Denesyuk, N. A. | bioRxiv Science

bioRxiv2018

Frictional effects on RNA folding: Speed limit and Kramers turnover

We investigated frictional effects on the folding rates of a human Telomerase hairpin (hTR HP) and H-type pseudoknot from the Beet Western Yellow Virus (BWYV PK) using simulations of the Three Interaction Site (TIS) model for RNA. The heat capacity from TIS model simulations, calculated using temperature replica exchange simulations, reproduces nearly quantitatively the available experimental data for the hTR HP. The corresponding results for BWYV PK serve as predictions. We calculated the folding rates (kFs) from more than 100 folding trajectories for each value of the solvent viscosity ({eta}) at a fixed salt concentration of 200 mM. Using the theoretical estimate ([Formula] where N is number of nucleotides) for folding free energy barrier, kF data for both the RNAs are quantitatively fit using one dimensional Kramers theory with two parameters specifying the curvatures in the unfolded basin and the barrier top. In the high-friction regime ({eta} {gtrsim} 10-5 Pa{middle dot}s), for both HP and PK, kFs decrease as 1/{eta} whereas in the low friction regime kFs increase as{eta} increases, leading to a maximum folding rate at a moderate viscosity (~ 10-6 Pa{middle dot}s), which is the Kramers turnover. From the fits, we find that the speed limit to RNA folding at water viscosity is between (1 - 4)s, which is in accord with our previous theoretical prediction as well as results from several single molecule experiments. Both the RNA constructs fold by parallel pathways. Surprisingly, we find that the flux through the pathways could be altered by changing solvent viscosity, a prediction that is more easily testable in RNA than proteins.

biophysics↗

bioRxiv2018

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

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.

biophysics↗