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A DNA palindrome is a sequence of DNA followed by an exact inverted copy of itself. Palindromes are associated with gross chromosomal instability in mammalian cells. This may be related to their ability to extrude a double-stranded cruciform structure. In mammalian cells, palindromes have been shown to undergo centre-directed rearrangements resulting in a central region of asymmetry. This process occurs via a mechanism termed â centre break palindrome revisionâ . In this thesis, I have investigated palindrome revision in mammalian cells using two existing assays. In the first, performed by transfection of an extrachromosomal palindromic dimer, I have shown that joining of palindrome-mediated double-strand breaks does not depend solely on NHEJ and instead relies heavily on an alternate end-joining pathway. Using the second assay, the Line78 mouse model which contains a 15.4kb transgenic palindrome, I have shown that small modifications near the centre of the palindrome prevent these centre-directed rearrangements possibly by inhibiting cruciform formation.

A DNA palindrome is a sequence of DNA followed by an exact inverted copy of itself. Palindromes are associated with gross chromosomal instability in mammalian cells. This may be related to their ability to extrude a double-stranded cruciform structure. In mammalian cells, palindromes have been shown to undergo centre-directed rearrangements resulting in a central region of asymmetry. This process occurs via a mechanism termed â centre break palindrome revisionâ . In this thesis, I have investigated palindrome revision in mammalian cells using two existing assays. In the first, performed by transfection of an extrachromosomal palindromic dimer, I have shown that joining of palindrome-mediated double-strand breaks does not depend solely on NHEJ and instead relies heavily on an alternate end-joining pathway. Using the second assay, the Line78 mouse model which contains a 15.4kb transgenic palindrome, I have shown that small modifications near the centre of the palindrome prevent these centre-directed rearrangements possibly by inhibiting cruciform formation.

Lorsqu'on s'intéresse à l'étude de la structure combinatoire d'un mot infini w, une stratégie classique consiste à calculer sa fonction de complexité, c'est-à-dire à décrire le nombre de mots de longueur n qui apparaissent dans w, pour chaque entier n ≥ 0. Récemment, des chercheurs se sont intéressés à un raffinement de cette notion en introduisant la fonction de complexité palindromique: pour chaque entier n ≥ 0, nous calculons le nombre de palindromes de longueur n apparaissant dans w. Rappelons qu'un palindrome est un mot qui se lit de la même façon de gauche à droite que de droite à gauche (par exemple, "radar" et "ressasser" sont des palindromes de la langue française). La connaissance des palindromes apparaissant dans un mot permet de déduire de nombreuses informations précieuses sur sa structure. Par exemple, un mot admettant une infinité de palindromes préfixes est nécessairement récurrent (tout facteur apparaît une infinité de fois) et son langage est fermé sous l'opération miroir. D'autre part, nous étudions également les occurrences de facteurs antipalindromiques (une généralisation de la notion de palindrome), qui semblent naturellement en interaction avec les palindromes usuels. En particulier, nous décrivons les complexités palindromique et antipalindromique de quelques familles importantes de mots: les mots périodiques, les mots sturmiens, le mot de Thue-Morse et les suites de Rote. Dans un deuxième temps, nous étudions le défaut palindromique des mots finis et infinis. Il s'agit d'une mesure de "richesse" ou de "pauvreté" en palindromes des mots. Nous montrons en particulier que certains mots associés aux suites de Rote, à l'instar des mots sturmiens (Droubay, Justin et Pirillo, 2001), sont aussi pleins, c'est-à-dire qu'ils réalisent la complexité palindromique maximale, et nous établissons aussi des conditions sous lesquelles les mots périodiques sont pleins. Une section supplémentaire est consacrée à l'étude des lacunes du mot de Thue-Morse, qui admet une infinité de palindromes, mais dont le défaut est infini (c'est-à-dire qu'il possède une infinité de lacunes palindromiques). En dernier lieu, nous mentionnons quelques problèmes ouverts dans ce passionnant champ de recherche. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Combinatoire, Mots, Palindromes, Antipalindromes, Complexité, Défaut.

This work is an exploration into the palindrome, both as a literary form and an expression of infinity. The first two chapters address the fascinating manner in which the mind contextualizes fragments of speech and ludicrous grammatical implications that are spawned by the poetic structure of the palindrome (third chapter). The thesis then departs from the literary aspect of the palindrome and focuses in the fourth chapter on structural likenesses in psychology and mythology. The fifth chapter argues the palindrome and parallel conceptual structures as examples of recursion, then presents examples of recursion in language/grammar, art, and computer science. The sixth chapter uses instances of the recursive equiangular spiral throughout nature to introduce recursion and therefore the palindrome as an archetypal expression of infinity. The thesis ends with a list of the author's palindromes.

Ce mémoire fait partie du domaine de la combinatoire des mots et plus particulièrement de l'étude de la complexité palindromique (le nombre de facteurs palindromes) des mots infinis. La conjecture de Hof, Knill et Simon, énoncée pour la première fois en 1995, donne une caractérisation des points fixes dont la complexité palindromique est infinie. Récemment, elle a été résolue pour les points fixes sur un alphabet binaire (Tan, 2007). Dans ce mémoire, nous la démontrons pour les points fixes de morphismes uniformes sur un alphabet binaire (ce n'est pas plus général que le résultat de Tan). De plus, notre approche permet d'obtenir une démonstration d'un résultat similaire pour les points fixes contenant une infinité d'antipalindromes. Afin d'atteindre notre objectif, nous établissons un ensemble de résultats combinatoires sur les mots. En effet, nous faisons une étude des ƒ-palindromes et de certaines équations qui en contiennent. Ensuite, nous introduisons les morphismes de classe P, P¹ et ƒ-P et nous démontrons notamment que l'ensemble des morphismes de classe P¹ est un monoïde. Nous rassemblons également les résultats d'un travail précédent sur les morphismes conjugués. Finalement, nous étudions les chevauchements de mots et nous construisons un graphe de chevauchements, assise de notre démonstration de la conjecture. Toutes ces recherches ont contribué au développement d'un outil informatique voué à l'étude de questions soulevées en combinatoire des mots. Ce dernier est constitué d'un ensemble de classes et de fonctions écrites en langage Python annexées à ce mémoire. Elles seront bientôt incluses dans un paquetage sur la combinatoire des mots associé au logiciel libre Sage. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Combinatoire des mots, ƒ-palindrome, Complexité palindromique, Conjecture de Hof, Knill et Simon, Point fixe de morphisme, Chevauchement, Automates.

Breaking Through is a single-movement composition for symphony orchestra based on a fourteen-note melody. Every harmonic and melodic figure except the bass line is derived from this source melody. The structure of the work is based on a number of musical dichotomies that work on both local and large-scale levels. The local dichotomies contrast consonance with dissonance and ambiguity with clarity (in respect to texture and rhythm). The dichotomy of two-part form versus three-part form and the dichotomy of simplicity versus complexity operate on the large scale. The unity lended by the single source melody coupled with the contrasts furnished by the aforementioned dichotomies allow Breaking Through to be both coherent and interesting.

Mycoplasma hyopneumoniae é uma bactéria de tamanho diminuto, caracterizada por um genoma pequeno, com baixo conteúdo GC. Está associada com doenças respiratórias de suínos, resultando em prejuízos produtivos e econômicos na indústria animal. A presença de sequências de DNA repetitivas, que ocorrem em grandes quantidades em células eucarióticas, vem sendo cada vez mais identificadas em genomas de procariotos, sendo também associadas a um potencial papel regulador. Uma vez que a regulação da transcrição nesses organismos ainda é pouco entendida, o objetivo do presente estudo foi realizar uma busca in silico por elementos repetitivos nas regiões intergênicas do genoma de M. hyopneumoniae linhagem 7448. Dois tipos de repetições foram selecionados para a busca inicial: tandem e palindromes. Regiões intergênicas de até 500 pb a montante do sítio de início da tradução de todas as CDSs do genoma de M. hyopneumoniae linhagem 7448 foram utilizadas para a predição. Para cada tipo de elemento dois programas computacionais independentes foram utilizados. As predições in silico resultaram em 144 repetições em tandem e 1.171 palindromes. O DNA repetitivo se encontra distribuído a montante de 86% das unidades transcricionais de M. hyopneumoniae linhagem 7448. Análises comparativas entre genomas de micoplasmas demonstraram diferentes níveis de conservação dos elementos repetitivos entre linhagens patogênicas e não-patogênicas. Linhagens patogênicas revelaram uma conservação de 59%, enquanto que a não patogênica, somente de 46%. Através de ensaios de amplificação quantitativa de DNA, foi observado diferentes níveis de expressão em genes codificantes para importantes proteínas, como glicina hidroximetiltransferase, lipoproteína, adesinas e proteína ligadora de GTP. Os genes codificantes para essas proteínas divergiam no número de repetições palindromes e tandens na sua respectiva região intergênica. Além disso, repetições encontradas em 206 genes já descritos como regulados em diferentes condições em M. hyopneumoniae linhagem 232 mostraram aproximadamente 80% de conservação em relação à linhagem M. hyopneumoniae linhagem 7448. Todos esses resultados sugerem um potencial papel regulador das repetições de DNA em tandem e palindromes em Mycoplasma. / Mycoplasma hyopneumoniae is a diminutive bacterium, characterized by a small genome with a low GC content. It is commonly associated with swine respiratory diseases, resulting in productivity and economic losses in the animal industry. Repetitive DNA, which occurs in large quantities in eukaryotic cells, has been increasingly identified in prokaryotic genomes, and has been associated with a potential regulatory function. Once transcription regulation in these organisms is still poorly understood, the aim of the current study was to perform an in silico search of repeat elements in the genomic intergenic regions of M. hyopneumoniae strain 7448. Two types of repeats were selected for initial search: Tandem and Palindromic. Intergenic regions up to 500 bp upstream from start codon of M. hyopneumoniae strain 7448 CDSs were used as input for the software’s prediction. For each type of repeat sequence, two independent software packages were used. Computational analysis results in 144 tandem repeats and 1,171 palindrome elements. The repeats were distributed in the upstream region of 86% of transcriptional units of M. hyopneumoniae strain 7448. Comparative analysis between distinct mycoplasmas, demonstrate different indices of repeat conservation among pathogenic and non-pathogenic strains. Pathogenic strains revealed 59% conservation, while non-pathogenic only 46%. Through assays of quantitative amplification of DNA, different levels of expression in genes coding important proteins have been demonstrated, as glycine hydroxymethyltransferase, lipoprotein, adhesins and GTP-binding protein. These protein coding genes differ in number of palindromes or tandem repeats in respective upstream regions. In addition, repeats found in 206 genes already described to be regulated in different grow conditions in M. hyopneumoniae strain 232 showed almost 80% of conservation in relation to M. hyopneumoniae strain 7448. All these findings, suggests a potential regulatory role of tandem and palindrome DNA repeats.

SbcCD has been shown to cleave a DNA hairpin formed by a palindromic DNA sequence on the lagging strand template of the E. coli chromosome. This activity was exploited to create a unique system for inducing a single site-specific DNA double-strand break (DSB) once per replication cycle. First, this work shows that the SOS response induced by this DSB is only essential for viability following multiple cycles of cleavage and repair. Next, the SOS-inducible inhibitor of cell division SfiA is shown to be dispensable for survival, despite demonstrating that cleavage of the palindrome causes both an increase in cell size and a delay in nucleoid segregation. A model of the E. coli cell cycle is presented to reconcile the observation that growth under chronic DSB induced conditions has no effect on generation time despite causing an increase in cell size. This system of DSB induction was then coupled with fluorescence markers on both sides of the palindrome to visualise the consequence of the DSB in vivo. Cleavage of the DNA hairpin by SbcCD in a recAmutant was used to selectively degrade the chromosome that replicated the palindrome on the lagging strand of replication, allowing two genetically identical sister chromosomes to be distinguished. This approach was used to show that chromosome segregation in E. coli is not random, but results in the segregation of lagging strand replicated DNA to mid-cell and leading strand replicated DNA to cell poles. Finally, this system for visualising the site of an inducible DSB was optimised for use in various other mutant backgrounds to allow the events of DSB repair to be dissected. This work provides a solid basis for further investigation into the relationship between replication, recombination and chromosome segregation in the model organism E. coli.

Dans cette thèse, différents problèmes de la combinatoire des mots et de géométrie discrète sont considérés. Nous étudions d'abord l'occurrence des palindromes dans les codages de rotations, une famille de mots incluant entre autres les mots sturmiens et les suites de Rote. En particulier, nous démontrons que ces mots sont pleins, c'est-à-dire qu'ils réalisent la complexité palindromique maximale. Ensuite, nous étudions une nouvelle famille de mots, appelés mots pseudostandards généralisés, qui sont générés à l'aide d'un opérateur appelé clôture pseudopalindromique itérée. Nous présentons entre autres une généralisation d'une formule décrite par Justin qui permet de générer de façon linéaire et optimale un mot pseudostandard généralisé. L'objet central, le f-palindrome ou pseudopalindrome est un indicateur des symétries présentes dans les objets géométriques. Dans les derniers chapitres, nous nous concentrons davantage sur des problèmes de nature géométrique. Plus précisément, nous donnons la solution à deux conjectures de Provençal concernant les pavages par translation, en exploitant la présence dé palindromes et de périodicité locale dans les mots de contour. À la fin de plusieurs chapitres, différents problèmes ouverts et conjectures sont brièvement présentés. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Palindrome, pseudopalindrome, clôture pseudopalindromique itérée, codages de rotations, symétries, chemins discrets, pavages.