Quantitative and comprehensive decomposition of the ion atmosphere around nucleic acids

Abstract

The ion atmosphere around nucleic acids critically affects biological and physical processes such as chromosome packing, RNA folding, and molecular recognition. However, the dynamic nature of the ion atmosphere renders it difficult to characterize. The basic thermodynamic description of this atmosphere, a full accounting of the type and number of associated ions, has remained elusive. Here we provide the first complete accounting of the ion atmosphere, using buffer equilibration and atomic emission spectroscopy (BE-AES) to accurately quantitate the cation association and anion depletion. We have examined the influence of ion size and charge on ion occupancy around simple, well-defined DNA molecules. The relative affinity of monovalent and divalent cations correlates inversely with their size. Divalent cations associate preferentially over monovalent cations; e.g., with Na+ in 4-fold excess of Mg2+ (20 vs 5 mM), the ion atmosphere nevertheless has 3-fold more Mg2+ than Na+. Further, the dicationic polyamine putrescine2+ does not compete effectively for association relative to divalent metal ions, presumably because of its lower charge density. These and other BE-AES results can be used to evaluate and guide the improvement of electrostatic treatments. As a first step, we compare the BE-AES results to predictions from the widely used nonlinear Poisson Boltzmann (NLPB) theory and assess the applicability and precision of this theory. In the future, BE-AES in conjunction with improved theoretical models, can be applied to complex binding and folding equilibria of nucleic acids and their complexes, to parse the electrostatic contribution from the overall thermodynamics of important biological processes.

Figure 1

The ion atmosphere around nucleic acids. The formation of a condensed layer of counterions around the DNA (A) is driven by and in return modulates the negative electrostatic potential surrounding the DNA (φ, B). In the PB model, the ion distribution, shown as a radial density function (ρ_ion(r), C), is determined by the potential (φ) at an indicated location via Boltzmann weighting.

Figure 2

Scheme of the buffer equilibration-atomic emission spectroscopy (BE-AES) approach.

Figure 3

Neutralization of 24L (−46 charges) by Na⁺ association (○) and anion depletion (▽). The associated Na⁺ ions plus the excluded anions gives the total charge of the ion atmosphere (□, solid line shows +46). Data are compared to the NLPB prediction for monovalent cations and anions (dashed lines).

Figure 4

The competitive association of monovalent cations (▵ for Li⁺, K⁺ or Rb⁺; NH₄+ and TMA⁺ are not detectable herein) against 50 mM Na⁺ (○) for 24L, compared with NLPB predictions (dashed lines). Data are fit with Eq. 2 (solid curved lines). The total charge of the ion atmosphere (□) is plotted as in Fig. 3.

Figure 5

The competitive association of divalent cations (▵ for Ca²⁺, Sr²⁺ or Ba²⁺; putrescine²⁺ is not detectable by AES) against 2 mM Mg²⁺ (○) for 24L. Data are fit to Eq. 2 (solid curved lines) and compared to the NLPB predictions (dashed and dotted lines). A small amount of Na⁺ from the buffer (5 mM for concentrations of competing divalent ions ≤ 2 mM; 10 mM otherwise) is present in the ion atmosphere (dotted points). The total charge of the ion atmosphere (□) is plotted as in Fig. 3.

Figure 6

The competitiveness of monovalent (A) and divalent (B) cations inversely correlate with ion size. The competition constants are obtained from data in Figs.4 & 5 by Eq. 2. The radii of the hydrated ions are approximated by the distance from the ion to the water oxygen atom in the first hydration shell ^, plus 1.4 Å for the water layer. The radius of putrescine²⁺ is crudely estimated as half of the average separation between N atoms (the closest: 3.3 Å, the furthest: 5.5 Å) plus the radius of an amine (1.65 Å) and a water layer (1.4 Å).

Figure 7

The competitive association between Na⁺ and Mg²⁺ with 24L. A: Na⁺ (○) was titrated into 5 mM Mg²⁺ background (▵). B: Mg²⁺ (▵) was titrated into 20 mM Na⁺ (○). Data are fit with Eq. 2 (solid curved lines) and compared to NLPB predictions (dashed lines). The total charge of the ion atmosphere (□) is plotted as in Fig. 3.

Figure 8

The competitive association of Na⁺ and Mg²⁺ with the 24 bp DNA triplex (T24L). A: Na⁺ (○) competes with 5 mM Mg²⁺ background (▵). B: Mg²⁺ (▵) competes with 20 mM Na⁺ background (○). Data are fitted with Eq. 2 (solid curved lines) and compared to NLPB predictions (dashed lines). Anions were not detected because neutral species of cacodylate (pK_a 6.3) present in the acidic solution (pH 5.1).