Sobre modelos de rearranjo de genomas

Orientador: João MeidanisTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Rearranjo de genomas é o nome dado a eventos onde grandes blocos de DNA trocam de posição durante o processo evolutivo. Com a crescente disponibilidade de sequências completas de DNA, a análise desse tipo de eventos pode ser uma importante ferramenta para o entendimento da genômica evolutiva. Vários modelos matemáticos de rearranjo de genomas foram propostos ao longo dos últimos vinte anos. Nesta tese, desenvolvemos dois novos modelos. O primeiro foi proposto como uma definição alternativa ao conceito de distância de breakpoint. Essa distância é uma das mais simples medidas de rearranjo, mas ainda não há um consenso quanto à sua definição para o caso de genomas multi-cromossomais. Pevzner e Tesler deram uma definição em 2003 e Tannier et al. a definiram de forma diferente em 2008. Nesta tese, nós desenvolvemos uma outra alternativa, chamada de single-cut-or-join (SCJ). Nós mostramos que, no modelo SCJ, além da distância, vários problemas clássicos de rearranjo, como a mediana de rearranjo, genome halving e pequena parcimônia são fáceis, e apresentamos algoritmos polinomiais para eles. O segundo modelo que apresentamos é o formalismo algébrico por adjacências, uma extensão do formalismo algébrico proposto por Meidanis e Dias, que permite a modelagem de cromossomos lineares. Esta era a principal limitação do formalismo original, que só tratava de cromossomos circulares. Apresentamos algoritmos polinomiais para o cálculo da distância algébrica e também para encontrar cenários de rearranjo entre dois genomas. Também mostramos como calcular a distância algébrica através do grafo de adjacências, para facilitar a comparação com outras distâncias de rearranjo. Por fim, mostramos como modelar todas as operações clássicas de rearranjo de genomas utilizando o formalismo algébricoAbstract: Genome rearrangements are events where large blocks of DNA exchange places during evolution. With the growing availability of whole genome data, the analysis of these events can be a very important and promising tool for understanding evolutionary genomics. Several mathematical models of genome rearrangement have been proposed in the last 20 years. In this thesis, we propose two new rearrangement models. The first was introduced as an alternative definition of the breakpoint distance. The breakpoint distance is one of the most straightforward genome comparison measures, but when it comes to defining it precisely for multichromosomal genomes, there is more than one way to go about it. Pevzner and Tesler gave a definition in a 2003 paper, and Tannier et al. defined it differently in 2008. In this thesis we provide yet another alternative, calling it single-cut-or-join (SCJ). We show that several genome rearrangement problems, such as genome median, genome halving and small parsimony, become easy for SCJ, and provide polynomial time algorithms for them. The second model we introduce is the Adjacency Algebraic Theory, an extension of the Algebraic Formalism proposed by Meidanis and Dias that allows the modeling of linear chromosomes, the main limitation of the original formalism, which could deal with circular chromosomes only. We believe that the algebraic formalism is an interesting alternative for solving rearrangement problems, with a different perspective that could complement the more commonly used combinatorial graph-theoretic approach. We present polynomial time algorithms to compute the algebraic distance and find rearrangement scenarios between two genomes. We show how to compute the rearrangement distance from the adjacency graph, for an easier comparison with other rearrangement distances. Finally, we show how all classic rearrangement operations can be modeled using the algebraic theoryDoutoradoCiência da ComputaçãoDoutor em Ciência da Computaçã

Genome Halving by Block Interchange

We address the problem of finding the minimal number of block interchanges (exchange of two intervals) required to transform a duplicated linear genome into a tandem duplicated linear genome. We provide a formula for the distance as well as a polynomial time algorithm for the sorting problem

Comparative genomics: multiple genome rearrangement and efficient algorithm development

Multiple genome rearrangement by signed reversal is discussed: For a collection of genomes represented by signed permutations, reconstruct their evolutionary history by using signed reversals, i.e. find a bifurcating tree where sampled genomes are assigned to leaf nodes and ancestral genomes (i.e. signed permutations) are hypothesized at internal nodes such that the total reversal distance summed over all edges of the tree is minimized. It is equivalent to finding an optimal Steiner tree that connects the given genomes by signed reversal paths. The key for the problem is to reconstruct all optimal Steiner nodes/ancestral genomes.;The problem is NP-hard and can only be solved by efficient approximation algorithms. Various algorithms/programs have been designed to solve the problem, such as BPAnalysis, GRAPPA, grid search algorithm, MGR greedy split algorithm (Chapter 1). However, they may have expensive computational costs or low inference accuracy. In this thesis, several new algorithms are developed, including nearest path search algorithm (Chapter 2), neighbor-perturbing algorithm (Chapter 3), branch-and-bound algorithm (Chapter 3), perturbing-improving algorithm (Chapter 4), partitioning algorithm (Chapter 5), etc. With theoretical proofs, computer simulations, and biological applications, these algorithms are shown to be 2-approximation algorithms and more efficient than the existing algorithms

Maximum likelihood estimates of pairwise rearrangement distances

Accurate estimation of evolutionary distances between taxa is important for many phylogenetic reconstruction methods. In the case of bacteria, distances can be estimated using a range of different evolutionary models, from single nucleotide polymorphisms to large-scale genome rearrangements. In the case of sequence evolution models (such as the Jukes-Cantor model and associated metric) have been used to correct pairwise distances. Similar correction methods for genome rearrangement processes are required to improve inference. Current attempts at correction fall into 3 categories: Empirical computational studies, Bayesian/MCMC approaches, and combinatorial approaches. Here we introduce a maximum likelihood estimator for the inversion distance between a pair of genomes, using the group-theoretic approach to modelling inversions introduced recently. This MLE functions as a corrected distance: in particular, we show that because of the way sequences of inversions interact with each other, it is quite possible for minimal distance and MLE distance to differently order the distances of two genomes from a third. This has obvious implications for the use of minimal distance in phylogeny reconstruction. The work also tackles the above problem allowing free rotation of the genome. Generally a frame of reference is locked, and all computation made accordingly. This work incorporates the action of the dihedral group so that distance estimates are free from any a priori frame of reference.Comment: 21 pages, 7 figures. To appear in the Journal of Theoretical Biolog

Phylogenetic reconstruction from transpositions

Background Because of the advent of high-throughput sequencing and the consequent reduction in the cost of sequencing, many organisms have been completely sequenced and most of their genes identified. It thus has become possible to represent whole genomes as ordered lists of gene identifiers and to study the rearrangement of these entities through computational means. As a result, genome rearrangement data has attracted increasing attentions from both biologists and computer scientists as a new type of data for phylogenetic analysis. The main events of genome rearrangements include inversions, transpositions and transversions. To date, GRAPPA and MGR are the most accurate methods for rearrangement phylogeny, both assuming inversion as the only event. However, due to the complexity of computing transposition distance, it is very difficult to analyze datasets when transpositions are dominant. Results We extend GRAPPA to handle transpositions. The new method is named GRAPPA-TP, with two major extensions: a heuristic method to estimate transposition distance, and a new transposition median solver for three genomes. Although GRAPPA-TP uses a greedy approach to compute the transposition distance, it is very accurate when genomes are relatively close. The new GRAPPA-TP is available from http://phylo.cse.sc.edu/ Conclusion Our extensive testing using simulated datasets shows that GRAPPA-TP is very accurate in terms of ancestor genome inference and phylogenetic reconstruction. Simulation results also suggest that model match is critical in genome rearrangement analysis: it is not accurate to simulate transpositions with other events including inversions