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We present a statistical-mechanical analysis of the positioning of nucleosomes along one of the chromosomes of yeast DNA as a function of the strength of the binding potential and of the chemical potential of the nucleosomes. We find a significant density of two-level nucleosome switching regions where, as a function of the chemical potential, the nucleosome distribution undergoes a micro first-order transition. The location of these nucleosome switches shows a strong correlation with the location of transcription-factor binding sites.
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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.
DNA is a flexible molecule, but the degree of its flexibility is subject to debate. The commonly-accepted persistence length of $l_p approx 500,$AA is inconsistent with recent studies on short-chain DNA that show much greater flexibility but do not probe its origin. We have performed X-ray and neutron small-angle scattering on a short DNA sequence containing a strong nucleosome positioning element, and analyzed the results using a modified Kratky-Porod model to determine possible conformations. Our results support a hypothesis from Crick and Klug in 1975 that some DNA sequences in solution can have sharp kinks, potentially resolving the discrepancy. Our conclusions are supported by measurements on a radiation-damaged sample, where single-strand breaks lead to increased flexibility and by an analysis of data from another sequence, which does not have kinks, but where our method can detect a locally enhanced flexibility due to an $AT$-domain.
Cells are known to utilize biochemical noise to probabilistically switch between distinct gene expression states. We demonstrate that such noise-driven switching is dominated by tails of probability distributions and is therefore exponentially sensitive to changes in physiological parameters such as transcription and translation rates. However, provided mRNA lifetimes are short, switching can still be accurately simulated using protein-only models of gene expression. Exponential sensitivity limits the robustness of noise-driven switching, suggesting cells may use other mechanisms in order to switch reliably.
We study electronic transport in long DNA chains using the tight-binding approach for a ladder-like model of DNA. We find insulating behavior with localizaton lengths xi ~ 25 in units of average base-pair seperation. Furthermore, we observe small, but significant differences between lambda-DNA, centromeric DNA, promoter sequences as well as random-ATGC DNA.
A method for estimating the cross-correlation $C_{xy}(tau)$ of long-range correlated series $x(t)$ and $y(t)$, at varying lags $tau$ and scales $n$, is proposed. For fractional Brownian motions with Hurst exponents $H_1$ and $H_2$, the asymptotic expression of $C_{xy}(tau)$ depends only on the lag $tau$ (wide-sense stationarity) and scales as a power of $n$ with exponent ${H_1+H_2}$ for $tauto 0$. The method is illustrated on (i) financial series, to show the leverage effect; (ii) genomic sequences, to estimate the correlations between structural parameters along the chromosomes.
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