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

TL;DR

This paper explores the statistical mechanics of single-stranded RNA within virus capsids, revealing a surprising equivalence between branched and linear polymers through dimensional reduction techniques.

Contribution

It introduces a novel mapping of the statistical mechanics of treelike polymers onto lower-dimensional systems, enabling exact analysis of RNA conformation in confined environments.

Findings

Exact mapping of treelike polymer statistics to linear polymer problems.

Key properties of branched polymers match those of linear polymers in certain conditions.

Dimensional reduction simplifies the analysis of RNA packing in virus capsids.

Abstract

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 one-dimensional 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.