Folding λ-repressor at its speed limit

Abstract

We show that the five-helix bundle λ6-85 can be engineered and solvent-tuned to make the transition from activated two-state folding to downhill folding. The transition manifests itself as the appearance of additional dynamics faster than the activated kinetics, followed by the disappearance of the activated kinetics when the bias toward the native state is increased. Our fastest value of 1 μs for the "speed" limit of λ6-85 is measured at low concentrations of a denaturant that smoothes the free-energy surface. Complete disappearance of the activated phase is obtained in stabilizing glucose buffer. Langevin dynamics on a rough free-energy surface with variable bias toward the native state provides a robust and quantitative description of the transition from activated to downhill folding. Based on our simulation, we estimate the residual energetic frustration of λ6-85 to be δ2 G ≈ 0.64 k 2T2. We show that λ6-86, as well as very fast folding proteins or folding intermediates estimated to lie near the speed limit, provide a better rate-topology correlation than proteins with larger energetic frustration. A limit of β ≥ 0.7 on any stretching of λ6-85 barrier-free dynamics suggests that a low-dimensional free-energy surface is sufficient to describe folding.