Alignments with non-overlapping moves, inversions and tandem duplications in O ( n 4) time

Sequence alignment is a central problem in bioinformatics. The classical dynamic programming algorithm aligns two sequences by optimizing over possible insertions, deletions and substitutions. However, other evolutionary events can be observed, such as inversions, tandem duplications or moves (transpositions). It has been established that the extension of the problem to move operations is NP-complete. Previous work has shown that an extension restricted to non-overlapping inversions can be solved in O(n 3) with a restricted scoring scheme. In this paper, we show that the alignment problem extended to non-overlapping moves can be solved in O(n 5) for general scoring schemes, O(n 4log n) for concave scoring schemes and O(n 4) for restricted scoring schemes. Furthermore, we show that the alignment problem extended to non-overlapping moves, inversions and tandem duplications can be solved with the same time complexities. Finally, an example of an alignment with non-overlapping moves is provide

Homoplastic Microinversions and the Avian Tree of Life

Background Microinversions are cytologically undetectable inversions of DNA sequences that accumulate slowly in genomes. Like many other rare genomic changes (RGCs), microinversions are thought to be virtually homoplasy-free evolutionary characters, suggesting that they may be very useful for difficult phylogenetic problems such as the avian tree of life. However, few detailed surveys of these genomic rearrangements have been conducted, making it difficult to assess this hypothesis or understand the impact of microinversions upon genome evolution. Results We surveyed non-coding sequence data from a recent avian phylogenetic study and found substantially more microinversions than expected based upon prior information about vertebrate inversion rates, although this is likely due to underestimation of these rates in previous studies. Most microinversions were lineage-specific or united well-accepted groups. However, some homoplastic microinversions were evident among the informative characters. Hemiplasy, which reflects differences between gene trees and the species tree, did not explain the observed homoplasy. Two specific loci were microinversion hotspots, with high numbers of inversions that included both the homoplastic as well as some overlapping microinversions. Neither stem-loop structures nor detectable sequence motifs were associated with microinversions in the hotspots. Conclusions Microinversions can provide valuable phylogenetic information, although power analysis indicates that large amounts of sequence data will be necessary to identify enough inversions (and similar RGCs) to resolve short branches in the tree of life. Moreover, microinversions are not perfect characters and should be interpreted with caution, just as with any other character type. Independent of their use for phylogenetic analyses, microinversions are important because they have the potential to complicate alignment of non-coding sequences. Despite their low rate of accumulation, they have clearly contributed to genome evolution, suggesting that active identification of microinversions will prove useful in future phylogenomic studies

Complete plastid genomes from Ophioglossum californicum, Psilotum nudum, and Equisetum hyemale reveal an ancestral land plant genome structure and resolve the position of Equisetales among monilophytes

BACKGROUND: Plastid genome structure and content is remarkably conserved in land plants. This widespread conservation has facilitated taxon-rich phylogenetic analyses that have resolved organismal relationships among many land plant groups. However, the relationships among major fern lineages, especially the placement of Equisetales, remain enigmatic. RESULTS: In order to understand the evolution of plastid genomes and to establish phylogenetic relationships among ferns, we sequenced the plastid genomes from three early diverging species: Equisetum hyemale (Equisetales), Ophioglossum californicum (Ophioglossales), and Psilotum nudum (Psilotales). A comparison of fern plastid genomes showed that some lineages have retained inverted repeat (IR) boundaries originating from the common ancestor of land plants, while other lineages have experienced multiple IR changes including expansions and inversions. Genome content has remained stable throughout ferns, except for a few lineage-specific losses of genes and introns. Notably, the losses of the rps16 gene and the rps12i346 intron are shared among Psilotales, Ophioglossales, and Equisetales, while the gain of a mitochondrial atp1 intron is shared between Marattiales and Polypodiopsida. These genomic structural changes support the placement of Equisetales as sister to Ophioglossales + Psilotales and Marattiales as sister to Polypodiopsida. This result is augmented by some molecular phylogenetic analyses that recover the same relationships, whereas others suggest a relationship between Equisetales and Polypodiopsida. CONCLUSIONS: Although molecular analyses were inconsistent with respect to the position of Marattiales and Equisetales, several genomic structural changes have for the first time provided a clear placement of these lineages within the ferns. These results further demonstrate the power of using rare genomic structural changes in cases where molecular data fail to provide strong phylogenetic resolution

Complete plastid genomes from \u3ci\u3eOphioglossum californicum, Psilotum nudum,\u3c/i\u3e and \u3ci\u3eEquisetum hyemale\u3c/i\u3e reveal an ancestral land plant genome structure and resolve the position of Equisetales among monilophytes

Background: Plastid genome structure and content is remarkably conserved in land plants. This widespread conservation has facilitated taxon-rich phylogenetic analyses that have resolved organismal relationships among many land plant groups. However, the relationships among major fern lineages, especially the placement of Equisetales, remain enigmatic. Results: In order to understand the evolution of plastid genomes and to establish phylogenetic relationships among ferns, we sequenced the plastid genomes from three early diverging species: Equisetum hyemale (Equisetales), Ophioglossum californicum (Ophioglossales), and Psilotum nudum (Psilotales). A comparison of fern plastid genomes showed that some lineages have retained inverted repeat (IR) boundaries originating from the common ancestor of land plants, while other lineages have experienced multiple IR changes including expansions and inversions. Genome content has remained stable throughout ferns, except for a few lineage-specific losses of genes and introns. Notably, the losses of the rps16 gene and the rps12i346 intron are shared among Psilotales, Ophioglossales, and Equisetales, while the gain of a mitochondrial atp1 intron is shared between Marattiales and Polypodiopsida. These genomic structural changes support the placement of Equisetales as sister to Ophioglossales + Psilotales and Marattiales as sister to Polypodiopsida. This result is augmented by some molecular phylogenetic analyses that recover the same relationships, whereas others suggest a relationship between Equisetales and Polypodiopsida. Conclusions: Although molecular analyses were inconsistent with respect to the position of Marattiales and Equisetales, several genomic structural changes have for the first time provided a clear placement of these lineages within the ferns. These results further demonstrate the power of using rare genomic structural changes in cases where molecular data fail to provide strong phylogenetic resolution

Clustering by compression

We present a new method for clustering based on compression. The method doesn't use subject-specific features or background knowledge, and works as follows: First, we determine a universal similarity distance, the normalized compression distance or NCD, computed from the lengths of compressed data files (singly and in pairwise concatenation). Second, we apply a hierarchical clustering method. The NCD is universal in that it is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal but uses the non-computable notion of Kolmogorov complexity. We propose precise notions of similarity metric, normal compressor, and show that the NCD based on a normal compressor is a similarity metric that approximates universality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (binary tree) by a new quartet method and a fast heuristic to implement it. The method is implemented and available as public software, and is robust under choice of different compressors. To substantiate our claims of universality and robustness, we report evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors. In genomics we presented new evidence for major questions in Mammalian evolution, based on whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta hypothesis against the Theria hypothesis.Comment: LaTeX, 27 pages, 20 figure

Algorithms and methods for large-scale genome rearrangements identification

Esta tesis por compendio aborda la definición formal de SB, empezando por Pares de Segmentos de alta puntuación (HSP), los cuales son bien conocidos y aceptados. El primer objetivo se centró en la detección de SB como una combinación de HSPs incluyendo repeticiones lo cual incrementó la complejidad del modelo. Como resultado, se obtuvo un método más preciso y que mejora la calidad de los resultados del estado del arte. Este método aplica reglas basadas en la adyacencia de SBs, permitiendo además detectar LSGR e identificarlos como inversiones, translocaciones o duplicaciones, constituyendo un framework capaz de trabajar con LSGR para organismos de un solo cromosoma. Más tarde en un segundo artículo, se utilizó este framework para refinar los bordes de los SBs. En nuestra novedosa propuesta, las repeticiones que flanquean los SB se utilizaron para refinar los bordes explotando la redundancia introducida por dichas repeticiones. Mediante un alineamiento múltiple de estas repeticiones se calculan los vectores de identidad del SB y de la secuencia consenso de las repeticiones alineadas. Posteriormente, una máquina de estados finitos diseñada para detectar los puntos de transición en la diferencia de ambos vectores determina los puntos de inicio y fin de los SB refinados. Este método también se mostró útil a la hora de detectar "puntos de ruptura" (conocidos como break points (BP)). Estos puntos aparecen como la región entre dos SBs adyacentes. El método no fuerza a que el BP sea una región o un punto, sino que depende de los alineamientos de las repeticiones y del SB en cuestión. El método es aplicado en un tercer trabajo, donde se afronta un caso de uso de análisis de metagenomas. Es bien sabido que la información almacenada en las bases de datos no corresponde necesariamente a las muestras no cultivadas contenidas en un metagenoma, y es posible imaginar que la asignación de una muestra de un metagenoma se vea dificultada por un evento reorganizativo. En el articulo se muestra que las muestras de un metagenoma que mapean sobre las regiones exclusivas de un genoma (aquellas que no comparte con otros genomas) respaldan la presencia de ese genoma en el metagenoma. Estas regiones exclusivas son fácilmente derivadas a partir de una comparación múltiple de genomas, como aquellas regiones que no forman parte de ningún SB. Una definición bajo un espacio de comparación múltiple de genomas es más precisa que las definiciones construidas a partir de una comparación de pares, ya que entre otras cosas, permite un refinamiento siguiendo un procedimiento similar al descrito en el segundo artículo (usando SBs, en vez de repeticiones). Esta definición también resuelve la contradicción existente en la definición de puntos de BPs (mencionado en la segunda publicación), por la cual una misma región de un genoma puede ser detectada como BP o formar parte de un SB dependiendo del genoma con el que se compare. Esta definición de SB en comparación múltiple proporciona además información precisa para la reconstrucción de LSGR, con vistas a obtener una aproximación del verdadero ancestro común entre especies. Además, proporciona una solución para el problema de la granularidad en la detección de SBs: comenzamos por SBs pequeños y bien conservados y a través de la reconstrucción de LSGR se va aumentando gradualmente el tamaño de dichos bloques. Los resultados que se esperan de esta línea de trabajo apuntan a una definición de una métrica destinada a obtener distancias inter genómicas más precisas, combinando similaridad entre secuencias y frecuencias de LSGR.Esta tesis es un compendio de tres artículos recientemente publicados en revistas de alto impacto, en los cuales mostramos el proceso que nos ha llevado a proponer la definición de Unidades Elementales de Conservación (regiones conservadas entre genomas que son detectadas después de una comparación múltiple), así como algunas operaciones básicas como inversiones, transposiciones y duplicaciones. Los tres artículos están transversalmente conectados por la detección de Bloques de Sintenia (SB) y reorganizaciones genómicas de gran escala (LSGR) (consultar sección 2), y respaldan la necesidad de elaborar el framework que se describe en la sección "Systems And Methods". De hecho, el trabajo intelectual llevado a cabo en esta tesis y las conclusiones aportadas por las publicaciones han sido esenciales para entender que una definición de SB apropiada es la clave para muchos de los métodos de comparativa genómica. Los eventos de reorganización del ADN son una de las principales causas de evolución y sus efectos pueden ser observados en nuevas especies, nuevas funciones biológicas etc. Las reorganizaciones a pequeña escala como inserciones, deleciones o substituciones han sido ampliamente estudiadas y existen modelos aceptados para detectarlas. Sin embargo, los métodos para identificar reorganizaciones a gran escala aún sufren de limitaciones y falta de precisión, debido principalmente a que no existe todavía una definición de SB aceptada. El concepto de SB hace referencia a regiones conservadas entre dos genomas que guardan el mismo orden y {strand. A pesar de que existen métodos para detectarlos, éstos evitan tratar con repeticiones o restringen la búsqueda centrándose solamente en las regiones codificantes en aras de un modelo más simple. El refinamiento de los bordes de estos bloques es a día de hoy un problema aún por solucionar

Évolution des génomes par mutations locales et globales : une approche d’alignement

Durant leur évolution, les génomes accumulent des mutations pouvant affecter d’un nucléotide à plusieurs gènes. Les modifications au niveau du nombre et de l’organisation des gènes dans les génomes sont dues à des mutations globales, telles que les duplications, les pertes et les réarrangements. En comparant les ordres de gènes des génomes, il est possible d’inférer les événements évolutifs les plus fréquents, le contenu en gènes des espèces ancestrales ainsi que les histoires évolutives ayant menées aux ordres observés. Dans cette thèse, nous nous intéressons au développement de nouvelles méthodes algorithmiques, par approche d’alignement, afin d’analyser ces différents aspects de l’évolution des génomes. Nous nous intéressons à la comparaison de deux ou d’un ensemble de génomes reliés par une phylogénie, en tenant compte des mutations globales. Pour commencer, nous étudions la complexité théorique de plusieurs variantes du problème de l’alignement de deux ordres de gènes par duplications et pertes, ainsi que de l’approximabilité de ces problèmes. Nous rappelons ensuite les algorithmes exacts, en temps exponentiel, existants, et développons des heuristiques efficaces. Nous proposons, dans un premier temps, DLAlign, une heuristique quadratique pour le problème d’alignement de deux ordres de gènes par duplications et pertes. Ensuite, nous présentons, OrthoAlign, une extension de DLAlign, qui considère, en plus des duplications et pertes, les réarrangements et les substitutions. Nous abordons également le problème de l’alignement phylogénétique de génomes. Pour commencer, l’heuristique OrthoAlign est adaptée afin de permettre l’inférence de génomes ancestraux au noeuds internes d’un arbre phylogénétique. Nous proposons enfin, MultiOrthoAlign, une heuristique plus robuste, basée sur la médiane, pour l’inférence de génomes ancestraux et d’histoires évolutives d’un ensemble de génomes représentés aux feuilles d’un arbre phylogénétique.During the evolution process, genomes accumulate mutations that may affect the genome at different levels, ranging from one base to the overall gene content. Global mutations affecting gene content and organization are mainly duplications, losses and rearrangements. By comparing gene orders, it is possible to infer the most frequent events, the gene content in the ancestral genomes and the evolutionary histories of the observed gene orders. In this thesis, we are interested in developing new algorithmic methods based on an alignment approach for comparing two or a set of genomes represented as gene orders and related through a phylogenetic tree, based on global mutations. We study the theoretical complexity and the approximability of different variants of the two gene orders alignment problem by duplications and losses. Then, we present the existing exact exponential time algorithms, and develop efficient heuristics for these problems. First, we developed DLAlign, a quadratic time heuristic for the two gene orders alignment problem by duplications and losses. Then, we developed OrthoAlign, a generalization of DLAlign, accounting for most genome-wide evolutionary events such as duplications, losses, rearrangements and substitutions. We also study the phylogenetic alignment problem. First, we adapt our heuristic OrthoAlign in order to infer ancestral genomes at the internal nodes of a given phylogenetic tree. Finally, we developed MultiOrthoAlign, a more robust heuristic, based on the median problem, for the inference of ancestral genomes and evolutionary histories of extent genomes labeling leaves of a phylogenetic tree

Accelerating phylogeny-aware alignment with indel evolution using short time Fourier transform

Recently we presented a frequentist dynamic pro- gramming (DP) approach for multiple sequence alignment based on the explicit model of indel evolution Poisson Indel Process (PIP). This phylogeny-aware approach produces evolutionary meaningful gap patterns and is robust to the ‘over-alignment’ bias. Despite linear time complexity for the computation of marginal likelihoods, the overall method’s complexity is cubic in sequence length. Inspired by the popular aligner MAFFT, we propose a new technique to accelerate the evolutionary indel based alignment. Amino acid sequences are converted to sequences representing their physicochemical properties, and homologous blocks are identified by multi-scale short-time Fourier transform. Three three-dimensional DP matrices are then created under PIP, with homologous blocks defining sparse structures where most cells are excluded from the calculations. The homologous blocks are connected through intermediate ‘linking blocks’. The homologous and linking blocks are aligned under PIP as independent DP sub-matrices and their tracebacks merged to yield the final alignment. The new algorithm can largely profit from parallel computing, yielding a theoretical speed-up estimated to be pro- portional to the cubic power of the number of sub-blocks in the DP matrices. We compare the new method to the original PIP approach and demonstrate it on real data