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Wang X, Wang L. Computing Nonoverlapping Inversion Distance Between Two Strings in Linear Average Time. J Comput Biol 2019; 26:193-201. [PMID: 30638400 DOI: 10.1089/cmb.2018.0136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Biological events like inversions are not automatically detected by the usual alignment algorithms. Alignment with inversions does not have a known polynomial time algorithm and Schöniger and Waterman introduced a simplification of the alignment problem with nonoverlapping inversions, where all regions will not be allowed to overlap. They presented an \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \cal O} ( {n^6} )$$ \end{document} algorithm to compute nonoverlapping inversion distance between two strings of length n. The time and space complexities were improved to \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \cal O} ( {n^3} )$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \cal O} ( {n^2} )$$ \end{document} later by Cho, Vellozo, and Ta. In this article, a linear space and linear average time algorithm to compute the inversion distance between two strings of the same length is presented. The recursive formula for this purpose is new to the best of our knowledge. The space costs of the algorithms to solve the same problem are quadratic in the literature, and thus our original algorithm is the first linear space and linear average time algorithm to solve the inversion distance problem.
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Affiliation(s)
- Xiaodong Wang
- 1 Computer Science Department, Fujian University of Technology, Fuzhou, China
| | - Lei Wang
- 2 Facebook, Inc., Menlo Park, California
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Braun EL, Kimball RT, Han KL, Iuhasz-Velez NR, Bonilla AJ, Chojnowski JL, Smith JV, Bowie RCK, Braun MJ, Hackett SJ, Harshman J, Huddleston CJ, Marks BD, Miglia KJ, Moore WS, Reddy S, Sheldon FH, Witt CC, Yuri T. Homoplastic microinversions and the avian tree of life. BMC Evol Biol 2011; 11:141. [PMID: 21612607 PMCID: PMC3123225 DOI: 10.1186/1471-2148-11-141] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2010] [Accepted: 05/25/2011] [Indexed: 11/26/2022] Open
Abstract
BACKGROUND Microinversions are cytologically undetectable inversions of DNA sequences that accumulate slowly in genomes. Like many other rare genomic changes (RGCs), microinversions are thought to be virtually homoplasy-free evolutionary characters, suggesting that they may be very useful for difficult phylogenetic problems such as the avian tree of life. However, few detailed surveys of these genomic rearrangements have been conducted, making it difficult to assess this hypothesis or understand the impact of microinversions upon genome evolution. RESULTS We surveyed non-coding sequence data from a recent avian phylogenetic study and found substantially more microinversions than expected based upon prior information about vertebrate inversion rates, although this is likely due to underestimation of these rates in previous studies. Most microinversions were lineage-specific or united well-accepted groups. However, some homoplastic microinversions were evident among the informative characters. Hemiplasy, which reflects differences between gene trees and the species tree, did not explain the observed homoplasy. Two specific loci were microinversion hotspots, with high numbers of inversions that included both the homoplastic as well as some overlapping microinversions. Neither stem-loop structures nor detectable sequence motifs were associated with microinversions in the hotspots. CONCLUSIONS Microinversions can provide valuable phylogenetic information, although power analysis indicates that large amounts of sequence data will be necessary to identify enough inversions (and similar RGCs) to resolve short branches in the tree of life. Moreover, microinversions are not perfect characters and should be interpreted with caution, just as with any other character type. Independent of their use for phylogenetic analyses, microinversions are important because they have the potential to complicate alignment of non-coding sequences. Despite their low rate of accumulation, they have clearly contributed to genome evolution, suggesting that active identification of microinversions will prove useful in future phylogenomic studies.
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Affiliation(s)
- Edward L Braun
- Department of Biology, University of Florida, Gainesville, FL 32611, USA
| | - Rebecca T Kimball
- Department of Biology, University of Florida, Gainesville, FL 32611, USA
| | - Kin-Lan Han
- Department of Biology, University of Florida, Gainesville, FL 32611, USA
| | | | - Amber J Bonilla
- Department of Biology, University of Florida, Gainesville, FL 32611, USA
| | - Jena L Chojnowski
- Department of Biology, University of Florida, Gainesville, FL 32611, USA
| | - Jordan V Smith
- Department of Biology, University of Florida, Gainesville, FL 32611, USA
| | - Rauri CK Bowie
- Zoology Department, Field Museum of Natural History, 1400 S. Lakeshore Drive, Chicago, IL 60605, USA
- Museum of Vertebrate Zoology and Department of Integrative Biology, University of California, Berkeley, Berkeley, CA 94720, USA
| | - Michael J Braun
- Department of Vertebrate Zoology, Smithsonian Institution, 4210 Silver Hill Road, Suitland, MD 20746, USA
- Behavior, Ecology, Evolution, and Systematics Program, University of Maryland, College Park, MD 20742, USA
| | - Shannon J Hackett
- Zoology Department, Field Museum of Natural History, 1400 S. Lakeshore Drive, Chicago, IL 60605, USA
| | - John Harshman
- Zoology Department, Field Museum of Natural History, 1400 S. Lakeshore Drive, Chicago, IL 60605, USA
- 4869 Pepperwood Way, San Jose, CA 95124, USA
| | - Christopher J Huddleston
- Department of Vertebrate Zoology, Smithsonian Institution, 4210 Silver Hill Road, Suitland, MD 20746, USA
| | - Ben D Marks
- Museum of Natural Science and Department of Biological Sciences, 119 Foster Hall, Louisiana State University, Baton Rouge, LA 70803, USA
| | - Kathleen J Miglia
- Department of Biological Sciences, Wayne State University, 5047 Gullen Mall, Detroit, MI 48202, USA
| | - William S Moore
- Department of Biological Sciences, Wayne State University, 5047 Gullen Mall, Detroit, MI 48202, USA
| | - Sushma Reddy
- Zoology Department, Field Museum of Natural History, 1400 S. Lakeshore Drive, Chicago, IL 60605, USA
- Biology Department, Loyola University Chicago, Chicago, IL 60626, USA
| | - Frederick H Sheldon
- Museum of Natural Science and Department of Biological Sciences, 119 Foster Hall, Louisiana State University, Baton Rouge, LA 70803, USA
| | - Christopher C Witt
- Museum of Natural Science and Department of Biological Sciences, 119 Foster Hall, Louisiana State University, Baton Rouge, LA 70803, USA
- Department of Biology and Museum of Southwestern Biology, University of New Mexico, Albuquerque, NM 87131, USA
| | - Tamaki Yuri
- Department of Biology, University of Florida, Gainesville, FL 32611, USA
- Department of Vertebrate Zoology, Smithsonian Institution, 4210 Silver Hill Road, Suitland, MD 20746, USA
- Sam Noble Oklahoma Museum of Natural History, University of Oklahoma, Norman, OK 73072, USA
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