Computational Molecular Biology

Computational Biology is a fairly new subject that arose in response to the computational problems posed by the analysis and the processing of biomolecular sequence and structure data. The field was initiated in the late 60's and early 70's largely by pioneers working in the life sciences. Physicists and mathematicians entered the field in the 70's and 80's, while Computer Science became involved with the new biological problems in the late 1980's. Computational problems have gained further importance in molecular biology through the various genome projects which produce enormous amounts of data. For this bibliography we focus on those areas of computational molecular biology that involve discrete algorithms or discrete optimization. We thus neglect several other areas of computational molecular biology, like most of the literature on the protein folding problem, as well as databases for molecular and genetic data, and genetic mapping algorithms. Due to the availability of review papers and a bibliography this bibliography

Models and Algorithms for Sorting Permutations with Tandem Duplication and Random Loss

A central topic of evolutionary biology is the inference of phylogeny, i. e., the evolutionary history of species. A powerful tool for the inference of such phylogenetic relationships is the arrangement of the genes in mitochondrial genomes. The rationale is that these gene arrangements are subject to different types of mutations in the course of evolution. Hence, a high similarity in the gene arrangement between two species indicates a close evolutionary relation. Metazoan mitochondrial gene arrangements are particularly well suited for such phylogenetic studies as they are available for a wide range of species, their gene content is almost invariant, and usually free of duplicates. With these properties gene arrangements of mitochondrial genomes are modeled by permutations in which each element represents a gene, i. e., a specific genetic sequence. The mutations that shape the gene arrangement of genomes are then represented by operations that rearrange elements in permutations, so-called genome rearrangements, and thereby bridge the gap between evolutionary biology and optimization. Many problems of phylogeny inference can be formulated as challenging combinatorial optimization problems which makes this research area especially interesting for computer scientists. The most prominent examples of such optimization problems are the sorting problem and the distance problem. While the sorting problem requires a minimum length sequence of rearrangements that transforms one given permutation into another given permutation, i. e., it aims for a hypothetical scenario of gene order evolution, the distance problem intends to determine only the length of such a sequence. This minimum length is called distance and used as a (dis)similarity measure quantifying the evolutionary relatedness. Most evolutionary changes occurring in gene arrangements of mitochondrial genomes can be explained by the tandem duplication random loss (TDRL) genome rearrangement model. A TDRL consists of a duplication of a consecutive set of genes in tandem followed by a random loss of one copy of each duplicated gene. In spite of the importance of the TDRL genome rearrangement in mitochondrial evolution, its combinatorial properties have rarely been studied. In addition, models of genome rearrangements which include all types of rearrangement that are relevant for mitochondrial genomes, i. e., inversions, transpositions, inverse transpositions, and TDRLs, while admitting computational tractability are rare. Nevertheless, especially for metazoan gene arrangements the TDRL rearrangement should be considered for the reconstruction of phylogeny. Realizing that a better understanding of the TDRL model is indispensable for the study of mitochondrial gene arrangements, the central theme of this thesis is to broaden the horizon of TDRL genome rearrangements with respect to mitochondrial genome evolution. For this purpose, this thesis provides combinatorial properties of the TDRL model and its variants as well as efficient methods for a plausible reconstruction of rearrangement scenarios between gene arrangements. The methods that are proposed consider all types of genome rearrangements that predominately occur during mitochondrial evolution. More precisely, the main points contained in this thesis are as follows: The distance problem and the sorting problem for the TDRL model are further examined in respect to circular permutations, a formal concept that reflects the circular structure of mitochondrial genomes. As a result, a closed formula for the distance is provided. Recently, evidence for a variant of the TDRL rearrangement model in which the duplicated set of genes is additionally inverted have been found. Initiating the algorithmic study of this new rearrangement model on a certain type of permutations, a closed formula solving the distance problem is proposed as well as a quasilinear time algorithm that solves the corresponding sorting problem. The assumption that only one type of genome rearrangement has occurred during the evolution of certain gene arrangements is most likely unrealistic, e. g., at least three types of rearrangements on top of the TDRL rearrangement have to be considered for the evolution metazoan mitochondrial genomes. Therefore, three different biologically motivated constraints are taken into account in this thesis in order to produce plausible evolutionary rearrangement scenarios. The first constraint is extending the considered set of genome rearrangements to the model that covers all four common types of mitochondrial genome rearrangements. For this 4-type model a sharp lower bound and several close additive upper bounds on the distance are developed. As a byproduct, a polynomial-time approximation algorithm for the corresponding sorting problem is provided that guarantees the computation of pairwise rearrangement scenarios that deviate from a minimum length scenario by at most two rearrangement operations. The second biologically motivated constraint is the relative frequency of the different types of rearrangements occurring during the evolution. The frequency is modeled by employing a weighting scheme on the 4-type model in which every rearrangement is weighted with respect to its type. The resulting NP-hard sorting problem is then solved by means of a polynomial size integer linear program. The third biologically motivated constraint that has been taken into account is that certain subsets of genes are often found in close proximity in the gene arrangements of many different species. This observation is reflected by demanding rearrangement scenarios to preserve certain groups of genes which are modeled by common intervals of permutations. In order to solve the sorting problem that considers all three types of biologically motivated constraints, the exact dynamic programming algorithm CREx2 is proposed. CREx2 has a linear runtime for a large class of problem instances. Otherwise, two versions of the CREx2 are provided: The first version provides exact solutions but has an exponential runtime in the worst case and the second version provides approximated solutions efficiently. CREx2 is evaluated by an empirical study for simulated artificial and real biological mitochondrial gene arrangements

Streaming Breakpoint Graph Analytics for Accelerating and Parallelizing the Computation of DCJ Median of Three Genomes

AbstractThe problem of finding the median of three genomes is the key process in building the most parsimonious phylogenetic trees from genome rearrangement data. The median problem using Double-Cut-and-Join (DCJ) distance is NP-hard and the best exact algorithm is based on a branch-and-bound best-first search strategy to explore sub-graph patterns in Multiple BreakPoint Graph (MBG). In this paper, by taking advantage of the “streaming” property of MBG, we introduce the “footprint-based” data structure to reduce the space requirement of a single search nodes from O(v2) to O(v); minimize the redundant computation in counting cycles/paths to update bounds, which leads to dramatically decrease of workload of a single search node. Additional heuristic of branching strategy is introduced to help reducing the searching space. Last but not least, the introduction of a multi-thread shared memory parallel algorithm with two load balancing strategies bring in additional benefit by distributing search work efficiently among different processors. We conduct extensive experiments on simulated datasets and our results show significant improvement on all datasets. And we test our DCJ median algorithm with GASTS, a state of the art software phylogenetic tree construction package. On the real high resolution Drosophila data set, our exact algorithm run as fast as the heuristic algorithm and help construct a better phylogenetic tree

On pairwise distances and median score of three genomes under DCJ

In comparative genomics, the rearrangement distance between two genomes (equal the minimal number of genome rearrangements required to transform them into a single genome) is often used for measuring their evolutionary remoteness. Generalization of this measure to three genomes is known as the median score (while a resulting genome is called median genome). In contrast to the rearrangement distance between two genomes which can be computed in linear time, computing the median score for three genomes is NP-hard. This inspires a quest for simpler and faster approximations for the median score, the most natural of which appears to be the halved sum of pairwise distances which in fact represents a lower bound for the median score. In this work, we study relationship and interplay of pairwise distances between three genomes and their median score under the model of Double-Cut-and-Join (DCJ) rearrangements. Most remarkably we show that while a rearrangement may change the sum of pairwise distances by at most 2 (and thus change the lower bound by at most 1), even the most "powerful" rearrangements in this respect that increase the lower bound by 1 (by moving one genome farther away from each of the other two genomes), which we call strong, do not necessarily affect the median score. This observation implies that the two measures are not as well-correlated as one's intuition may suggest. We further prove that the median score attains the lower bound exactly on the triples of genomes that can be obtained from a single genome with strong rearrangements. While the sum of pairwise distances with the factor 2/3 represents an upper bound for the median score, its tightness remains unclear. Nonetheless, we show that the difference of the median score and its lower bound is not bounded by a constant.Comment: Proceedings of the 10-th Annual RECOMB Satellite Workshop on Comparative Genomics (RECOMB-CG), 2012. (to appear

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

Phylogeny and Ancestral Genome Reconstruction from Gene Order Using Maximum Likelihood and Binary Encoding

Over the long history of genome evolution, genes get rearranged under events such as rearrangements, losses, insertions and duplications, which in all change the ordering and content along the genome. Recent progress in genome-scale sequencing renews the challenges in the reconstructions of phylogeny and ancestral genomes with gene-order data. Such problems have been proved so interesting that a large number of algorithms have been developed rigorously over the past few years in attempts to tackle these problems following various principles. However, difficulties and limitations in performance and scalability largely prevent us from analyzing emerging modern whole-genome data, our study presented in this dissertation focuses on developing appropriate evolutionary models and robust algorithms for solving the phylogenetic and ancestral inference problems using gene-order data under the whole-genome evolution, along with their applications. To reconstruct phylogenies from gene-order data, we developed a collection of closely-related methods following the principle of likelihood maximization. To the best of our knowledge, it was the first successful attempt to apply maximum likelihood optimization technique into the analysis of gene-order phylogenetic problem. Later we proposed MLWD (in collaboration with Lin and Moret) in which we described an effective transition model to account for the transitions between presence and absence states of an gene adjacency. Besides genome rearrangements, other evolutionary events modify gene contents such as gene duplications and gene insertion/deletion (indels) can be naturally processed as well. We present our results from extensive testing on simulated data showing that our approach returns very accurate results very quickly. With a known phylogeny, a subsequent problem is to reconstruct the gene-order of ancestral genomes from their living descendants. To solve this problem, we adopted an adjacency-based probabilistic framework, and developed a method called PMAG. PMAG decomposes gene orderings into a set of gene adjacencies and then infers the probability of observing each adjacency in the ancestral genome. We conducted extensive simulation experiments and compared PMAG with InferCarsPro, GASTS, GapAdj and SCJ. According to the results, PMAG demonstrated great performance in terms of the true positive rate of gene adjacency. PMAG also achieved comparable running time to the other methods, even when the traveling sales man problem (TSP) were exactly solved. Although PMAG can give good performance, it is strongly restricted from analyzing datasets underwent only rearrangements. To infer ancestral genomes under a more general model of evolution with an arbitrary rate of indels , we proposed an enhanced method PMAG+ based on PMAG. PMAG+ includes a novel approach to infer ancestral gene contents and a detail description to reduce the adjacency assembly problem to an instance of TSP. We designed a series of experiments to validate PMAG+ and compared the results with the most recent and comparable method GapAdj. According to the results, ancestral gene contents predicted by PMAG+ coincided highly with the actual contents with error rates less than 1%. Under various degrees of indels, PMAG+ consistently achieved more accurate prediction of ancestral gene orders and at the same time, produced contigs very close to the actual chromosomes