An important problem in genome comparison is the genome sorting problem, that is, the problem of finding a sequence of basic operations that transforms one genome into another whose length (possibly weighted) equals the distance between them. These sequences are called optimal sorting scenarios. However, there is usually a large number of such scenarios, and a naïve algorithm is very likely to be biased towards a specific type of scenario, impairing its usefulness in real-world applications. One way to go beyond the traditional sorting algorithms is to explore all possible solutions, looking at all the optimal sorting scenarios instead of just an arbitrary one. Another related approach is to analyze all the intermediate genomes, that is, all the genomes that can occur in an optimal sorting scenario. In this article, we show how to enumerate the optimal sorting scenarios and the intermediate genomes between any two given genomes, under the rank distance.

MOTIVATION: The rank distance model represents genome rearrangements in multi-chromosomal genomes as matrix operations, which allows the reconstruction of parsimonious histories of evolution by rearrangements. We seek to generalize this model by allowing for genomes with different gene content, to accommodate a broader range of biological contexts. We approach this generalization by using a matrix representation of genomes. This leads to simple distance formulas and sorting algorithms for genomes with different gene contents, but without duplications. RESULTS: We generalize the rank distance to genomes with different gene content in two different ways. The first approach adds insertions, deletions and the substitution of a single extremity to the basic operations. We show how to efficiently compute this distance. To avoid genomes with incomplete markers, our alternative distance, the rank-indel distance, only uses insertions and deletions of entire chromosomes. We construct phylogenetic trees with our distances and the DCJ-Indel distance for simulated data and real prokaryotic genomes, and compare them against reference trees. For simulated data, our distances outperform the DCJ-Indel distance using the Quartet metric as baseline. This suggests that rank distances are more robust for comparing distantly related species. For real prokaryotic genomes, all rearrangement-based distances yield phylogenetic trees that are topologically distant from the reference (65% similarity with Quartet metric), but are able to cluster related species within their respective clades and distinguish the Shigella strains as the farthest relative of the Escherichia coli strains, a feature not seen in the reference tree. AVAILABILITY AND IMPLEMENTATION: Code and instructions are available at https://github.com/meidanis-lab/rank-indel. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We outline an integrated approach to speciation and whole genome doubling (WGD) to resolve the occurrence of these events in phylogenetic analysis. We propose a more principled way of estimating the parameters of gene divergence and fractionation than the standard mixture of normals analysis. We formulate an algorithm for resolving data on local peaks in the distributions of duplicate gene similarities for a number of related genomes. We illustrate with a comprehensive analysis of WGD-origin duplicate gene data from the family Brassicaceae.

BACKGROUND: Recently, Pereira Zanetti, Biller and Meidanis have proposed a new definition of a rearrangement distance between genomes. In this formulation, each genome is represented as a matrix, and the distance d is the rank distance between these matrices. Although defined in terms of matrices, the rank distance is equal to the minimum total weight of a series of weighted operations that leads from one genome to the other, including inversions, translocations, transpositions, and others. The computational complexity of the median-of-three problem according to this distance is currently unknown. The genome matrices are a special kind of permutation matrices, which we study in this paper. In their paper, the authors provide an [Formula: see text] algorithm for determining three candidate medians, prove the tight approximation ratio [Formula: see text], and provide a sufficient condition for their candidates to be true medians. They also conduct some experiments that suggest that their method is accurate on simulated and real data. RESULTS: In this paper, we extend their results and provide the following: Three invariants characterizing the problem of finding the median of 3 matrices A sufficient condition for uniqueness of medians that can be checked in O(n) A faster, [Formula: see text] algorithm for determining the median under this condition A new heuristic algorithm for this problem based on compressed sensing A [Formula: see text] algorithm that exactly solves the problem when the inputs are orthogonal matrices, a class that includes both permutations and genomes as special cases. CONCLUSIONS: Our work provides the first proof that, with respect to the rank distance, the problem of finding the median of 3 genomes, as well as the median of 3 permutations, is exactly solvable in polynomial time, a result which should be contrasted with its NP-hardness for the DCJ (double cut-and-join) distance and most other families of genome rearrangement operations. This result, backed by our experimental tests, indicates that the rank distance is a viable alternative to the DCJ distance widely used in genome comparisons.

Recently, the Single-Cut-or-Join (SCJ) operation was proposed as a basis for a new rearrangement distance between multichromosomal genomes, leading to very fast algorithms, both in theory and in practice. However, it was not clear how well this new distance fares when it comes to using it to solve relevant problems, such as the reconstruction of evolutionary history. In this paper, we advance current knowledge, by testing SCJ's ability regarding evolutionary reconstruction in two aspects: 1) How well does SCJ reconstruct evolutionary topologies? and 2) How well does SCJ reconstruct ancestral genomes? In the process of answering these questions, we implemented SCJ-based methods, and made them available to the community. We ran experiments using as many as 200 genomes, with as many as 3,000 genes. For the first question, we found out that SCJ can recover typically between 60 percent and more than 95 percent of the topology, as measured through the Robinson-Foulds distance (a.k.a. split distance) between trees. In other words, 60 percent to more than 95 percent of the original splits are also present in the reconstructed tree. For the second question, given a topology, SCJ's ability to reconstruct ancestral genomes depends on how far from the leaves the ancestral is. For nodes close to the leaves, about 85 percent of the gene adjacencies can be recovered. This percentage decreases as we move up the tree, but, even at the root, about 50 percent of the adjacencies are recovered, for as many as 64 leaves. Our findings corroborate the fact that SCJ leads to very conservative genome reconstructions, yielding very few false-positive gene adjacencies in the ancestrals, at the expense of a relatively larger amount of false negatives. In addition, experiments with real data from the Campanulaceae and Protostomes groups show that SCJ reconstructs topologies of quality comparable to the accepted trees of the species involved. As far as time is concerned, the methods we implemented can find a topology for 64 genomes with 2,000 genes each in about 10.7 minutes, and reconstruct the ancestral genomes in a 64-leaf tree in about 3 seconds, both on a typical desktop computer. It should be noted that our code is written in Java and we made no significant effort to optimize it.

Algebraic rearrangement theory, as introduced by Meidanis and Dias, focuses on representing the order in which genes appear in chromosomes, and applies to circular chromosomes only. By shifting our attention to genome adjacencies, we introduce the adjacency algebraic theory, extending the original algebraic theory to linear chromosomes in a very natural way, also allowing the original algebraic distance formula to be used to the general multichromosomal case, with both linear and circular chromosomes. The resulting distance, which we call algebraic distance here, is very similar to, but not quite the same as, double-cut-and-join distance. We present linear time algorithms to compute it and to sort genomes. We show how to compute the rearrangement distance from the adjacency graph, for an easier comparison with other rearrangement distances. A thorough discussion on the relationship between the chromosomal and adjacency representation is also given, and we show how all classic rearrangement operations can be modeled using the algebraic theory.

For the last 10 years, SinBiota, the information system of the Biota-FAPESP Program, has served the community storing and displaying data in maps, and providing a common base for researchers in different areas to communicate and exchange biodiversity data. State administration has also used the system to support new laws and regulations. Now it is time to rethink the system, which has grown in an ad-hoc, unstructured way, aiming at the support that will be needed for the next 10 years. In a project jointly funded by Microsoft Research and FAPESP, we aim at the creation of a specification for the new SinBiota 2.0 system, including cutting-edge services and technologies on information technology, in order to achieve a number of goals, namely: guarantee the use and expansion of the system for the next ten years, support the availability of a larger volume of higher quality environmental data, oriented also to the educational and public administration sectors, provide more efficient sharing of data among BIOTA researchers, inter-operate with international initiatives, provide effective tools to assist researchers in finding relevant information amongst a large amount of environment data. The expected results at the end of this project are the composition of a specification (Reference Document) of the SinBiota 2.0 system, and the implementation of a prototype that will gradually replace the current system. We propose in this work the system architecture and our vision of the main features that would allow SinBiota 2.0 to meet the expectations of the biodiversity research community and other stakeholders. We also describe a prototype application that implements most of the features present in the current SinBiota 1.0 system, as well as some of the new features envisaged for the new version.

The breakpoint distance is one of the most straightforward genome comparison measures. Surprisingly, when it comes to defining it precisely for multichromosomal genomes with both linear and circular chromosomes, there is more than one way to go about it. Pevzner and Tesler gave a definition in a 2003 paper, Tannier et al. defined it differently in 2008, and in this paper we provide yet another alternative, calling it SCJ for single-cut-or-join, in analogy to the popular double cut and join (DCJ) measure. We show that several genome rearrangement problems, such as median and halving, become easy for SCJ, and provide linear and higher polynomial time algorithms for them. For the multichromosomal linear genome median problem, this is the first polynomial time algorithm described, since for other distances this problem is NP-hard. In addition, we show that small parsimony under SCJ is also easy, and can be solved by a variant of Fitch's algorithm. In contrast, big parsimony is NP-hard under SCJ. This new distance measure may be of value as a speedily computable, first approximation to distances based on more realistic rearrangement models.

Given two genomes represented as circularly ordered sequences of genes, we show a polynomial time algorithm for the minimum weight series of fusion, jissions, and transpositions (with transpositions weighing twice as much as fusions and$ssions) that transforms one genome into the other. The algorithm is based on classical results ofpermutation group theory and is the jirst polynomial result for a genome rearrangement problem involving transpositions. It has been observed in real biological instances that transpositions occur with about ha&- the frequency of reversals. Although we are not using reversals in this study, this observation motivated the double weight assigned to transpositions.

One of the proposed ways to compare genomes or other large DNA molecules is by computing a rearrangement distance, defined as the minimum number of rearrangement events necessary to transform one molecule into another taking into account only the relative order of similar genes. In this work, we study the problem of computing the transposition distance between two linear gene orders, represented by permutations. To help solve it, we present a very simple structure, the breakpoint diagram, and a 2.25-approximation algorithm for the problem based on this structure. While there are better approximation algorithms, they are based on more complex data structures. Our algorithm was implemented in the C programming language and we show experimental results obtained with it on all permutations of up to 11 genes, plus selected permutations of higher size.

In recent years we are seeing increasing interest in research on mutational events acting on large portions of chromosomes. Among these events, a reversal acts on a fragment of a chromosome, reversing the order and orientation of the genes, and a transposition moves fragments from one region to another within a chromosome. We analyze genomes evolving by reversals and transpositions. We present approximation algorithms to compute the reversal and transposition distance for linear permutations, and a lower bound on the reversal and transposition diameter of signed linear permutations.

DNA fragment assembly is an area which makes intensive use of computers. However, computer users in this field are typically not experts in computer science, but build their working environment on an ad-hoc basis. In this situation, it seems appropriate to offer a kind of support which can contribute to a better organization of working environments, and a better exploitation of computer hardware and software. The authors describe an approach in this direction based on the emerging paradigms of workflow modeling and management. In particular they offer three contributions: first, they discuss why workflow management can be fruitfully adopted in DNA fragment assembly, and describe one way to perceive and model sequencing processes as workflows. Second, they outline an architecture of a system intended to support sequencing applications, whose core component is a workflow management system. Finally, they sketch their experience of building a prototype using commercial workflow management technology.