  In the nuclei of eukaryotic cells, DNA is packaged through several levels of
compaction in an orderly retrievable way that enables the correct regulation of
gene expression. The functional dynamics of this assembly involves the
unwinding of the so-called 30 nm chromatin fiber and accordingly imposes strong
topological constraints. We present a general method for computing both the
twist and the writhe of any winding pattern. An explicit derivation is
implemented for the chromatin fiber which provides the linking number of DNA in
eukaryotic chromosomes. We show that there exists one and only one unwinding
path which satisfies both topological and mechanical constraints that DNA has
to deal with during condensation/decondensation processes.
