Measuring internal friction of an ultrafast-folding protein

Nanosecond laser T-jump was used to measure the viscosity dependence of the folding kinetics of the villin subdomain under conditions where the viscogen has no effect on its equilibrium properties. The dependence of the unfolding/refolding relaxation time on solvent viscosity indicates a major contribution to the dynamics from internal friction. The internal friction increases with increasing temperature, suggesting a shift in the transition state along the reaction coordinate toward the native state with more compact structures, and therefore, a smaller diffusion coefficient due to increased landscape roughness. Fitting the data with an Ising-like model yields a relatively small position dependence for the diffusion coefficient. This finding is consistent with the excellent correlation found between experimental and calculated folding rates based on free energy barrier heights using the same diffusion coefficient for every protein.

[1]  Bojan Zagrovic,et al.  Solvent viscosity dependence of the folding rate of a small protein: Distributed computing study , 2003, J. Comput. Chem..

[2]  T R Sosnick,et al.  Viscosity dependence of the folding kinetics of a dimeric and monomeric coiled coil. , 1999, Biochemistry.

[3]  D. Baker,et al.  Contact order, transition state placement and the refolding rates of single domain proteins. , 1998, Journal of molecular biology.

[4]  V. Muñoz,et al.  Folding dynamics and mechanism of β-hairpin formation , 1997, Nature.

[5]  D Baker,et al.  Limited internal friction in the rate-limiting step of a two-state protein folding reaction. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Peter G Wolynes,et al.  Scanning malleable transition state ensembles: comparing theory and experiment for folding protein U1A. , 2005, Biochemistry.

[7]  T. Schindler,et al.  Diffusion control in an elementary protein folding reaction. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[8]  E. Henry,et al.  Relaxation rate for an ultrafast folding protein is independent of chemical denaturant concentration. , 2007, Journal of the American Chemical Society.

[9]  William A. Eaton,et al.  Combinatorial modeling of protein folding kinetics: free energy profiles and rates , 2004 .

[10]  J. Onuchic,et al.  Protein folding funnels: a kinetic approach to the sequence-structure relationship. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[11]  V. Muñoz,et al.  A simple model for calculating the kinetics of protein folding from three-dimensional structures. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[12]  J. Onuchic,et al.  Understanding protein folding with energy landscape theory Part II: Quantitative aspects , 2002, Quarterly Reviews of Biophysics.

[13]  J. Onuchic,et al.  Folding time predictions from all-atom replica exchange simulations. , 2007, Journal of molecular biology.

[14]  A limiting speed for protein folding at low solvent viscosity. , 2004, Journal of the American Chemical Society.

[15]  E. Henry,et al.  Chemical, physical, and theoretical kinetics of an ultrafast folding protein , 2008, Proceedings of the National Academy of Sciences.

[16]  H. Kramers Brownian motion in a field of force and the diffusion model of chemical reactions , 1940 .

[17]  J. Hofrichter,et al.  Laser temperature jump study of the helix<==>coil kinetics of an alanine peptide interpreted with a 'kinetic zipper' model. , 1997, Biochemistry.

[18]  Benjamin Schuler,et al.  Ultrafast dynamics of protein collapse from single-molecule photon statistics , 2007, Proceedings of the National Academy of Sciences.

[19]  Gerhard Hummer,et al.  Intrinsic rates and activation free energies from single-molecule pulling experiments. , 2006, Physical review letters.

[20]  Amyn S. Teja,et al.  Density, Viscosity, and Thermal Conductivity of Aqueous Ethylene, Diethylene, and Triethylene Glycol Mixtures between 290 K and 450 K , 2003 .

[21]  V Muñoz,et al.  A statistical mechanical model for beta-hairpin kinetics. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Jorge Chahine,et al.  Configuration-dependent diffusion can shift the kinetic transition state and barrier height of protein folding , 2007, Proceedings of the National Academy of Sciences.

[23]  S. Hagen,et al.  Internal friction controls the speed of protein folding from a compact configuration. , 2004, Biochemistry.

[24]  Linlin Qiu,et al.  Internal friction in the ultrafast folding of the tryptophan cage , 2004 .

[25]  Gerhard Hummer,et al.  Diffusive model of protein folding dynamics with Kramers turnover in rate. , 2006, Physical review letters.

[26]  John E. Straub,et al.  Classical and modern methods in reaction rate theory , 1988 .

[27]  C. M. Jones,et al.  The role of solvent viscosity in the dynamics of protein conformational changes. , 1992, Science.

[28]  S. Plotkin,et al.  Three-body interactions improve the prediction of rate and mechanism in protein folding models. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[29]  J. Udgaonkar,et al.  Diffusional barrier in the unfolding of a small protein. , 2007, Journal of molecular biology.

[30]  D. Thirumalai,et al.  Measuring the energy landscape roughness and the transition state location of biomolecules using single molecule mechanical unfolding experiments , 2006, Journal of Physics: Condensed Matter.

[31]  P. Wolynes,et al.  The experimental survey of protein-folding energy landscapes , 2005, Quarterly Reviews of Biophysics.

[32]  Shoji Takada,et al.  Microscopic Theory of Protein Folding Rates.II: Local Reaction Coordinates and Chain Dynamics , 2000, cond-mat/0008455.

[33]  J. Hofrichter,et al.  Effect of Viscosity on the Kinetics of α-Helix and β-Hairpin Formation , 2001 .

[34]  J. Onuchic,et al.  DIFFUSIVE DYNAMICS OF THE REACTION COORDINATE FOR PROTEIN FOLDING FUNNELS , 1996, cond-mat/9601091.

[35]  Regine Herbst-Irmer,et al.  High-resolution x-ray crystal structures of the villin headpiece subdomain, an ultrafast folding protein. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[36]  V. Muñoz,et al.  A statistical mechanical model for β-hairpin kinetics , 1998 .

[37]  Alessandro Pelizzola,et al.  Exact solution of the Muñoz-Eaton model for protein folding. , 2002, Physical review letters.

[38]  F. Schmid,et al.  Diffusional barrier crossing in a two-state protein folding reaction , 1999, Nature Structural Biology.

[39]  Jan Kubelka,et al.  Estimating free-energy barrier heights for an ultrafast folding protein from calorimetric and kinetic data. , 2008, The journal of physical chemistry. B.

[40]  V. Muñoz,et al.  The Helix-Coil Kinetics of a Heteropeptide , 2000 .

[41]  V Muñoz,et al.  Folding dynamics and mechanism of beta-hairpin formation. , 1997, Nature.

[42]  H. Frauenfelder,et al.  Protein folding is slaved to solvent motions , 2006, Proceedings of the National Academy of Sciences.

[43]  A. Fersht Structure and mechanism in protein science , 1998 .

[44]  John E. Straub,et al.  Time scales and pathways for kinetic energy relaxation in solvated proteins: Application to carbonmonoxy myoglobin , 2000 .

[45]  Lisa J Lapidus,et al.  How fast is protein hydrophobic collapse? , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[46]  J. Onuchic,et al.  Funnels, pathways, and the energy landscape of protein folding: A synthesis , 1994, Proteins.

[47]  James T. Hynes,et al.  The stable states picture of chemical reactions. II. Rate constants for condensed and gas phase reaction models , 1980 .

[48]  A. Szabó,et al.  Electron transfer reaction dynamics in non-Debye solvents , 1998 .

[49]  J. Telis‐Romero,et al.  Viscosity of Aqueous Carbohydrate Solutions at Different Temperatures and Concentrations , 2007 .

[50]  M. Karplus,et al.  Parametrization of the friction constant for stochastic simulations of polymers , 1988 .