Single-Molecule FRET Shows Folding Transition Path Time for All-Alpha Protein Slowed by Internal Friction

Abstract

The transition-path is the tiny fraction of an equilibrium, single-molecule trajectory when a transition occurs between two states. The importance of the transition-path in protein folding is that it contains all the mechanistic information on how a protein folds and unfolds. However, a transition-path has never been observed experimentally for any molecular system in the condensed phase because it is too fast to measure. Even determining the average transition-path time, 〈tTP〉, is challenging. Previously, we determined 〈tTP〉∼2μs for the all-β protein, FBP28 WW-domain (1/kF=100μs) and an upper bound of 〈tTP〉∼10μs for the much slower αβ-protein GB1 (1/kF =1s) by employing the Gopich-Szabo maximum likelihood analysis of photon trajectories in single-molecule FRET experiments and a kinetic model in which the lifetime of an additional state in a one-step discretization of the transition path corresponds to 〈tTP〉 (Chung et al., Science 2012). Surprisingly, the 〈tTP〉s for the two proteins differ by <5-fold, while the folding rates differ by ∼10,000-fold. Even more surprising is that this result can be explained by the theory for diffusion of a Brownian particle over a barrier on a one-dimensional free-energy surface, which predicts 〈tTP〉 to be insensitive to the barrier height but to scale as 1/D∗, the diffusion coefficient at the barrier top, i.e. 〈tTP〉μln(3βΔG∗)/D∗. Maximum likelihood analysis of photon trajectories for α3D, an all-α protein (1/kF=2ms), reveals an additional-state lifetime of 12μs. While the folding time for all-β proteins scales linearly with the solvent viscosity, like other all-α proteins, the folding time of α3D scales sub-linearly with viscosity (1/kF∼η1/2), as does the 12μs lifetime. These results indicate that this additional lifetime corresponds to 〈tTP〉, slowed compared to the WW-domain by a larger contribution of internal friction to D∗.