A 1-dimensional statistical mechanics model for nucleosome positioning on genomic DNA

TL;DR

This paper introduces a 1D statistical mechanics model to analyze nucleosome positioning on genomic DNA, comparing homogeneous and sheep DNA, and predicting experimental outcomes based on sequence effects.

Contribution

The work develops a novel 1D model for nucleosome positioning that incorporates sequence-specific potentials and finite nucleosome size effects, extending previous simplified models.

Findings

Finite nucleosome size influences positioning probabilities.

Sequence-dependent potentials affect nucleosome distribution.

Model predictions align with experimental digestion patterns.

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 (approx. 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 1 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.