Semi-primary lattices and tableau algorithms

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995.Includes bibliographical references (leaves 194-195).by Glenn Paul Tesler.Ph.D

The Fragile Breakage versus Random Breakage Models of Chromosome Evolution

For many years, studies of chromosome evolution were dominated by the random breakage theory, which implies that there are no rearrangement hot spots in the human genome. In 2003, Pevzner and Tesler argued against the random breakage model and proposed an alternative “fragile breakage” model of chromosome evolution. In 2004, Sankoff and Trinh argued against the fragile breakage model and raised doubts that Pevzner and Tesler provided any evidence of rearrangement hot spots. We investigate whether Sankoff and Trinh indeed revealed a flaw in the arguments of Pevzner and Tesler. We show that Sankoff and Trinh's synteny block identification algorithm makes erroneous identifications even in small toy examples and that their parameters do not reflect the realities of the comparative genomic architecture of human and mouse. We further argue that if Sankoff and Trinh had fixed these problems, their arguments in support of the random breakage model would disappear. Finally, we study the link between rearrangements and regulatory regions and argue that long regulatory regions and inhomogeneity of gene distribution in mammalian genomes may be responsible for the breakpoint reuse phenomenon

Reconstructing the Genomic Architecture of Mammalian Ancestors Using Multispecies Comparative Maps

Rapidly developing comparative gene maps in selected mammal species are providing an opportunity to reconstruct the genomic architecture of mammalian ancestors and study rearrangements that transformed this ancestral genome into existing mammalian genomes. Here, the recently developed Multiple Genome Rearrangement (MGR) algorithm is applied to human, mouse, cat and cattle comparative maps (with 311-470 shared markers) to impute the ancestral mammalian genome. Reconstructed ancestors consist of 70-100 conserved segments shared across the genomes that have been exchanged by rearrangement events along the ordinal lineages leading to modern species genomes. Genomic distances between species, dominated by inversions (reversals) and translocations, are presented in a first multispecies attempt using ordered mapping data to reconstruct the evolutionary exchanges that preceded modern placental mammal genomes

Lattice Diagram Polynomials and Extended Pieri Rules

The lattice cell in the ${i+1}^{st}$ row and ${j+1}^{st}$ column of the positive quadrant of the plane is denoted $(i,j)$. If $\mu$ is a partition of $n+1$, we denote by $\mu/ij$ the diagram obtained by removing the cell $(i,j)$ from the (French) Ferrers diagram of $\mu$. We set $\Delta_{\mu/ij}=\det \| x_i^{p_j}y_i^{q_j} \|_{i,j=1}^n$, where $(p_1,q_1),... ,(p_n,q_n)$ are the cells of $\mu/ij$, and let ${\bf M}_{\mu/ij}$ be the linear span of the partial derivatives of $\Delta_{\mu/ij}$. The bihomogeneity of $\Delta_{\mu/ij}$ and its alternating nature under the diagonal action of $S_n$ gives ${\bf M}_{\mu/ij}$ the structure of a bigraded $S_n$-module. We conjecture that ${\bf M}_{\mu/ij}$ is always a direct sum of $k$ left regular representations of $S_n$, where $k$ is the number of cells that are weakly north and east of $(i,j)$ in $\mu$. We also make a number of conjectures describing the precise nature of the bivariate Frobenius characteristic of ${\bf M}_{\mu/ij}$ in terms of the theory of Macdonald polynomials. On the validity of these conjectures, we derive a number of surprising identities. In particular, we obtain a representation theoretical interpretation of the coefficients appearing in some Macdonald Pieri Rules.Comment: 77 pages, Te

Viral population estimation using pyrosequencing

The diversity of virus populations within single infected hosts presents a major difficulty for the natural immune response as well as for vaccine design and antiviral drug therapy. Recently developed pyrophosphate based sequencing technologies (pyrosequencing) can be used for quantifying this diversity by ultra-deep sequencing of virus samples. We present computational methods for the analysis of such sequence data and apply these techniques to pyrosequencing data obtained from HIV populations within patients harboring drug resistant virus strains. Our main result is the estimation of the population structure of the sample from the pyrosequencing reads. This inference is based on a statistical approach to error correction, followed by a combinatorial algorithm for constructing a minimal set of haplotypes that explain the data. Using this set of explaining haplotypes, we apply a statistical model to infer the frequencies of the haplotypes in the population via an EM algorithm. We demonstrate that pyrosequencing reads allow for effective population reconstruction by extensive simulations and by comparison to 165 sequences obtained directly from clonal sequencing of four independent, diverse HIV populations. Thus, pyrosequencing can be used for cost-effective estimation of the structure of virus populations, promising new insights into viral evolutionary dynamics and disease control strategies.Comment: 23 pages, 13 figure

Initial Sequence and Comparative Analysis of the Cat Genome

The genome sequence (1.9-fold coverage) of an inbred Abyssinian domestic cat was assembled, mapped, and annotated with a comparative approach that involved cross-reference to annotated genome assemblies of six mammals (human, chimpanzee, mouse, rat, dog, and cow). The results resolved chromosomal positions for 663,480 contigs, 20,285 putative feline gene orthologs, and 133,499 conserved sequence blocks (CSBs). Additional annotated features include repetitive elements, endogenous retroviral sequences, nuclear mitochondrial (numt) sequences, micro-RNAs, and evolutionary breakpoints that suggest historic balancing of translocation and inversion incidences in distinct mammalian lineages. Large numbers of single nucleotide polymorphisms (SNPs), deletion insertion polymorphisms (DIPs), and short tandem repeats (STRs), suitable for linkage or association studies were characterized in the context of long stretches of chromosome homozygosity. In spite of the light coverage capturing ∼65% of euchromatin sequence from the cat genome, these comparative insights shed new light on the tempo and mode of gene/genome evolution in mammals, promise several research applications for the cat, and also illustrate that a comparative approach using more deeply covered mammals provides an informative, preliminary annotation of a light (1.9-fold) coverage mammal genome sequence

Erratum: Corrigendum: Sequence and comparative analysis of the chicken genome provide unique perspectives on vertebrate evolution

International Chicken Genome Sequencing Consortium. The Original Article was published on 09 December 2004. Nature432, 695–716 (2004). In Table 5 of this Article, the last four values listed in the ‘Copy number’ column were incorrect. These should be: LTR elements, 30,000; DNA transposons, 20,000; simple repeats, 140,000; and satellites, 4,000. These errors do not affect any of the conclusions in our paper. Additional information. The online version of the original article can be found at 10.1038/nature0315