Salt-Dependent DNA-DNA Spacings in Intact Bacteriophage $\lambda$ Reflect 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 $\lambda$ with mono-, di-, and polyvalent salt concentrations, for wild-type [$48.5\times {10}^3$ 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.

Figure 1

(a) Raw SAXS 2D image of the wild-type $\lambda$ phage (48.5 kbp genomic DNA length) in the TM buffer. (b) Radially integrated scattering intensity $I(Q)$ where $Q=\frac{4\pi }{\lambda }\sin \theta$, $2\theta$ is the scattering angle, and $\lambda$ here is the x-ray wavelength. The blue and green $I(Q)$ curves are the raw profiles from the wild-type $\lambda$ phage solution and from the buffer. The red (“$\lambda$ phage”) and aqua (empty “capsid”) curves have the buffer $I(Q)$ subtracted. Note that the scattering from phage is an order of magnitude smaller than the background at high $Q$.

Figure 2

(a) The DNA-DNA diffraction peaks from the $\lambda$ $cI60$ and $b221$ strains with DNA lengths of 100% and 78% of the wild-type, respectively. Solid lines are the fits to the peak using a Lorentz function with a linear background. (b) DNA-DNA $d$ spacing as a function of added multivalent cation concentration for $\lambda$ $cI60$ phage; the background buffer is TM buffer for all three series. There is no [${\mathrm{Na}}^{+}$] series because the $cI60$ phage did not survive the dialysis against 50 $\mathrm{m}M$ Tris only, probably due to the elevated DNA pressure breaking the capsid. (c) DNA-DNA $d$ spacing as a function of added mono- and divalent cation concentration for $\lambda$ $b221$ phage; the background buffer is 50 $\mathrm{m}M$ $p\mathrm{H}$ 7.5 Tris only. The dotted line indicates the $d$ spacing with no added salt (i.e., 50 $\mathrm{m}M$ Tris only). (d) DNA-DNA $d$ spacing as a function of added tri- and tetravalent cation concentration for $\lambda$ $b221$ phage; the background buffer is TM buffer. The dotted line indicates the $d$ spacing with no added salt (i.e., TM buffer only). The $Y$ axis range in panels (b), (c), & (d) is set to 2 Å for easy comparison.

Figure 3

(a) Measured DNA-DNA pressure vs $d$ spacing curves for bulk DNA solutions in the TM buffer, without and with 2 $\mathrm{m}M$ ${\mathrm{Co}}^{3+}$. The arrow indicates the $d$ spacing under zero osmotic pressure. (b) Interaction energy per unit length, vs $d$ spacing, obtained by integration of pressures from (a). (c) and (d) Total interaction energies of DNA inside phage capsids, for two DNA lengths, determined from results like those in (b). Background buffer is 50 $\mathrm{m}M$ Tris $p\mathrm{H}$ 7.5 for (c), and TM buffer for (d). The energies for zero [${\mathrm{Mg}}^{2+}$] and for zero [${\mathrm{Co}}^{3+}$], determined experimentally, are indicated by dotted horizontal lines in (c) and (d), respectively. Note again that there is no “zero [${\mathrm{Mg}}^{2+}$]” point for the 100% DNA strain ($cI60$).