Generalized Manning Condensation Model Captures the RNA Ion Atmosphere

RNA is highly sensitive to the ionic environment and typically requires ${\mathrm{Mg}}^{2+}$ to form compact structures. There is a need for models capable of describing the ion atmosphere surrounding RNA with quantitative accuracy. We present a model of RNA electrostatics and apply it within coarse-grained molecular dynamics simulation. The model treats ${\mathrm{Mg}}^{2+}$ ions explicitly to account for ion-ion correlations neglected by mean-field theories. Since mean-field theories capture KCl well, it is treated implicitly by a generalized Manning counterion condensation model. The model extends Manning condensation to deal with arbitrary RNA conformations, nonlimiting KCl concentrations, and the ion inaccessible volume of RNA. The model is tested against experimental measurements of the excess ${\mathrm{Mg}}^{2+}$ associated with the RNA, ${\mathrm{\Gamma }}_{2+}$, because ${\mathrm{\Gamma }}_{2+}$ is directly related to the ${\mathrm{Mg}}^{2+}$-RNA interaction free energy. The excellent agreement with experiment demonstrates that the model captures the ionic dependence of the RNA free energy landscape.

Figure 1

The model captures excess ${\mathrm{Mg}}^{2+}$ over a wide range of concentrations for both (a) the adenine riboswitch at 50 mM KCl, and (b) a 58 nucleotide ribosomal fragment. Experimental results are plotted as lines and simulation results are plotted as dots.

Figure 2

Predictions by the model are too high for the beet western yellow virus pseudoknot in the rigid simulation where the RNA is fixed in the crystal structure (the open circles). The agreement with experiment [17] is quite close if native basin fluctuations are included (the solid circles).