Mg²⁺ binding to tRNA revisited: The nonlinear Poisson-Boltzmann model

Our current understanding of Mg²⁺ binding to RNA, in both thermodynamic and structural terms, is largely based on classical studies of transfer RNAs. Based on these studies, it is clear that magnesium ions are crucial for stabilizing the folded structure of tRNA. We present here a rigorous theoretical model based on the nonlinear Poisson-Boltzmann (NLPB) equation for understanding Mg²⁺ binding to yeast tRNA(Phe). We use this model to interpret a variety of experimental Mg²⁺ binding data. In particular, we find that the NLPB equation provides a remarkably accurate description of both the overall stoichiometry and the free energy of Mg²⁺ binding to yeast tRNA(Phe) without any fitted parameters. In addition, the model accurately describes the interaction of Mg²⁺ with localized regions of the RNA as determined by the pK(a) shift of differently bound fluorophores. In each case, we find that the model also reproduces the univalent salt-dependence and the anticooperativity of Mg²⁺ binding. Our results lead us to a thermodynamic description of Mg²⁺ binding to yeast tRNA(Phe) based on the NLPB equation. In this model, Mg²⁺ binding is simply explained by an ensemble of ions distributed according to a Boltzmann weighted average of the mean electrostatic potential around the RNA. It appears that the entire ensemble of electrostatically bound ions superficially mimics a few strongly coordinated ions. In this regard, we find that Mg²⁺ stabilizes the tertiary structure of yeast tRNA(Phe) in part by accumulating in regions of high negative electrostatic potential. These regions of Mg²⁺ localization correspond to bound ions that are observed in the X-ray crystallographic structures of yeast tRNA(Phe). Based on our results and the available thermodynamic data, there is no evidence that specifically coordinated Mg ions have a significant role in stabilizing the native tertiary structure of yeast tRNA(Phe) in solution. (C) 2000 Academic Press.