Thermodynamics of DNA packaging inside a viral capsid: the role of DNA intrinsic thickness

Abstract

We characterize the equilibrium thermodynamics of a thick polymer confined in a spherical region of space. This is used to gain insight into the DNA packaging process. The experimental reference system for the present study is the recent characterization of the loading process of the genome inside the $ϕ$29 bacteriophage capsid. Our emphasis is on the modelling of double-stranded DNA as a flexible thick polymer (tube) instead of a beads-and-springs chain. By using finite-size scaling to extrapolate our results to genome lengths appropriate for $ϕ$29, we find that the thickness-induced force may account for up to half the one measured experimentally at high packing densities. An analogous agreement is found for the total work that has to be spent in the packaging process. Remarkably, such agreement can be obtained in the absence of any tunable parameters and is a mere consequence of the DNA thickness. Furthermore, we provide a quantitative estimate of how the persistence length of a polymer depends on its thickness. The expression accounts for the significant difference in the persistence lengths of single- and double-stranded DNA (again with the sole input of their respective sections and natural nucleotide/base-pair spacing).