Impact of Ion-Mixing Entropy on Orientational Preferences of DNA Helices: FRET Measurements and Computer Simulations

Abstract

Biological processes require DNA and RNA helices to pack together in specific interhelical orientations. While electrostatic repulsion between backbone charges is expected to be maximized when helices are in parallel alignment, such orientations are commonplace in nature. To better understand how the repulsion is overcome, we used experimental and computational approaches to investigate how the orientational preferences of DNA helices depend on the concentration and valence of mobile cations. We used Förster resonance energy transfer (FRET) to probe the relative orientations of two 24-bp helices held together via a freely rotating PEG linker. At low cation concentrations, the helices preferred more "cross"-like orientations over those closer to parallel, and this preference was reduced with increasing salt concentrations. The results were in good quantitative agreement with Poisson-Boltzmann (PB) calculations for monovalent salt (Na⁺). However, PB underestimated the ability of mixtures of monovalent and divalent ions (Mg²⁺) to reduce the conformational preference. As a complementary approach, we performed all-atom molecular dynamics (MD) simulations and found better agreement with the experimental results. While MD and PB predict similar electrostatic forces, MD predicts a greater accumulation of Mg²⁺ in the ion atmosphere surrounding the DNA. Mg²⁺ occupancy is predicted to be greater in conformations close to the parallel orientation than in conformations close to the crossed orientation, enabling a greater release of Na⁺ ions and providing an entropic gain (one bound ion for two released). MD predicts an entropy gain larger than that of PB because of the increased Mg²⁺ occupancy. The entropy changes have a negligible effect at low Mg²⁺ concentrations because the free energies are dominated by electrostatic repulsion. However, as the Mg²⁺ concentration increases, charge screening is more effective and the mixing entropy produces readily detectable changes in packing preferences. Our results underline the importance of mixing entropy of counterions in nucleic acid interactions and provide a new understanding on the impact of a mixed ion atmosphere on the packing of DNA helices.

Figure 1.

FRET-based assay of interhelical orientations. A) Cartoon depicting DNA helices (cylinders) in different orientations. In a parallel orientation (θ = 0°), backbone charges repel one another at close range across the entire length of each helix. Rotation through an interaxial angle θ increases charge-charge distances, until these mutual distances are maximized in a crossed orientation (θ = 90°). B) An experimental system comprising two 24-bp helices (total charge = 92e) tethered by a short, centrally connected PEG₃ linker was used to monitor interhelical orientations by FRET. One helix (blue) bore a single Cy3 donor, while the second tethered helix (green) bore a Cy5 acceptor dye at each end.

Figure 2.

PB electrostatic free energy for the relative orientation of a pair of 24-bp DNA helices computed with varying solution conditions. A,B) PB-calculated free energy penalties associated with the interhelical orientation θ, referenced against the crossed orientation at θ = 90°, shown with various concentrations of A) NaCl and B) MgCl₂. Solution conditions in B) also include 50 mM NaCl background. C,D) Maximum free energy penalty associated with rotating from the crossed orientation (θ = 90°) to the parallel orientation (θ = 0°) as a function of C) Na⁺ and D) Mg²⁺ concentration.

Figure 3.

Experiment FRET efficiency (points) E_Tot across various concentrations of NaCl (blue) and MgCl₂ (orange), along with ensemble predictions from free energy profiles computed by PB (solid curves) and entropy mixing adjustments from MD (green). Dashed horizontal line shows the expectation value for E_Tot under a free rotation regime. All MgCl₂ conditions also include 50 mM NaCl. Error bars show standard error over the complete sample of replicates at each solution condition. The replicas include repeated measurements using the same sample and repeated measurements of newly prepared systems. All points have error bars with some being smaller than the data points.

Figure 4.

The accumulation of the total mobile ion charge subtracting the bulk contribution. The difference from the bulk at large distances is an estimate of the number of ions bound to the DNA. We consider this difference as a function of distance from the center of the DNA system. The solutions in panels (A) and (B) are of 50mM NaCl and two concentrations of MgCl₂: Panel (A) 9mM Mg²⁺, and Panel (B) 77mM Mg²⁺ for the parallel conformation. The differences between this plot and the slash and cross conformations at a given concentration are small and are shown in Fig S11. In all the plots the difference in the total charge distributions when comparing different packing or computational methods is small. In panel B the differences between constant concentration (PB) and a constant number of ions (MD) lead to deviation in the charge at large distances, that do not impact significantly the shorter-range DNA energetics.

Figure 5.

Accumulated charge of different ion types subtracting the bulk charge as a function of distance from the origin. The charges are partitioned into contributions of ion types and alternative DNA conformations. We also report separately the results for PB and MD calculations. Panels A-C analyze the solution of 9 mM MgCl₂ and Panels D-F for the solution of 77 mM MgCl₂ (both with a 50mM NaCl background). Panels A and D report the result for magnesium ion, panels B and E for the sodium ion, and panels C and F for the chloride. The results for the parallel conformation are shown with an orange line (PB) and a green line (MD). For the cross-conformation, we have the PB data in red line and the results from MD in blue.

Figure 6.

The difference between the ion compositions of the surrounding ions near the cross and parallel packing of the DNA helices. In orange, we show the difference between the parallel and the cross states computed with PB and in green with MD. Panels A-C are for a Mg²⁺ concentration of 9mM and panels D-F for the 77mM concentration. In both Mg²⁺ concentrations, MD has a greater accumulation of Mg²⁺ in the parallel state than PB, with greater Na⁺ release into the aqueous solution.