Title: 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 ($\eta$) 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 ($\eta\gtrsim10^{-5}\,\textrm{Pa\ensuremath{\cdot}s}$), for both HP and
PK, $k_\mathrm{F}$s decrease as $1/\eta$ whereas in the low friction regime,
$k_\mathrm{F}$ values increase as $\eta$ 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 $\mathrm{\mu s}$, 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 in proteins.