Expression of chirality in columnar hexagonal phases or DNA and nucleosomes

It is surprising to see how eukaryotic chromosomes or sperm nuclei are highly condensed chromatin materials and how they can sometimes present spectacular helical morphologies. We may suspect that these helical shapes originate from the chiral properties of DNA and other components of chromatin. Dense solutions of DNA and nucleosomes can be prepared in vitro to reproduce some of the characteristics of chromatin. They form multiple ordered phases, either mesophases or 3D crystals, that can be useful to analyze precisely how chiral structures can emerge, or not, from interactions between these constitutive elements. We address the question of the competition between twist and hexagonal packing in dense states of DNA, nucleosomes, chromatin and chromosomes. From the microscopic analysis of many examples, we show how the twist arising from the chirality of the objects can be diluted in the phase and/or expelled along twist walls. These walls are either parallel or normal to the direction of the columns. In the first case, we determine that the twist axis lies parallel to one θ2 direction of the hexagonal network. Helical shapes of chromosomes and bundles of DNA and chromatin may also be consequences of this competition, as illustrated here.