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 regular chromatin fibers if their rotational setting (defined by the DNA helical twist) is conserved. We describe nucleosome positions along the fiber using a thermodynamic model of finite-size particles with both intrinsic histone-DNA interactions and an effective two-body potential. We infer one- and two-body energies directly from high-throughput maps of nucleosome positions. We show that higher-order chromatin structure helps explains in vitro and in vivo nucleosome ordering in transcribed regions, and plays a leading role in establishing well-known 10-11 bp genome-wide periodicity of nucleosome positions.