Ulisses Dias

SIS: a program to generate draft genome sequence scaffolds for prokaryotes

BackgroundDecreasing costs of DNA sequencing have made prokaryotic draft genome sequences increasingly common. A contig scaffold is an ordering of contigs in the correct orientation. A scaffold can help genome comparisons and guide gap closure efforts. One popular technique for obtaining contig scaffolds is to map contigs onto a reference genome. However, rearrangements that may exist between the query and reference genomes may result in incorrect scaffolds, if these rearrangements are not taken into account. Large-scale inversions are common rearrangement events in prokaryotic genomes. Even in draft genomes it is possible to detect the presence of inversions given sufficient sequencing coverage and a sufficiently close reference genome.ResultsWe present a linear-time algorithm that can generate a set of contig scaffolds for a draft genome sequence represented in contigs given a reference genome. The algorithm is aimed at prokaryotic genomes and relies on the presence of matching sequence patterns between the query and reference genomes that can be interpreted as the result of large-scale inversions; we call these patterns inversion signatures. Our algorithm is capable of correctly generating a scaffold if at least one member of every inversion signature pair is present in contigs and no inversion signatures have been overwritten in evolution. The algorithm is also capable of generating scaffolds in the presence of any kind of inversion, even though in this general case there is no guarantee that all scaffolds in the scaffold set will be correct. We compare the performance of sis, the program that implements the algorithm, to seven other scaffold-generating programs. The results of our tests show that sis has overall better performance.Conclusionssis is a new easy-to-use tool to generate contig scaffolds, available both as stand-alone and as a web server. The good performance of sis in our tests adds evidence that large-scale inversions are widespread in prokaryotic genomes.

Length and Symmetry on the Sorting by Weighted Inversions Problem

Large-scale mutational events that occur when stretches of DNA sequence move throughout genomes are called genome rearrangement events. In bacteria, inversions are one of the most frequently observed rearrangements. In some bacterial families, inversions are biased in favor of symmetry as shown by recent research [6, 8, 10]. In addition, several results suggest that short segment inversions are more frequent in the evolution of microbial genomes [4,6,15]. Despite the fact that symmetry and length of the reversed segments seem very important, they have not been considered together in any problem in the genome rearrangement field. Here, we define the problem of sorting genomes (or permutations) using inversions whose costs are assigned based on their lengths and asymmetries. We present five procedures and we assess these procedure performances on small sized permutations. The ideas presented in this paper provide insights to solve the problem and set the stage for a proper theoretical analysis.

A general heuristic for genome rearrangement problems.

In this paper, we present a general heuristic for several problems in the genome rearrangement field. Our heuristic does not solve any problem directly, it is rather used to improve the solutions provided by any non-optimal algorithm that solve them. Therefore, we have implemented several algorithms described in the literature and several algorithms developed by ourselves. As a whole, we implemented 23 algorithms for 9 well known problems in the genome rearrangement field. A total of 13 algorithms were implemented for problems that use the notions of prefix and suffix operations. In addition, we worked on 5 algorithms for the classic problem of sorting by transposition and we conclude the experiments by presenting results for 3 approximation algorithms for the sorting by reversals and transpositions problem and 2 approximation algorithms for the sorting by reversals problem. Another algorithm with better approximation ratio can be found for the last genome rearrangement problem, but it is purely theoretical with no practical implementation. The algorithms we implemented in addition to our heuristic lead to the best practical results in each case. In particular, we were able to improve results on the sorting by transpositions problem, which is a very special case because many efforts have been made to generate algorithms with good results in practice and some of these algorithms provide results that equal the optimum solutions in many cases. Our source codes and benchmarks are freely available upon request from the authors so that it will be easier to compare new approaches against our results.

Heuristics for the Sorting by Length-Weighted Inversions Problem on Signed Permutations

Genome Rearrangement is a field that addresses the problem of finding the minimum number of global operations that transform a given genome into another. In this work, we deal with inversion events, which occur when a segment of DNA sequence in the genome is reversed. In our model, each inversion costs the number of elements in the reversed segment. We present a new heuristic for this problem and we show that our method outperforms a previous approach. Our method uses the metaheuristic called Greedy Randomized Adaptive Search Procedure (GRASP) that has been routinely used to find solutions for combinatorial optimization problems. In essence, we implemented an iterative process in which each iteration receives a feasible solution whose neighborhood is investigated for a better solution. We use as initial solution a sequence of inversions of minimum length when each inversion costs one unit, which is a problem that already has several polynomial time algorithms. In almost every case, we were able to improve that initial solution by providing a less-costly sequence of inversions.

Extending Bafna-Pevzner algorithm

Genome Rearrangement is a field that addresses the problem of finding the minimum number of global operations, such as transpositions, reversals, fusions and fissions that transform a given genome into another. In this work we deal with transposition events, which are events that change the position of two contiguous block of genes in the same chromosome. Some approximation algorithms for this problem were published so far. Bafna and Pevzner [1] proposed the first 1.5-approximation algorithm for the transposition distance problem and recently Elias and Hartman [4] delineated a 1.375-approximation algorithm, which is currently the best performance ratio known. Many other algorithms achieve good performance on experimental results and provide new insights to solve the problem [2, 5, 8, 9, 11]. In this paper we present two main results. The first result is the implementation of the 1.375-algorithm described by Elias and Hartman [4]. We also compared the experimental results from Elias-Hartman algorithm with other approaches. It is important to realize that no implementation of Elias-Hartman algorithm was provided before this work and the approximation proof was assisted by a computer program. Although the approximation ratio is an important issue, we need to know how the algorithm behaves on practical experiments. For this reason, we show the experimental results of Elias-Hartman algorithm using our datasets. The second result is the description of our algorithm based on Bafna and Pevzner [1] 1.5-approximation algorithm. Our algorithm uses a set of heuristics that allowed us to improve the solution quality of the original algorithm, but keeping the original 1.5-approximation ratio. We compare our experimental results with the best results published so far. The results indicate that our algorithm performs best in practice. The solution quality analysis also shows that our algorithm outperforms Elias and Hartman 1.375-approximation algorithm on longer permutations, despite the approximation ratio. We delineate an algorithm for the transposition distance problem. Our algorithm is the first polynomial time algorithm that sorts by transposition any permutation π, for |π| = 9. We show that our algorithm is better than the other algorithms using sequences π, for π < 11. We also show that our algorithm keeps the good performance on longer permutations. We claim that the heuristics proposed in this work contribute for discovering the complexity of sorting by transposition, which remains open.

Sorting by Prefix Reversals and Prefix Transpositions

In this paper, we present a new algorithm for the Sorting by Prefix Reversals and Prefix Transpositions Problem. The previous approximation algorithm was bounded by factor 3, and here we present an asymptotic 2-approximation algorithm. We consider theoretical and practical aspects in our analysis, and we show that our method is better than other approaches in both cases.

Heuristics for the Sorting by Length-Weighted Inversion Problem

In this paper we present a polynomial-time algorithm for the length-weighted inversion problem on unsigned permutations. We consider the linear cost function where each inversion costs the number of elements in the reversed segment. We evaluate our method by comparing its results against a previous known approximation algorithm. The results from two batches of tests using all possible small permutations and a sample of large permutations show that our algorithm has significantly better results.

Sorting genomes using almost-symmetric inversions

Inversions are one of the most frequent large-scale rearrangements observed in actual genomes. While a large body of literature exists on mathematical problems related to the computation of the inversion distance between abstract genomes, these works generally do not take into account that most inversions in bacterial chromosomes are symmetric or roughly symmetric with respect to the origin of replication. We define a new problem: how to sort genomes (or permutations) using almost-symmetric inversions. We show an algorithm that can sort any permutation using only almost-symmetric inversions. Two variants of this algorithm are presented that have better performance in practice. We explore the question of determining the minimum number of almost-symmetric inversions needed to sort a genome by presenting lower and upper bounds and results for special permutation families. The results obtained are the first steps in exploring this interesting new problem.

A simulation tool for the study of symmetric inversions in bacterial genomes

We present the tool SIB that simulates genomic inversions in bacterial chromosomes. The tool simulates symmetric inversions but allows the appearance of nonsymmetric inversions by simulating small syntenic blocks frequently observed on bacterial genome comparisons. We evaluate SIB by comparing its results to real genome alignments. We develop measures that allow quantitative comparisons between real pairwise alignments (in terms of dotplots) and simulated ones. These measures allow an evaluation of SIB in terms of dendrograms. We evaluate SIB by comparing its results to whole chromosome alignments and maximum likelihood trees for three bacterial groups (the Pseudomonadaceae family and the Xanthomonas and Shewanella genera). We demonstrate an application of SIB by using it to evaluate the ancestral genome reconstruction tool MGR.

Sorting by weighted inversions considering length and symmetry

Large-scale mutational events that occur when stretches of DNA sequence move throughout genomes are called genome rearrangements. In bacteria, inversions are one of the most frequently observed rearrangements. In some bacterial families, inversions are biased in favor of symmetry as shown by recent research. In addition, several results suggest that short segment inversions are more frequent in the evolution of microbial genomes. Despite the fact that symmetry and length of the reversed segments seem very important, they have not been considered together in any problem in the genome rearrangement field. Here, we define the problem of sorting genomes (or permutations) using inversions whose costs are assigned based on their lengths and asymmetries. We consider two formulations of the same problem depending on whether we know the orientation of the genes. Several procedures are presented and we assess these procedure performances on a large set of more than 4.4 × 109 permutations. The ideas presented in this paper provide insights to solve the problem and set the stage for a proper theoretical analysis.