Simulation of protein folding by reaction path annealing

We present a systematic application of reaction path sampling to computer simulations of the folding of peptides and small proteins at atomic resolution in the presence of solvent. We use a simulated annealing protocol to generate an ensemble of room temperature folding trajectories of fixed length, which connect predetermined initial and final states. The trajectories are distributed according to a discretized version of the Onsager–Machlup action functional. We show that, despite the enormous practical restrictions placed on the number of time slices which can be explored, some of the basic kinetic features found experimentally for the folding of peptides and small proteins are exhibited in the nature of the reaction paths sampled. We test the method on three systems: A 12 residue α-helical peptide, a 16 residue β-hairpin peptide, and the 36 residue avian Pancreatic Polypeptide (aPP). All systems are represented at atomic resolution, and include explicit water molecules. For the 12 residue α-helix, we f...

[1]  Ron Elber,et al.  Calculation of classical trajectories with a very large time step: Formalism and numerical examples , 1996 .

[2]  B. Zimm,et al.  Theory of the Phase Transition between Helix and Random Coil in Polypeptide Chains , 1959 .

[3]  P. Kollman,et al.  Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. , 1998, Science.

[4]  D. Chandler,et al.  Transition pathways in a many-body system: Application to hydrogen-bond breaking in water , 1998 .

[5]  Berk Hess,et al.  LINCS: A linear constraint solver for molecular simulations , 1997 .

[6]  B. Brooks,et al.  Protein hydration elucidated by molecular dynamics simulation. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[7]  G. Parisi,et al.  Statistical Field Theory , 1988 .

[8]  Lars Onsager,et al.  Fluctuations and Irreversible Processes , 1953 .

[9]  A. Fersht.  Nucleation mechanisms in protein folding. , 1997, Current opinion in structural biology.

[10]  N Go,et al.  The effect of amino acid substitution on protein‐folding and ‐unfolding transition studied by computer simulation , 1988, Biopolymers.

[11]  V. Pande,et al.  Pathways for protein folding: is a new view needed? , 1998, Current opinion in structural biology.

[12]  K. Schulten,et al.  Unfolding of titin immunoglobulin domains by steered molecular dynamics simulation. , 1998, Biophysical journal.

[13]  S Doniach,et al.  Multiple time step diffusive Langevin dynamics for proteins , 1998, Proteins.

[14]  T. Woolf,et al.  DYNAMIC REACTION PATHS AND RATES THROUGH IMPORTANCE-SAMPLED STOCHASTIC DYNAMICS , 1999 .

[15]  Barry Honig,et al.  Calculating total electrostatic energies with the nonlinear Poisson-Boltzmann equation , 1990 .

[16]  E I Shakhnovich,et al.  Identifying the protein folding nucleus using molecular dynamics. , 1998, Journal of molecular biology.

[17]  A Kitao,et al.  Energy landscape of a native protein: Jumping‐among‐minima model , 1998, Proteins.

[18]  Christopher M. Dobson,et al.  Mutational analysis of acylphosphatase suggests the importance of topology and contact order in protein folding , 1999, Nature Structural Biology.

[19]  S Rackovsky,et al.  Unfolding and refolding of the native structure of bovine pancreatic trypsin inhibitor studied by computer simulations. , 1993, Biochemistry.

[20]  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.

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

[22]  I. R. Mcdonald,et al.  Theory of simple liquids , 1998 .

[23]  David Baker,et al.  Important role of hydrogen bonds in the structurally polarized transition state for folding of the src SH3 domain , 1998, Nature Structural &Molecular Biology.

[24]  W. L. Jorgensen,et al.  The OPLS [optimized potentials for liquid simulations] potential functions for proteins, energy minimizations for crystals of cyclic peptides and crambin. , 1988, Journal of the American Chemical Society.

[25]  P. Wolynes,et al.  Folding dynamics with nonadditive forces: A simulation study of a designed helical protein and a random heteropolymer , 1999 .

[26]  P A Kollman,et al.  Study of the stability and unfolding mechanism of BBA1 by molecular dynamics simulations at different temperatures , 1999, Protein science : a publication of the Protein Society.

[27]  V S Pande,et al.  Molecular dynamics simulations of unfolding and refolding of a beta-hairpin fragment of protein G. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[28]  H. Scheraga,et al.  Accessible surface areas as a measure of the thermodynamic parameters of hydration of peptides. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[29]  Kentaro Shimizu,et al.  Parallel algorithm for efficient calculation of second derivatives of conformational energy function in internal coordinates , 1998 .

[30]  V. Daggett,et al.  Mapping the interactions present in the transition state for unfolding/folding of FKBP12. , 1999, Journal of molecular biology.

[31]  M Levitt,et al.  Hierarchy of structure loss in MD simulations of src SH3 domain unfolding. , 1999, Journal of molecular biology.

[32]  Charles L. Brooks,et al.  Helix−Coil Kinetics: Folding Time Scales for Helical Peptides from a Sequential Kinetic Model , 1996 .

[33]  A V Finkelstein,et al.  Can protein unfolding simulate protein folding? , 1997, Protein engineering.

[34]  W. F. van Gunsteren,et al.  Effect of constraints on the dynamics of macromolecules , 1982 .

[35]  Lawrence R. Pratt,et al.  A statistical method for identifying transition states in high dimensional problems , 1986 .

[36]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[37]  Fumiaki Kanô,et al.  Dynamics of folding and unfolding transition in a globular protein studied by time correlation functions from computer simulation , 1982, Biopolymers.

[38]  T. Blundell,et al.  X-ray analysis (1. 4-A resolution) of avian pancreatic polypeptide: Small globular protein hormone. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[39]  L. Serrano,et al.  Obligatory steps in protein folding and the conformational diversity of the transition state , 1998, Nature Structural &Molecular Biology.

[40]  K. Dill,et al.  Protein folding in the landscape perspective: Chevron plots and non‐arrhenius kinetics , 1998, Proteins.

[41]  M. Karplus,et al.  A comparison between molecular dynamics and X-ray results for dissociated CO in myoglobin , 1997, Nature Structural Biology.

[42]  R. L. Baldwin,et al.  Parameters of helix–coil transition theory for alanine‐based peptides of varying chain lengths in water , 1991, Biopolymers.

[43]  K Schulten,et al.  Stability and dynamics of G-actin: back-door water diffusion and behavior of a subdomain 3/4 loop. , 1997, Biophysical journal.

[44]  M Karplus,et al.  Ligand-induced conformational changes in ras p21: a normal mode and energy minimization analysis. , 1997, Journal of molecular biology.

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

[46]  M. Levitt,et al.  Protein unfolding pathways explored through molecular dynamics simulations. , 1993, Journal of molecular biology.

[47]  S. R. Kimura,et al.  Surface of active polarons: A semiexplicit solvation method for biomolecular dynamics , 2000 .

[48]  C. Schiffer,et al.  Investigation of protein unfolding and stability by computer simulation. , 1995, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[49]  S. Chandrasekhar.  Stochastic problems in Physics and Astronomy , 1943 .

[50]  A. Fersht,et al.  The structure of the transition state for folding of chymotrypsin inhibitor 2 analysed by protein engineering methods: evidence for a nucleation-condensation mechanism for protein folding. , 1995, Journal of molecular biology.

[51]  Ron Elber,et al.  Stochastic path approach to compute atomically detailed trajectories: Application to the folding of C peptide , 1999 .

[52]  Harold A. Scheraga,et al.  An efficient, differentiable hydration potential for peptides and proteins , 1996, J. Comput. Chem..

[53]  J. Straub,et al.  The MaxFlux algorithm for calculating variationally optimized reaction paths for conformational transitions in many body systems at finite temperature , 1997 .

[54]  G. Careri,et al.  Protein hydration and function. , 1991, Advances in protein chemistry.

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

[56]  G. Millhauser,et al.  Estimating the relative populations of 3(10)-helix and alpha-helix in Ala-rich peptides: a hydrogen exchange and high field NMR study. , 1997, Journal of molecular biology.

[57]  D. Eisenberg,et al.  Atomic solvation parameters applied to molecular dynamics of proteins in solution , 1992, Protein science : a publication of the Protein Society.

[58]  H. Risken.  The Fokker-Planck equation : methods of solution and applications , 1985 .

[59]  U. Singh,et al.  A NEW FORCE FIELD FOR MOLECULAR MECHANICAL SIMULATION OF NUCLEIC ACIDS AND PROTEINS , 1984 .

[60]  E. Shakhnovich.  Theoretical studies of protein-folding thermodynamics and kinetics. , 1997, Current opinion in structural biology.

[61]  Sebastian Doniach,et al.  Simulations of the thermodynamic properties of a short polyalanine peptide using potentials of mean force , 1997 .

[62]  Ron Elber,et al.  Temperature dependent reaction coordinates , 2000 .

[63]  M. Totrov,et al.  Contact area difference (CAD): a robust measure to evaluate accuracy of protein models. , 1997, Journal of molecular biology.

[64]  G. Millhauser.  Views of helical peptides: a proposal for the position of 3(10)-helix along the thermodynamic folding pathway. , 1995, Biochemistry.

[65]  J. Straub,et al.  Direct computation of long time processes in peptides and proteins: Reaction path study of the coil‐to‐helix transition in polyalanine , 1999, Proteins.

[66]  A. Gronenborn,et al.  A novel, highly stable fold of the immunoglobulin binding domain of streptococcal protein G. , 1993, Science.

[67]  A. Fersht,et al.  The changing nature of the protein folding transition state: implications for the shape of the free-energy profile for folding. , 1998, Journal of molecular biology.

[68]  Sebastian Doniach,et al.  Protein flexibility in solution and in crystals , 1999 .

[69]  M Karplus,et al.  "New view" of protein folding reconciled with the old through multiple unfolding simulations. , 1997, Science.

[70]  Ron Elber,et al.  A method for determining reaction paths in large molecules: application to myoglobin , 1987 .

[71]  Christoph Dellago,et al.  On the calculation of reaction rate constants in the transition path ensemble , 1999 .

[72]  R. Dyer,et al.  Fast events in protein folding: helix melting and formation in a small peptide. , 1996, Biochemistry.