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Chromatin is a key assembly in eucariotic cell nuclei. Despite the efforts to elucidate chromatin fiber structure, the detail of its organization remains still unknown. Historically, there are two principal classes of competing models of the 30-nm fiber: the solenoid models and the two-start helix models, though a whole series of indications of complex multi-start helix organization appeared quite recently. At the present it is impossible to resolve experimentally which model describes better the fiber structure under physiological conditions. However, certain observable features in the fiber organization are generally accepted, namely: (1) the nucleosomes are peripherally situated in the fiber and at low ionic strength form a zig-zag chain, (2) DNA linker is situated in the interior of the fiber, and (3) nucleosome-nucleosome interactions play an active role in condensation-decondensation processes. Theoretical analysis helps to elucidate which geometries are most plausibles for the fiber structure. One of the new ways to approach the problem is to consider the fiber as an ordered structure resulting from the balance of thermal disorder and electrostatic (and mechanical) interactions of its constituants. To achive this, it is necessary to identify robust parameters of the DNA-protein assembly at the smaller scale and to show how they control the fiber structure ordering at the bigger scale. Here, we propose a model based on the interactions between nucleosomes. The type of interaction proposed has allowed us previously to describe with success the condensed phases in acqueous solutions of nucleosomes with digested linker DNA, both in physiological conditions and in a wide range of monovalent salt concentration [1]. Taking into account the polar and chiral nature of nucleosomes, we perform detailed group theory analysis to construct the free energy of the native fiber and to reveal the thermodynamically favorable helical fiber structures. The effects of homogeneous mechanical torsion applied over the fiber (in biochemical experiments, rather than in single molecule ones) are also studied. We show that even in the case of very low load the helix unwinding is a multistep process and we give its geometrical and thermodynamical details. Such a scenario, known in biology since many years, had no simple explanation in previous theoretical works. 1. Lorman V., Podgornik R., Žekš B., Europhys. Lett., 69, 1017 (2005)