  One-dimensional arrays of nucleosomes (DNA-bound histone octamers separated
by stretches of linker DNA) fold into higher-order chromatin structures which
ultimately make up eukaryotic chromosomes. Chromatin structure formation leads
to 10-11 base pair (bp) discretization of linker lengths caused by the smaller
free energy cost of packaging nucleosomes into a regular chromatin fiber if
their rotational setting (defined by DNA helical twist) is conserved. We
describe nucleosome positions along the fiber using a thermodynamic model of
finite-size particles with effective two-body interactions, subject to an
arbitrary external potential. We infer both one-body and two-body energies from
readily available large-scale maps of nucleosome positions. We show that
two-body forces play a leading role in establishing well-known 10-11 bp
genome-wide periodicity of nucleosome occupancies. They also explain nucleosome
ordering over transcribed regions observed in both in vitro and in vivo
high-throughput experiments.
