Molecular Simulations of ion effects on the Thermodynamics of RNA Folding

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, {Delta}G(c), of RNA upon folding varies with the salt concentration (c) as, {Delta}G(c) = kc ln c + const, where the coefficient kc is proportional to the difference in the uptake of ions (ion preferential coefficient), {Delta}{Gamma}, between the folded and unfolded states. 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 folding free energy and ion preferential coefficient. Without any input from experiments, the simulations quantitatively reproduce the heat capacity for the -1 frame shifting pseudoknot (PK) from Beet Western Yellow Virus, thus validating the model. We show that {Delta}G(c) calculated directly from {Delta}{Gamma} varies linearly with ln c (c < 0.2M), for a hairpin and the PK, thus demonstrating a molecular link between the two quantities for RNA molecules that undergo substantial conformational changes during folding. Explicit ion simulations also show the linear dependence of {Delta}G(c) on ln c at all c with kc = 2kBT, except that {Delta}G(c) values are shifted by about 2 kcal/mol higher than experiments at all salt concentrations. The discrepancy is due to an underestimate the {Gamma} values for both the folded and unfolded states, while giving accurate values for {Delta}{Gamma}. The predictions for the salt dependence of {Delta}{Gamma} are amenable to test using single molecule pulling experiments. Our simulations, representing a significant advance in quantitatively describing ion effects in RNA, show that the framework provided here can be used to obtain accurate thermodynamics of RNA folding.