Protein folding trajectories can be described quantitatively by one-dimensional diffusion over measured energy landscapes

Protein folding features a diffusive search over a multi-dimensional energy landscape in conformational space for the minimum-energy structure(1). Experiments, however, are usually interpreted in terms of a one-dimensional (1D) projection of the full landscape onto a practical reaction coordinate. Although simulations have shown that folding kinetics can be described well by diffusion over a 1D projection(2,3), 1D approximations have not yet been fully validated experimentally. We used folding trajectories of single molecules held under tension in optical tweezers to compare the conditional probability of being on a transition path(4), calculated from the trajectory(5), with the prediction for ideal 1D diffusion over the measured 1D landscape(6), calculated from committor statistics(7,8). We found good agreement for the protein PrP (refs 9,10) and for one of the structural transitions in a leucine-zipper coiled-coil(11), but not for a second transition in the coiled-coil, owing to poor reaction-coordinate quality(12). These results show that 1D descriptions of folding can indeed be good, even for complex tertiary structures. More fundamentally, they also provide a fully experimental validation of the basic physical picture of folding as diffusion over a landscape.