Geometrical, Conformational, and Topological Restraints in Nucleosome Compaction along Chromatin Fibers

Compaction of nucleosomes in chromatin is directed by their positioning along DNA. The statistical analysis of the nucleosome repeat length in chromatin fibers reveals the presence of a ten-fold periodicity suggesting the existence of orientation constraints of the nucleosome units that provide the geometrical conditions of helical conformations. We investigated the architectures of the chromatin fiber by integrating the experimental results with geometrical, conformational and topological restraints, under the hypothesis of the minimum distortion of the nucleosome and linker DNA structures. The periodical repeats of nucleosomes can be investigated assuming the principle of conformational equivalence of the repeating units. The problem of selecting the compact architectures of the chromatin fiber for different linker lengths can be factorized in one in which only orientational parameters are taken into account and the other in which the lengths of DNA linkers are considered. The best packing of nucleosomes requires the uniformity of orientational parameters and “quasi-conformational equivalence” of the repeating units, even though linker lengths are not strictly equal. We showed that the path of the linkers in compact nucleosome packing is severely constrained by steric hindrances and topological conditions and that the excluded volume at linker crossing and the torsional energy limit the possible close packing of the nucleosomes in the chromatin fiber. In particular, the torsional energy of the chromatin fiber appears crucial in determining the kind of nucleosome packing for short nucleosome repeat lengths as in telomeres and yeast chromatin.