷 290-290页

作者： zu Belzen, Julius Upmeier Buergel, Thore Holderbach, Stefan Bubeck, Felix Adam, Lukas Gandor, Catharina Klein, Marita Mathony, Jan Pfuderer, Pauline Platz, Lukas Przybilla, Moritz Schwendemann, Max Heid, Daniel Hoffmann, Mareike Daniela Jendrusch, Michael Schmelas, Carolin Waldhauer, Max Lehmann, Irina Niopek, Dominik Eils, Roland University of Heidelberg Synthetic Biology Group Institute for Pharmacy and Molecular Biotechnology and Center for Quantitative Analysis of Molecular and Cellular Biosystems Heidelberg Germany (GRID:grid.7700.0) (ISNI:0000 0001 2190 4373) Digital Health Center Berlin Institute of Health (BIH) and Charité University Medicine Berlin Germany (GRID:grid.6363.0) (ISNI:0000 0001 2218 4662) University of Heidelberg Synthetic Biology Group Institute for Pharmacy and Molecular Biotechnology and Center for Quantitative Analysis of Molecular and Cellular Biosystems Heidelberg Germany (GRID:grid.7700.0) (ISNI:0000 0001 2190 4373) University of Heidelberg Synthetic Biology Group Institute for Pharmacy and Molecular Biotechnology and Center for Quantitative Analysis of Molecular and Cellular Biosystems Heidelberg Germany (GRID:grid.7700.0) (ISNI:0000 0001 2190 4373) German Cancer Research Center (DKFZ) Department of Theoretical Bioinformatics Heidelberg Germany (GRID:grid.7497.d) (ISNI:0000 0004 0492 0584) University Hospital Heidelberg Department of Infectious Diseases Virology Heidelberg Germany (GRID:grid.5253.1) (ISNI:0000 0001 0328 4908) BioQuant Center and Cluster of Excellence CellNetworks at Heidelberg University Heidelberg Germany (GRID:grid.7700.0) (ISNI:0000 0001 2190 4373) Berlin Institute of Health (BIH) and Charité University Medicine Molecular Epidemiology Unit Berlin Germany (GRID:grid.484013.a) University of Heidelberg Synthetic Biology Group Institute for Pharmacy and Molecular Biotechnology and Center for Quantitative Analysis of Molecular and Cellular Biosystems Heidelberg Germany (GRID:grid.7700.0) (ISNI:0000 0001 2190 4373) University Hospital Heidelberg Health Data Science Unit Heidelberg Germany (GRID:grid.5253.1) (ISNI:0000 0001 0328 4908) Digital Health Center Berlin Institute of Health (BIH) and Charité University Medicine Berlin Germany (GRID:grid.6363.0) (ISNI:0000 0001 2218 4662) University Hospital Heidelberg Health Data Science Unit Heidelberg Germany (GRI

Proteins are nature’s most versatile molecular machines. Deep neural networks trained on large protein datasets have recently been used to tackle the unmet complexity of protein sequence–function relationships. The implicit knowledge contained in these networks represents a powerful, but thus far inaccessible, resource for understanding protein biology. Here, we show that occlusion-based sensitivity analysis can leverage the knowledge present in deep-neural-network-based protein sequence classifiers to identify functionally relevant parts of proteins. We first validated our approach by successfully predicting positions that mediate small molecule binding or catalytic activity across different protein classes. Next, we inferred the impact of point mutations on the activity of ERK and HRas, signalling factors frequently deregulated in cancer. Finally, we used our approach to identify engineering hotspots in CRISPR–Cas9 and anti-CRISPR protein AcrIIA4. Our work demonstrates how implicit knowledge in neural networks can be harnessed for protein functional dissection and protein *** neural networks are a powerful tool for predicting protein function, but identifying the specific parts of a protein sequence that are relevant to its functions remains a challenge. An occlusion-based sensitivity technique helps interpret these deep neural networks, and can guide protein engineering by locating functionally relevant protein positions.

关键词： Proteins

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Complete Characterization of Incorrect Orthology Assignments in Best Match Graphs

arXiv

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arXiv 2020年

作者： Schaller, David Geiß, Manuela Stadler, Peter F. Hellmuth, Marc Max Planck Institute for Mathematics in the Sciences Inselstraße 22 LeipzigD-04103 Germany Bioinformatics Group Department of Computer Science & Interdisciplinary Center for Bioinformatics Universität Leipzig Härtelstraße 16–18 LeipzigD-04107 Germany Software Competence Center Hagenberg GmbH Softwarepark 21 HagenbergA-4232 Austria Halle-Jena-Leipzig Competence Center for Scalable Data Services and Solutions Dresden-Leipzig Leipzig Research Center for Civilization Diseases Centre for Biotechnology and Biomedicine at Leipzig University Universität Leipzig Institute for Theoretical Chemistry University of Vienna Währingerstrasse 17 WienA-1090 Austria Facultad de Ciencias Universidad National de Colombia Sede Bogotá Colombia Santa Fe Insitute 1399 Hyde Park Rd. Santa FeNM87501 United States School of Computing University of Leeds EC Stoner Building LeedsLS2 9JT United Kingdom

Genome-scale orthology assignments are usually based on reciprocal best matches. In the absence of horizontal gene transfer (HGT), every pair of orthologs forms a reciprocal best match. Incorrect orthology assignments therefore are always false positives in the Reciprocal Best Match Graph. We consider duplication/loss scenarios and characterize unambiguous false-positive (u-fp) orthology assignments, that is, edges in the Best Match Graphs (BMGs) that cannot correspond to orthologs for any gene tree that explains the BMG. We characterize u-fp edges in terms of subgraphs of the BMG and show that, given a BMG, there is a unique "augmented tree" that explains the BMG and identifies all u-fp edges in terms of overlapping sets of species in certain subtrees. The augmented tree can be constructed as a refinement of the unique least resolved tree of the BMG in polynomial time. Removal of the u-fp edges from the reciprocal best matches results in a unique orthology *** Codes 92-08, MSC 92D15, MSC 68R01 Copyright © 2020, The Authors. All rights reserved.

关键词： Forestry

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