Thermodynamics of nucleosome breathing and positioning

Nucleosomes are fundamental units of chromatin in which a length of genomic DNA is wrapped around a histone octamer spool in a left-handed superhelix. Large-scale nucleosome maps show a wide distribution of DNA wrapping lengths, which in some cases are tens of base pairs (bp) shorter than the 147 bp canonical wrapping length observed in nucleosome crystal structures. Here, we develop a thermodynamic model that assumes a constant free energy cost of unwrapping a nucleosomal bp. Our model also incorporates linker DNA-short DNA segments between neighboring nucleosomes imposed by the folding of nucleosome arrays into chromatin fibers and other higher-order chromatin structures. We use this model to study nucleosome positioning and occupancy in the presence of nucleosome "breathing"-partial unwrapping and rewrapping of nucleosomal DNA due to interactions with the neighboring particles. We find that, as the unwrapping cost per bp and the chemical potential are varied, the nucleosome arrays are characterized by three distinct states, with low, intermediate, and high densities. The transition between the latter two states proceeds through an equiprobable state in which all nucleosome wrapping lengths are equally likely. We study the equiprobable state theoretically using a mean-field approach, obtaining an excellent agreement with numerical simulations. Finally, we use our model to reproduce S. cerevisiae nucleosome occupancy profiles observed in the vicinity of transcription start sites, as well as genome-wide distributions of nucleosome wrapping lengths. Overall, our results highlight the key role of partial nucleosome unwrapping in shaping the genome-wide patterns of nucleosome positioning and occupancy.