Radial Distribution of RNA Genomes Packaged inside Spherical Viruses

The problem of RNA genomes packaged inside spherical viruses is studied. The RNA-capsid attraction is assumed to be nonspecific and occurs at the inner capsid surface only. For weak attraction, RNA concentration is maximum at the center of the capsid to maximize their configurational entropy. For stronger attraction, RNA concentration peaks near the capsid surface. In the latter case, the competition between the branching of RNA secondary structure and its adsorption to the inner capsid results in the formation of a dense layer of RNA near capsid surface. The layer thickness is a slowly varying (logarithmic) function of the capsid inner radius. Consequently, the amount of RNA packaged is proportional to the capsid area (or the number of proteins) instead of its volume. The numerical profiles describe reasonably well the observed RNA concentration profiles of various viruses.

Figure 1

Two different profiles for RNA monomer concentration inside spherical viruses. Points are experimental data and solid lines are theoretical fit. (a) Profile II, Eq. (9), fitted to RNA concentration of Dengue virus obtained from cryoelectron microscopy experiment [16]. (b) Profile III, Eq. (11), fitted to RNA concentration of Bacteriophage ${\mathrm{MS}}_2$ obtained from small angle neutron scattering experiment [17].

Figure 2

Schematic representation of the secondary structure of a single-stranded RNA molecule as a collection of linear sections, branch points, and end points. The molecule can freely fluctuate between different branching configurations.