Structural Origin of Landscape Roughness in Protein Folding from Single-Molecule FRET and All-Atom Molecular Dynamics Simulations

Abstract

Folding of most single-domain proteins has been successfully described by diffusion on a one-dimensional (1D) free energy surface. Although the 1D surface is smooth, there are many local minima in the underlying energy landscape, giving rise to landscape “roughness”. According to Kramers’ reaction-rate theory, roughness slows folding kinetics by reducing the diffusion coefficient at the top of the free energy barrier that separates folded and unfolded states. By measuring the transition-path time (tTP) from a maximum likelihood analysis of photon trajectories in single molecule FRET experiments, we have recently shown that the Kramers diffusion coefficient for a designed α-helical protein, α3D, is markedly reduced (Chung and Eaton, Nature,2013). To discover the structural origin of this slow diffusion, we have combined additional single-molecule FRET measurements with all-atom molecular dynamics (MD) calculations. α3D contains 12 negatively-charged and 10 positively-charged side-chains. Analysis of the transition paths in the MD simulations shows that many non-native salt-bridges form during the folding transition path, suggesting them as the structural origin of long tTP. To test this idea, we lowered the pH to neutralize the carboxylates and eliminate salt-bridges, which increased the folding rate by about 10-fold and significantly reduced tTP. Although it was only possible to determine an upper bound for tTP, even at the highest possible solvent viscosity (15 cP), simulations of photon trajectories suggested that most, if not all, of the increase in folding rate could be accounted for by a decreased tTP and an increased Kramers diffusion coefficient. Neutralizing the carboxylates in MD simulations also increases the folding rate and diffusion coefficient and decreases tTP. These results provide the first quantitative glimpse of the effect of specific intra-molecular interactions on barrier crossing dynamics in protein folding.