Mechanical model of the nucleosome and chromatin

A theoretical framework for evaluating the approximate energy and dynamic properties associated with the folding of DNA into nucleosomes and chromatin is presented. Experimentally determined elastic constants of linear DNA and a simple fold geometry are assumed in order to derive elastic constants for extended and condensed chromatin. The model predicts the Young's modulus of extended and condensed chromatin to within an order of magnitude of experimentally determined values. Thus we demonstrate that the elastic properties of DNA are a primary determinant of the elastic properties of the higher order folded states. The derived elastic constants are used to predict the speed of propagation of small amplitude waves that excite an extension(sound), twist, bend or shear motion in each folded state. Taken together the results demonstrate that folding creates a hierarchy of time, length and energy scales.