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High-Resolution Free-Energy Landscape Analysis of α-Helical Protein Folding: HP35 and Its Double Mutant.

Banushkina PV, Krivov SV - J Chem Theory Comput (2013)

Bottom Line: Natl.Four different estimations of the pre-exponential factor for both proteins give k 0 (-1) values of approximately a few tens of nanoseconds.Our analysis gives detailed information about folding of the proteins and can serve as a rigorous common language for extensive comparison between experiment and simulation.

View Article: PubMed Central - PubMed

Affiliation: Astbury Center for Structural Molecular Biology, Faculty of Biological Sciences, University of Leeds , Leeds LS2 9JT, United Kingdom.

ABSTRACT
The free-energy landscape can provide a quantitative description of folding dynamics, if determined as a function of an optimally chosen reaction coordinate. Here, we construct the optimal coordinate and the associated free-energy profile for all-helical proteins HP35 and its norleucine (Nle/Nle) double mutant, based on realistic equilibrium folding simulations [Piana et al. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 17845]. From the obtained profiles, we directly determine such basic properties of folding dynamics as the configurations of the minima and transition states (TS), the formation of secondary structure and hydrophobic core during the folding process, the value of the pre-exponential factor and its relation to the transition path times, the relation between the autocorrelation times in TS and minima. We also present an investigation of the accuracy of the pre-exponential factor estimation based on the transition-path times. Four different estimations of the pre-exponential factor for both proteins give k 0 (-1) values of approximately a few tens of nanoseconds. Our analysis gives detailed information about folding of the proteins and can serve as a rigorous common language for extensive comparison between experiment and simulation.

No MeSH data available.


Related in: MedlinePlus

Plot of theposition autocorrelation function in the native (N)state (dashed line), the denatured (D) state (dash-dotted line), andthe transition state (TS) (solid line). Dotted line shows ln C(τ) = −1 – τ/70, which is anautocorrelation function with a time decay τcorr =70 ns to mimic the experiment.34
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fig9: Plot of theposition autocorrelation function in the native (N)state (dashed line), the denatured (D) state (dash-dotted line), andthe transition state (TS) (solid line). Dotted line shows ln C(τ) = −1 – τ/70, which is anautocorrelation function with a time decay τcorr =70 ns to mimic the experiment.34

Mentions: Experimental estimatesof k0 for theNle/Nle double mutant were obtained by Kubelka et al.34 A “very rough estimate” was made by assumingthat the empirical protein folding “speed limit” tf = N/100 μs, where N is the number of residues in the polypeptide chain,2 corresponds to k0–1; for N = 35, one obtains k0–1 ≈ 350 ns. The secondestimate is based on the decay time of the autocorrelation functionin the folded state. A value of τcorr = 70 ns wasobtained from a biexponential fit of the relaxation after a temperaturejump.34 Assuming that the decay times inthe native and transition states are the same (i.e., that these stateshave similar curvature and diffusion coefficients), one finds k0–1 = 2πτcorr ≈ 420 ns. Having the folding trajectory, we cantest the assumptions: in particular, how similar are the autocorrelationdecay times at different regions on the FEP? Figure 9 shows the logarithm of the position autocorrelation functionln C(τ) in the N, D, and TS states, whereandAs one can see, the autocorrelation functiondoes not have a simple single-exponential decay C(τ) = exp(−τ/τcorr), and, thus,τcorr cannot be unambiguously determined. However,it is clear that the “effective” decay time at the transitionstate, which actually determines the pre-exponential factor, is significantlysmaller than that in the basins, indicating that the assumption aboveis likely to be poor. Note that the long-time slope of lnC(τ) in the D and N states is close to the experimentally measuredτcorr value (τcorr = 70 ns).


High-Resolution Free-Energy Landscape Analysis of α-Helical Protein Folding: HP35 and Its Double Mutant.

Banushkina PV, Krivov SV - J Chem Theory Comput (2013)

Plot of theposition autocorrelation function in the native (N)state (dashed line), the denatured (D) state (dash-dotted line), andthe transition state (TS) (solid line). Dotted line shows ln C(τ) = −1 – τ/70, which is anautocorrelation function with a time decay τcorr =70 ns to mimic the experiment.34
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Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3860327&req=5

fig9: Plot of theposition autocorrelation function in the native (N)state (dashed line), the denatured (D) state (dash-dotted line), andthe transition state (TS) (solid line). Dotted line shows ln C(τ) = −1 – τ/70, which is anautocorrelation function with a time decay τcorr =70 ns to mimic the experiment.34
Mentions: Experimental estimatesof k0 for theNle/Nle double mutant were obtained by Kubelka et al.34 A “very rough estimate” was made by assumingthat the empirical protein folding “speed limit” tf = N/100 μs, where N is the number of residues in the polypeptide chain,2 corresponds to k0–1; for N = 35, one obtains k0–1 ≈ 350 ns. The secondestimate is based on the decay time of the autocorrelation functionin the folded state. A value of τcorr = 70 ns wasobtained from a biexponential fit of the relaxation after a temperaturejump.34 Assuming that the decay times inthe native and transition states are the same (i.e., that these stateshave similar curvature and diffusion coefficients), one finds k0–1 = 2πτcorr ≈ 420 ns. Having the folding trajectory, we cantest the assumptions: in particular, how similar are the autocorrelationdecay times at different regions on the FEP? Figure 9 shows the logarithm of the position autocorrelation functionln C(τ) in the N, D, and TS states, whereandAs one can see, the autocorrelation functiondoes not have a simple single-exponential decay C(τ) = exp(−τ/τcorr), and, thus,τcorr cannot be unambiguously determined. However,it is clear that the “effective” decay time at the transitionstate, which actually determines the pre-exponential factor, is significantlysmaller than that in the basins, indicating that the assumption aboveis likely to be poor. Note that the long-time slope of lnC(τ) in the D and N states is close to the experimentally measuredτcorr value (τcorr = 70 ns).

Bottom Line: Natl.Four different estimations of the pre-exponential factor for both proteins give k 0 (-1) values of approximately a few tens of nanoseconds.Our analysis gives detailed information about folding of the proteins and can serve as a rigorous common language for extensive comparison between experiment and simulation.

View Article: PubMed Central - PubMed

Affiliation: Astbury Center for Structural Molecular Biology, Faculty of Biological Sciences, University of Leeds , Leeds LS2 9JT, United Kingdom.

ABSTRACT
The free-energy landscape can provide a quantitative description of folding dynamics, if determined as a function of an optimally chosen reaction coordinate. Here, we construct the optimal coordinate and the associated free-energy profile for all-helical proteins HP35 and its norleucine (Nle/Nle) double mutant, based on realistic equilibrium folding simulations [Piana et al. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 17845]. From the obtained profiles, we directly determine such basic properties of folding dynamics as the configurations of the minima and transition states (TS), the formation of secondary structure and hydrophobic core during the folding process, the value of the pre-exponential factor and its relation to the transition path times, the relation between the autocorrelation times in TS and minima. We also present an investigation of the accuracy of the pre-exponential factor estimation based on the transition-path times. Four different estimations of the pre-exponential factor for both proteins give k 0 (-1) values of approximately a few tens of nanoseconds. Our analysis gives detailed information about folding of the proteins and can serve as a rigorous common language for extensive comparison between experiment and simulation.

No MeSH data available.


Related in: MedlinePlus