Dependence of Internal Friction on Folding Mechanism

An outstanding challenge in protein folding is understanding the origin of “internal friction” in folding dynamics, experimentally identified from the dependence of folding rates on solvent viscosity. A possible origin suggested by simulation is the crossing of local torsion barriers. However, it was unclear why internal friction varied from protein to protein or for different folding barriers of the same protein. Using all-atom simulations with variable solvent viscosity, in conjunction with transition-path sampling to obtain reaction rates and analysis via Markov state models, we are able to determine the internal friction in the folding of several peptides and miniproteins. In agreement with experiment, we find that the folding events with greatest internal friction are those that mainly involve helix formation, while hairpin formation exhibits little or no evidence of friction. Via a careful analysis of folding transition paths, we show that internal friction arises when torsion angle changes are an important part of the folding mechanism near the folding free energy barrier. These results suggest an explanation for the variation of internal friction effects from protein to protein and across the energy landscape of the same protein.

[1]  R. Best,et al.  Correction to Balanced Protein–Water Interactions Improve Properties of Disordered Proteins and Non-Specific Protein Association , 2015, Journal of chemical theory and computation.

[2]  R. Best,et al.  Molecular Origins of Internal Friction Effects on Protein Folding Rates , 2014, Nature Communications.

[3]  G. Papoian,et al.  Concerted dihedral rotations give rise to internal friction in unfolded proteins. , 2014, Journal of the American Chemical Society.

[4]  Frank Noé,et al.  Markov state models of biomolecular conformational dynamics. , 2014, Current opinion in structural biology.

[5]  William A. Eaton,et al.  Single molecule fluorescence probes dynamics of barrier crossing , 2013, Nature.

[6]  R. Best,et al.  Engineering Folding Dynamics from Two-State to Downhill: Application to λ-Repressor , 2013, The journal of physical chemistry. B.

[7]  K. Lindorff-Larsen,et al.  Atomic-level description of ubiquitin folding , 2013, Proceedings of the National Academy of Sciences.

[8]  R. Best,et al.  Folding Kinetics and Unfolded State Dynamics of the GB1 Hairpin from Molecular Simulation. , 2013, Journal of chemical theory and computation.

[9]  R. Best,et al.  Force-field dependence of chignolin folding and misfolding: comparison with experiment and redesign. , 2012, Biophysical journal.

[10]  R. R. Cheng,et al.  Quantifying internal friction in unfolded and intrinsically disordered proteins with single-molecule spectroscopy , 2012, Proceedings of the National Academy of Sciences.

[11]  J. Dzubiella,et al.  Peptide chain dynamics in light and heavy water: zooming in on internal friction. , 2012, Journal of the American Chemical Society.

[12]  Kevin J. McHale,et al.  Single-Molecule Fluorescence Experiments Determine Protein Folding Transition Path Times , 2012, Science.

[13]  Jane Clarke,et al.  Localizing internal friction along the reaction coordinate of protein folding by combining ensemble and single-molecule fluorescence spectroscopy , 2012, Nature Communications.

[14]  Robert B Best,et al.  Microscopic events in β-hairpin folding from alternative unfolded ensembles , 2011, Proceedings of the National Academy of Sciences.

[15]  Frank Noé,et al.  Markov models of molecular kinetics: generation and validation. , 2011, The Journal of chemical physics.

[16]  R. Best,et al.  What is the time scale for α-helix nucleation? , 2011, Journal of the American Chemical Society.

[17]  R. Best,et al.  Protein simulations with an optimized water model: cooperative helix formation and temperature-induced unfolded state collapse. , 2010, The journal of physical chemistry. B.

[18]  Dmitry M Korzhnev,et al.  A Transient and Low-Populated Protein-Folding Intermediate at Atomic Resolution , 2010, Science.

[19]  H. Schwalbe,et al.  Intrinsic propensities of amino acid residues in GxG peptides inferred from amide I' band profiles and NMR scalar coupling constants. , 2010, Journal of the American Chemical Society.

[20]  Jane Clarke,et al.  Experimental evidence for a frustrated energy landscape in a 3-helix bundle protein family , 2009, Nature.

[21]  Feng Liu,et al.  The transition state transit time of WW domain folding is controlled by energy landscape roughness. , 2009, The Journal of chemical physics.

[22]  Vijay S Pande,et al.  Progress and challenges in the automated construction of Markov state models for full protein systems. , 2009, The Journal of chemical physics.

[23]  C. Schubert,et al.  Context-independent, temperature-dependent helical propensities for amino acid residues. , 2009, Journal of the American Chemical Society.

[24]  William A Eaton,et al.  Experimental determination of upper bound for transition path times in protein folding from single-molecule photon-by-photon trajectories , 2009, Proceedings of the National Academy of Sciences.

[25]  William A Eaton,et al.  Measuring internal friction of an ultrafast-folding protein , 2008, Proceedings of the National Academy of Sciences.

[26]  Carsten Kutzner,et al.  GROMACS 4:  Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. , 2008, Journal of chemical theory and computation.

[27]  G. Hummer,et al.  Coarse master equations for peptide folding dynamics. , 2008, The journal of physical chemistry. B.

[28]  Martin Gruebele,et al.  Tuning λ6- 85 towards downhill folding at its melting temperature , 2007 .

[29]  M. Parrinello,et al.  Canonical sampling through velocity rescaling. , 2007, The Journal of chemical physics.

[30]  P. Bolhuis,et al.  Sampling the multiple folding mechanisms of Trp-cage in explicit solvent , 2006, Proceedings of the National Academy of Sciences.

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

[32]  刘金明,et al.  IL-13受体α2降低血吸虫病肉芽肿的炎症反应并延长宿主存活时间[英]/Mentink-Kane MM,Cheever AW，Thompson RW，et al//Proc Natl Acad Sci U S A , 2005 .

[33]  Cecilia Clementi,et al.  Quantifying the roughness on the free energy landscape: entropic bottlenecks and protein folding rates. , 2004, Journal of the American Chemical Society.

[34]  Peter G Wolynes,et al.  Protein topology determines binding mechanism. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[35]  G. Hummer.  From transition paths to transition states and rate coefficients. , 2004, The Journal of chemical physics.

[36]  Wei Zhang,et al.  A point‐charge force field for molecular mechanics simulations of proteins based on condensed‐phase quantum mechanical calculations , 2003, J. Comput. Chem..

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

[38]  Martin Gruebele,et al.  Folding at the speed limit , 2003, Nature.

[39]  J. W. Neidigh,et al.  Designing a 20-residue protein , 2002, Nature Structural Biology.

[40]  Sheena E. Radford,et al.  Im7 folding mechanism: misfolding on a path to the native state , 2002, Nature Structural Biology.

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

[42]  D. Thirumalai,et al.  Native topology determines force-induced unfolding pathways in globular proteins. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[43]  J. Onuchic,et al.  Topological and energetic factors: what determines the structural details of the transition state ensemble and "en-route" intermediates for protein folding? An investigation for small globular proteins. , 2000, Journal of molecular biology.

[44]  Y. Sugita,et al.  Replica-exchange molecular dynamics method for protein folding , 1999 .

[45]  C L Brooks,et al.  Exploring the origins of topological frustration: design of a minimally frustrated model of fragment B of protein A. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

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

[47]  L Serrano,et al.  A tale of two secondary structure elements: when a beta-hairpin becomes an alpha-helix. , 1999, Journal of molecular biology.

[48]  David J. Wales,et al.  Energy Landscape of a Model Protein , 1999, cond-mat/9904304.

[49]  A. Mark,et al.  On the validity of Stokes' law at the molecular level , 1999 .

[50]  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.

[51]  C. Dellago,et al.  Transition path sampling and the calculation of rate constants , 1998 .

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

[53]  D. Thirumalai,et al.  Viscosity Dependence of the Folding Rates of Proteins , 1997, cond-mat/9705309.

[54]  J. Onuchic,et al.  Navigating the folding routes , 1995, Science.

[55]  G L Gilliland,et al.  Two crystal structures of the B1 immunoglobulin-binding domain of streptococcal protein G and comparison with NMR. , 1994, Biochemistry.

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

[57]  Matthews Cr,et al.  Role of diffusion in the folding of the alpha subunit of tryptophan synthase from Escherichia coli. , 1990 .

[58]  P. Wolynes,et al.  Intermediates and barrier crossing in a random energy model , 1989 .

[59]  W. Kabsch,et al.  Dictionary of protein secondary structure: Pattern recognition of hydrogen‐bonded and geometrical features , 1983, Biopolymers.

[60]  M. Parrinello,et al.  Polymorphic transitions in single crystals: A new molecular dynamics method , 1981 .

[61]  H Frauenfelder,et al.  Solvent viscosity and protein dynamics. , 1980, Biochemistry.

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

[63]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

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

[65]  K. Dill,et al.  From Levinthal to pathways to funnels , 1997, Nature Structural Biology.

[66]  W. Kuhn,et al.  Modellmässige Deutung der inneren Viskosität (der Formzähigkeitskonstante) von Fadenmolekeln I , 1946 .