A new Monte Carlo model for the structure of chromatin is presented here. Based on our previous work on superhelical DNA and polynucleosomes, it reintegrates aspects of the "solenoid" and the "zig-zag" models. The DNA is modeled as a flexible elastic polymer chain, consisting of segments connected by elastic bending, torsional, and stretching springs. The electrostatic interaction between the DNA segments is described by the Debye-Hückel approximation. Nucleosome core particles are represented by oblate ellipsoids; their interaction potential has been parameterized by a comparison with data from liquid crystals of nucleosome solutions. DNA and chromatosomes are linked either at the surface of the chromatosome or through a rigid nucleosome stem. Equilibrium ensembles of 100-nucleosome chains at physiological ionic strength were generated by a Metropolis-Monte Carlo algorithm. For a DNA linked at the nucleosome stem and a nucleosome repeat of 200 bp, the simulated fiber diameter of 32 nm and the mass density of 6.1 nucleosomes per 11 nm fiber length are in excellent agreement with experimental values from the literature. The experimental value of the inclination of DNA and nucleosomes to the fiber axis could also be reproduced. Whereas the linker DNA connects chromatosomes on opposite sides of the fiber, the overall packing of the nucleosomes leads to a helical aspect of the structure. The persistence length of the simulated fibers is 265 nm. For more random fibers where the tilt angles between two nucleosomes are chosen according to a Gaussian distribution along the fiber, the persistence length decreases to 30 nm with increasing width of the distribution, whereas the other observable parameters such as the mass density remain unchanged. Polynucleosomes with repeat lengths of 212 bp also form fibers with the expected experimental properties. Systems with larger repeat length form fibers, but the mass density is significantly lower than the measured value. The theoretical characteristics of a fiber with a repeat length of 192 bp where DNA and nucleosomes are connected at the core particle are in agreement with the experimental values. Systems without a stem and a repeat length of 217 bp do not form fibers.

Based on model structures with atomic resolution, a coarse-grained model for the nucleosome geometry was implemented. The dependence of the chromatin fiber conformation on the spatial orientation of nucleosomes and the path and length of the linker DNA was systematically explored by Monte Carlo simulations. Two fiber types were analyzed in detail that represent nucleosome chains without and with linker histones, respectively: two-start helices with crossed-linker DNA (CL conformation) and interdigitated one-start helices (ID conformation) with different nucleosome tilt angles. The CL conformation was derived from a tetranucleosome crystal structure that was extended into a fiber. At thermal equilibrium, the fiber shape persisted but relaxed into a structure with a somewhat lower linear mass density of 3.1 +/- 0.1 nucleosomes/11 nm fiber. Stable ID fibers required local nucleosome tilt angles between 40 degrees and 60 degrees. For these configurations, much higher mass densities of up to 7.9 +/- 0.2 nucleosomes/11 nm fiber were obtained. A model is proposed, in which the transition between a CL and ID fiber is mediated by relatively small changes of the local nucleosome geometry. These were found to be in very good agreement with changes induced by linker histone H1 binding as predicted from the high resolution model structures.

DNA-DNA interactions are important for the assembly of DNA nanostructures and during biological processes such as genome compaction and transcription regulation. In studies of these complex processes, DNA is commonly modeled as a homogeneously charged cylinder and its electrostatic interactions are calculated within the framework of the Poisson-Boltzmann equation. Commonly, a charge adaptation factor is used to address limitations of this theoretical approach. Despite considerable theoretical and experimental efforts, a rigorous quantitative assessment of this parameter is lacking. Here, we comprehensively characterized DNA-DNA interactions in the presence of monovalent ions by analyzing the supercoiling behavior of single DNA molecules held under constant tension. Both a theoretical model and coarse-grained simulations of this process revealed a surprisingly small effective DNA charge of 40% of the nominal charge density. These findings were directly supported by atomic-scale molecular dynamics simulations that determined the effective force between two DNA molecules. Our new parameterization has direct impact on many physical models involving DNA-DNA interactions.

No abstract