The trajectory of a stiff rod in a curved potential energy trough. An initial result for short nucleosomal rods

Analytical ultracentrifugation and the characterization of chromatin structure

This mini review consists of two parts. The first part will provide a brief overview of the theoretical aspects involved in the two kinds of experiments that can be conducted with the analytical ultracentrifuge (sedimentation velocity and sedimentation equilibrium) as they pertain to the study of chromatin. In the following sections, I describe the analytical ultracentrifuge experiments which, in my opinion, have contributed the most to our understanding of chromatin. Few other biophysical techniques, with the exception of X-ray scattering and diffraction, have contributed as extensively as the analytical ultracentrifuge to the characterization of so many different aspects of chromatin structure. In the course of his scientific career, Professor Henryk Eisenberg has made many important contributions to the theoretical aspects underlying ultracentrifuge analysis, especially in the analysis of solutions of polyelectrolytes and biological macromolecules [H. Eisenberg, Biological macromolecules and polyelectrolytes in solution, Clarendon Press, Oxford, 1976]. As an example he has devoted some of his research effort to the characterization of chromatin in solution. This review includes these important contributions.

The elastic resilience of DNA can induce all-or-none structural transitions in the nucleosome core particle

DNA on the surface of the histone octamer in the native nucleosome core particle is modeled as a circumferentially wound elastic line on the surface of a cylinder. In a model for the radial transition, the line is allowed to straighten, and thus lose energy, by swinging off the surface, but it is impeded in such an excursion by a radial force field representing the attractive interaction between DNA and histone octamer. In a model for the axial transition, the line may straighten by becoming more parallel to a generator of the cylinder while remaining on the surface. In this mode of straightening, dimer-tetramer or tetramer-tetramer interfaces are disrupted, and the resulting energy gain impedes the transition. Both radial and axial transitions are predicted to occur in all-or-none fashion. We propose that these models are related to the abrupt transitions actually observed in the nucleosome core particle.

An estimate of the extent of folding of nucleosomal DNA by laterally asymmetric neutralization of phosphate groups

We attempt quantitative implementation of a previous suggestion that asymmetric charge neutralization of DNA phosphate groups may provide part of the driving force for nucleosome folding. Polyelectrolyte theory can be used to estimate the effective compressive force acting along the length of one side of the DNA surface when a fraction of the phosphate groups are neutralized by histones bound to that side. A standard engineering formula then relates the force to the bending amplitude caused by it. Calculated bending amplitudes are consistent with the curvature of nucleosomal DNA and the overall extent of charge neutralization by the histones. The relation of the model to various aspects of nucleosome folding, including the detailed path of core-particle DNA, is discussed. Several other DNA-protein complexes are listed as examples of possible asymmetric charge-induced bending.