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RNA folding is enabled by interactions between the nucleic acid and its ion atmosphere, the mobile sheath of aqueous ions that surrounds and stabilizes it. Understanding the ion atmosphere requires the interplay of experiment and theory. However, even an apparently simple experiment to probe the ion atmosphere, measuring the dependence of DNA duplex stability upon ion concentration and identity, suffers from substantial complexity, because the unfolded ensemble contains many conformational states that are difficult to treat accurately with theory. To minimize this limitation, we measured the unfolding equilibrium of a DNA hairpin using a single-molecule optical trapping assay, in which the unfolded state is constrained to a limited set of elongated conformations. The unfolding free energy increased linearly with the logarithm of monovalent cation concentration for several cations, such that smaller cations tended to favor the folded state. Mg(2+) stabilized the hairpin much more effectively at low concentrations than did any of the monovalent cations. Poisson-Boltzmann theory captured trends in hairpin stability measured for the monovalent cation titrations with reasonable accuracy, but failed to do so for the Mg(2+) titrations. This finding is consistent with previous work, suggesting that Poisson-Boltzmann and other mean-field theories fail for higher valency cations where ion-ion correlation effects may become significant. The high-resolution data herein, because of the straightforward nature of both the folded and the unfolded states, should serve as benchmarks for the development of more accurate electrostatic theories that will be needed for a more quantitative and predictive understanding of nucleic acid folding.

Electrostatic forces, acting between helices and modulated by the presence of the ion atmosphere, are key determinants in the energetic balance that governs RNA folding. Previous studies have employed Poisson-Boltzmann (PB) theory to compute the energetic contribution of these forces in RNA folding. However, the complex interaction of these electrostatic forces with RNA features such as tertiary contact formation, specific ion-binding, and complex interhelical junctions present in prior studies precluded a rigorous evaluation of PB theory, especially in physiologically important Mg(2+) solutions. To critically assess PB theory, we developed a model system that isolates these electrostatic forces. The model system, composed of two DNA duplexes tethered by a polyethylene glycol junction, is an analog for the unfolded state of canonical helix-junction-helix motifs found in virtually all structured RNAs. This model system lacks the complicating features that have precluded a critical assessment of PB in prior studies, ensuring that interhelical electrostatic forces dominate the behavior of the system. The system's simplicity allows PB predictions to be directly compared with small-angle X-ray scattering experiments over a range of monovalent and divalent ion concentrations. These comparisons indicate that PB is a reasonable description of the underlying electrostatic energies for monovalent ions, but large deviations are observed for divalent ions. The validation of PB for monovalent solutions allows analysis of the change in the conformational ensemble of this simple motif as salt concentration is changed. Addition of ions allows the motif to sample more compact microstates, increasing its conformational entropy. The increase of conformational entropy presents an additional barrier to folding by stabilizing the unfolded state. Neglecting this effect will adversely impact the accuracy of folding analyses and models.

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 four-fold excess of Mg2+ (20 vs. 5 mM), the ion atmosphere nevertheless has three-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.

Linearly polarized synchrotron radiation has been used to investigate the orientation dependence of the K absorption edge of a single crystal of ammonium dithiomolybdate, the crystal structure of which is also reported herein. Following the collection of spectra with the polarization vector parallel to the oxygen-oxygen interatomic vector, the sulfur-sulfur vector, and the twofold rotation axis, self-consistent field X..cap alpha.. multiple scattered wave (SCF X..cap alpha.. MSW) calculations were done to interpret the observed orientation dependence. It is shown that this orientation dependence can be used to highlight the edge features which derive from molecular orbitals contributed to principally by the oxygen of the sulfur ligands. Anisotropy is also apparent in the extended X-ray absorption fine structure (EXAFS) spectra, which were recorded for orientations along the S-S and O-O interatomic vectors. It is thus demonstrated that polarized single-crystal X-ray absorption spectroscopy can provide orientationally selective information about the absorbing atom. It could, in principle, be used to deduce certain types of geometric information about the x-ray absorbing species.