Long‐Time Protein Folding Dynamics from Short‐Time Molecular Dynamics Simulations
Abstract
Protein folding involves physical timescales—microseconds to seconds—that are too long to be studied directly by straightforward molecular dynamics simulation, where the fundamental timestep is constrained to femtoseconds. Here we show how the long‐time statistical dynamics of a simple solvated biomolecular system can be well described by a discrete‐state Markov chain model constructed from trajectories that are an order of magnitude shorter than the longest relaxation times of the system. This suggests that such models, appropriately constructed from short molecular dynamics simulations, may have utility in the study of long‐time conformational dynamics.
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References
1.
M. Andrec, A. K. Felts, E. Gallicchio, and R. M. Levy, Protein folding pathways from replica exchange simulations and a kinetic network model, Proc. Natl. Acad. Sci. USA, 102 (2005), pp. 6801–6806.
2.
C. B. Anfinsen, Principles that govern folding of protein chains, Science, 181 (1973), pp. 223–230.
3.
K. D. Ball and R. S. Berry, Realistic master equation modeling of relaxation on complete potential energy surfaces: Kinetic results, J. Chem. Phys., 109 (1998), pp. 8557–8572.
4.
H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak, Molecular dynamics with coupling to an external bath, J. Chem. Phys., 81 (1984), pp. 3684–3690.
5.
P. G. Bolhuis, C. Dellago, and D. Chandler, Reaction coordinates of biomolecular isomerization, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 5877–5882.
6.
D. A. Case, D. A. Pearlman, J. W. Caldwell, T. E. Cheatham, III, J. Wang, W. S. Ross, C. L. Simmerling, T. A. Darden, K. M. Merz, R. V. Stanton, A. L. Cheng, J. J. Vincent, M. Crowley, V. Tsui, H. Gohlke, R. J. Radmer, Y. Duan, J. Pitera, I. Massova, G. L. Seibel, U. C. Singh, P. K. Weiner, and P. A. Kollman, AMBER7, University of California, San Francisco, CA, 2002.
7.
J. D. Chodera, An MPI‐Based Parallel perl Wrapper to Conduct Replica‐Exchange Dynamics for the sander Molecular Dynamics Program from amber7, http://www.dillgroup.ucsf.edu/∼jchodera/code/rex.
8.
J. D. Chodera, W. C. Swope, J. W. Pitera, C. Seok, and K. A. Dill, Use of the weighted histogram analysis method for the analysis of simulated and parallel tempering simulations, J. Chem. Theor. Comput., to appear.
9.
R. Czerminski and R. Elber, Reaction path study of conformational transitions in flexible systems: Application to peptides, J. Chem. Phys., 92 (1990), pp. 5580–5601.
10.
T. A. Darden, D. M. York, and L. G. Pedersen, Particle mesh Ewald—An N log(N) method for Ewald sums in large systems, J. Chem. Phys., 98 (1993), pp. 10089–10092.
11.
B. L. de Groot, X. Daura, A. E. Mark, and H. Grubmüller, Essential dynamics of reversible peptide folding: Memory‐free conformational dynamics governed by internal hydrogen bonds, J. Mol. Biol., 309 (2001), pp. 299–313.
12.
C. Dellago, P. G. Bolhuis, and D. Chandler, Efficient transition path sampling: Application to the Lennard‐Jones cluster rearrangements, J. Chem. Phys., 108 (1998), pp. 9236–9245.
13.
W. E, W. Ren, and E. Vanden‐Eijnden, String method for the study of rare events, Phys. Rev. B, 66 (2002), 052301.
14.
B. Efron, Bootstrap methods: Another look at the jackknife, Ann. Statist., 7 (1979), pp. 1–26.
15.
A. K. Faradjian and R. Elber, Computing time scales from reaction coordinates by milestoning, J. Chem. Phys., 120 (2004), pp. 10880–10889.
16.
A. R. Fersht, On the simulation of protein folding by short time scale molecular dynamics and distributed computing, Proc. Natl. Acad. Sci. USA, 99 (2002), pp. 14122–14125.
17.
B. G. Fitch, R. S. Germain, M. Mendell, J. Pitera, M. Pitman, A. Rayshubskiy, Y. Sham, F. Suits, W. Swope, T. J. C. Ward, Y. Zhestkov, and R. Zhou, Blue Matter, an application framework for molecular simulation on Blue Gene, J. Parallel Distrib. Comput., 63 (2003), pp. 759–773.
18.
A. Gara, M. A. Blumrich, D. Chen, G. L.‐T. Chiu, P. Coteus, M. E. Giampapa, R. A. Haring, P. Heidelberger, D. Hoenicke, G. V. Kopcsay, T. A. Liebsch, M. Ohmacht, B. D. Steinmacher‐Burow, T. Takken, and P. Vranas, Overview of the Blue Gene/L system architecture, IBM J. Res. Develop., 49 (2005), pp. 195–212.
19.
R. S. Germain, B. Fitch, A. Rayshubskiy, M. Eleftheriou, M. C. Pitman, F. Suits, M. Giampapa, and T. J. C. Ward, Blue Matter on Blue Gene/L: Massively parallel computation for biomolecular simulation, in CODES+ISSS ’05: Proceedings of the 3rd IEEE/ACM/IFIP International Conference on Hardware/Software Codesign and System Synthesis, ACM, New York, 2005, pp. 207–212.
20.
F. A. Hamprecht, C. Peter, X. Daura, W. Thiel, and W. F. van Gunsteren, A strategy for analysis of (molecular) equilibrium simulations: Configuration space density estimation, clustering, and visualization, J. Chem. Phys., 114 (2001), pp. 2079–2089.
21.
W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, Comparison of simple potential functions for simulating liquid water, J. Chem. Phys., 79 (1983), pp. 926–935.
22.
M. E. Karpen, D. J. Tobias, and C. L. Brooks, III, Statistical clustering techniques for the analysis of long molecular dynamics trajectories: Analysis of 2.2–ns trajectories of YPGDV, Biochemistry, 32 (1993), pp. 412–420.
23.
P. A. Kollman, R. Dixon, W. Cornell, T. Vox, C. Chipot, and A. Pohorille, The development/application of a “minimalist” organic/biochemical molecular mechanic force field using a combination of ab initio calculations and experimental data, in Computer Simulation of Biomolecular Systems, Vol. 3, A. Wilkinson, P. Weiner, and W. F. van Gunsteren, eds., Kluwer/Escom, The Netherlands, 1997, pp. 83–96.
24.
J. Kubelka, J. Hofrichter, and W. A. Eaton, The protein folding “speed limit,”, Curr. Opin. Struct. Biol., 14 (2004), pp. 76–88.
25.
S. Kumar, D. Bouzida, R. H. Swendsen, P. A. Kollman, and J. M. Rosenberg, The weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method, J. Comput. Chem., 13 (1992), pp. 1011–1021.
26.
R. E. Kunz and R. S. Berry, Statistical interpretation of topographies and dynamics of multidimensional potentials, J. Chem. Phys., 103 (1995), pp. 1904–1912.
27.
P. Lenz, B. Zagrovic, J. Shapiro, and V. S. Pande, Folding probabilities: A novel approach to folding transitions and the two‐dimensional Ising‐model, J. Chem. Phys., 120 (2004), pp. 6769–6778.
28.
Y. Levy, J. Jortner, and O. M. Becker, Dynamics of hierarchical folding on energy landscapes of hexapeptides, J. Chem. Phys., 115 (2001), pp. 10533–10547.
29.
A. Ma and A. R. Dinner, Automatic method for identifying reaction coordinates in complex systems, J. Phys. Chem. B, 109 (2005), pp. 6769–6779.
30.
N. J. Marianayagam, N. L. Fawzi, and T. Head‐Gordon, Protein folding by distributed computing and the denatured state ensemble, Proc. Natl. Acad. Sci. USA, 102 (2005), pp. 16684–16689.
31.
D. Moroni, T. S. van Erp, and P. G. Bolhuis, Investigating rare events by transition interface sampling, Phys. A, 340 (2004), pp. 395–401.
32.
P. N. Mortenson, D. A. Evans, and D. J. Wales, Energy landscapes of model polyalanines, J. Chem. Phys., 117 (2002), pp. 1363–1376.
33.
P. N. Mortenson and D. J. Wales, Energy landscapes, global optimization and dynamics of the polyalanine Ac(ala)$_8$NHMe, J. Chem. Phys., 114 (2001), pp. 6443–6454.
34.
S. B. Ozkan, K. A. Dill, and I. Bahar, Fast‐folding protein kinetics, hidden intermediates, and the sequential stabilization model, Protein Science, 11 (2002), pp. 1958–1970.
35.
E. Paci, A. Cavalli, M. Vendruscolo, and A. Caflisch, Analysis of the distributed computing approach applied to the folding of a small β peptide, Proc. Natl. Acad. Sci. USA, 100 (2003), pp. 8217–8222.
36.
V. S. Pande, I. Baker, J. Chapman, S. P. Elmer, S. Khaliq, S. M. Larson, Y. M. Rhee, M. R. Shirts, C. D. Snow, E. J. Sorin, and B. Zagrovic, Atomistic protein folding simulations on the submillisecond time scale using worldwide distributed computing, Biopolymers, 68 (2003), pp. 91–109.
37.
S. Park and V. S. Pande, Validation of Markov state models using Shannon’s entropy, J. Chem. Phys., 124 (2006), 054118.
38.
I. K. Roterman, M. H. Lambert, K. D. Gibson, and H. A. Scheraga, A comparison of the CHARMM, AMBER and ECEPP potentials for peptides. II. $\phi-\psi$ maps for N‐acetyl alanine N’‐methyl amide: Comparisons, contrasts and simple experimental tests, J. Biomol. Struct. Dyn., 78 (1989), pp. 421–453.
39.
J. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, Numerical integration of the cartesian equations of motion of a system with constraints: Molecular dynamics of n‐alkanes, J. Comput. Phys., 23 (1977), pp. 327–341.
40.
V. Schultheis, T. Hirschberger, H. Carstens, and P. Tavan, Extracting Markov models of peptide conformational dynamics from simulation data, J. Chem. Theor. Comput., 1 (2005), pp. 515–526.
41.
Ch. Schütte, A. Fischer, W. Huisinga, and P. Deuflhard, A direct approach to conformational dynamics based on hybrid Monte Carlo, J. Comput. Phys., 151 (1999), pp. 146–168.
42.
Ch. Schütte and W. Huisinga, Biomolecular conformations can be identified as metastable states of molecular dynamics, in Handbook of Numerical Analysis—Special Volume on Computational Chemistry, Vol. X, P. G. Ciarlet and J.‐L. Lions, eds., North–Holland, Amsterdam, 2002, pp. 699–744.
43.
D. Shalloway, Macrostates of classical stochastic systems, J. Chem. Phys., 105 (1996), pp. 9986–10007.
44.
M.‐y. Shen and K. F. Freed, Long time dynamics of met‐enkephalin: Tests of mode‐coupling theory and implicit solvent models, J. Chem. Phys., 118 (2003), pp. 5143–5156.
45.
N. Singhal, J. D. Chodera, J. W. Pitera, V. S. Pande, K. A. Dill, and W. C. Swope, An Automatic State Decomposition Method for the Construction of Discrete‐State Markov Models of Protein Dynamics, manuscript, 2006.
46.
N. Singhal, C. D. Snow, and V. S. Pande, Using path sampling to build better Markovian state models: Predicting the folding rate and mechanism of a tryptophan zipper beta hairpin, J. Chem. Phys., 121 (2004), pp. 415–425.
47.
S. Sriraman, I. G. Kevrekidis, and G. Hummer, Coarse master equation from Bayesian analysis of replica molecular dynamics simulations, J. Phys. Chem. B, 109 (2005), pp. 6479–6484.
48.
Y. Sugita and Y. Okamoto, Replica‐exchange molecular dynamics method for protein folding, Chem. Phys. Lett., 314 (1999), pp. 141–151.
49.
W. C. Swope, J. W. Pitera, and F. Suits, Describing protein folding kinetics by molecular dynamics simulations: 1. Theory, J. Phys. Chem. B, 108 (2004), pp. 6571–6581.
50.
W. C. Swope, J. W. Pitera, F. Suits, M. Pitman, M. Eleftheriou, B. G. Fitch, R. S. Germain, A. Rayshubski, T. J. C. Ward, Y. Zhestkov, and R. Zhou, Describing protein folding kinetics by molecular dynamics simulations: 2. Example applications to alanine dipeptide and a beta‐hairpin peptide, J. Phys. Chem. B, 108 (2004), pp. 6582–6594.
51.
A. Ulitsky and D. Shalloway, Variational calculation of macrostate transition rates, J. Chem. Phys., 109 (1998), pp. 1670–1686.
52.
T. S. van Erp, D. Moroni, and P. G. Bolhuis, A novel path sampling method for the calculation of rate constants, J. Chem. Phys., 118 (2003), pp. 7762–7774.
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Copyright © 2006 Society for Industrial and Applied Mathematics.
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Submitted: 2 February 2006
Accepted: 5 May 2006
Published online: 28 December 2006
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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