Magnesium Dependence of the RNA Free Energy Landscape

The RNA free energy landscape is highly sensitive to ionic concentrations, and especially to Mg$^{2+}$, as most RNA tertiary structure will not form in the absence of Mg$^{2+}$. At physiological concentrations, the energy landscape must be smooth and funneled to fold on biological time scales, but changes in ionic concentration may affect the relative stability of alternative states. We perturb a structure-based model, which captures the funneled nature of the energy landscape, to include electrostatic effects. Our model includes explicit Mg$^{2+}$ and screening by implicit KCl. A dynamic model for the local competition between Manning condensed Mg$^{2+}$ and KCl is introduced, which makes the model more broadly applicable and transferable than a previous static model. We use the excess Mg$^{2+}$ ions associated with the RNA ($\Gamma_{2+}$) to test the model. $\Gamma _{2+}$ is an ideal metric because it is closely related to the Mg$^{2+}$-RNA interaction free energy, and is easily measurable in both experiment and simulation. The model captures intermediate states of a small pseudoknot missed by models without electrostatics.