  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.
