Mg ²⁺ –RNA interaction free energies and their relationship to the folding of RNA tertiary structures

Abstract

Mg 2؉ ions are very effective at stabilizing tertiary structures in RNAs. In most cases, folding of an RNA is so strongly coupled to its interactions with Mg 2؉ that it is difficult to separate free energies of Mg 2؉ -RNA interactions from the intrinsic free energy of RNA folding. To devise quantitative models accounting for this phenomenon of Mg 2؉ -induced RNA folding, it is necessary to independently determine Mg 2؉ -RNA interaction free energies for folded and unfolded RNA forms. In this work, the energetics of Mg 2؉ -RNA interactions are derived from an assay that measures the effective concentration of Mg 2؉ in the presence of RNA. These measurements are used with other measures of RNA stability to develop an overall picture of the energetics of Mg 2؉ -induced RNA folding. Two different RNAs are discussed, a pseudoknot and an rRNA fragment. Both RNAs interact strongly with Mg 2؉ when partially unfolded, but the two folded RNAs differ dramatically in their inherent stability in the absence of Mg 2؉ and in the free energy of their interactions with Mg 2؉ . From these results, it appears that any comprehensive framework for understanding Mg 2؉ -induced stabilization of RNA will have to (i) take into account the interactions of ions with the partially unfolded RNAs and (ii) identify factors responsible for the widely different strengths with which folded tertiary structures interact with Mg 2؉ .cations ͉ ion interaction coefficients ͉ Wyman linkage relations M g 2ϩ ions strongly stabilize RNA tertiary structures under conditions that only weakly affect RNA secondary structure stability, a phenomenon first studied in the folding of transfer RNA (1, 2). Although the sensitivity of RNA folding to Mg 2ϩ has been amply documented for many RNAs, it is still unknown how this sensitivity is quantitatively related to the strengths of Mg 2ϩ -RNA interactions. Thus, for most RNAs, the magnitude of the intrinsic RNA instability is unknown, nor is it known how much more favorably Mg 2ϩ interacts with the native RNA structure than with structures from which folding takes place. Lacking this fundamental overview of Mg 2ϩ -RNA interaction free energies, it has not been possible to carry out extensive evaluations of theoretical models that seek to explain Mg 2ϩ -induced RNA folding in terms of the underlying physical interactions (3, 4).In this article, we parse the tertiary folding of two different RNAs into the intrinsic free energy of folding in the absence of Mg 2ϩ and the free energies of Mg 2ϩ interactions with folded and partially folded states. To obtain the relevant free energies, we devised a practical experimental method for measuring the effect of RNA on Mg 2ϩ ion activities and derived the equations necessary for extracting Mg 2ϩ -RNA interaction free energies from the experimental data. The two RNAs have vastly different stabilities in the absence of Mg 2ϩ and correspondingly large differences in the favorable interactions of the native RNA structures with Mg 2ϩ . Clearly, different RNAs use different strategies ...

Unwinding RNA's secrets: advances in the biology, physics, and modeling of complex RNAs

“…However, the opposite conclusion has been drawn from fitting RNA folding transitions to PB predictions [70][71][72][73][74]. Ion-counting and SAXS experiments have provided a simple test for these effects and have revealed effects of ion size and valence that are not accounted for by PB theory, with deviations up to an order of magnitude in the systems investigated [58,75].…”

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“…PB theory has been successfully applied to predict the composition of the ion atmosphere and ion induced folding of nucleic acids Draper 1999, 2000;Grilley et al 2006;Bai et al 2007Bai et al , 2008Chu et al 2007), although limitations in its accuracy are also known; in particular, the neglect of ion size and ion-ion correlations (Antypov et al 2005;Chu et al 2007;Bai et al 2008;Chu et al 2008;Grochowski and Trylska 2008). Under the simplifying assumption that the U-to-M transition does not involve specific ion binding, we can compute the purely electrostatic contributions to the free energy by calculating the dependence of the PB energies on salt concentration for the U and M states: To solve the PB equation and to compute properties such as the composition of the ion atmosphere or electrostatic energies, it is necessary to define the geometry and charge distribution of the molecular conformations of interest.…”

“…Ions in this atmosphere are in fast exchange and remain fully hydrated. The properties and thermodynamic consequences of this ion atmosphere have been modeled using electrostatic theories, with PoissonBoltzmann (PB) theory prominently used (Chin et al 1999;Misra and Draper 2000;Tan and Chen 2005;Grilley et al 2006;Bai et al 2007Bai et al , 2008Chu et al 2007). At the other end of the spectrum are specifically bound ions, which are in slow exchange and often at least partially dehydrated (Burkhardt and Zacharias 2001;van Buuren et al 2002;Draper 2004;Draper et al 2005;Stefan et al 2006).…”

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