dsDNA PACKAGING IN VIRUSES: STRUCTURE AND THERMODYNAMICS
It was long believed that dsDNA forms coaxial spools inside viral capsids, because such conformations would minimize the elastic bending energy. But electrostatic repulsions and thermal motions guarantee that DNA will not press up against the capid walls but will, instead, fill most of the available volume. We have shown that the final conformations contain considerable disorder, but that they have features that reflect the size and shape of the capsid, and the size and shape of that part of the protein portal that projects into the capsid's interior. Phi29, for example, has a slightly elongated capsid, and the portal is very small; this leads to the folded toroid structure (figure at left), a conformation first proposed by Nick Hud. Other phage genomes exhibit other conformations that include twisted toroids, coaxial spools, and concentric spools.
What are the components of the free energy cost of packaging ds-stranded DNA into the capsid?
The motors that load dsDNA into bacteriophage capsids are among the strongest of all biological motors, because packaging is opposed by a variety of large forces.
Our coarse-grain modeling approach allowed a direct determination of the free energy cost of packaging, and a decomposition of ΔG into its components. As expected, DNA-DNA electrostatic repulsions account for ~40-50% of the cost, but we were the first to show that the conformational entropy penalty is large, representing another 40-50% of the cost; the elastic deformations are ~10-20% of the total (publication).
What is the conformation of double-stranded DNA inside bacteriophage capsids?
An independent calculation of the entropic penalties for confining polymers into small spaces
We developed a Monte Carlo method for determining the entropic cost for the confinement of a semi-flexible polymer with persistence length P in the long-chain limit, where the length of the chain L >> P. In this limit, the confinement entropy ΔS is generally an extensive function (proportional to L), so we report the penalty per unit length, ΔS/P. We treated both ideal chains (zero diameter and no excluded volume effects) and chains with finite diameter. We examined three different confinement geometries: between parallel plates (a "slit", or one-dimensional confinement), a circular tube (two-dimensional confinement) and a sphere (three-dimensional confinement). We covered four orders of magnitude for the characteristic distance d of the confining volume.
We used a wormlike coil model for cases of modest to tight confinement (d/P < 10), and a freely-jointed (Gaussian) chain for cases involving modest to weak confinement (d/P ≥ 1). The two models agreed in the region of modest confinement (1 ≤ d/P ≤ 10), validating the model parameters.
The figure above shows the confinement penalties in the long-chain limit for ideal chains (D = 0, black) and one chain with nonzero diameter (D = 0.06P, red; this ratio of D/P corresponds to that of B-DNA). Results are shown for confinement between parallel plates separated by distance d (squares), a circular tube of diameter d (triangles), and a sphere of diameter d (circles). The red curves are dashed for values of d/P < 1 because the polymer diameter D becomes a significant fraction of the characteristic distance of the confining volume, d, in this region. The red arrows show that, when d = 0.1P, the entropic penalty for a chain of nonzero diameter D is the same as it would be for an ideal chain of in a space with d' = d-D = 0.04P. (There is no red curve for spherical confinement; when chains with nonzero diameter are confined to spheres, ΔS is not an extensive property of the polymer length L. In this case, the penalty can be determined using coarse-grained MD simulations, as described above.) . (publication).