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Hartmann T, Middendorf M, Bernt M. Genome Rearrangement Analysis : Cut and Join Genome Rearrangements and Gene Cluster Preserving Approaches. Methods Mol Biol 2024; 2802:215-245. [PMID: 38819562 DOI: 10.1007/978-1-0716-3838-5_9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/01/2024]
Abstract
Genome rearrangements are mutations that change the gene content of a genome or the arrangement of the genes on a genome. Several years of research on genome rearrangements have established different algorithmic approaches for solving some fundamental problems in comparative genomics based on gene order information. This review summarizes the literature on genome rearrangement analysis along two lines of research. The first line considers rearrangement models that are particularly well suited for a theoretical analysis. These models use rearrangement operations that cut chromosomes into fragments and then join the fragments into new chromosomes. The second line works with rearrangement models that reflect several biologically motivated constraints, e.g., the constraint that gene clusters have to be preserved. In this chapter, the border between algorithmically "easy" and "hard" rearrangement problems is sketched and a brief review is given on the available software tools for genome rearrangement analysis.
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Affiliation(s)
- Tom Hartmann
- Swarm Intelligence and Complex Systems Group, Institute of Computer Science, University Leipzig, Leipzig, Germany
| | - Martin Middendorf
- Swarm Intelligence and Complex Systems Group, Institute of Computer Science, University Leipzig, Leipzig, Germany.
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Alexandrino AO, Oliveira AR, Jean G, Fertin G, Dias U, Dias Z. Reversal and Transposition Distance on Unbalanced Genomes Using Intergenic Information. J Comput Biol 2023; 30:861-876. [PMID: 37222724 DOI: 10.1089/cmb.2023.0087] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/25/2023] Open
Abstract
The most common way to calculate the rearrangement distance between two genomes is to use the size of a minimum length sequence of rearrangements that transforms one of the two given genomes into the other, where the genomes are represented as permutations using only their gene order, based on the assumption that genomes have the same gene content. With the advance of research in genome rearrangements, new works extended the classical models by either considering genomes with different gene content (unbalanced genomes) or including more genomic characteristics to the mathematical representation of the genomes, such as the distribution of intergenic regions sizes. In this study, we study the Reversal, Transposition, and Indel (Insertion and Deletion) Distance using intergenic information, which allows comparing unbalanced genomes, because indels are included in the rearrangement model (i.e., the set of possible rearrangements allowed when we compute the distance). For the particular case of transpositions and indels on unbalanced genomes, we present a 4-approximation algorithm, improving a previous 4.5 approximation. This algorithm is extended so as to deal with gene orientation and to maintain the 4-approximation factor for the Reversal, Transposition, and Indel Distance on unbalanced genomes. Furthermore, we evaluate the proposed algorithms using experiments on simulated data.
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Affiliation(s)
| | | | - Géraldine Jean
- Nantes Université, École Centrale Nantes, CNRS, LS2N, UMR 6004, Nantes, France
| | - Guillaume Fertin
- Nantes Université, École Centrale Nantes, CNRS, LS2N, UMR 6004, Nantes, France
| | - Ulisses Dias
- School of Technology, University of Campinas, Limeira, Brazil
| | - Zanoni Dias
- Institute of Computing, University of Campinas, Campinas, Brazil
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Brito KL, Oliveira AR, Alexandrino AO, Dias U, Dias Z. An improved approximation algorithm for the reversal and transposition distance considering gene order and intergenic sizes. Algorithms Mol Biol 2021; 16:24. [PMID: 34965857 PMCID: PMC8717661 DOI: 10.1186/s13015-021-00203-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2021] [Accepted: 12/15/2021] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND In the comparative genomics field, one of the goals is to estimate a sequence of genetic changes capable of transforming a genome into another. Genome rearrangement events are mutations that can alter the genetic content or the arrangement of elements from the genome. Reversal and transposition are two of the most studied genome rearrangement events. A reversal inverts a segment of a genome while a transposition swaps two consecutive segments. Initial studies in the area considered only the order of the genes. Recent works have incorporated other genetic information in the model. In particular, the information regarding the size of intergenic regions, which are structures between each pair of genes and in the extremities of a linear genome. RESULTS AND CONCLUSIONS In this work, we investigate the SORTING BY INTERGENIC REVERSALS AND TRANSPOSITIONS problem on genomes sharing the same set of genes, considering the cases where the orientation of genes is known and unknown. Besides, we explored a variant of the problem, which generalizes the transposition event. As a result, we present an approximation algorithm that guarantees an approximation factor of 4 for both cases considering the reversal and transposition (classic definition) events, an improvement from the 4.5-approximation previously known for the scenario where the orientation of the genes is unknown. We also present a 3-approximation algorithm by incorporating the generalized transposition event, and we propose a greedy strategy to improve the performance of the algorithms. We performed practical tests adopting simulated data which indicated that the algorithms, in both cases, tend to perform better when compared with the best-known algorithms for the problem. Lastly, we conducted experiments using real genomes to demonstrate the applicability of the algorithms.
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Alexandrino AO, Oliveira AR, Dias U, Dias Z. Incorporating intergenic regions into reversal and transposition distances with indels. J Bioinform Comput Biol 2021; 19:2140011. [PMID: 34775923 DOI: 10.1142/s0219720021400114] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Problems in the genome rearrangement field are often formulated in terms of pairwise genome comparison: given two genomes [Formula: see text] and [Formula: see text], find the minimum number of genome rearrangements that may have occurred during the evolutionary process. This broad definition lacks at least two important considerations: the first being which features are extracted from genomes to create a useful mathematical model, and the second being which types of genome rearrangement events should be represented. Regarding the first consideration, seminal works in the genome rearrangement field solely used gene order to represent genomes as permutations of integer numbers, neglecting many important aspects like gene duplication, intergenic regions, and complex interactions between genes. Regarding the second consideration, some rearrangement events are widely studied such as reversals and transpositions. In this paper, we shed light on the first consideration and created a model that takes into account gene order and the number of nucleotides in intergenic regions. In addition, we consider events of reversals, transpositions, and indels (insertions and deletions) of genomic material. We present a 4-approximation algorithm for reversals and indels, a [Formula: see text]-approximation algorithm for transpositions and indels, and a 6-approximation for reversals, transpositions, and indels.
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Affiliation(s)
| | - Andre Rodrigues Oliveira
- Institute of Computing, University of Campinas, 1251 Albert Einstein Ave., 13083-852 Campinas, São Paulo, Brazil
| | - Ulisses Dias
- School of Technology, University of Campinas, 1888 Paschoal Marmo St., 13484-332 Limeira, São Paulo, Brazil
| | - Zanoni Dias
- Institute of Computing, University of Campinas, 1251 Albert Einstein Ave., 13083-852 Campinas, São Paulo, Brazil
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Oliveira AR, Jean G, Fertin G, Brito KL, Dias U, Dias Z. Sorting Permutations by Intergenic Operations. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2021; 18:2080-2093. [PMID: 33945484 DOI: 10.1109/tcbb.2021.3077418] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Genome Rearrangements are events that affect large stretches of genomes during evolution. Many mathematical models have been used to estimate the evolutionary distance between two genomes based on genome rearrangements. However, most of them focused on the (order of the) genes of a genome, disregarding other important elements in it. Recently, researchers have shown that considering regions between each pair of genes, called intergenic regions, can enhance distance estimation in realistic data. Two of the most studied genome rearrangements are the reversal, which inverts a sequence of genes, and the transposition, which occurs when two adjacent gene sequences swap their positions inside the genome. In this work, we study the transposition distance between two genomes, but we also consider intergenic regions, a problem we name Sorting by Intergenic Transpositions. We show that this problem is NP-hard and propose two approximation algorithms, with factors 3.5 and 2.5, considering two distinct definitions for the problem. We also investigate the signed reversal and transposition distance between two genomes considering their intergenic regions. This second problem is called Sorting by Signed Intergenic Reversals and Intergenic Transpositions. We show that this problem is NP-hard and develop two approximation algorithms, with factors 3 and 2.5. We check how these algorithms behave when assigning weights for genome rearrangements. Finally, we implemented all these algorithms and tested them on real and simulated data.
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Siqueira G, Alexandrino AO, Oliveira AR, Dias Z. Approximation algorithm for rearrangement distances considering repeated genes and intergenic regions. Algorithms Mol Biol 2021; 16:21. [PMID: 34645469 PMCID: PMC8513232 DOI: 10.1186/s13015-021-00200-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2021] [Accepted: 08/31/2021] [Indexed: 01/02/2023] Open
Abstract
The rearrangement distance is a method to compare genomes of different species. Such distance is the number of rearrangement events necessary to transform one genome into another. Two commonly studied events are the transposition, which exchanges two consecutive blocks of the genome, and the reversal, which reverts a block of the genome. When dealing with such problems, seminal works represented genomes as sequences of genes without repetition. More realistic models started to consider gene repetition or the presence of intergenic regions, sequences of nucleotides between genes and in the extremities of the genome. This work explores the transposition and reversal events applied in a genome representation considering both gene repetition and intergenic regions. We define two problems called Minimum Common Intergenic String Partition and Reverse Minimum Common Intergenic String Partition. Using a relation with these two problems, we show a \documentclass[12pt]{minimal}
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\begin{document}$$\Theta \left( k \right)$$\end{document}Θk-approximation for the Intergenic Transposition Distance, the Intergenic Reversal Distance, and the Intergenic Reversal and Transposition Distance problems, where k is the maximum number of copies of a gene in the genomes. Our practical experiments on simulated genomes show that the use of partitions improves the estimates for the distances.
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Martín-Vide C, Vega-Rodríguez MA, Wheeler T. A 3.5-Approximation Algorithm for Sorting by Intergenic Transpositions. ALGORITHMS FOR COMPUTATIONAL BIOLOGY 2020. [PMCID: PMC7197096 DOI: 10.1007/978-3-030-42266-0_2] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/02/2022]
Abstract
Genome Rearrangements affect large stretches of genomes during evolution. One of the most studied genome rearrangement is the transposition, which occurs when a sequence of genes is moved to another position inside the genome. Mathematical models have been used to estimate the evolutionary distance between two different genomes based on genome rearrangements. However, many of these models have focused only on the (order of the) genes of a genome, disregarding other important elements in it. Recently, researchers have shown that considering existing regions between each pair of genes, called intergenic regions, can enhance the distance estimation in realistic data. In this work, we study the transposition distance between two genomes, but we also consider intergenic regions, a problem we name Sorting Permutations by Intergenic Transpositions (SbIT). We show that this problem is NP-hard and propose a 3.5-approximation algorithm for it.
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