Fig. 7.

Comparison between Mg²⁺ and Ca²⁺ binding to phosphate groups and RNA. (A) Effective potentials for Mg²⁺ and Ca²⁺ with the phosphate group show that the transition barrier between inner-shell–outer-shell coordination for Ca²⁺ is considerably lower than for Mg²⁺. However, the depths of the inner- and outer-shell minima are comparable. (B) Radial distribution function between the ions and phosphate groups in BWYV. Also shown are the results for Mg²⁺ ions in which Mg²⁺–phosphate interactions are modeled using the Debye–Hückel potential (green). (C and D) Preferential interaction coefficient ${\mathrm{\Gamma }}_X$ (C) and radius of gyration $R_g$ (D) computed for 58-nt rRNA. Only data for 150 mM KCl are presented here; data for other KCl concentrations can be found in SI Appendix, Fig. S6. The rRNA reaches its native states at high divalent ion concentrations using our model, but does not easily fold at any Mg²⁺ concentration should the Debye–Hückel potential be used.