Specific details concerning the spatial organization of nucleosomes in 30 nm fibers remain unknown. To investigate this, we analyzed all stereochemically possible configurations of two-start nucleosome fibers with short DNA linkers L = 13-37 bp (nucleosome repeat length (NRL) = 160-184 bp). Four superhelical parameters-inclination of nucleosomes, twist, rise, and diameter-uniquely describe a regular symmetric fiber. The energy of a fiber is defined as the sum of four terms: elastic energy of the linker DNA, steric repulsion, electrostatics, and a phenomenological (H4 tail-acidic patch) interaction between two stacked nucleosomes. By optimizing the fiber energy with respect to the superhelical parameters, we found two types of topological transition in fibers (associated with the change in inclination angle): one caused by an abrupt 360° change in the linker DNA twisting (change in the DNA linking number, ΔLk = 1), and another caused by overcrossing of the linkers (ΔLk = 2). To the best of our knowledge, this topological polymorphism of the two-start fibers was not reported in the computations published earlier. Importantly, the optimal configurations of the fibers with linkers L = 10n and 10n + 5 bp are characterized by different values of the DNA linking number-that is, they are topologically different. Our results are consistent with experimental observations, such as the inclination 60° to 70° (the angle between the nucleosomal disks and the fiber axis), helical rise, diameter, and left-handedness of the fibers. In addition, we make several testable predictions, among them different degrees of DNA supercoiling in fibers with L = 10n and 10n + 5 bp, different flexibility of the two types of fibers, and a correlation between the local NRL and the level of transcription in different parts of the yeast genome.

During interphase the eukaryotic genome is organized into chromosome territories that are spatially segregated into compartment domains. The extent to which interacting domains or chromosomes are entangled is not known. We analyze series of co-occurring chromatin interactions using multi-contact 3C (MC-3C) in human cells to provide insights into the topological entanglement of chromatin. Multi-contact interactions represent percolation paths (C-walks) through 3D chromatin space. We find that the order of interactions within C-walks that occur across interfaces where chromosomes or compartment domains interact is not random. Polymer simulations show that such C-walks are consistent with distal domains being topologically insulated, i.e. not catenated. Simulations show that even low levels of random strand passage, e.g. by topoisomerase II, would result in entanglements, increased mixing at domain interfaces and an order of interactions within C-walks not consistent with experimental MC-3C data. Our results indicate that during interphase entanglements between chromosomes and chromosomal domains are rare.

It has long been suggested that chromatin may form a fiber with a diameter of ~30 nm that suppresses transcription. Despite nearly four decades of study, the structural nature of the 30-nm chromatin fiber and conclusive evidence of its existence in vivo remain elusive. The key support for the existence of specific 30-nm chromatin fiber structures is based on the determination of the structures of reconstituted nucleosome arrays using X-ray crystallography and single-particle cryo-electron microscopy coupled with glutaraldehyde chemical cross-linking. Here we report the characterization of these nucleosome arrays in solution using analytical ultracentrifugation, NMR, and small-angle X-ray scattering. We found that the physical properties of these nucleosome arrays in solution are not consistent with formation of just a few discrete structures of nucleosome arrays. In addition, we obtained a crystal of the nucleosome in complex with the globular domain of linker histone H5 that shows a new form of nucleosome packing and suggests a plausible alternative compact conformation for nucleosome arrays. Taken together, our results challenge the key evidence for the existence of a limited number of structures of reconstituted nucleosome arrays in solution by revealing that the reconstituted nucleosome arrays are actually best described as an ensemble of various conformations with a zigzagged arrangement of nucleosomes. Our finding has implications for understanding the structure and function of chromatin in vivo.