(64e) Wrapping Transitions in a Single Nucleosome under Tension

All of the processes necessary for the survival of a eukaryotic cell hinge on the cell's ability to store and read the genetic information encoded in its DNA. The daunting task of packaging its long DNA into a micron-sized nucleus is complicated by the necessity of maintaining the accessibility of the DNA to the cell's enzymatic machinery. The fundamental unit of packaged DNA, the nucleosome core particle, contains 146 base pairs of DNA wrapped 1.7 times around a cationic protein complex called the histone octamer. A string of nucleosomes is organized into higher-order structures at several hierarchical levels to form chromatin, a remarkable complex that is compact yet maintains accessibility for gene expression.

We develop a theoretical model of the nucleosome core particle in order to extract detailed quantitative information from single-molecule measurements of a single nucleosome under tension. We employ the wormlike chain model to describe the DNA strand as a thermally fluctuating polymer chain; the chain adsorbs on a helical spool that represents the histone octamer. The free energy of binding the polymer chain to the spool incorporates a site-dependent interaction strength, representing the specific binding sites on the histone-octamer surface. Despite the detailed nature of the model, we maintain an exact analytical formalism, which greatly simplifies comparison of our model with experimental data. We explore the role that thermal fluctuations play in wrapping transitions for a spool under tension. Our theory gives the physical justification for the experimentally observed hopping phenomenon associated with wrapping transitions and predicts the conditions where hopping occurs. We then test two models for the binding free energy against experimental results for a single nucleosome under tension. The first model is a constant binding affinity, i.e. a constant DNA-DNA interaction parameter; the second model for DNA binding is a structurally inspired interaction model with site-dependent binding free energies. We find that the model with site-dependent binding results in a patch of high affinity that captures the experimentally observed distance between hopping states, whereas constant binding affinity deviates from the observed experimental trend.