Helical packaging of semiflexible polymers in bacteriophages

We investigate multilayered helical packaging of double-stranded DNA, or of a general polymer chain with persistence length lb, into an ideal, inert cylindrical container, reaching densities slightly below close packaging. We calculate the free energy as a function of the packaged length, based on the energies for bending, twisting, the suffered entropy loss, and the electrostatic energy in a Debye–Hückel model. In the absence of charges on the packaged polymer, a critical packaging force can be determined, similar to the mechanism involved in DNA unzipping models. When charges are taken into consideration, in the final packaging state the charges which are chemically distant become geometrically close, and therefore a steep rise is seen in the free energy. We argue that due to the extremely ordered and almost closely packaged final state the actual packaging geometry does not influence the behaviour of the free energy, pointing towards a certain universality of this state of the polymer. Our findings are compared to a recent simulations study, showing that the model is sensitive to the screening length.