Potential Function Describing the Folding of the 30 nm Fiber

Genome Dashboards: Framework and Examples

Genomics is a sequence-based informatics science and a three-dimensional-structure-based material science. However, in practice, most genomics researchers utilize sequence-based informatics approaches or three-dimensional-structure-based material science techniques, not both. This division is, at least in part, the result of historical developments rather than a fundamental necessity. The underlying computational tools, experimental techniques, and theoretical models were developed independently. The primary result presented here is a framework for the unification of informatics- and physics-based data associated with DNA, nucleosomes, and chromatin. The framework is based on the mathematical representation of geometrically exact rods and the generalization of DNA basepair step parameters. Data unification enables researchers to integrate computational, experimental, and theoretical approaches for the study of chromatin biology. The framework can be implemented using model-view-controller design principles, existing genome browsers, and existing molecular visualization tools. We developed a minimal, web-based genome dashboard, G-Dash-min, and applied it to two simple examples to demonstrate the usefulness of data unification and proof of concept. Genome dashboards developed using the framework and design principles presented here are extensible and customizable and are therefore more broadly applicable than the examples presented. We expect a number of purpose-specific genome dashboards to emerge as a novel means of investigating structure-function relationships for genomes that range from basepairs to entire chromosomes and for generating, validating, and testing mechanistic hypotheses.

Molecular Dynamics Simulations of a Nucleosome and Free DNA

All atom molecular dynamics simulations (10ns) of a nucleosome and of its 146 basepairs of DNA free in solution have been conducted. DNA helical parameters (Roll, Tilt, Twist, Shift, Slide, Rise) were extracted from each trajectory to compare the conformation, effective force constants, persistence length measures, and fluctuations of nucleosomal DNA to free DNA. The conformation of DNA in the nucleosome, as determined by helical parameters, is found to be largely within the range of thermally accessible values obtained for free DNA. DNA is found to be less flexible on the nucleosome than when free in solution, however such measures are length scale dependent. A method for disassembling and reconstructing the conformation and dynamics of the nucleosome using Fourier analysis is presented. Long length variations in the conformation of nucleosomal DNA are identified other than those associated with helix repeat. These variations are required to create a proposed tetrasome conformation or to qualitatively reconstruct the 1.75 turns of the nucleosome's superhelix. Reconstruction of free DNA using selected long wavelength variations in conformation can produce either a left-handed or a right-handed superhelix. The long wavelength variations suggest 146 basepairs is a natural length of DNA to wrap around the histone core.

Exploring the conformational space of chromatin fibers and their stability by numerical dynamic phase diagrams

The three-dimensional structure of chromatin affects DNA accessibility and is therefore a key regulator of gene expression. However, the path of the DNA between consecutive nucleosomes, and the resulting chromatin fiber organization remain controversial. The conformational space available for the folding of the nucleosome chain has been analytically described by phase diagrams with a two-angle model, which describes the chain trajectory by a DNA entry-exit angle at the nucleosome and a torsion angle between consecutive nucleosomes. Here, a novel type of numerical phase diagrams is introduced that relates the geometric phase space to the energy associated with a given chromatin conformation. The resulting phase diagrams revealed differences in the energy landscape that reflect the probability of a given conformation to form in thermal equilibrium. Furthermore, we investigated the effects of entropy and additional degrees of freedom in the dynamic phase diagrams by performing Monte Carlo simulations of the initial chain trajectories. Using our approach, we were able to demonstrate that conformations that initially were geometrically impossible could evolve into energetically favorable states in thermal equilibrium due to DNA bending and torsion. In addition, dynamic phase diagrams were applied to identify chromatin fibers that reflect certain experimentally determined features.

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.