Protein folding is slaved to solvent motions - PubMed (original) (raw)

Protein folding is slaved to solvent motions

H Frauenfelder et al. Proc Natl Acad Sci U S A. 2006.

Abstract

Proteins, the workhorses of living systems, are constructed from chains of amino acids, which are synthesized in the cell based on the instructions of the genetic code and then folded into working proteins. The time for folding varies from microseconds to hours. What controls the folding rate is hotly debated. We postulate here that folding has the same temperature dependence as the alpha-fluctuations in the bulk solvent but is much slower. We call this behavior slaving. Slaving has been observed in folded proteins: Large-scale protein motions follow the solvent fluctuations with rate coefficient k(alpha) but can be slower by a large factor. Slowing occurs because large-scale motions proceed in many small steps, each determined by k(alpha). If conformational motions of folded proteins are slaved, so a fortiori must be the motions during folding. The unfolded protein makes a Brownian walk in the conformational space to the folded structure, with each step controlled by k(alpha). Because the number of conformational substates in the unfolded protein is extremely large, the folding rate coefficient, k(f), is much smaller than k(alpha). The slaving model implies that the activation enthalpy of folding is dominated by the solvent, whereas the number of steps n(f) = k(alpha)/k(f) is controlled by the number of accessible substates in the unfolded protein and the solvent. Proteins, however, undergo not only alpha- but also beta-fluctuations. These additional fluctuations are local protein motions that are essentially independent of the bulk solvent fluctuations and may be relevant at late stages of folding.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.

Fig. 1.

A schematic description of protein folding. In real space, the unfolded polypeptide (U) folds into the working protein (N). In conformational space, the protein makes a random walk through the high-dimensional energy landscape. (a) A 1D cross-section through the energy landscape showing the U (blue), TSE (red), and N (green) conformational basins. The long arrow represents a folding path with an overall rate _k_f, whereas the short arrow shows a single step, with a rate _k_α, in the conformational diffusion during folding. (b) A 2D cross-section through the energy landscape illustrating two different paths for the folding motions of proteins. Starting from a U conformation, proteins make a Brownian walk in the conformational space until they finally fall into the ensemble of N substates.

Fig. 2.

Fig. 2.

The folding rates for various polypeptides and proteins versus the solvent viscosity: (Gly-Ser)n (n = 1 and 3) polypeptide chains (17) (from Eq. 4, κ = 0.95 and 0.80, respectively), tryptophan cage (21) (κ = 0.84), cytochrome c (14, 15) (κ = 0.55), α-helix (κ = 0.53), β-hairpin (18) (κ = 0.93), and protein L (19) (κ = 0.93). The rate coefficients for the bulk α-fluctuations for glycerol–water mixtures (kα) and for kexit also are plotted for comparison.

Fig. 3.

Fig. 3.

The viscosity dependence of large-scale protein motions. (a) Viscosity dependence of the folding time at 293 K for cytochrome c (14, 15). The solid line is a linear fit predicting an internal friction within the protein (14, 15), and the dashed line is a fit to Eq. 4 for a power-law viscosity dependence of folding, with κ = 0.55. Error bars are the standard deviation. (b) Plot of the isothermal rate coefficients versus viscosity. The dotted lines are the rates for the exit of CO from Mb (kexit) at the indicated temperatures; the solid and dashed lines are the folding rates (kf) corresponding to the linear (solid line) and power-law (dashed line) fits in a, respectively.

Fig. 4.

Fig. 4.

The exit of CO from Mb (23). (a) Arrhenius plot of the CO exit rate. The symbols are the experimental data (23), the solid lines connect the data points measured in different glycerol–water mixtures [99% (wt/wt), 79% (wt/wt), and 60% (wt/wt)], and the dashed lines are the Arrhenius fits to the isoviscous data for five viscosities [log(η/cP) = 1, 2, 3, 4, and 5]. (b) Arrhenius plot of _n_exit. The solid line shows the data for the 79% (wt/wt) mixture, and the dashed lines show the data for three of the viscosities.

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