Spatial Distribution of Competing Ions around DNA in Solution

The competition of monovalent and divalent cations for proximity to negatively charged DNA is of biological importance and can provide strong constraints for theoretical treatments of polyelectrolytes. Resonant x-ray scattering experiments have allowed us to monitor the number and distribution of each cation in a mixed ion cloud around DNA. These measurements provide experimental evidence to support a general theoretical prediction: the normalized distribution of each ion around polyelectrolytes remains constant when ions are mixed at different ratios. In addition, the amplitudes of the scattering signals throughout the competition provide a measurement of the surface concentration parameter that predicts the competition behavior of these cations. The data suggest that ion size needs to be taken into account in applying Poisson-Boltzmann treatments to polyelectrolytes such as DNA.

Figure 1

In part (a), the measured anomalous signal for monovalent rubidium ions in Rb-DNA is shown. The smooth, dashed curve is the best fit to the analytical theory described in the text. The inset shows a cartoon of the sample and indicates density variations of the counterions by shading. Part (b) shows measured and predicted curves for divalent ${\mathrm{S}\mathrm{r}}^{2+}$ ions in Sr-DNA. The inset illustrates the difference in the shape of the anomalous signals for monovalent ions (lower, blue curve) and divalent ions (upper, red curve). The tighter spatial localization of divalent ions is reflected by the higher intensity at larger scattering angle. In parts (c) and (d) anomalous signals for both types of ions are shown in two different bulk solutions. The curve amplitudes have been scaled to illustrate the shape similarity under different solution conditions. In (c), the darker (black) curve was acquired in a pure rubidium solution (0.1 M ${\mathrm{R}\mathrm{b}}^{+}$); the lighter (cyan) curve was acquired in 0.09 M ${\mathrm{R}\mathrm{b}}^{+}$ and 0.01 M ${\mathrm{S}\mathrm{r}}^{2+}$. In (d), the darker (black) curve was acquired in an all strontium solution (0.1 M ${\mathrm{S}\mathrm{r}}^{2+}$). The lighter (magenta) curve was acquired in 0.09 M ${\mathrm{R}\mathrm{b}}^{+}$, 0.01 M ${\mathrm{S}\mathrm{r}}^{2+}$.

Figure 2

The measured reduced surface concentrations of ${\mathrm{R}\mathrm{b}}^{+}$ (solid blue circles) and ${\mathrm{S}\mathrm{r}}^{2+}$ (solid red triangles) ions are shown as the bulk solution composition is varied. The solid lines represent the best fit of Eq. (3) to the data. The dashed lines represent the predictions of numerical calculations with finite ionic radius, i.e., the distance of closest approach of both types of ions to the DNA. A curve corresponding to a representative value of $2\AA$ is shown. Both approaches result in good agreement with the data. The inset shows that the sum of the reduced surface concentrations equals unity (solid line), within error.