Variational tensor approach for approximating the rare-event kinetics of macromolecular systems

Journal of Chemical Physics

Volumn 144, Issue 5, 2016, Pages

  Nüske, Feliks ^a   Schneider, Reinhold ^b   Vitalini, Francesca ^a   Noé, Frank ^a  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL CHEMISTRY; DIHEDRAL ANGLE; FUNCTIONS; MACROMOLECULES; MOLECULAR DYNAMICS; TENSORS;

BASIS FUNCTIONS; COMBINATORIAL EXPLOSION; HIGH-DIMENSIONAL; KINETIC PROPERTIES; MACROMOLECULAR SYSTEMS; MOLECULAR COORDINATES; SPARSE TENSOR PRODUCTS; VARIATIONAL FORMULATION;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 84957072943     PISSN: 00219606     EISSN: 10897690     Source Type: Journal    
DOI: 10.1063/1.4940774     Document Type: Article

References (43)

1. W. van Gunsteren, J. Dolenc, and A. Mark, "Molecular simulation as an aid to experimentalists," Curr. Opin. Struct. Biol. 18, 149-153 (2008). 10.1016/j.sbi.2007.12.007
2. C. Schütte, A. Fischer, W. Huisinga, and P. Deuflhard, "A direct approach to conformational dynamics based on hybrid Monte Carlo," J. Comput. Phys. 151, 146-168 (1999). 10.1006/jcph.1999.6231
3. N. Singhal and V. S. Pande, "Error analysis and efficient sampling in Markovian state models for molecular dynamics," J. Chem. Phys. 123, 204909 (2005). 10.1063/1.2116947
4. F. Noé, I. Horenko, C. Schütte, and J. C. Smith, "Hierarchical analysis of conformational dynamics in biomolecules: Transition networks of metastable states," J. Chem. Phys. 126, 155102 (2007). 10.1063/1.2714539
5. J. D. Chodera, K. A. Dill, N. Singhal, V. S. Pande, W. C. Swope, and J. W. Pitera, "Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics," J. Chem. Phys. 126, 155101 (2007). 10.1063/1.2714538
6. J.-H. Prinz, H. Wu, M. Sarich, B. Keller, M. Senne, M. Held, J. D. Chodera, C. Schütte, and F. Noé, "Markov models of molecular kinetics: Generation and validation," J. Chem. Phys. 134, 174105 (2011). 10.1063/1.3565032
7. W. C. Swope, J. W. Pitera, F. Suits, M. Pitman, and M. Eleftheriou, "Describing protein folding kinetics by molecular dynamics simulations. 2. Example applications to alanine dipeptide and beta-hairpin peptide," J. Phys. Chem. B 108, 6582-6594 (2004). 10.1021/jp037422q
8. M. K. Scherer, B. Trendelkamp-Schroer, F. Paul, G. Pérez-Hernández, M. Hoffmann, N. Plattner, C. Wehmeyer, J.-H. Prinz, and F. Noé, "PyEMMA 2: A software package for estimation, validation, and analysis of Markov models," J. Chem. Theory Comput. 11, 5525-5542 (2015). 10.1021/acs.jctc.5b00743
9. K. A. Beauchamp, G. R. Bowman, T. J. Lane, L. Maibaum, I. S. Haque, and V. S. Pande, "MSMBuilder2: Modeling conformational dynamics at the picosecond to millisecond scale," J. Chem. Theory Comput. 7, 3412-3419 (2011). 10.1021/ct200463m
10. F. Noé, C. Schütte, E. Vanden-Eijnden, L. Reich, and T. R. Weikl, "Constructing the full ensemble of folding pathways from short off-equilibrium simulations," Proc. Natl. Acad. Sci. U. S. A. 106, 19011-19016 (2009). 10.1073/pnas.0905466106
11. A. Berezhkovskii, G. Hummer, and A. Szabo, "Reactive flux and folding pathways in network models of coarse-grained protein dynamics," J. Chem. Phys. 130, 205102 (2009). 10.1063/1.3139063
12. W. Zhuang, R. Z. Cui, D.-A. Silva, and X. Huang, "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 115, 5415-5424 (2011). 10.1021/jp109592b
13. F. Noé, S. Doose, I. Daidone, M. Löllmann, J. D. Chodera, M. Sauer, and J. C. Smith, "Dynamical fingerprints for probing individual relaxation processes in biomolecular dynamics with simulations and kinetic experiments," Proc. Natl. Acad. Sci. U. S. A. 108, 4822-4827 (2011). 10.1073/pnas.1004646108
14. B. Lindner, Z. Yi, J.-H. Prinz, J. C. Smith, and F. Noé, "Dynamic neutron scattering from conformational dynamics. I. Theory and Markov models," J. Chem. Phys. 139, 175101 (2013). 10.1063/1.4824070
15. K. A. Beauchamp, D. L. Ensign, R. Das, and V. S. Pande, "Quantitative comparison of villin headpiece subdomain simulations and triplet-triplet energy transfer experiments," Proc. Natl. Acad. Sci. U. S. A. 108, 12734-12739 (2011). 10.1073/pnas.1010880108
16. G. R. Bowman and P. L. Geissler, "Equilibrium fluctuations of a single folded protein reveal a multitude of potential cryptic allosteric sites," Proc. Natl. Acad. Sci. U. S. A. 109, 11681-11686 (2012). 10.1073/pnas.1209309109
17. K. A. Beauchamp, R. McGibbon, Y. S. Lin, and V. S. Pande, "Simple few-state models reveal hidden complexity in protein folding," Proc. Natl. Acad. Sci. U. S. A. 109, 17807-17813 (2012). 10.1073/pnas.1201810109
18. I. Buch, T. Giorgino, and G. de Fabritiis, "Complete reconstruction of an enzyme-inhibitor binding process by molecular dynamics simulations," Proc. Natl. Acad. Sci. U. S. A. 108, 10184-10189 (2011). 10.1073/pnas.1103547108
19. S. K. Sadiq, F. Noé, and G. de Fabritiis, "Kinetic characterization of the critical step in HIV-1 protease maturation," Proc. Natl. Acad. Sci. U. S. A. 109, 20449-20454 (2012). 10.1073/pnas.1210983109
20. M. Sarich, F. Noé, and C. Schütte, "On the approximation quality of Markov state models," SIAM Multiscale Model. Simul. 8, 1154-1177 (2010). 10.1137/090764049
21. F. Noé and F. Nüske, "A variational approach to modeling slow processes in stochastic dynamical systems," SIAM Multiscale Model. Simul. 11, 635-655 (2013). 10.1137/110858616
22. F. Nüske, B. G. Keller, G. Pérez-Hernández, A. S. J. S. Mey, and F. Noé, "Variational approach to molecular kinetics," J. Chem. Theory Comput. 10, 1739-1752 (2014). 10.1021/ct4009156
23. F. Vitalini, F. Noé, and B. G. Keller, "A basis set for peptides for the variational approach to conformational kinetics," J. Chem. Theory Comput. 11, 3992-4004 (2015). 10.1021/acs.jctc.5b00498
24. I. Oseledets and E. Tyrtyshnikov, "Breaking the curse of dimensionality, Or how to use SVD in many dimensions," SIAM J. Sci. Comput. 31, 3744-3759 (2009). 10.1137/090748330
25. I. Oseledets, "Tensor-train decomposition," SIAM J. Sci. Comput. 33, 2295-2317 (2011). 10.1137/090752286
26. S. Ostlund and S. Rommer, "Thermodynamic limit of density matrix renormalization," Phys. Rev. Lett. 75, 3537-3540 (1995). 10.1103/PhysRevLett.75.3537
27. S. R. White, "Density matrix formulation for quantum renormalization groups," Phys. Rev. Lett. 69, 2863-2866 (1992). 10.1103/PhysRevLett.69.2863
28. S. Szalay, M. Pfeffer, V. Murg, G. Barcza, F. Verstraete, R. Schneider, and Ö. Legeza, "Tensor product methods and entanglement optimization for ab initio quantum chemistry," Int. J. Quantum Chem. 115, 1342-1391 (2015). 10.1002/qua.24898
29. W. Hackbusch and S. Kühn, "A new scheme for the tensor representation," J. Fourier Anal. Appl. 15, 706-722 (2009). 10.1007/s00041-009-9094-9
30. W. Hackbusch, Tensor Spaces and Numerical Tensor Calculus (Springer, Berlin Heidelberg, 2012).
31. S. Holtz, T. Rohwedder, and R. Schneider, "The alternating linear scheme for tensor optimization in the tensor train format," SIAM J. Sci. Comput. 34, A683-A713 (2012). 10.1137/100818893
32. J. Chodera, W. Swope, J. Pitera, and K. Dill, "Long-time protein folding dynamics from short-time molecular dynamics simulations," SIAM Multiscale Model. Simul. 5, 1214-1226 (2006). 10.1137/06065146X
33. K. Fan, "On a theorem of Weyl concerning eigenvalues of linear transformations," Proc. Natl. Acad. Sci. U. S. A. 35, 652-655 (1949). 10.1073/pnas.35.11.652
34. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry (Dover Publications, Mineola, NY, 1982).
35. H. Wu and F. Noé, "Gaussian Markov transition models of molecular kinetics," J. Chem. Phys. 142, 084104 (2015). 10.1063/1.4913214
36. G. Perez-Hernandez, F. Paul, T. Giorgino, G. de Fabritiis, and F. Noé, "Identification of slow molecular order parameters for Markov model construction," J. Chem. Phys. 139, 015102 (2013). 10.1063/1.4811489
37. C. R. Schwantes and V. S. Pande, "Improvements in Markov state model construction reveal many non-native interactions in the folding of NTL9," J. Chem. Theory Comput. 9, 2000-2009 (2013). 10.1021/ct300878a
38. S. V. Dolgov, B. N. Khoromskij, I. V. Oseledets, and D. V. Savostyanov, "Computation of extreme eigenvalues in higher dimensions using block tensor train format," Comput. Phys. Commun. 185, 1207-1216 (2014). 10.1016/j.cpc.2013.12.017
39. D. Kressner, M. Steinlechner, and A. Uschmajew, "Low-rank tensor methods with subspace correction for symmetric eigenvalue problems," SIAM J. Sci. Comput. 36, A2346-A2368 (2014). 10.1137/130949919
40. D. E. Shaw, P. Maragakis, K. Lindorff-Larsen, S. Piana, R. O. Dror, M. P. Eastwood, J. A. Bank, J. M. Jumper, J. K. Salmon, Y. Shan, and W. Wriggers, "Atomic-level characterization of the structural dynamics of proteins," Science 330, 341-346 (2010). 10.1126/science.1187409
41. F. Noé, H. Wu, J.-H. Prinz, and N. Plattner, "Projected and hidden Markov models for calculating kinetics and metastable states of complex molecules," J. Chem. Phys. 139, 184114 (2013). 10.1063/1.4828816
42. Y. Duan, C. Wu, S. Chowdhury, M. C. Lee, G. Xiong, W. Zhang, R. Yang, P. Cieplak, R. Luo, T. Lee, J. Caldwell, J. Wang, and P. Kollman, "A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations," J. Comput. Chem. 24, 1999-2012 (2003). 10.1002/jcc.10349
43. J. R. Magnus, "On differentiating eigenvalues and eigenvectors," Econometric Theory 1, 179-191 (1985). 10.1017/S0266466600011129