Abstract
The first level of folding of DNA in eukaryotes is provided by the so-called ‘10 nm chromatin fibre’, where DNA wraps around histone proteins (∼10 nm in size) to form nucleosomes, which go on to create a zig-zagging bead-on-a-string structure. In this work we present a one-dimensional statistical mechanics model to study nucleosome positioning within one such 10 nm fibre. We focus on the case of genomic sheep DNA, and we start from effective potentials valid at infinite dilution and determined from high-resolution in vitro salt dialysis experiments. We study positioning within a polynucleosome chain, and compare the results for genomic DNA to that obtained in the simplest case of homogeneous DNA, where the problem can be mapped to a Tonks gas []. First, we consider the simple, analytically solvable, case where nucleosomes are assumed to be point-like. Then, we perform numerical simulations to gauge the effect of their finite size on the nucleosomal distribution probabilities. Finally we compare nucleosome distributions and simulated nuclease digestion patterns for the two cases (homogeneous and sheep DNA), thereby providing testable predictions of the effect of sequence on experimentally observable quantities in experiments on polynucleosome chromatin fibres reconstituted in vitro.
Highlights
Chromatin is the building block of chromosomes within eukaryotes [2,3,4,5,6]
Results for the positional probability distribution functions (PDFs) with finite histone size we study the same polynucleosome chain of N = 10 nucleosomes, on a DNA with L = 4600 base pairs, where, the histone size is set to 146 base pairs
Our main focus was on the effect of sequence on the 1D organisation of nucleosomes along the chromatin fibre, and to address this we have compared the statistics of a DNA molecule with uniform DNA: histone interaction to another case, of a genomic DNA region, where the DNA:histone potential was informed by existing experimental high-resolution nucleosome positioning data
Summary
Chromatin is the building block of chromosomes within eukaryotes [2,3,4,5,6]. It is made up by histone proteins (normally octamers) and DNA, which wraps around the histones to form a left-handed superhelix [7]. Electron microscopy and atomic force microscopy revealed that when spread on a surface, chromatin fibres (a DNA chain containing many nucleosome) adopts a characteristic bead-on-a-string structure (figure 1). This is the first level of compaction of DNA within eukaryotic nuclei, which needs to be complemented by higher orders of compactions which are to date not fully understood [2, 3]. Because in the test tube there are no other constituents than DNA and histone octamers, it follows that, at least under those conditions, the positioning of the nucleosome must be dictated by simple biophysical laws: nucleosome– nucleosome interactions along the chain [10], and the nucleosome: DNA interaction. The latter interaction is partly given by electrostatic attractions between the negatively charged DNA and the positively charged histone octamer [11,12,13,14], but it includes a sequence-specific component, which is largely due to the sequence-dependent elastic properties of the genetic material [15,16,17,18]
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