Salt-Dependent DNA-DNA Spacings in Intact BacteriophageλReflect Relative Importance of DNA Self-Repulsion and Bending Energies

Using solution synchrotron x-ray scattering, we measure the variation of DNA-DNA $d$ spacings in bacteriophage $\ensuremath{\lambda}$ with mono-, di-, and polyvalent salt concentrations, for wild-type [$48.5\ifmmode\times\else\texttimes\fi{}{10}^{3}$ base pairs (bp)] and short-genome-mutant (37.8 kbp) strains. From the decrease in $d$ spacings with increasing salt, we deduce the relative contributions of DNA self-repulsion and bending to the energetics of packaged phage genomes. We quantify the DNA-DNA interaction energies within the intact phage by combining the measured $d$ spacings in the capsid with measurements of osmotic pressure in DNA assemblies under the same salt conditions in bulk solution. In the commonly used Tris-Mg buffer, the DNA-DNA interaction energies inside the phage capsids are shown to be about $1kT/\mathrm{bp}$, an order of magnitude larger than the bending energies.