Crystalline toroidal globules of DNA and other semi-flexible polymers: Jumps in radius caused by hexagonal packing

We study a single semiflexible polymer chain immersed in a poor solvent. Such chains are stiff and are known to form toroidal globules. Here we examine the effects of hexagonally ordered packing of the chains. This packing induces a series of sharp transitions in the circuit number (number of complete circuits of the toroid) and major radius of the torus as a function of chain length. Circuit numbers corresponding to closed shells are strongly favoured and circuit numbers corresponding to a spare loop are forbidden. The potential landscape as a function of the circuit number consists of a series of minima separated by barriers. In some cases these barriers may be high enough to produce long-lived non-equilibrium tori.