Estimating Free-Energy Barrier Heights for an Ultrafast Folding Protein from Calorimetric and Kinetic Data

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• 作者：Raquel Godoy-Ruiz ; Eric R. Henry ; Jan Kubelka ; James Hofrichter ; Victor Muñ ; oz ; Jose M. Sanchez-Ruiz ; William A. Eaton
• 刊名：Journal of Physical Chemistry B
• 出版年：2008
• 出版时间：May 15, 2008
• 年：2008
• 卷：112
• 期：19
• 页码：5938 - 5949
• 全文大小：385K
• 年卷期：v.112,no.19(May 15, 2008)
• ISSN：1520-5207

文摘

Differential scanning calorimetry was used to measure the temperature dependence of the absolute heat capacityof the 35-residue subdomain of the villin headpiece, a protein that folds in 5 mages/entities/mgr.gif">s and is therefore assumed tohave a small free-energy barrier separating folded and unfolded states. To obtain an estimate of the barrierheight from the calorimetric data, two models, a variable-barrier model and an Ising-like model, were usedto fit the heat capacity in excess of the folded state over the temperature range 15-125 mages/entities/deg.gif">C. The variable-barrier model is based on an empirical mathematical form for the density of states, with four adjustableparameters and the enthalpy (H) as a reaction coordinate. The Ising-like model is based on the inter-residuecontact map of the X-ray structure with exact enumeration of ~10⁵ possible conformations, with two adjustableparameters in the partition function, and either the fraction of native contacts (Q) or the number of orderedresidues (P) as reaction coordinates. The variable-barrier model provides an excellent fit to the data andyields a barrier height at the folding temperature ranging from 0.4 to 1.1 kcal mol^-1, while the Ising-likemodel provides a less good fit and yields barrier heights of 2.3 ± 0.1 kcal mol^-1 and 2.1 ± 0.1 kcal mol^-1for the Q and P reaction coordinates, respectively. In both models, the barrier to folding increases with increasingtemperature. Assuming a sufficiently large activation energy for diffusion on the free-energy surfaces, bothmodels are consistent with the observation of a temperature-independent folding rate in previously publishedlaser temperature-jump experiments. Analysis of this kinetic data, using an approximate form for the pre-exponential factor of Kramers theory and the 70 ns relaxation time for the fast phase that precedes the unfolding/refolding relaxation to determine the diffusion coefficient, results in a barrier height of 1.6 ± 0.3 kcal mol^-1for an unspecified reaction coordinate. Although no independent test of the validity of the H, Q, or P reactioncoordinates is given, the barrier-height estimates obtained with the three reaction coordinates are in quitegood agreement with the value derived from a Kramers analysis of the kinetics that makes no assumptionsabout the reaction coordinate. However, the higher estimates obtained using Q or P appear more consistentwith the finding of barrier-crossing kinetics of a villin mutant that folds in 700 ns, corresponding to a 1.3kcal mol^-1 reduction in the folding barrier relative to wild-type. All of the results suggest that the free-energybarrier to folding is sufficiently low that it should be possible to engineer this protein or find solution conditionsthat would eliminate the barrier to create the "downhill" folding scenario of Wolynes and Onuchic.