Theoretical Studies On Ion-dependent RNA Folding Stability

RNA structure and folding stability determine RNA cellular functions. RNA folding into a stable structure is remarkably sensitive to the around ionic conditions. In order to understand the mechanism and accurately predict the electrostatic thermodynamic parameters of ion-induced RNA folding, many theoretical studies focus on ion-RNA interactions and the effect on RNA folding stability.Recently, a new model, Tightly Bound Ion (TBI) model, was developed to account for the correlation and the fluctuation effects of ions around RNA structures. Comparisons of the theoretical predictions and experiment data suggested that the TBI model led to much improved results than other models such as the mean field-based Poisson-Boltzmann (PB) model for ion-dependent RNA folding stability.One of the great challenges in RNA folding is to predict the ions effects on the formation of RNA tertiary structures, where the different helices and loops are brought together for form a stable3D structure. Tetraloop-receptor is a frequently occurring basic building block for RNA tertiary structure. Understanding the mechanism of its formation can provide useful insights into the physical mechanism for general tertiary folding. Combining the TBI model and a coarse-grained RNA conformational model (Vfold), we study the tetraloop-receptor docking (folding) stability in the different ionic solutions. Our goal is to understand the physical mechanism for ion-promoted RNA tertiary structure folding.By using the Vfold model to sample the conformational ensemble of the flexible loops in the tetraloop-receptor system, we generate the conformational ensembles of both the folded (docked) and the unfolded (undocked) states. Based on the tetraloop-receptor conformational ensemble, the TBI theory for ion-RNA interactions predicts the electrostatic thermodynamics of the system in a salt solution with the different Mg2+ion concentrations. The predicted docking free energy agrees well with the experimental data. Furthermore, the free energy landscape and the component free energy contributions lead to several important conclusions:(a) the ion entropy provides the major stabilizing force for tetraloop-receptor docking;(b) the dominant contribution to the ion entropy force comes from the redistribution of the diffusive ions;(c) through the electrostatic screening/charge neutralization effect, the Coulomb force can also play a(albeit minor) role in the docking process. Our method of combining Vfold and TBI models provides a new paradigm for studying the folding of more complex RNA structures.A notable limitation of the original TBI model is its systematic over-estimation of the RNA folding stability at high Mg2+ion concentrations. This error is likely caused by neglecting the many-body effect among the bound ions. To enhance the accuracy of the theoretical predictions, we developed a new improved TBI model by including the many-body effect between the ions. Applying the modified model to BWYV and T2RNAs, we found that including the many-body effect can indeed lead to much improved predictions for RNA folding stability at high Mg2+ion concentrations. Furthermore, the new model results in several new insights into ion-RNA interactions:(a) The many-body effect can be important for ion effect in RNA folding at high Mg2+concentration;(b) The many-body effect could lower the overall number of the bound ions and could cause a minor shift in the distribution of the bound ions;(c) The results of the many-body effect can be dependent on the RNA structure. In general, more compact structures can cause more densely populated bound ions and a stronger many-body effect;(d) Although the many-body effect for monovalent ions is weak, the concentration of monovalent ions can modulate the binding of the multivalent ions and the resultant many-body effect through ion binding competitions.