Molecular simulations of the monovalent-ion dependent Folding Thermodynamics of RNA

Abstract A quantitative description of how ions affect RNA folding thermodynamics and kinetics is a vexing problem. Experiments have shown that the free energy change, ΔG(c), upon folding on the salt concentration (c) varies as, ΔG(c) = kc ln c + const. The coefficient kc is proportional to the difference in the ion preferential coefficient, ΔΓ, between the folded and unfolded states. In order to calculate the dependence of ΔG(c) on ln c, we performed simulations using the Three Interaction Site (TIS) model, which accounts for the electrostatic interactions implicitly by the Debye-Hückel potential. The simulations quantitatively reproduce the heat capacity for the ?1 frame shifting pseudoknot (PK) from Beet Western Yellow Virus. We also establish that ΔG(c) from simulations varies linearly with ln c in accord with experiments. Above c > 0.2M there is a curvature in the dependence of ΔG(c) on ln c. We find that ΔG(c) calculated directly from ΔΓ also varies linearly with ln c (c < 0.2M), for a hairpin and the PK, thus demonstrating a direct link between the two quantities for RNA molecules that undergo substantial conformational changes during folding. We also performed simulations for the hairpin by explicitly modeling the monovalent ions. Explicit ion simulations show the linear dependence of ΔG(c) on ln c at all c with kc = 2kBT, the value obtained using implicit ion simulations. However, at all c the calculated ΔG(c) values are about 2 kcal/mol higher than experiments. The discrepancy occurs because explicit ion simulations underestimate the Γ values for both the folded and unfolded states, while giving a relatively accurate value for ΔΓ. In contrast, ΔG(c) calculated from implicit ion simulations are in quantitative agreement with experiments except at c = 1M. Because effects ion size and shape cannot be taken into account using implicit ion simulations, we conclude that it will be necessary to use the more demanding explicit ion simulations for treating many aspects of RNA folding thermodynamics.