Computational analysis of nucleosome positioning datasets

Chromatin is a complex of DNA and histone proteins that constitutes the elemental material of eukaryotic chromosomes. The basic repeating sub-unit of chromatin, the nucleosome core particle, is comprised of approximately 146 base pairs (bp) of DNA wrapped around an octamer of core histones. Core particles are joined together by variable lengths of linker DNA to form chains of nucleosomes that are folded into higher-order structures. The specific distribution of nucleosomes along the DNA fibre is known to influence this folding process. Furthermore, on a local level, the positioning of nucleosomes can control access to DNA sequence motifs, and thus plays a fundamental role in regulating gene expression. Despite considerable experimental effort, neither the folding process nor the mechanisms for gene regulation are currently well understood.Monomer extension (ME) is an established in vitro experimental technique which maps the positions adopted by reconstituted core histone octamers on a defined DNA sequence. It provides quantitative positioning information, at high resolution, over long continuous stretches of DNA sequence. This technique has been employed to map several genes: globin genes (8 kbp), the beta-lactoglobulin gene (10 kbp) and various imprinting genes (4 kbp).This study explores and analyses this unique dataset, utilising computational and stochastic techniques, to gain insight into the potential influence of nucleosomal positioning on the structure and function of chromatin. The first section of this thesis expands upon prior analyses, explores general features of the dataset using common bioinformatics tools, and attempts to relate the quantitative positioning information from ME to data from other commonly used competitive reconstitution protocols. Finally, evidence of a correlation between the in vitro ME dataset and in vivo nucleosome positions for the beta-lactoglobulin gene region is presented.The second section presents the development of a novel method for the analysis of ME maps using Monte Carlo simulation methods. The goal was to use the ME datasets to simulate a higher order chromatin fibre, taking advantage of the longrange and quantitative nature of the ME datasets.The Monte Carlo simulations have allowed new insights to be gleaned from the datasets. Analysis of the beta-lactoglobulin positioning map indicates the potential for discrete disruption of nucleosomal organisation, at specific physiological nucleosome densities, over regions found to have unusual chromatin structure in vivo. This suggests a correspondence between the quantitative histone octamer positioning information in vitro and the positioning of nucleosomes in vivo.Further, the simulations demonstrate that histone density-dependent changes in nucleosomal organisation, in both the beta-lactoglobulin and globin positioning maps, often occur in regions involved in gene regulation. This implies that irregular chromatin structures may form over certain biologically significant regions.Taken together, these studies lend weight to the hypothesis that nucleosome positioning information encoded within DNA plays a fundamental role in directing chromatin structure in vivo

Arithmetic patches, weak tangents, and dimension

The first named author is supported by a Leverhulme Trust Research Fellowship (RF-2016-500) and the second named author is supported by a PhD scholarship provided bythe School of Mathematics in the University of St AndrewsWe investigate the relationships between several classical notions in arithmetic combinatorics and geometry including the presence (or lack of) arithmetic progressions (or patches in dimensions at least 2), the structure of tangent sets, and the Assouad dimension. We begin by extending a recent result of Dyatlov and Zahl by showing that a set cannot contain arbitrarily large arithmetic progressions (patches) if it has Assouad dimension strictly smaller than the ambient spatial dimension. Seeking a partial converse, we go on to prove that having Assouad dimension equal to the ambient spatial dimension is equivalent to having weak tangents with non-empty interior and to ‘asymptotically’ containing arbitrarily large arithmetic patches. We present some applications of our results concerning sets of integers, which include a weak solution to the Erdös–Turán conjecture on arithmetic progressions.PostprintPeer reviewe

An update on nuclear calcium signalling

Over the past 15 years or so, numerous studies have sought to characterise how nuclear calcium (Ca2+) signals are generated and reversed, and to understand how events that occur in the nucleoplasm influence cellular Ca2+ activity, and vice versa. In this Commentary, we describe mechanisms of nuclear Ca2+ signalling and discuss what is known about the origin and physiological significance of nuclear Ca2+ transients. In particular, we focus on the idea that the nucleus has an autonomous Ca2+ signalling system that can generate its own Ca2+ transients that modulate processes such as gene transcription. We also discuss the role of nuclear pores and the nuclear envelope in controlling ion flux into the nucleoplasm

Uniform scaling limits for ergodic measures

J. M. Fraser and M. Pollicott were financially supported in part by the EPSRC grant EP/J013560/1.We provide an elementary proof that ergodic measures on one-sided shift spaces are ‘uniformly scaling’ in the following sense: at almost every point the scenery distributions weakly converge to a common distribution on the space of measures. Moreover, we show how the limiting distribution can be expressed in terms of, and derived from, a 'reverse Jacobian’ function associated with the corresponding measure on the space of left infinite sequences. Finally we specialise to the setting of Gibbs measures, discuss some statistical properties, and prove a Central Limit Theorem for ergodic Markov measures.PostprintPeer reviewe

Editorial: If the settler never came

If the settler never came and the (Australian) continent developed herself, what kinds of conversations would we consider? Perhaps, we would highlight the fact that the Country and Island landscape did not have an estimated number of languages but significantly more than the speculated 250 (or “over 300”, or “hundreds of”) Aboriginal and Torres Strait Islander languages across the island and continental landscape. It would be a given continuance that every year across the Country, and not just 2019 declared by the United Nations General assembly, as the year to celebrate the Indigenous languages. Perhaps the ways we define, discuss and distinguish these numerous, living languages would be very different from our current forensic approaches

Effects of supply and demand disturbances on real commodity prices: the US, UK and Japanese experience

Using forty-one years of monthly data, this paper assesses the impact of economy-wide supply and demand shocks on commodity prices in three of the world?s major economies. Utilising a small theoretical macro model, empirical results support the hypothesis that the relationship between real commodity prices and inflation can be either positive or negative depending on the relative importance of supply and demand shocks in the national economy. Our results also show that differences occur across economies with the UK commodity returns registering more sensitivity to demand shocks than those of US and Japanese markets. Supply and demand components of commodity prices have also varied over time and across economies, suggesting that commodity markets are not fully globally integrated but are highly sensitive to national influences

The dimensions of inhomogeneous self-affine sets

Funding: SAB thanks the Carnegie Trust for financially supporting this work. JMF was financially supported by a Leverhulme Trust Research Fellowship (RF-2016-500) and an EPSRC Standard Grant (EP/R015104/1).We prove that the upper box dimension of an inhomogeneous self-affine set is bounded above by the maximum of the affinity dimension and the dimension of the condensation set. In addition, we determine sufficient conditions for this upper bound to be attained, which, in part, constitutes an exploration of the capacity for the condensation set to mitigate dimension drop between the affinity dimension and the corresponding homogeneous attractor. Our work improves and unifies previous results on general inhomogeneous attractors, low-dimensional affine systems, and inhomogeneous self-affine carpets, while providing inhomogeneous analogues of Falconer’s seminal results on homogeneous self-affine sets.Publisher PDFPeer reviewe

Seasonal Variation in 25(OH)D at Aberdeen (57°N) and Bone Health Indicators- Could Holidays in the Sun and Cod Liver Oil Supplements Alleviate Deficiency?

Vitamin D has been linked with many health outcomes. The aim of this longitudinal study, was to assess predictors of seasonal variation of 25-hydroxy-vitamin D (25(OH)D) (including use of supplements and holidays in sunny destinations) at a northerly latitude in the UK (57°N) in relation to bone health indicators. 365 healthy postmenopausal women (mean age 62.0 y (SD 1.4)) had 25(OH)D measurements by immunoassay, serum C-telopeptide (CTX), estimates of sunlight exposure (badges of polysulphone film), information regarding holidays in sunny destinations, and diet (from food diaries, including use of supplements such as cod liver oil (CLO)) at fixed 3-monthly intervals over 15 months (subject retention 88%) with an additional 25(OH)D assessment in spring 2008. Bone mineral density (BMD) at the lumbar spine (LS) and dual hip was measured in autumn 2006 and spring 2007 (Lunar I-DXA). Deficiency prevalence (25(OH)