The linkage between magnesium binding and RNA folding

Understanding the linkage between Mg2+ binding and RNA folding requires a proper theoretical model describing the energetics of Mg2+ binding to the folded and unfolded states of RNA. Our current understanding of Mg2+ binding to these different RNA states derives from empirical thermodynamic models that depend on a number of unjustified assumptions. We present a rigorous theoretical model describing the linkage between RNA folding and magnesium ion binding. In this model, based on the non-linear Poisson-Boltzmann (NLPB) equation, the stabilization of RNA by Mg2+ arises from two distinct binding modes, diffuse binding and site binding. Diffusely bound Mg2+ are described as an ensemble of hydrated ions that are attracted to the negative charge of the RNA. Site-bound Mg2+ are partially desolvated ions that are attracted to electronegative pockets on the RNA surface. We explore two systems, yeast tRNAPhe and a 58-nucleotide rRNA fragment, with different Mg2+ binding properties. The NLPB equation accurately describes both the stoichiometric and energetic linkage between Mg2+ binding and RNA folding for both of these systems without requiring any fitted parameters in the calculation. Moreover, the NLPB model presents a well-defined physical description of how Mg2+ binding helps fold an RNA. For both of the molecules studied here, the relevant unfolded state is a disordered intermediate state (I) that contains stable helical secondary structure without any tertiary contacts. Diffusely bound Mg2+ interact with these secondary structure elements to stabilize the I state. The secondary structural elements of the I state fold into a compact, native tertiary structure (the N state). Diffuse binding plays a dominant role in stabilizing the N state for both RNAs studied. However, for the rRNA fragment, site-binding to a location with extraordinarily high electrostatic potential is also coupled to folding. Our results suggest that much experimental data measuring the linkage between Mg2+ binding and RNA folding must be reinterpreted.