Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2006 Mar;15(3):564-82.
doi: 10.1110/ps.051758206.

Role of unfolded state heterogeneity and en-route ruggedness in protein folding kinetics

Paul A Ellison  1 , Silvia Cavagnero
Affiliations

Role of unfolded state heterogeneity and en-route ruggedness in protein folding kinetics

Paul A Ellison et al. Protein Sci. 2006 Mar.

Abstract

In order to improve our understanding of the physical bases of protein folding, there is a compelling need for better connections between experimental and computational approaches. This work addresses the role of unfolded state conformational heterogeneity and en-route intermediates, as an aid for planning and interpreting protein folding experiments. The expected kinetics were modeled for different types of energy landscapes, including multiple parallel folding routes, preferential paths dominated by one primary folding route, and distributed paths with a wide spectrum of microscopic folding rate constants. In the presence of one or more preferential routes, conformational exchange among unfolded state populations slows down the observed rates for native protein formation. We find this to be a general phenomenon, taking place even when unfolded conformations interconvert much faster than the "escape" rate constants to folding. Dramatic kinetic deceleration is expected in the presence of an increasing number of folding-incompetent unfolded conformations. This argues for the existence of parallel folding paths involving several folding-competent unfolded conformations, during the early stages of protein folding. Deviations from single-exponential behavior are observed for unfolded conformations exchanging at comparable rates or more slowly than folding events. Analysis of the effect of en-route (on-path) intermediate formation and landscape ruggedness on folding kinetics leads to the following unexpected conclusions: (1) intermediates, which often retard native state formation, may in some cases accelerate folding, and (2) rugged landscapes, usually associated with stretched exponentials, display single-exponential behavior in the presence of late high-friction paths.

PubMed Disclaimer

Figures

Scheme 1.
Scheme 1.
Figure 1.
Figure 1.
Kinetic models examined in this work for the folding of proteins that do not populate kinetic intermediates. U, U1…10, and N denote the total unfolded state population, the individual unfolded subpopulations, and the native state, respectively. The thickness of the lines for the folding events correspond to the value of the respective rate constants.
Figure 2.
Figure 2.
Time course for protein folding according to the kinetic Models I through IV, defined in Figure 1. The rate constants for the folding events in Models I to IV are listed in Table 1. The rate constants for unfolded state interconversion are as labeled on the figure. The initial total unfolded state population was set to one. Initial unfolded state populations for Models II to IV were equally partitioned among the different unfolded states.
Figure 3.
Figure 3.
(A) Illustration of the effect of multiple parallel folding pathways on predicted folding kinetics, according to five different kinetic models. Rapid interconversion of unfolded state populations is assumed. Folding rate constants and initial unfolded state populations were set to the same values as in Figure 2. Unfolded state interconversion rates were set to kinter-U = 106 sec−1. (B) Effect of number of unfolded state conformations on the observed single-exponential kinetic rate constant for folding. Simulations have been run under identical conditions to those used in A except that the number of unfolded state microscopic states has been varied, as shown in the plot. The folding rate constants for Model IV, for different number of unfolded states, were determined according to Equations 5 and 6, as discussed in Materials and Methods.
Figure 4.
Figure 4.
Flux for native state formation through individual folding routes corresponding to Models II (upper panel), III (middle panel), and IV (lower panel) of Figure 1. Folding rate constants and initial unfolded state populations were set to the same values as in Figure 2. Unfolded state interconversion rates were set to kinter-U = 106 sec−1.
Figure 5.
Figure 5.
Deviation from exponentiality during the time course of native state formation for the folding of a protein according to kinetic Models II, III, and IV. Rate constants for folding are as in Figure 2, except for the rate constants for the interconversion of unfolded state conformations (kinter-U), which are as indicated on the figure. The captions to the curves represent (a) kinetic simulation output, (b) single-exponential, (c) double-exponential, and (d) multiple (i.e., deca-) exponential fits to the simulated data. Plot residuals, i.e., differences between computation output and its matching curve fit, are shown above each panel.
Figure 6.
Figure 6.
Kinetic models examined in this work for the folding of proteins populating one class of kinetic intermediates. Symbols are defined as in the legend to Figure 1. In addition, I denotes a folding intermediate and I1…10 denote individual folding intermediates.
Figure 7.
Figure 7.
Expected time courses for native state formation according to the kinetic models illustrated in the upper portion of the figure. Each model involves at least one folding intermediate. Specific kinetic parameters are reported in Table 2. The step(s) connecting unfolded and intermediate state(s) are reversible, for intermediates of types 2 to 6. Unfolded state and intermediate interconversion rates were set to kinter-U = kinter-I = 1010 sec−1. The graphs on the left side of the figure illustrate the folding progress through the fastest path for each kinetic model. The different kinetic models are named according to the general models of Figure 1, for the U to I, and I to N steps, respectively. The asterisks refer to modified model types characterized by non–mutually interconverting intermediates.
Figure 8.
Figure 8.
Predicted time courses for native state formation according to kinetic models involving at least one folding intermediate. The specific models are illustrated in the upper portion of the figure. Kinetic parameters are reported in Table 2. Unfolded state and intermediate interconversion rates were set to kinter-U = kinter-I = 1010 sec−1. The graphs on the left side of the figure illustrate the folding progress through the fastest path for each kinetic model. The asterisks have the same meaning as in Figure 7.
Figure 9.
Figure 9.
Expected time courses for native state formation according to kinetic models involving one preferential folding pathway and at least one folding intermediate. The specific models are illustrated in the upper portion of the figure. Kinetic parameters are reported in Table 2. Unfolded state and intermediate interconversion rates were set to kinter-U = kinter-I = 1010 sec−1. The graphs on the left side of the figure illustrate the folding progress through the fastest path for each kinetic model. The asterisks have the same meaning as in Figure 7.
Figure 10.
Figure 10.
Kinetic impact of folding landscape ruggedness on protein folding. The simulations were carried out for en-route (or on-path) intermediates. The cases of a monotonically downhill (top panels) and a downhill followed by an energy barrier (bottom panels) bumpy landscapes were considered. The predicted populations of native state, kinetic intermediates, and single-, multiple (deca-), and stretched-exponential fits to the computation output are plotted as a function of time. Residuals illustrate differences between simulated outputs and curve fits. The kinetic parameters used in the calculations are provided in Table 3. Unfolded state and intermediate interconversion rates were set to kinter-U = kinter-I = 1010 sec−1. Labels to the intermediates have been omitted in the landscape images, for clarity. The kinetic models were named based on the general nomenclature of Figure 1, according the following additional criteria The first numeral refers to the transitions from U up to I3. The second numeral refers to the last transition, from I3 to N. The tilde between numerals indicates that the fast folding routes are not linked to the same intermediate. The asterisk refers to a modified model type with non–mutually interconverting intermediates. The results from stretched exponential curve fitting, for the graphs illustrating type 1 intermediates, are, from left to right: α = 2.2, k = 7.1 × 107 sec−1; α = 1.5, k = 3.6 × 107 sec−1; α = 1.4, k = 1.9 × 107 sec−1; α = 2.1, k = 1.4 × 107 sec−1; and α = 2.2, k = 1.8 × 107 sec−1, respectively.
Scheme 2.
Scheme 2.
Scheme 3.
Scheme 3.
See this image and copyright information in PMC

Similar articles

See all similar articles

Cited by

See all "Cited by" articles

References

    1. Ansari, A., Jones, C.M., Henry, E.R., Hofrichter, J., and Eaton, W.A. 1992. The role of solvent viscosity in the dynamics of protein conformational changes. Science 256: 1796–1798. - PubMed
    1. Baldwin, R.L. 1995. The nature of protein folding pathways: The classical versus the new view. J. Biomol. NMR 5: 103–109. - PubMed
    1. Brooks III, C.L. 2002. Protein and peptide folding explored with molecular simulations. Acc. Chem. Res. 35: 447–454. - PubMed
    1. Brooks III, C.L., Gruebele, M., Onuchic, J.N., and Wolynes, P.G. 1998. Chemical physics of protein folding. Proc.Natl. Acad. Sci. 95: 11037–11038. - PMC - PubMed
    1. Bryngelson, J.D., Onuchic, J.N., Socci, N.D., and Wolynes, P.G. 1995. Funnels, pathways, and the energy landscape of protein folding: A synthesis. Proteins 21: 167–195. - PubMed

Publication types

LinkOut - more resources