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

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.