Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies

We propose a method for computing any Gelfand-Dickey tau function living in Segal-Wilson Grassmannian as the asymptotics of block Toeplitz determinant associated to a certain class of symbols. Also truncated block Toeplitz determinants associated to the same symbols are shown to be tau function for rational reductions of KP. Connection with Riemann-Hilbert problems is investigated both from the point of view of integrable systems and block Toeplitz operator theory. Examples of applications to algebro-geometric solutions are given.Comment: 35 pages. Typos corrected, some changes in the introductio

Quantitative test of the barrier nucleosome model for statistical positioning of nucleosomes up- and downstream of transcription start sites

The positions of nucleosomes in eukaryotic genomes determine which parts of the DNA sequence are readily accessible for regulatory proteins and which are not. Genome-wide maps of nucleosome positions have revealed a salient pattern around transcription start sites, involving a nucleosome-free region (NFR) flanked by a pronounced periodic pattern in the average nucleosome density. While the periodic pattern clearly reflects well-positioned nucleosomes, the positioning mechanism is less clear. A recent experimental study by Mavrich et al. argued that the pattern observed in S. cerevisiae is qualitatively consistent with a `barrier nucleosome model', in which the oscillatory pattern is created by the statistical positioning mechanism of Kornberg and Stryer. On the other hand, there is clear evidence for intrinsic sequence preferences of nucleosomes, and it is unclear to what extent these sequence preferences affect the observed pattern. To test the barrier nucleosome model, we quantitatively analyze yeast nucleosome positioning data both up- and downstream from NFRs. Our analysis is based on the Tonks model of statistical physics which quantifies the interplay between the excluded-volume interaction of nucleosomes and their positional entropy. We find that although the typical patterns on the two sides of the NFR are different, they are both quantitatively described by the same physical model, with the same parameters, but different boundary conditions. The inferred boundary conditions suggest that the first nucleosome downstream from the NFR (the +1 nucleosome) is typically directly positioned while the first nucleosome upstream is statistically positioned via a nucleosome-repelling DNA region. These boundary conditions, which can be locally encoded into the genome sequence, significantly shape the statistical distribution of nucleosomes over a range of up to ~1000 bp to each side.Comment: includes supporting materia

Preferentially Quantized Linker DNA Lengths in Saccharomyces cerevisiae

The exact lengths of linker DNAs connecting adjacent nucleosomes specify the intrinsic three-dimensional structures of eukaryotic chromatin fibers. Some studies suggest that linker DNA lengths preferentially occur at certain quantized values, differing one from another by integral multiples of the DNA helical repeat, ∼10 bp; however, studies in the literature are inconsistent. Here, we investigate linker DNA length distributions in the yeast Saccharomyces cerevisiae genome, using two novel methods: a Fourier analysis of genomic dinucleotide periodicities adjacent to experimentally mapped nucleosomes and a duration hidden Markov model applied to experimentally defined dinucleosomes. Both methods reveal that linker DNA lengths in yeast are preferentially periodic at the DNA helical repeat (∼10 bp), obeying the forms 10n+5 bp (integer n). This 10 bp periodicity implies an ordered superhelical intrinsic structure for the average chromatin fiber in yeast

Monte Carlo Simulations indicate that Chromati: Nanostructure is accessible by Light Microscopy

A long controversy exists about the structure of chromatin. Theoretically, this structure could be resolved by scattering experiments if one determines the scattering function - or equivalently the pair distribution function - of the nucleosomes. Unfortunately, scattering experiments with live cells are very difficult and limited to only a couple of nucleosomes

Chromatin and epigenetics: current biophysical views

Recent advances in high-throughput sequencing experiments and their theoretical descriptions have determined fast dynamics of the "chromatin and epigenetics" field, with new concepts appearing at high rate. This field includes but is not limited to the study of DNA-protein-RNA interactions, chromatin packing properties at different scales, regulation of gene expression and protein trafficking in the cell nucleus, binding site search in the crowded chromatin environment and modulation of physical interactions by covalent chemical modifications of the binding partners. The current special issue does not pretend for the full coverage of the field, but it rather aims to capture its development and provide a snapshot of the most recent concepts and approaches. Eighteen open-access articles comprising this issue provide a delicate balance between current theoretical and experimental biophysical approaches to uncover chromatin structure and understand epigenetic regulation, allowing free flow of new ideas and preliminary results

Oligonucleotide Sequence Motifs as Nucleosome Positioning Signals

To gain a better understanding of the sequence patterns that characterize positioned nucleosomes, we first performed an analysis of the periodicities of the 256 tetranucleotides in a yeast genome-wide library of nucleosomal DNA sequences that was prepared by in vitro reconstitution. The approach entailed the identification and analysis of 24 unique tetranucleotides that were defined by 8 consensus sequences. These consensus sequences were shown to be responsible for most if not all of the tetranucleotide and dinucleotide periodicities displayed by the entire library, demonstrating that the periodicities of dinucleotides that characterize the yeast genome are, in actuality, due primarily to the 8 consensus sequences. A novel combination of experimental and bioinformatic approaches was then used to show that these tetranucleotides are important for preferred formation of nucleosomes at specific sites along DNA in vitro. These results were then compared to tetranucleotide patterns in genome-wide in vivo libraries from yeast and C. elegans in order to assess the contributions of DNA sequence in the control of nucleosome residency in the cell. These comparisons revealed striking similarities in the tetranucleotide occurrence profiles that are likely to be involved in nucleosome positioning in both in vitro and in vivo libraries, suggesting that DNA sequence is an important factor in the control of nucleosome placement in vivo. However, the strengths of the tetranucleotide periodicities were 3–4 fold higher in the in vitro as compared to the in vivo libraries, which implies that DNA sequence plays less of a role in dictating nucleosome positions in vivo. The results of this study have important implications for models of sequence-dependent positioning since they suggest that a defined subset of tetranucleotides is involved in preferred nucleosome occupancy and that these tetranucleotides are the major source of the dinucleotide periodicities that are characteristic of positioned nucleosomes

Genomic Organization of H2Av Containing Nucleosomes in Drosophila Heterochromatin

H2Av is a versatile histone variant that plays both positive and negative roles in transcription, DNA repair, and chromatin structure in Drosophila. H2Av, and its broader homolog H2A.Z, tend to be enriched toward 5′ ends of genes, and exist in both euchromatin and heterochromatin. Its organization around euchromatin genes and other features have been described in many eukaryotic model organisms. However, less is known about H2Av nucleosome organization in heterochromatin. Here we report the properties and organization of individual H2Av nucleosomes around genes and transposable elements located in Drosophila heterochromatic regions. We compare the similarity and differences with that found in euchromatic regions. Our analyses suggest that nucleosomes are intrinsically positioned on inverted repeats of DNA transposable elements such as those related to the “1360” element, but are not intrinsically positioned on retrotransposon-related elements

Plasmodium falciparum Nucleosomes Exhibit Reduced Stability and Lost Sequence Dependent Nucleosome Positioning

The packaging and organization of genomic DNA into chromatin represents an additional regulatory layer of gene expression, with specific nucleosome positions that restrict the accessibility of regulatory DNA elements. The mechanisms that position nucleosomes in vivo are thought to depend on the biophysical properties of the histones, sequence patterns, like phased di-nucleotide repeats and the architecture of the histone octamer that folds DNA in 1.65 tight turns. Comparative studies of human and P. falciparum histones reveal that the latter have a strongly reduced ability to recognize internal sequence dependent nucleosome positioning signals. In contrast, the nucleosomes are positioned by AT-repeat sequences flanking nucleosomes in vivo and in vitro. Further, the strong sequence variations in the plasmodium histones, compared to other mammalian histones, do not present adaptations to its AT-rich genome. Human and parasite histones bind with higher affinity to GC-rich DNA and with lower affinity to AT-rich DNA. However, the plasmodium nucleosomes are overall less stable, with increased temperature induced mobility, decreased salt stability of the histones H2A and H2B and considerable reduced binding affinity to GC-rich DNA, as compared with the human nucleosomes. In addition, we show that plasmodium histone octamers form the shortest known nucleosome repeat length (155bp) in vitro and in vivo. Our data suggest that the biochemical properties of the parasite histones are distinct from the typical characteristics of other eukaryotic histones and these properties reflect the increased accessibility of the P. falciparum genome