Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes

Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic codes over GR(p^a,m) and generating sets for its ideals are considered. Along with some structure details of the ambient ring, the existance of a certain type of generating set for an ideal is proven.Comment: arXiv admin note: text overlap with arXiv:0906.400

An optimized kit-free method for making strand-specific deep sequencing libraries from RNA fragments

Deep sequencing of strand-specific cDNA libraries is now a ubiquitous tool for identifying and quantifying RNAs in diverse sample types. The accuracy of conclusions drawn from these analyses depends on precise and quantitative conversion of the RNA sample into a DNA library suitable for sequencing. Here, we describe an optimized method of preparing strand-specific RNA deep sequencing libraries from small RNAs and variably sized RNA fragments obtained from ribonucleoprotein particle footprinting experiments or fragmentation of long RNAs. Our approach works across a wide range of input amounts (400 pg to 200 ng), is easy to follow and produces a library in 2-3 days at relatively low reagent cost, all while giving the user complete control over every step. Because all enzymatic reactions were optimized and driven to apparent completion, sequence diversity and species abundance in the input sample are well preserved

Measuring the reproducibility and quality of Hi-C data

BACKGROUND: Hi-C is currently the most widely used assay to investigate the 3D organization of the genome and to study its role in gene regulation, DNA replication, and disease. However, Hi-C experiments are costly to perform and involve multiple complex experimental steps; thus, accurate methods for measuring the quality and reproducibility of Hi-C data are essential to determine whether the output should be used further in a study. RESULTS: Using real and simulated data, we profile the performance of several recently proposed methods for assessing reproducibility of population Hi-C data, including HiCRep, GenomeDISCO, HiC-Spector, and QuASAR-Rep. By explicitly controlling noise and sparsity through simulations, we demonstrate the deficiencies of performing simple correlation analysis on pairs of matrices, and we show that methods developed specifically for Hi-C data produce better measures of reproducibility. We also show how to use established measures, such as the ratio of intra- to interchromosomal interactions, and novel ones, such as QuASAR-QC, to identify low-quality experiments. CONCLUSIONS: In this work, we assess reproducibility and quality measures by varying sequencing depth, resolution and noise levels in Hi-C data from 13 cell lines, with two biological replicates each, as well as 176 simulated matrices. Through this extensive validation and benchmarking of Hi-C data, we describe best practices for reproducibility and quality assessment of Hi-C experiments. We make all software publicly available at http://github.com/kundajelab/3DChromatin_ReplicateQC to facilitate adoption in the community

Large domains of heterochromatin direct the formation of short mitotic chromosome loops

During mitosis chromosomes reorganise into highly compact, rod-shaped forms, thought to consist of consecutive chromatin loops around a central protein scaffold. Condensin complexes are involved in chromatin compaction, but the contribution of other chromatin proteins, DNA sequence and histone modifications is less understood. A large region of fission yeast DNA inserted into a mouse chromosome was previously observed to adopt a mitotic organisation distinct from that of surrounding mouse DNA. Here, we show that a similar distinct structure is common to a large subset of insertion events in both mouse and human cells and is coincident with the presence of high levels of heterochromatic H3 lysine nine trimethylation (H3K9me3). Hi-C and microscopy indicate that the heterochromatinised fission yeast DNA is organised into smaller chromatin loops than flanking euchromatic mouse chromatin. We conclude that heterochromatin alters chromatin loop size, thus contributing to the distinct appearance of heterochromatin on mitotic chromosomes

The HoxD cluster is a dynamic and resilient TAD boundary controlling the segregation of antagonistic regulatory landscapes

The mammalian HoxD cluster lies between two topologically associating domains (TADs) matching distinct enhancer-rich regulatory landscapes. During limb development, the telomeric TAD controls the early transcription of Hoxd genes in forearm cells, whereas the centromeric TAD subsequently regulates more posterior Hoxd genes in digit cells. Therefore, the TAD boundary prevents the terminal Hoxd13 gene from responding to forearm enhancers, thereby allowing proper limb patterning. To assess the nature and function of this CTCF-rich DNA region in embryos, we compared chromatin interaction profiles between proximal and distal limb bud cells isolated from mutant stocks where various parts of this boundary region were removed. The resulting progressive release in boundary effect triggered inter-TAD contacts, favored by the activity of the newly accessed enhancers. However, the boundary was highly resilient, and only a 400-kb deletion, including the whole-gene cluster, was eventually able to merge the neighboring TADs into a single structure. In this unified TAD, both proximal and distal limb enhancers nevertheless continued to work independently over a targeted transgenic reporter construct. We propose that the whole HoxD cluster is a dynamic TAD border and that the exact boundary position varies depending on both the transcriptional status and the developmental context. Press

Systematic evaluation of chromosome conformation capture assays [preprint]

Chromosome conformation capture (3C)-based assays are used to map chromatin interactions genome-wide. Quantitative analyses of chromatin interaction maps can lead to insights into the spatial organization of chromosomes and the mechanisms by which they fold. A number of protocols such as in situ Hi-C and Micro-C are now widely used and these differ in key experimental parameters including cross-linking chemistry and chromatin fragmentation strategy. To understand how the choice of experimental protocol determines the ability to detect and quantify aspects of chromosome folding we have performed a systematic evaluation of experimental parameters of 3C-based protocols. We find that different protocols capture different 3D genome features with different efficiencies. First, the use of cross-linkers such as DSG in addition to formaldehyde improves signal-to-noise allowing detection of thousands of additional loops and strengthens the compartment signal. Second, fragmenting chromatin to the level of nucleosomes using MNase allows detection of more loops. On the other hand, protocols that generate larger multi-kb fragments produce stronger compartmentalization signals. We confirmed our results for multiple cell types and cell cycle stages. We find that cell type-specific quantitative differences in chromosome folding are not detected or underestimated by some protocols. Based on these insights we developed Hi-C 3.0, a single protocol that can be used to both efficiently detect chromatin loops and to quantify compartmentalization. Finally, this study produced ultra-deeply sequenced reference interaction maps using conventional Hi-C, Micro-C and Hi-C 3.0 for commonly used cell lines in the 4D Nucleome Project

The non-canonical SMC protein SmcHD1 antagonises TAD formation and compartmentalisation on the inactive X chromosome.

The inactive X chromosome (Xi) in female mammals adopts an atypical higher-order chromatin structure, manifested as a global loss of local topologically associated domains (TADs), A/B compartments and formation of two mega-domains. Here we demonstrate that the non-canonical SMC family protein, SmcHD1, which is important for gene silencing on Xi, contributes to this unique chromosome architecture. Specifically, allelic mapping of the transcriptome and epigenome in SmcHD1 mutant cells reveals the appearance of sub-megabase domains defined by gene activation, CpG hypermethylation and depletion of Polycomb-mediated H3K27me3. These domains, which correlate with sites of SmcHD1 enrichment on Xi in wild-type cells, additionally adopt features of active X chromosome higher-order chromosome architecture, including A/B compartments and partial restoration of TAD boundaries. Xi chromosome architecture changes also occurred following SmcHD1 knockout in a somatic cell model, but in this case, independent of Xi gene derepression. We conclude that SmcHD1 is a key factor in defining the unique chromosome architecture of Xi

On a class of repeated-root monomial-like abelian codes

In this paper we study polycyclic codes of length $p^{s_1} \times \cdots \times p^{s_n}$\ over \F_{p^a}\ generated by a single monomial. These codes form a special class of abelian codes. We show that these codes arise from the product of certain single variable codes and we determine their minimum Hamming distance. Finally we extend the results of Massey et. al. on the weight retaining property of monomials in one variable to the weight retaining property of monomials in several variables

ASPeak: an abundance sensitive peak detection algorithm for RIP-Seq

SUMMARY: Unlike DNA, RNA abundances can vary over several orders of magnitude. Thus, identification of RNA-protein binding sites from high-throughput sequencing data presents unique challenges. Although peak identification in ChIP-Seq data has been extensively explored, there are few bioinformatics tools tailored for peak calling on analogous datasets for RNA-binding proteins. Here we describe ASPeak (abundance sensitive peak detection algorithm), an implementation of an algorithm that we previously applied to detect peaks in exon junction complex RNA immunoprecipitation in tandem experiments. Our peak detection algorithm yields stringent and robust target sets enabling sensitive motif finding and downstream functional analyses. AVAILABILITY: ASPeak is implemented in Perl as a complete pipeline that takes bedGraph files as input. ASPeak implementation is freely available at https://sourceforge.net/projects/as-peak under the GNU General Public License. ASPeak can be run on a personal computer, yet is designed to be easily parallelizable. ASPeak can also run on high performance computing clusters providing efficient speedup. The documentation and user manual can be obtained from http://master.dl.sourceforge.net/project/as-peak/manual.pdf