How charge fluctuations modulate complexation of DNA around a histone cylinder

It is an enigma that in a nucleosome complex, a single DNA winds around a histone protein core about 1.6-1.8 times. We find that the optimal winding can be given by the charge density fluctuations on the DNA contour due to multivalent counterions binding and unbinding in a physiological ionic background. From a model free energy of the DNA wound on the histone cylinder, where the charge fluctuations induce the intra-DNA attraction, we establish the conditions and a phase diagram for stability of the complex as a function of the salt and divalent cations concentrations.