Multichromosomal median and halving problems under different genomic distances

<p>Abstract</p> <p>Background</p> <p>Genome median and genome halving are combinatorial optimization problems that aim at reconstructing ancestral genomes as well as the evolutionary events leading from the ancestor to extant species. Exploring complexity issues is a first step towards devising efficient algorithms. The complexity of the median problem for unichromosomal genomes (permutations) has been settled for both the breakpoint distance and the reversal distance. Although the multichromosomal case has often been assumed to be a simple generalization of the unichromosomal case, it is also a relaxation so that complexity in this context does not follow from existing results, and is open for all distances.</p> <p>Results</p> <p>We settle here the complexity of several genome median and halving problems, including a surprising polynomial result for the breakpoint median and guided halving problems in genomes with circular and linear chromosomes, showing that the multichromosomal problem is actually easier than the unichromosomal problem. Still other variants of these problems are NP-complete, including the DCJ double distance problem, previously mentioned as an open question. We list the remaining open problems.</p> <p>Conclusion</p> <p>This theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes.</p

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

Sampling and counting genome rearrangement scenarios

Even for moderate size inputs, there are a tremendous number of optimal rearrangement scenarios, regardless what the model is and which specific question is to be answered. Therefore giving one optimal solution might be misleading and cannot be used for statistical inferring. Statistically well funded methods are necessary to sample uniformly from the solution space and then a small number of samples are sufficient for statistical inferring

Étude de l’évolution des génomes par duplications, pertes et réarrangements

La duplication est un des évènements évolutifs les plus importants, car elle peut mener à la création de nouvelles fonctions géniques. Durant leur évolution, les génomes sont aussi affectés par des inversions, des translocations (incluant des fusions et fissions de chromosomes), des transpositions et des délétions. L'étude de l'évolution des génomes est importante, notamment pour mieux comprendre les mécanismes biologiques impliqués, les types d'évènements qui sont les plus fréquents et quels étaient les contenus en gènes des espèces ancestrales. Afin d'analyser ces différents aspects de l'évolution des génomes, des algorithmes efficaces doivent être créés pour inférer des génomes ancestraux, des histoires évolutives, des relations d'homologies et pour calculer les distances entre les génomes. Dans cette thèse, quatre projets reliés à l'étude et à l'analyse de l'évolution des génomes sont présentés : 1) Nous proposons deux algorithmes pour résoudre des problèmes reliés à la duplication de génome entier : un qui généralise le problème du genome halving aux pertes de gènes et un qui permet de calculer la double distance avec pertes. 2) Nous présentons une nouvelle méthode pour l'inférence d'histoires évolutives de groupes de gènes orthologues répétés en tandem. 3) Nous proposons une nouvelle approche basée sur la théorie des graphes pour inférer des gènes in-paralogues qui considère simultanément l'information provenant de différentes espèces afin de faire de meilleures prédictions. 4) Nous présentons une étude de l'histoire évolutive des gènes d'ARN de transfert chez 50 souches de Bacillus.Gene duplication is one of the most important types of events affecting genomes during their evolution because it can create novel gene function. During the evolution process, genomes are also affected by inversions, translocations (including chromosome fusions and fissions), transpositions and deletions. Studying the evolution of genomes is important to get a better understanding of the biological mechanisms involved, which types of events are more frequent than others and what was the gene content in the ancestral species just to name a few. In order to analyze these different aspects of genome evolution, efficient algorithms need to be developed to infer ancestral genomes, evolutionary histories, homology relationships between genes and to compute distances between genomes. In this thesis, four different projects related to the study and analysis of genome evolution are presented: 1) We developed two algorithms to solve problems related to whole genome duplication: one that generalizes the genome halving problem to gene losses, and one that allows to compute the double distance with losses. 2) We developed a new method to infer evolutionary histories of orthologous tandemly arrayed gene clusters. 3) We proposed a new graph-theoretic approach to infer inparalogs that simultaneously considers the information given by multiple species in order to make better inferences of inparalogous gene pairs. 4) We studied the evolutionary history of the tRNA genes of 50 Bacillus strains

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

A mathematical model for germinal centre kinetics and affinity maturation

We present a mathematical model which reproduces experimental data on the germinal centre (GC) kinetics of the primed primary immune response and on affinity maturation observed during the reaction. We show that antigen masking by antibodies which are produced by emerging plasma cells can drive affinity maturation and provide a feedback mechanism by which the reaction is stable against variations in the initial antigen amount over several orders of magnitude. This provides a possible answer to the long-standing question of the role of antigen reduction in driving affinity maturation. By comparing model predictions with experimental results, we propose that the selection probability of centrocytes and the recycling probability of selected centrocytes are not constant but vary during the GC reaction with respect to time. It is shown that the efficiency of affinity maturation is highest if clones with an affinity for the antigen well above the average affinity in the GC leave the GC for either the memory or plasma cell pool. It is further shown that termination of somatic hypermutation several days before the end of the germinal centre reaction is beneficial for affinity maturation. The impact on affinity maturation of simultaneous initiation of memory cell formation and somatic hypermutation vs. delayed initiation of memory cell formation is discussed

The Semiotics of Global Warming: Combating Semiotic Corrruption

The central focus of this paper is the disjunction between the findings of climate science in revealing the threat of global warming and the failure to act appropriately to these warnings. The development of climate science can be illuminated through the perspective provided by Peircian semiotics, but efforts to account for its success as a science and its failure to convince people to act accordingly indicate the need to supplement Peirce’s ideas. The more significant gaps, it is argued, call for the integration of major new ideas. It will be argued that Peirce should be viewed as a Schellingian philosopher, and it will then be shown how this facilitates integration into his philosophy of concepts developed by other philosophers and theorists within this tradition. In particular, Bourdieu’s concepts of the ‘habitus’ and ‘field’ will be integrated with Peirce’s semiotics and used to analyse the achievements and failures of climate science. It will be suggested that the resulting synthesis can augment Peirce’s evolutionary cosmology and so provide a better basis for comprehending and responding to the situation within which we find ourselves

Necessary Conditions for Open-Ended Evolution

Evolution on Earth is widely considered to be an effectively endless process. Though this phenomenon of open-ended evolution (OEE) has been a topic of interest in the artificial life community since its beginnings, the field still lacks an empirically validated theory of what exactly is necessary to reproduce the phenomenon in general (including in domains quite unlike Earth). This dissertation (1) enumerates a set of conditions hypothesized to be necessary for OEE in addition to (2) introducing an artificial life world called Chromaria that incorporates each of the hypothesized necessary conditions. It then (3) describes a set of experiments with Chromaria designed to empirically validate the hypothesized necessary conditions. Thus, this dissertation describes the first scientific endeavor to systematically test an OEE framework in an alife world and thereby make progress towards solving an open question not just for evolutionary computation and artificial life, but for science in general

Development of efficient De Bruijn graph-based algorithms for genome assembly

Programa Oficial de Doutoramento en Computación. 5009V01[Abstract] During the last two decades, thanks to the development of new sequencing techniques, the study of the genome has become very popular in order to discover the genetic variation present in both humans and other organisms. The predominant mode of genome analysis is through the assembly of reads in one or multiple chains for as long as possible. The most traditional way of assembly is the one that involves reads from a single genome. In this field, in the last decade, third-generation readings have emerged with new challenges for which there are no efficient solutions. The first contribution that has been made in this thesis is Compact-Flye, a tool for the efficient assembly of third-generation reads on the Flye algorithm. This tool is based on the ingenious use of compact data structures to improve typical assembly steps such as counting and indexing k-mers. Apart from the assembly of a genome, there are techniques that seek to assemble all the genomes contained in a given sample. This assembly is known as multiple sequence assembly or haplotype reconstruction, a subject also treated in this thesis. Our first approach to solving this has been viaDBG, which is the first solution based on de Bruijn graphs that offers results comparable to current techniques in viral genome assembly while maintaining the efficiency of these graphs. Our second contribution is ViQUF, which is a natural improvement on its predecessor. ViQUF completely changes the algorithm of viaDBG but continues to be based on the same structures, although with some variations that allow it not only to improve results in terms of time and quality, but also to provide additionalinformation such as an estimate of the relative presence of each species in the sample.[Resumen] Durante las últimas dos décadas, gracias al desarrollo de nuevas técnias secuenciación, el estudio del genoma ha ganado mucha popularidad de cara a conocer la variación genética presente tanto seres humanos como otros organismos. El modo predominante de análisis del genoma es a través del ensamblaje de lecturas en una o múltiples cadenas lo más largas posibles. La manera más tradicional de ensamblaje es el que implica lecturas provenientes de un solo genoma. En este campo, en la última década han surgido las lecturas de tercera generación con nuevos retos para los que no existen soluciones eficientes. La primera aportación que se ha realizado en esta tesis es Compact-Flye una herramienta para el ensamblaje eficiente de lecturas de tercera generación sobre el algoritmo Flye. Esta herramienta está basada en el uso igenioso de estructuras compactas de datos para mejorar etapas típicas del ensamblaje como el conteo e indexación de k-mers. Al margen del ensamblaje de un genoma existen técnicas que buscan ensamblar todos los genomas contenidos en una muestra determinada. Este ensamblaje es conocido como ensamblaje múltiple de secuencias o reconstrucción de haplotipos, tema también tratado en esta tesis. Nuestra primera aproximación para la resolución de este ha sido viaDBG, que es la primera solución basada en grafos de de Bruijn que ofrece resultados comparables a las técnicas vigentes en ensamblaje de genomas víricos, mientras que mantiene la eficiencia de estos grafos. Nuestra segunda aportación es ViQUF, que es una mejora natural de su predecesor. ViQUF cambia totalmente la algoritmia de viaDBG, pero sigue cimentándose en las mismas estructuras aunque con alguna variación que le permite no solo mejorar resultados en tiempo y calidad. Sino que además le permite aportar más información como estimaciones relativa de cada especie en la muestra.[Resumo] Durante as dúas últimas décadas, grazas ao desenvolvemento de novas técnicas de secuenciación, o estudo do xenoma fíxose moi popular para descubrir a variación xenética presente tanto nos humanos como noutros organismos. O modo predominante de análise do xenoma é a través da ensamblaxe de lecturas nunha ou varias cadeas o maior tempo posible. A forma máis tradicional de ensamblar é a que implica lecturas dun só xenoma. Neste campo, na última década xurdiron lecturas de terceira xeración con novos retos para os que non existen solucións eficientes. A primeira contribución que se fixo nesta tese é Compact-Flye, unha ferramenta para a montaxe eficiente de lecturas de terceira xeración sobre o algoritmo Flye. Esta ferramenta baséase no uso intelixente de estruturas de datos compactas para mellorar os pasos típicos de montaxe, como contar e indexar k-mers. Ademais da montaxe dun xenoma, existen técnicas que buscan ensamblar todos os xenomas contidos nunha determinada mostra. Este conxunto coñécese como conxunto de secuencias múltiples ou reconstrución de haplotipos, tema tamén tratado nesta tesis. O noso primeiro enfoque para resolver isto foi viaDBG, que é a primeira solución baseada en gráficos de Bruijn que ofrece resultados comparables ás técnicas actuais de ensamblaxe de xenoma viral, mantendo a eficiencia destes gráficos. A nosa segunda incorporación é ViQUF, que é unha mellora natural con respecto ao seu predecesor. ViQUF cambia completamente o algoritmo de viaDBG pero segue baseándose nas mesmas estruturas, aínda que con algunha variación que lle permite non só mellorar os resultados en tempo e calidade. Pero tamén permite achegar máis información como estimacións relativas de cada especie da mostra.Xunta de Galicia; ED431G 2019/01Xunta de Galicia; ED431C 2021/53Xunta de Galicia; IG240.2020.1.185Xunta de Galicia; IN852A 2018/14Quiero agradecer al Centro de Investigación de Galicia “CITIC”, financiado por la Xunta de Galicia y la Unión Europea (European Regional Development Fund- Galicia 2014-2020 Program), con la beca ED431G 2019/01. También agradecer a la Xunta de Galicia/FEDER-UE que ha financiado esta tesis a través de las becas [ED431C 2021/53; IG240.2020.1.185; IN852A 2018/14]; al Ministerio de Ciencia e Innovación con las becas [TIN2016- 78011-C4-1-R; FPU17/02742; PID2019-105221RB-C41; PID2020-114635RB-I00]; y a la academia de Finlandia [grants 308030 and 323233 (LS)]