Investigating Molecular Kinetics by Variationally Optimized Diffusion Maps

Journal of Chemical Theory and Computation

Volumn 11, Issue 12, 2015, Pages 5947-5960

  Boninsegna, Lorenzo ^a   Gobbo, Gianpaolo ^b   Noé, Frank ^c   Clementi, Cecilia ^a  

^a RICE UNIVERSITY   (United States)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

^c FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

NIMA-INTERACTING PEPTIDYLPROLYL ISOMERASE; PEPTIDYLPROLYL ISOMERASE; PROTEIN;

CHEMISTRY; DIFFUSION; GENETICS; HUMAN; KINETICS; MARKOV CHAIN; METABOLISM; MOLECULAR DYNAMICS; MUTAGENESIS; PROTEIN FOLDING; PROTEIN TERTIARY STRUCTURE;

DIFFUSION; HUMANS; KINETICS; MARKOV CHAINS; MOLECULAR DYNAMICS SIMULATION; MUTAGENESIS; PEPTIDYLPROLYL ISOMERASE; PROTEIN FOLDING; PROTEIN STRUCTURE, TERTIARY; PROTEINS;

EID: 84949638655     PISSN: 15499618     EISSN: 15499626     Source Type: Journal    
DOI: 10.1021/acs.jctc.5b00749     Document Type: Article

References (68)

1. Shirts, M.; Pande, V. S. Screen Savers of the World Unite! Science 2000, 290, 1903-1904 10.1126/science.290.5498.1903
2. Shaw, D. E.; Maragakis, P.; Lindorff-Larsen, K.; Piana, S.; Dror, R.; Eastwood, M.; Bank, J.; Jumper, J.; Salmon, J.; Shan, Y.; Wriggers, W. Atomic-Level Characterization of the Structural Dynamics of Proteins Science 2010, 330, 341-346 10.1126/science.1187409
3. Eastman, P.; Pande, V. S. Efficient Nonbonded Interactions for Molecular Dynamics on a Graphics Processing Unit J. Comput. Chem. 2010, 31, 1268-1272 10.1002/jcc.21413
4. Harvey, M.; Giupponi, G.; Fabritiis, G. D. ACEMD: Accelerated Molecular Dynamics Simulations in the Microseconds Timescale J. Chem. Theory Comput. 2009, 5, 1632-1639 10.1021/ct9000685
5. Le Grand, S.; Goetz, A. W.; Walker, R. C. SPFP: Speed Without Compromise-a Mixed Precision Model for GPU Accelerated Molecular Dynamics Simulations Comput. Phys. Commun. 2013, 184, 374-380 10.1016/j.cpc.2012.09.022
6. Schütte, C.; Fischer, A.; Huisinga, W.; Deuflhard, P. A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo J. Comput. Phys. 1999, 151, 146-168 10.1006/jcph.1999.6231
7. Swope, W. C.; Pitera, J. W.; Suits, F. Describing Protein Folding Kinetics by Molecular Dynamics Simulations: 1. Theory J. Phys. Chem. B 2004, 108, 6571-6581 10.1021/jp037421y
8. Singhal, N.; Pande, V. S. Error Analysis and Efficient Sampling in Markovian State Models for Molecular Dynamics J. Chem. Phys. 2005, 123, 204909 10.1063/1.2116947
9. Noé, F.; Horenko, I.; Schütte, C.; Smith, J. C. Hierarchical Analysis of Conformational Dynamics in Biomolecules: Transition Networks of Metastable States J. Chem. Phys. 2007, 126, 155102 10.1063/1.2714539
10. Chodera, J. D.; Dill, K. A.; Singhal, N.; Pande, V. S.; Swope, W. C.; Pitera, J. W. Automatic Discovery of Metastable States for the Construction of Markov Models of Macromolecular Conformational Dynamics J. Chem. Phys. 2007, 126, 155101 10.1063/1.2714538
11. Buchete, N. V.; Hummer, G. Coarse Master Equations for Peptide Folding Dynamics J. Phys. Chem. B 2008, 112, 6057-6069 10.1021/jp0761665
12. Bowman, G. R.; Pande, V. S.; Noé, F., Eds. An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation; Advances in Experimental Medicine and Biology 797; Springer: Heidelberg, 2014.
13. McGibbon, R. T.; Ramsundar, B.; Sultan, M. M.; Kiss, G.; Pande, V. S. Understanding Protein Dynamics with L1-Regularized Reversible Hidden Markov Models. Proceedings of the 31st International Conference on Machine Learning, Beijing, China, 2014.
14. Noé, F.; Wu, H.; Prinz, J.-H.; Plattner, N. Projected and Hidden Markov Models for Calculating Kinetics and Metastable States of Complex Molecules J. Chem. Phys. 2013, 139, 184114 10.1063/1.4828816
15. Coifman, R. R.; Lafon, S.; Lee, A. B.; Maggioni, M.; Nadler, B.; Warner, F.; Zucker, S. W. Geometric Diffusions As a Tool for Harmonic Analysis and Structure Deffnition of Data: Diffusion Maps Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 7426-7431 10.1073/pnas.0500334102
16. Rohrdanz, M. A.; Zheng, W.; Maggioni, M.; Clementi, C. Determination of Reaction Coordinates Via Locally Scaled Diffusion Map J. Chem. Phys. 2011, 134, 124116 10.1063/1.3569857
17. Rao, F.; Caflisch, A. the Protein Folding Network J. Mol. Biol. 2004, 342, 299-306 10.1016/j.jmb.2004.06.063
18. Noé, F.; Krachtus, D.; Smith, J. C.; Fischer, S. Transition Networks for the Comprehensive Characterization of Complex Conformational Change in Proteins J. Chem. Theory Comput. 2006, 2, 840-857 10.1021/ct050162r
19. Muff, S.; Caflisch, A. Kinetic Analysis of Molecular Dynamics Simulations Reveals Changes in the Denatured State and Switch of Folding Pathways upon Single-Point Mutation of a -Sheet Miniprotein Proteins: Struct., Funct., Genet. 2008, 70, 1185-1195 10.1002/prot.21565
20. Hegger, R.; Stock, G. Multidimensional Langevin Modeling of Biomolecular Dynamics J. Chem. Phys. 2009, 130, 034106 10.1063/1.3058436
21. Deuflhard, P.; Huisinga, W.; Fischer, A.; Schütte, C. Identification of Almost Invariant Aggregates in Reversibly Nearly Uncoupled Markov Chains Lin. Alg. Appl. 2000, 315, 39-59 10.1016/S0024-3795(00)00095-1
22. Bowman, G. R. Improved Coarse-Graining of Markov State Models Via Explicit Consideration of Statistical Uncertainty J. Chem. Phys. 2012, 137, 134111 10.1063/1.4755751
23. Yao, Y.; Cui, R. Z.; Bowman, G. R.; Silva, D.-A.; Sun, J.; Huang, X. Hierarchical Nyström Methods for Constructing Markov State Models for Conformational Dynamics J. Chem. Phys. 2013, 138, 174106 10.1063/1.4802007
24. Hummer, G.; Szabo, A. Optimal Dimensionality Reduction of Multistate Kinetic and Markov-State Models J. Phys. Chem. B 2015, 119, 9029-9037 10.1021/jp508375q
25. Prinz, J.-H.; Wu, H.; Sarich, M.; Keller, B.; Senne, M.; Held, M.; Chodera, J. D.; Schütte, C.; Noé, F. Markov Models of Molecular Kinetics: Generation and Validation J. Chem. Phys. 2011, 134, 174105 10.1063/1.3565032
26. Schütte, C.; Noé, F.; Lu, J.; Sarich, M.; Vanden-Eijnden, E. Markov State Models Based on Milestoning J. Chem. Phys. 2011, 134, 204105 10.1063/1.3590108
27. Noé, F.; Doose, S.; Daidone, I.; Löllmann, M.; Chodera, J. D.; Sauer, M.; Smith, J. C. Dynamical Fingerprints for Probing Individual Relaxation Processes in Biomolecular Dynamics with Simulations and Kinetic Experiments Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 4822-4827 10.1073/pnas.1004646108
28. E, W.; Vanden-Eijnden, E. Towards a Theory of Transition Paths J. Stat. Phys. 2006, 123, 503-523 10.1007/s10955-005-9003-9
29. Metzner, P.; Schütte, C.; Vanden-Eijnden, E. Transition Path Theory for Markov Jump Processes Multiscale Model. Simul. 2009, 7, 1192-1219 10.1137/070699500
30. Noé, F.; Schütte, C.; Vanden-Eijnden, E.; Reich, L.; Weikl, T. Constructing the Full Ensemble of Folding Pathways from Short Off-Equilibrium Simulations Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 19011-19016 10.1073/pnas.0905466106
31. Held, M.; Metzner, P.; Prinz, J.-H.; Noé, F. Mechanisms of Protein-Ligand Association and Its Modulation by Protein Mutations Biophys. J. 2011, 100, 701-710 10.1016/j.bpj.2010.12.3699
32. Silva, D.-A.; Bowman, G. R.; Sosa-Peinado, A.; Huang, X. A Role for Both Conformational Selection and Induced Fit in Ligand Binding by the LAO Protein PLoS Comput. Biol. 2011, 7, e1002054 10.1371/journal.pcbi.1002054
33. Zheng, W.; Qi, B.; Rohrdanz, M. A.; Caflisch, A.; Dinner, A. R.; Clementi, C. Delineation of Folding Pathways of a β-Sheet Miniprotein J. Phys. Chem. B 2011, 115, 13065-13074 10.1021/jp2076935
34. Kube, S.; Weber, M. a Coarse Graining Method for the Identification of Transition Rates Between Molecular Conformations J. Chem. Phys. 2007, 126, 024103 10.1063/1.2404953
35. Keller, B.; Prinz, J.-H.; Noé, F. Markov Models and Dynamical Fingerprints: Unraveling the Complexity of Molecular Kinetics Chem. Phys. 2012, 396, 92-107 10.1016/j.chemphys.2011.08.021
36. Zheng, W.; Rohrdanz, M. A.; Maggioni, M.; Clementi, C. Polymer Reversal Rate Calculated Via Locally Scaled Diffusion Map J. Chem. Phys. 2011, 134, 144109 10.1063/1.3575245
37. Prinz, J.-H.; Chodera, J. D.; Noé, F. Spectral Rate Theory for Two-State Kinetics Phys. Rev. X 2014, 4, 011020 10.1103/PhysRevX.4.011020
38. Zheng, W.; Rohrdanz, M. A.; Clementi, C. Rapid Exploration of Configuration Space with Diffusion-Map-Directed Molecular Dynamics J. Phys. Chem. B 2013, 117, 12769-76 10.1021/jp401911h
39. Preto, J.; Clementi, C. Fast Recovery of Free Energy Landscapes Via Diffusion-Map-Directed Molecular Dynamics Phys. Chem. Chem. Phys. 2014, 16, 19181-19191 10.1039/C3CP54520B
40. Sarich, M.; Noé, F.; Schütte, C. On the Approximation Quality of Markov State Models Multiscale Model. Simul. 2010, 8, 1154-1177 10.1137/090764049
41. Molgedey, L.; Schuster, H. G. Separation of a Mixture of Independent Signals Using Time Delayed Correlations Phys. Rev. Lett. 1994, 72, 3634-3637 10.1103/PhysRevLett.72.3634
42. Perez-Hernandez, G.; Paul, F.; Giorgino, T.; de Fabritiis, G.; Noé, F. Identification of Slow Molecular Order Parameters for Markov Model Construction J. Chem. Phys. 2013, 139, 015102 10.1063/1.4811489
43. Schwantes, C. R.; Pande, V. S. Improvements in Markov State Model Construction Reveal Many Non-Native Interactions in the Folding of NTL9 J. Chem. Theory Comput. 2013, 9, 2000-2009 10.1021/ct300878a
44. Nüske, F.; Keller, B.; Pérez-Hernández, G.; Mey, A. S. J. S.; Noé, F. Variational Approach to Molecular Kinetics J. Chem. Theory Comput. 2014, 10, 1739-1752 10.1021/ct4009156
45. Noé, F.; Nüske, F. A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems Multiscale Model. Simul. 2013, 11, 635-655 10.1137/110858616
46. Krivov, S. V. The Free Energy Landscape Analysis of Protein (FIP35) Folding Dynamics J. Phys. Chem. B 2011, 115, 12315-12324 10.1021/jp208585r
47. Berezovska, G.; Prada-Gracia, D.; Rao, F. Consensus for the Fip35 Folding Mechanism? J. Chem. Phys. 2013, 139, 035102 10.1063/1.4812837
48. Mori, T.; Saito, S. Dynamic Heterogeneity in the Folding/unfolding Transitions of FiP35 J. Chem. Phys. 2015, 142, 135101 10.1063/1.4916641
49. Lane, T. J.; Bowman, G. R.; Beauchamp, K.; Voelz, V. a.; Pande, V. S. Markov State Model Reveals Folding and Functional Dynamics in Ultra-Long MD Trajectories J. Am. Chem. Soc. 2011, 133, 18413-18419 10.1021/ja207470h
50. McGibbon, R. T.; Pande, V. S. Learning Kinetic Distance Metrics for Markov State Models of Protein Conformational Dynamics J. Chem. Theory Comput. 2013, 9, 2900-2906 10.1021/ct400132h
51. Gardiner, C. Stochastic Methods: A Handbook for the Natural and Social Sciences; Springer Series in Synergetics; Springer: Berlin/Heidelberg, 2009.
52. Zhuang, W.; Cui, R. Z.; Silva, D.-A.; Huang, X. Simulating the T-Jump-Triggered Unfolding Dynamics of Trpzip2 Peptide and Its Time-Resolved IR and Two-Dimensional IR Signals Using the Markov State Model Approach J. Phys. Chem. B 2011, 115, 5415-5424 10.1021/jp109592b
53. Lindner, B.; Yi, Z.; Prinz, J.-H.; Smith, J. C.; Noé, F. Dynamic Neutron Scattering from Conformational Dynamics. I. Theory and Markov Models J. Chem. Phys. 2013, 139, 175101 10.1063/1.4824070
54. Deuflhard, P.; Weber, M. Linear Algebra Appl. 2005, 398, 161-184 10.1016/j.laa.2004.10.026
55. Weber, M. Meshless Methods in Conformation Dynamics. Ph.D. thesis, Freie Universität Berlin, 2006.
56. Coifman, R. R.; Kevrekidis, I. G.; Lafon, S.; Maggioni, M.; Nadler, B. Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Processes Multiscale Model. Simul. 2008, 7, 842-864 10.1137/070696325
57. Cossio, P.; Laio, A.; Pietrucci, F. Which Similarity Measure Is Better for Analyzing Protein Structures in a Molecular Dynamics Trajectory? Phys. Chem. Chem. Phys. 2011, 13, 10421-10425 10.1039/c0cp02675a
58. Zhou, T.; Caflisch, A. Distribution of Reciprocal of Interatomic Distances: A Fast Structural Metric J. Chem. Theory Comput. 2012, 8, 2930-2937 10.1021/ct3003145
59. Jäger, M.; Nguyen, H.; Crane, J. C.; Kelly, J. W.; Gruebele, M. The Folding Mechanism of a Beta-Sheet: The WW Domain J. Mol. Biol. 2001, 311, 373-393 10.1006/jmbi.2001.4873
60. Caprara, A.; Carr, R.; Istrail, S.; Lancia, G.; Walenz, B. 1001 Optimal PDB Structure Alignments: Integer Programming Methods for Finding the Maximum Contact Map Overlap J. Comput. Biol. 2004, 11, 27-52 10.1089/106652704773416876
61. Noé, F.; Clementi, C. Kinetic Distance and Kinetic Maps from Molecular Dynamics Simulation J. Chem. Theory Comput. 2015, 11, 5002-5011 10.1021/acs.jctc.5b00553
62. Scherer, M. K.; Trendelkamp-Schroer, B.; Paul, F.; Perez-Hernandez, G.; Hoffmann, M.; Plattner, N.; Wehmeyer, C.; Prinz, J.-H.; Noé, F. PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models J. Chem. Theory Comput. 2015, 10.1021/acs.jctc.5b00743
63. Freddolino, P. L.; Park, S.; Roux, B.; Schulten, K. Force Field Bias in Protein Folding Simulations Biophys. J. 2009, 96, 3772-3780 10.1016/j.bpj.2009.02.033
64. Freddolino, P. L.; Liu, F.; Gruebele, M.; Schulten, K. Ten-Microsecond Molecular Dynamics Simulation of a Fast-Folding WW Domain Biophys. J. 2008, 94, L75-L77 10.1529/biophysj.108.131565
65. Ensign, D. L.; Pande, V. S. The Fip35 WW Domain Folds with Structural and Mechanistic Heterogeneity in Molecular Dynamics Simulations Biophys. J. 2009, 96, L53-L55 10.1016/j.bpj.2009.01.024
66. a Beccara, S.; Škrbić, T.; Covino, R.; Faccioli, P. Dominant Folding Pathways of a WW Domain Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 2330-2335 10.1073/pnas.1111796109
67. a Beccara, S.; Fant, L.; Faccioli, P. Variational Scheme to Compute Protein Reaction Pathways Using Atomistic Force Fields with Explicit Solvent Phys. Rev. Lett. 2015, 114, 098103 10.1103/PhysRevLett.114.098103
68. Faccioli, P.; Sega, M.; Pederiva, F.; Orland, H. Dominant Pathways in Protein Folding Phys. Rev. Lett. 2006, 97, 108101 10.1103/PhysRevLett.97.108101