Critical assessment of nucleic acid electrostatics via experimental and computational investigation of an unfolded state ensemble

Abstract

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.

Figure 1

Schematic and sequence of the tethered duplex system. The system consists of two 12 bp DNA duplexes (red) joined by a flexible PEG tether (green). Under low ionic conditions, extended conformers dominate the unfolded ensemble; as ions are added, the ensemble relaxes to more relaxed states.

Figure 2

Scattering intensities I(s), weighted by momentum transfer s at different ionic concentrations as a function of s for Na⁺ (A) and Mg²⁺ (B). Open circles represent experimental data and solid black lines represent predictions from PB theory. Na⁺ concentrations (top to bottom): 2, 0.6, 0.3, 0.15, 0.08, 0.02, 0 M (in 16 mM Na⁺ background from Na-MOPS buffer). Mg²⁺ concentrations (top to bottom): 100, 10, 2, 0.6, 0.2, 0.05 mM (in 16 mM Na⁺ background from Na-MOPS buffer). For clarity, profiles are vertically offset and the number of data points are reduced. Error bars are smaller than symbols for some points.

Figure 3

Ion-mediated structural relaxation fit to the empirical Hill model for Na⁺ (A) and Mg²⁺ (B). Fraction relaxed reflects the overall relaxation of the ensemble as determined by projection onto the experimental scattering profiles taken at low- and high-ionic concentration (see Eq. 1). For both plots, solid lines show the Hill fit to the experimental data and the dashed lines show the same relaxation derived from PB.

Figure 4

Visualization of the computationally-derived unfolded ensemble at various ionic conditions. From left to right, top to bottom: 0, 0.04, 0.15, 0.3, 2 M monovalent ions (in 16 mM monovalent background). The last figure shows the ensemble in the absence of electrostatics (i.e., steric effects only). One duplex is rendered in gray while the colored balls represent the distal end of the other duplex. Colors represent the energetic difference between the conformer and the minimum-energy conformer observed in the ensemble. Red, 0 – 1 k_BT; Orange, 1 – 2k_BT; Yellow, 2 – 3 k_BT; Blue, > 3 k_BT. The representation of each duplex by a single point occasionally results in the juxtaposition of a high-energy conformer close to a low-energy one; these cases correspond to conformers whose distal ends are in close proximity to low-energy conformers, but whose orientations (hidden in this representation) are energetically unfavorable (e.g., stretch the PEG tether unfavorably).