Measuring Inter-DNA Potentials in Solution

Interactions between short strands of DNA can be tuned from repulsive to attractive by varying solution conditions and have been quantified using small angle x-ray scattering techniques. The effective DNA interaction charge was extracted by fitting the scattering profiles with the generalized one-component method and inter-DNA Yukawa pair potentials. A significant charge is measured at low to moderate monovalent counterion concentrations, resulting in strong inter-DNA repulsion. The charge and repulsion diminish rapidly upon the addition of divalent counterions. An intriguing short range attraction is observed at surprisingly low divalent cation concentrations, $\sim 16\mathrm{mM}$ ${\mathrm{Mg}}^{2+}$. Quantitative measurements of inter-DNA potentials are essential for improving models of fundamental interactions in biological systems.

Figure 1

The experimental $I(Q)$ of 0.05 mM DNA (□) is compared with the calculated $I(Q)$ from DNA atoms only (dashed line) and the $I(Q)$ including solvent effects (see text) (solid line). Note that $I(Q)=NP(Q)$ in the absence of inter-DNA interference [$S(Q)=1$] under such dilute conditions. The curves are matched between $Q$ values of 0.1 and $0.25{\AA }^{-1}$. The inset shows a model consisting of DNA, distributed ${\mathrm{Na}}^{+}$ counterions, and dummy HS atoms.

Figure 2

Experimental $I(Q)$s are indicated with symbols; fits are shown as lines. The data are offset for clarity. (a) data with no excess salt. (b),(c), and (d) data at fixed DNA concentrations (around 0.60 mM) as counterion concentration and valence are varied as indicated.

Figure 3

(a) and (b) show the experimental effective charge $Z_{\mathrm{eff}}$ (symbols) and the theoretical renormalized charge $Z_{\mathrm{ren}}$ (lines) with scaling factors denoted below. Only the results from the one Yukawa repulsive potential refinements are shown. (c) The fitted inter-DNA potentials are shown as functions of inter-DNA distance. (d) The model $S(Q)$s corresponding to the inter-DNA potentials in (c).