Statistical mechanics of nucleosome ordering by chromatin structure-induced two-body interactions

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.