Frictional Effects on RNA Folding: Speed Limit and Kramers Turnover

Abstract

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 ($k_\mathrm{F}$) from more than 100 folding trajectories for each value of the solvent viscosity ($η$) at a fixed salt concentration of 200 mM. By using the theoretical estimate ($\propto$$\sqrt{N}$ where $N$ is the number of nucleotides) for folding free energy barrier, $k_\mathrm{F}$ 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 ($η\gtrsim10^{-5}\,\textrm{Pa\ensuremath{\cdot}s}$), for both HP and PK, $k_\mathrm{F}$s decrease as $1/η$ whereas in the low friction regime, $k_\mathrm{F}$ values increase as $η$ increases, leading to a maximum folding rate at a moderate viscosity ($\sim10^{-6}\,\textrm{Pa\ensuremath{\cdot}s}$), which is the Kramers turnover. From the fits, we find that the speed limit to RNA folding at water viscosity is between 1 and 4 $\mathrm{μs}$, 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 in proteins.