An implicit divalent counterion force field for RNA molecular dynamics.

How to properly account for polyvalent counterions in a molecular dynamics simulation of polyelectrolytes such as nucleic acids remains an open question. Not only do counterions such as Mg(2+) screen electrostatic interactions, they also produce attractive intrachain interactions that stabilize secondary and tertiary structures. Here, we show how a simple force field derived from a recently reported implicit counterion model can be integrated into a molecular dynamics simulation for RNAs to realistically reproduce key structural details of both single-stranded and base-paired RNA constructs. This divalent counterion model is computationally efficient. It works with existing atomistic force fields, or coarse-grained models may be tuned to work with it. We provide optimized parameters for a coarse-grained RNA model that takes advantage of this new counterion force field. Using the new model, we illustrate how the structural flexibility of RNA two-way junctions is modified under different salt conditions.

Free energy of RNA-counterion interactions in a tight-binding model computed by a discrete space mapping.

The thermodynamic stability of a folded RNA is intricately tied to the counterions and the free energy of this interaction must be accounted for in any realistic RNA simulations. Extending a tight-binding model published previously, in this paper we investigate the fundamental structure of charges arising from the interaction between small functional RNA molecules and divalent ions such as Mg(2+) that are especially conducive to stabilizing folded conformations. The characteristic nature of these charges is utilized to construct a discretely connected energy landscape that is then traversed via a novel application of a deterministic graph search technique. This search method can be incorporated into larger simulations of small RNA molecules and provides a fast and accurate way to calculate the free energy arising from the interactions between an RNA and divalent counterions. The utility of this algorithm is demonstrated within a fully atomistic Monte Carlo simulation of the P4-P6 domain of the Tetrahymena group I intron, in which it is shown that the counterion-mediated free energy conclusively directs folding into a compact structure.

Ions and RNAs: Free Energies of Counterion-Mediated RNA Fold Stabilities.

We present an implicit ion model fo the calculation of the electrostatic free energies of RNA conformations in the presence of divalent counterions such as Mg(2+). The model was applied to the native and several non-native structures of the hammerhead ribozyme and the group I intron in Tetrahymena to study the stability of candidate unfolding intermediates. Based on a rigorous statistical mechanical treatment of the counterions that are closely associated with the RNA while handling the rest of the ions in the solution via a mean field theory in the Grand Canonical ensemble, the implicit ion model accurately reproduces the ordering of their free energies, correctly identifying the native fold as the most stable structure out of the other alternatives. For RNA concentrations in the range below 0.1 µM, divalent concentrations of ∼0.5 mM or above, and over a wide range of solvent dielectric constants, the equilibrium number of divalent ions associated with the RNA remains close to what is needed to exactly neutralize the phosphate negative charges, but the stability of compact RNA folds can be reversed when the divalent ion concentration is lower than ∼0.1 mM, causing the number of associated ions to underneutralize the RNA. In addition to calculating counterion-mediated free energies, the model is also able to identify potential high-affinity electronegative ion binding pockets on the RNA. The model can be easily integrated into an all-atom Monte Carlo RNA simulation as an implicit counterion model.