Authors: Tine Curk, James Daniel Farrell, Jure Dobnikar, and Rudolf Podgornik.

Viruses are amongst the simplest biological systems, and as such they have attracted the attention of experimental and theoretical physicists for over half a century now. A fundamental structural unit of a virus is a protein shell - the capsid - that surrounds and protects the genome, which can be either RNA or DNA, single- or double stranded, and is in a number of cases known to Angstrom-level precision, determined by x-ray diffraction and cryo-electron microscopy. In many cases the capsids exhibit spherical shape and a local hexagonal crystal-like order, compatible with the global icosahedral organization, and in some cases this capsid symmetry is reflected also in the structure of the packaged genome, which is the second fundamental structural unit of a virus. Contrary to dense DNA solutions in the bulk, no atomistic simulations of DNA packaging in viral capsids are available. Detailed coarse grained simulations of the DNA packing inside the capsid are mostly performed by feeding the chain into the capsid cavity and therefore possibly exhibit strong non-equilibrium trapping into one of energetically vicinal entrapments.

To avoid non-equilibrium external driving effects and to uniquely specify the equilibrium configuration of a confined semiflexible polymer chain in the context not exclusively related to viral DNA encapsidation, we therefore modifyied the original question, focusing on the nature of the optimal equilibrium ground-state packing configuration of a confined quasi-one-dimensional object in a spherical enclosure at strictly equilibrium conditions.

Fig.1 Morphologies for short and long chains. 

Using analytical calculations and computer simulations of a long elastic filament confined to a spherical container, we showed that the ground state is not a single spool as assumed hitherto, but an ordering mosaic of multiple homogeneously ordered domains. At low densities, we observe concentric spools, while at higher densities, other morphologies emerge, which resemble topological links, see Fig. 1 for short and long chains (number of particles). We discussed our results in the context of metallic wires, viral DNA, and flexible polymers. According to our results, at low temperatures, spherical confinement is sufficient to order the majority of the filament into tight spools. We predict a variety of multidomain morphologies such as nested spools and links of two or three components competing in the low temperature regime. Their energetic ordering may be sensitive to the interplay between elastic and repulsive forces and other microscopic details of the system. Our low-temperature results can be compared with previous experiments and simulations of packing metallic wires into spheres, where ringlike coiling was observed, reminiscent of our nested spools.

Article Link: Phys. Rev. Lett. 123, 047801