Tests of Kramers' Theory at the Single-Molecule Level: Evidence for Folding of an Isolated RNA Tertiary Interaction at the Viscous Speed Limit.

Dissipation and friction influence the conformational dynamics of biological polymers as they traverse barriers on rugged free energy surfaces. It is well established that the "speed limit" for macromolecular folding is dictated by a combination of (i) solvent friction, which depends on solvent viscosity, η, and (ii) internal friction, which is independent of solvent and depends solely on the molecular folding pathway. In this work, single-molecule Förster resonance energy transfer (FRET) confocal spectroscopy is used to study viscosity-dependent folding kinetics of an isolated RNA tertiary motif, that of the GAAA tetraloop receptor, allowing both solvent and internal frictional contributions to be investigated and extracted independently for both flexible PEG- and RNA-based (rU7, rA7) linkers in the unimolecular construct. Specifically, our single-molecule data reveal that (i) folding rate constants scale linearly with the inverse solvent viscosity (η), which supports Kramers'/Grote-Hynes' rate theory for η-dependent RNA folding and that (ii) they provide quantitative upper limits for the intrinsic viscosity, [ηint ≈ 0.1(2) cP], arising from internal friction associated with folding/unfolding of an isolated RNA tertiary interaction. Furthermore, in contrast to strong viscosity-induced shifts in the folding/unfolding rate constants, temperature-dependent studies demonstrate that the enthalpic, entropic, and free energy contributions to the transition state barrier are largely insensitive to the solvent viscosity. This supports a very simple picture for the conformational kinetics of isolated RNA tertiary interactions wherein rate constants for folding/unfolding are both inversely dependent on viscosity and limited by diffusional access to the transition state region on a multidimensional free energy surface. Particularly under cellular conditions, where ηsolv > 1 cp, this suggests that RNAs fold/unfold at a "speed limit" dictated by solvent viscosity and transition-state barrier thermodynamics rather than internal molecular friction.