Reduced Model Captures Mg2+-RNA Interaction Free Energy of Riboswitches

Abstract

The stability of RNA tertiary structures depends heavily on Mg2+. The Mg2+-RNA interaction free energy that stabilizes an RNA structure can be computed experimentally through fluorescence-based assays that measure Γ2+, the number of excess Mg2+ associated with an RNA molecule. Previous explicit-solvent simulations predict that the majority of excess Mg2+ ions interact closely and strongly with the RNA, unlike monovalent ions such as K+, suggesting that an explicit treatment of Mg2+ is important for capturing RNA dynamics. Here we present a reduced model that accurately reproduces the thermodynamics of Mg2+-RNA interactions. This model is able to characterize long-timescale RNA dynamics coupled to Mg2+ through the explicit representation of Mg2+ ions. KCl is described by Debye-Hückel screening and a Manning condensation parameter, which represents condensed K+ and models its competition with condensed Mg2+. The model contains one fitted parameter, the number of condensed K+ ions in the absence of Mg2+. Values of Γ2+ computed from molecular dynamics simulations using the model show excellent agreement with both experimental data on the adenine riboswitch and previous explicit-solvent simulations of the SAM-I riboswitch. This agreement confirms the thermodynamic accuracy of the model via the direct relation of Γ2+ to the Mg2+-RNA interaction free energy, and provides further support for the predictions from explicit-solvent calculations. This reduced model will be useful for future studies of the interplay between Mg2+ and RNA dynamics.