Abstract
How ions affect RNA folding thermodynamics and kinetics is an important but a vexing problem that remains unsolved. Experiments have shown that the free-energy change, Δ G( c), of RNA upon folding varies with the salt concentration ( c) as, Δ G( c) = k c ln c + const, where the coefficient k c is proportional to the difference in the ion preferential coefficient, ΔΓ. We performed simulations of a coarse-grained model, by modeling electrostatic interactions implicitly and with explicit representation of ions, to elucidate the molecular underpinnings of the relationship between Δ G and ΔΓ. The simulations quantitatively reproduce the heat capacity for a pseudoknot, thus validating the model. We show that Δ G( c), calculated directly from ΔΓ, varies linearly with ln c ( c < 0.2 M), for a hairpin and the pseudoknot, demonstrating a molecular link between the two quantities. Explicit ion simulations also show the linear dependence of Δ G( c) on ln c at all c with k c = 2 kB T, except that Δ G( c) values are shifted by ∼2 kcal/mol higher than experiments. The discrepancy is due to an underestimation of Γ for both the folded and unfolded states while giving accurate values for ΔΓ. The predictions for the salt dependence of ΔΓ are amenable to test using single-molecule pulling experiments. The framework provided here can be used to obtain accurate thermodynamics for other RNA molecules as well.
Highlights
In common with proteins, RNA molecules that carry out cellular functions adopt specific, compact conformations, which require ions
We demonstrated the model is thermodynamically accurate for several RNA molecules over a wide range of monovalent salt concentration c, and temperature T
We present the results of the same simulation model for the folding thermodynamics of the BWYV PK
Summary
RNA molecules that carry out cellular functions adopt specific, compact conformations, which require ions. In the absence of counter ions, compact RNA structures are energetically unfavorable due to the close proximity of negatively charged phosphate groups. To enable RNA molecules to fold, counterions from the buffer solution must condense onto the sugar-phosphate backbone, which would reduce the charges on the phosphate groups. Typically Mg2+, are efficient in stabilizing RNA folded structures [3, 12,13,14,15,16,17]. Representative high resolution structures of folded RNA show individual Mg2+ ions are bound to multiple phosphate groups [18, 19]. The presence of divalent ions is not essential for the stability of many RNAs with relatively simple architectures. The 1 frameshifting pseudoknot from beet western yellow virus (BWYV PK, Figure 1) [14, 20, 21] is
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