Protein folded states are kinetic hubs

Understanding molecular kinetics, and particularly protein folding, is a classic grand challenge in molecular biophysics. Network models, such as Markov state models (MSMs), are one potential solution to this problem. MSMs have recently yielded quantitative agreement with experimentally derived structures and folding rates for specific systems, leaving them positioned to potentially provide a deeper understanding of molecular kinetics that can lead to experimentally testable hypotheses. Here we use existing MSMs for the villin headpiece and NTL9, which were constructed from atomistic simulations, to accomplish this goal. In addition, we provide simpler, humanly comprehensible networks that capture the essence of molecular kinetics and reproduce qualitative phenomena like the apparent two-state folding often seen in experiments. Together, these models show that protein dynamics are dominated by stochastic jumps between numerous metastable states and that proteins have heterogeneous unfolded states (many unfolded basins that interconvert more rapidly with the native state than with one another) yet often still appear two-state. Most importantly, we find that protein native states are hubs that can be reached quickly from any other state. However, metastability and a web of nonnative states slow the average folding rate. Experimental tests for these findings and their implications for other fields, like protein design, are also discussed.

[1]  Vladimir N Uversky,et al.  Intrinsic disorder in proteins associated with neurodegenerative diseases. , 2009, Frontiers in bioscience.

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

[3]  Jia-Cherng Horng,et al.  Rapid Cooperative Two-state Folding of a Miniature α–β Protein and Design of a Thermostable Variant , 2003 .

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

[5]  D. Wetlaufer Nucleation, rapid folding, and globular intrachain regions in proteins. , 1973, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Vijay S. Pande,et al.  On the role of conformational geometry in protein folding , 1999 .

[7]  V. Pande,et al.  Rapid equilibrium sampling initiated from nonequilibrium data , 2009, Proceedings of the National Academy of Sciences.

[8]  G. Ulrich Nienhaus,et al.  Single-molecule Förster resonance energy transfer study of protein dynamics under denaturing conditions , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Martin Gruebele,et al.  Low barrier kinetics: Dependence on observables and free energy surface , 2006, J. Comput. Chem..

[10]  Vijay S Pande,et al.  Simulating oligomerization at experimental concentrations and long timescales: A Markov state model approach. , 2008, The Journal of chemical physics.

[11]  Peter G Wolynes,et al.  P versus Q: structural reaction coordinates capture protein folding on smooth landscapes. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[12]  J. Onuchic,et al.  KINETICS OF PROTEINLIKE MODELS : THE ENERGY LANDSCAPE FACTORS THAT DETERMINE FOLDING , 1995 .

[13]  Bing Shan,et al.  The unfolded state of the C-terminal domain of the ribosomal protein L9 contains both native and non-native structure. , 2009, Biochemistry.

[14]  Xuhui Huang,et al.  Using generalized ensemble simulations and Markov state models to identify conformational states. , 2009, Methods.

[15]  K. Zamaraev,et al.  Molybdenum Oxide Cluster Ions in the Gas Phase: Structure and Reactivity with Small Molecules , 1997 .

[16]  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.

[17]  J. Hofrichter,et al.  Sub-microsecond protein folding. , 2006, Journal of molecular biology.

[18]  Kunihiro Kuwajima,et al.  Multiple parallel-pathway folding of proline-free Staphylococcal nuclease. , 2003, Journal of molecular biology.

[19]  Vincent A Voelz,et al.  Unfolded-state dynamics and structure of protein L characterized by simulation and experiment. , 2010, Journal of the American Chemical Society.

[20]  S. Marqusee,et al.  Destabilization of the Escherichia coli RNase H kinetic intermediate: switching between a two-state and three-state folding mechanism. , 2004, Journal of molecular biology.

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

[22]  R. Hochstrasser,et al.  Peptide Conformational Dynamics and Vibrational Stark Effects Following Photoinitiated Disulfide Cleavage , 1997 .

[23]  V. Pande,et al.  Calculation of the distribution of eigenvalues and eigenvectors in Markovian state models for molecular dynamics. , 2007, The Journal of chemical physics.

[24]  Kwang-Hwi Cho,et al.  BIOPHYSICS AND COMPUTATIONAL BIOLOGY , 2009 .

[25]  F. Noé,et al.  Transition networks for modeling the kinetics of conformational change in macromolecules. , 2008, Current opinion in structural biology.

[26]  A. Fersht On the simulation of protein folding by short time scale molecular dynamics and distributed computing , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[27]  H. Scheraga,et al.  Global optimization of clusters, crystals, and biomolecules. , 1999, Science.

[28]  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.

[29]  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.

[30]  D. Raleigh,et al.  Rapid cooperative two-state folding of a miniature alpha-beta protein and design of a thermostable variant. , 2003, Journal of molecular biology.

[31]  KINETICS IN A GLOBALLY CONNECTED, CORRELATED RANDOM ENERGY MODEL , 1996 .

[32]  C. Schütte Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules , 1999 .

[33]  Shimon Weiss,et al.  Ruggedness in the folding landscape of protein L , 2008, HFSP journal.

[34]  M. Gruebele,et al.  Observation of strange kinetics in protein folding. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[35]  K. Dill,et al.  The protein folding problem. , 1993, Annual review of biophysics.

[36]  Protein folding in high-dimensional spaces: hypergutters and the role of nonnative interactions. , 2003, Biophysical journal.

[37]  Kyle A. Beauchamp,et al.  Molecular simulation of ab initio protein folding for a millisecond folder NTL9(1-39). , 2010, Journal of the American Chemical Society.

[38]  R. Levy,et al.  Protein folding pathways from replica exchange simulations and a kinetic network model. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[39]  V. Pande,et al.  The Roles of Entropy and Kinetics in Structure Prediction , 2009, PloS one.

[40]  V. Pande,et al.  Heterogeneity even at the speed limit of folding: large-scale molecular dynamics study of a fast-folding variant of the villin headpiece. , 2007, Journal of molecular biology.

[41]  M. Gruebele,et al.  Tuning lambda6-85 towards downhill folding at its melting temperature. , 2007, Journal of molecular biology.

[42]  K. Dill,et al.  The ultimate speed limit to protein folding is conformational searching. , 2007, Journal of the American Chemical Society.

[43]  K. Dill,et al.  Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics. , 2007, The Journal of chemical physics.

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

[45]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[46]  Vijay S Pande,et al.  Enhanced modeling via network theory: Adaptive sampling of Markov state models. , 2010, Journal of chemical theory and computation.

[47]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

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

[49]  F. Rao,et al.  The protein folding network. , 2004, Journal of molecular biology.

[50]  S Walter Englander,et al.  Order of steps in the cytochrome C folding pathway: evidence for a sequential stabilization mechanism. , 2006, Journal of molecular biology.

[51]  C. Dobson,et al.  The folding of hen lysozyme involves partially structured intermediates and multiple pathways , 1992, Nature.

[52]  Martin Suter,et al.  Small World , 2002 .

[53]  P. S. Kim,et al.  Intermediates in the folding reactions of small proteins. , 1990, Annual review of biochemistry.

[54]  Terrence G. Oas,et al.  Preorganized secondary structure as an important determinant of fast protein folding , 2001, Nature Structural Biology.

[55]  Sharon L. Milgram,et al.  The Small World Problem , 1967 .

[56]  C. Schütte,et al.  Supplementary Information for “ Constructing the Equilibrium Ensemble of Folding Pathways from Short Off-Equilibrium Simulations ” , 2009 .

[57]  D. Barrick What have we learned from the studies of two-state folders, and what are the unanswered questions about two-state protein folding? , 2009, Physical biology.

[58]  K. Dill,et al.  Protein folding by zipping and assembly , 2007, Proceedings of the National Academy of Sciences.

[59]  Jeffery G. Saven,et al.  Kinetics of protein folding: The dynamics of globally connected rough energy landscapes with biases , 1994 .

[60]  A. Fersht,et al.  Folding of chymotrypsin inhibitor 2. 1. Evidence for a two-state transition. , 1991, Biochemistry.

[61]  Benoît Roux,et al.  Mapping the conformational transition in Src activation by cumulating the information from multiple molecular dynamics trajectories , 2009, Proceedings of the National Academy of Sciences.

[62]  M. Gruebele,et al.  A one-dimensional free energy surface does not account for two-probe folding kinetics of protein alpha(3)D. , 2009, The Journal of chemical physics.