Packaged DNA. An elastic model.

We review and deepen a theory of elastic bending of DNA on a persistence length scale. In a regime of extensive charge neutralization the axis of the double helix is elastically unstable when straight. Its stable bent conformation allows nucleation of DNA toruses and in principle could direct the supercoiled (solenoid) form of a polynucleosome. The Euler theory of elastic instability of macroscopic rods gives a partial description of the intrinsic ability of DNA to form locally stable bends. A different, quasi-Eulerian theory can be based on what is probably the dominant bending mechanism of DNA in solution-flexible kinking at the sites of open base pairs. This predictive theory is in quantitative agreement with the observed value (about 16 nm) for the minimum radius of torus holes. Stability of the inner torus ring is achieved when DNA phosphate groups are about 90% neutralized by trivalent cations, another prediction that is consistent with the observed formation of toruses in these conditions. The predicted stable radius of curvature of charge-neutralized DNA is also equal to the radial dimension of a maximally contracted polynucleosome supercoil as measured by neutron scattering (17 nm), but further experimental investigation of the geometrical disposition of the spacer DNA regions in the solenoid will be necessary to rule out the possibility of accidental agreement for this complex system. We stress again the experimental reality and probable importance of open base pairs in the equilibrium solution conformation of DNA.