Conformation of single-stranded RNA in a virus capsid: implications of dimensional reduction

The statistical mechanics of a treelike polymer in a confining volume is relevant to the packaging of the genome in RNA viruses. Making use of the mapping of the grand partition function of this system onto the statistical mechanics of a hard-core gas in two fewer spatial dimensions and of techniques developed for the evaluation of the equilibrium properties of a one-dimensional hard rod gas, we show how it is possible to determine the density and other key properties of a collection of rooted excluded-volume tress confined between two walls, both in the absence and in the presence of a onedimensional external potential. We find, somewhat surprisingly, that in the case of key quantities, the statistical mechanics of the excluded volume, randomly branched polymer map exactly into corresponding problems for an unrestricted linear polymer.