  We investigate the mechanical stability of a segment of DNA wrapped around a
histone in the nucleosome configuration. The assumption underlying this
investigation is that the proper model for this packaging arrangement is that
of an elastic rod that is free to twist and that writhes subject to mechanical
constraints. We find that the number of constraints required to stabilize the
nuclesome configuration is determined by the length of the segment, the number
of times the DNA wraps around the histone spool, and the specific constraints
utilized. While it can be shown that four constraints suffice, in principle, to
insure stability of the nucleosome, a proper choice must be made to guarantee
the effectiveness of this minimal number. The optimal choice of constraints
appears to bear a relation to the existence of a spiral ridge on the surface of
the histone octamer. The particular configuration that we investigate is
related to the 30 nanometer spiral, a higher-order organization of DNA in
chromatin.
