Variational cross-validation of slow dynamical modes in molecular kinetics

Journal of Chemical Physics

Volumn 142, Issue 12, 2015, Pages

  McGibbon, Robert T ^a   Pande, Vijay S ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MOLECULAR DYNAMICS; SYSTEMATIC ERRORS; UNCERTAINTY ANALYSIS;

BIOMOLECULAR SYSTEM; MARKOV STATE MODELS; OBJECTIVE FUNCTIONS; PROJECTION OPERATOR; RAYLEIGH QUOTIENTS; STATISTICAL KINETICS; STATISTICAL UNCERTAINTY; THEORETICAL FRAMEWORK;

BIOLOGICAL SYSTEMS;

ALANINE; PEPTIDE;

ALGORITHM; CHEMISTRY; CLUSTER ANALYSIS; COMPUTER SIMULATION; KINETICS; MARKOV CHAIN; MOLECULAR MODEL; VALIDATION STUDY;

ALANINE; ALGORITHMS; CLUSTER ANALYSIS; COMPUTER SIMULATION; KINETICS; MARKOV CHAINS; MODELS, MOLECULAR; PEPTIDES;

EID: 84961290952     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4916292     Document Type: Article

References (87)

1. K. A. Dill, S. B. Ozkan, M. S. Shell, and T. R. Weikl, Annu. Rev. Biophys. 37, 289 (2008). 10.1146/annurev.biophys.37.092707.153558
2. M. Huse and J. Kuriyan, Cell 109, 275 (2002). 10.1016/S0092-8674(02)00741-9
3. E. Vargas, V. Yarov-Yarovoy, F. Khalili-Araghi, W. A. Catterall, M. L. Klein, M. Tarek, E. Lindahl, K. Schulten, E. Perozo, F. Bezanilla et al., J. Gen. Physiol. 140, 587 (2012). 10.1085/jgp.201210873
4. A. H. Phillips, Y. Zhang, C. N. Cunningham, L. Zhou, W. F. Forrest, P. S. Liu, M. Steffek, J. Lee, C. Tam, E. Helgason et al., Proc. Natl. Acad. Sci. U. S. A. 110, 11379 (2013). 10.1073/pnas.1302407110
5. G. Careri, P. Fasella, E. Gratton, and W. Jencks, Crit. Rev. Biochem. Mol. Biol. 3, 141 (1975). 10.3109/10409237509102555
6. H. B. Buergi and J. D. Dunitz, Acc. Chem. Res. 16, 153 (1983). 10.1021/ar00089a002
7. A. Mittermaier and L. E. Kay, Science 312, 224 (2006). 10.1126/science.1124964
8. L.-P. Wang, J. Chen, and T. Van Voorhis, J. Chem. Theory Comput. 9, 452 (2012). 10.1021/ct300826t
9. L. Huang and B. Roux, J. Chem. Theory Comput. 9, 3543 (2013). 10.1021/ct4003477
10. J. W. Ponder, C. Wu, P. Ren, V. S. Pande, J. D. Chodera, M. J. Schnieders, I. Haque, D. L. Mobley, D. S. Lambrecht, R. A. DiStasio, Jr. et al., J. Phys. Chem. B 114, 2549 (2010). 10.1021/jp910674d
11. R. B. Best, X. Zhu, J. Shim, P. E. Lopes, J. Mittal, M. Feig, and A. D. MacKerell, Jr., J. Chem. Theory Comput. 8, 3257 (2012). 10.1021/ct300400x
12. P. E. Lopes, J. Huang, J. Shim, Y. Luo, H. Li, B. Roux, and A. D. MacKerell, Jr., J. Chem. Theory Comput. 9, 5430 (2013). 10.1021/ct400781b
13. J. E. Stone, D. J. Hardy, I. S. Ufimtsev, and K. Schulten, J. Mol. Graphics Modell. 29, 116 (2010). 10.1016/j.jmgm.2010.06.010
14. D. E. Shaw, R. O. Dror, J. K. Salmon, J. P. Grossman, K. M. Mackenzie, J. A. Bank, C. Young, M. M. Deneroff, B. Batson, K. J. Bowers, E. Chow, M. P. Eastwood, D. J. Ierardi, J. L. Klepeis, J. S. Kuskin, R. H. Larson, K. Lindorff-Larsen, P. Maragakis, M. A. Moraes, S. Piana, Y. Shan, and B. Towles, in Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis (ACM, New York, 2009), pp. 39:1-39:11.
15. M. Shirts and V. S. Pande, Science 290, 5498 (2000). 10.1126/science.290.5498.1903
16. I. Buch, M. J. Harvey, T. Giorgino, D. Anderson, and G. De Fabritiis, J. Chem. Inf. Model. 50, 397 (2010). 10.1021/ci900455r
17. K. J. Kohlhoff, D. Shukla, M. Lawrenz, G. R. Bowman, D. E. Konerding, D. Belov, R. B. Altman, and V. S. Pande, Nat. Chem. 6, 15 (2014). 10.1038/nchem.1821
18. J. D. Chodera, N. Singhal, V. S. Pande, K. A. Dill, and W. C. Swope, J. Chem. Phys. 126, 155101 (2007). 10.1063/1.2714538
19. P. Deuflhard and M. Weber, Linear Algebra Appl. 398, 161 (2005). 10.1016/j.laa.2004.10.026
20. M. A. Rohrdanz, W. Zheng, M. Maggioni, and C. Clementi, J. Chem. Phys. 134, 124116 (2011). 10.1063/1.3569857
21. A. Altis, P. H. Nguyen, R. Hegger, and G. Stock, J. Chem. Phys. 126, 244111 (2007). 10.1063/1.2746330
22. P. Das, M. Moll, H. Stamati, L. E. Kavraki, and C. Clementi, Proc. Natl. Acad. Sci. U. S. A. 103, 9885 (2006). 10.1073/pnas.0603553103
23. S. V. Krivov and M. Karplus, Proc. Natl. Acad. Sci. U. S. A. 101, 14766 (2004). 10.1073/pnas.0406234101
24. W. E and E. Vanden-Eijnden, J. Stat. Phys. 123, 503 (2006). 10.1007/s10955-005-9003-9
25. R. T. McGibbon, C. R. Schwantes, and V. S. Pande, J. Phys. Chem. B 118, 6475 (2014). 10.1021/jp411822r
26. V. N. Vapnik and V. Vapnik, Statistical Learning Theory (Wiley, New York, 1998), Vol. 2.
27. S. C. Larson, J. Educ. Psychol. 22, 45 (1931). 10.1037/h0072400
28. J.-H. Prinz, H. Wu, M. Sarich, B. Keller, M. Senne, M. Held, J. D. Chodera, C. Schütte, and F. Noé, J. Chem. Phys. 134, 174105 (2011). 10.1063/1.3565032
29. C. R. Schwantes and V. S. Pande, J. Chem. Theory Comput. 9, 2000 (2013). 10.1021/ct300878a
30. G. Pérez-Hernández, F. Paul, T. Giorgino, G. De Fabritiis, and F. Noé, J. Chem. Phys. 139, 015102 (2013). 10.1063/1.4811489
31. O. Z. Maimon and L. Rokach, Data Mining and Knowledge Discovery Handbook (Springer, 2005), Vol. 1.
32. C. Schütte, " Conformational dynamics: Modelling, theory, algorithm, and application to biomolecules," Habilitation thesis (Free University Berlin, 1998).
33. E. Schmidt, Math. Ann. 63, 433 (1907). 10.1007/BF01449770
34. R. Courant and D. Hilbert, Methods of Mathematical Physics, Methods of Mathematical Physics Vol. 1 (Wiley, 2008).
35. C. A. Micchelli and A. Pinkus, J. Approximation Theory 24, 51 (1978). 10.1016/0021-9045(78)90036-9
36. F. Noé and S. Fischer, Curr. Opin. Struct. Biol. 18, 154 (2008). 10.1016/j.sbi.2008.01.008
37. G. R. Bowman, K. A. Beauchamp, G. Boxer, and V. S. Pande, J. Chem. Phys. 131, 124101 (2009). 10.1063/1.3216567
38. V. S. Pande, K. Beauchamp, and G. R. Bowman, Methods 52, 99 (2010). 10.1016/j.ymeth.2010.06.002
39. J. D. Chodera and F. F. Noé, Curr. Opin. Stuct. Biol. 25, 135 (2014). 10.1016/j.sbi.2014.04.002
40. F. Noé and F. Nüske, Multiscale Model. Simul. 11, 635 (2013). 10.1137/110858616
41. F. Nüske, B. G. Keller, G. Pérez-Hernández, A. S. J. S. Mey, and F. Noé, J. Chem. Theory Comput. 10, 1739 (2014). 10.1021/ct4009156
42. K. Fan, Proc. Natl. Acad. Sci. U. S. A. 35, 652 (1949). 10.1073/pnas.35.11.652
43. M. L. Overton and R. S. Womersley, SIAM J. Matrix Anal. Appl. 13, 41 (1992). 10.1137/0613006
44. P.-A. Absil, R. Mahony, R. Sepulchre, and P. Van Dooren, SIAM Rev. 44, 57 (2002). 10.1137/S0036144500378648
45. D. Sezer, J. H. Freed, and B. Roux, J. Phys. Chem. B 112, 11014 (2008). 10.1021/jp801608v
46. S. Muff and A. Caflisch, J. Chem. Phys. 130, 125104 (2009). 10.1063/1.3099705
47. I. Buch, T. Giorgino, and G. De Fabritiis, Proc. Natl. Acad. Sci. U. S. A. 108, 10184 (2011). 10.1073/pnas.1103547108
48. V. A. Voelz, G. R. Bowman, K. Beauchamp, and V. S. Pande, J. Am. Chem. Soc. 132, 1526 (2010). 10.1021/ja9090353
49. K. A. Beauchamp, R. T. McGibbon, Y.-S. Lin, and V. S. Pande, Proc. Natl. Acad. Sci. U. S. A. 109, 17807 (2012). 10.1073/pnas.1201810109
50. W. Zhuang, R. Z. Cui, D.-A. Silva, and X. Huang, J. Phys. Chem. B 115, 5415 (2011). 10.1021/jp109592b
51. S. K. Sadiq, F. Noé, and G. De Fabritiis, Proc. Natl. Acad. Sci. U. S. A. 109, 20449 (2012). 10.1073/pnas.1210983109
52. O. P. Choudhary, A. Paz, J. L. Adelman, J.-P. Colletier, J. Abramson, and M. Grabe, Nat. Struct. Mol. Biol. 21, 626 (2014). 10.1038/nsmb.2841
53. D. Shukla, Y. Meng, B. Roux, and V. S. Pande, Nat. Commun. 5 (2014). 10.1038/ncomms4397
54. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users' Guide, 3rd ed. (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1999).
55. B. Schölkopf, A. Smola, and K.-R. Müller, Neural Comput. 10, 1299 (1998). 10.1162/089976698300017467
56. U. Kjems, L. K. Hansen, and S. C. Strother, in Advances in Neural Information Processing Systems 13 (MIT Press, 2000), pp. 549-555.
57. T. J. Abrahamsen and L. K. Hansen, J. Mach. Learn. Res. 12, 2027 (2011).
58. M. Cornec, "Concentration inequalities of the cross-validation estimator for Empirical Risk Minimiser," preprint arXiv:1011.0096 (2010).
59. S. Park and V. S. Pande, J. Chem. Phys. 124, 054118 (2006). 10.1063/1.2166393
60. M. Sarich, F. Noé, and C. Schütte, Multiscale Model. Simul. 8, 1154 (2010). 10.1137/090764049
61. T. Zhou and A. Caflisch, J. Chem. Theory Comput. 8, 2930 (2012). 10.1021/ct3003145
62. D. L. Theobald, Acta Crystallogr., Sect. A: Found. Crystallogr. 61, 478 (2005). 10.1107/S0108767305015266
63. K. A. Beauchamp, G. R. Bowman, T. J. Lane, L. Maibaum, I. S. Haque, and V. S. Pande, J. Chem. Theory Comput. 7, 3412 (2011). 10.1021/ct200463m
64. S. Lloyd, IEEE Trans. Inf. Theory 28, 129-137 (1982). 10.1109/TIT.1982.1056489
65. M. Senne, B. Trendelkamp-Schroer, A. S. Mey, C. Schütte, and F. Noé, J. Chem. Theory Comput. 8, 2223 (2012). 10.1021/ct300274u
66. A. K. Theophilou, J. Phys. C: Solid State Phys. 12, 5419 (1979). 10.1088/0022-3719/12/24/013
67. E. K. U. Gross, L. N. Oliveira, and W. Kohn, Phys. Rev. A 37, 2805 (1988). 10.1103/PhysRevA.37.2805
68. N. Gidopoulos, P. Papaconstantinou, and E. Gross, Physica B 318, 328 (2002). 10.1016/S0921-4526(02)00799-8
69. R. Lai, J. Lu, and S. Osher, "Density matrix minimization with â.,"1 regularization," e-prints arXiv (2014).
70. C. R. Rao, J. R. Stat. Soc. Ser. B Stat. Methodol. 10, 159 (1948).
71. G. Baudat and F. Anouar, Neural Comput. 12, 2385 (2000). 10.1162/089976600300014980
72. L. Clemmensen, T. Hastie, D. Witten, and B. Ersbøll, Technometrics 53 (2011). 10.1198/TECH.2011.08118
73. B. K. Sriperumbudur, D. Torres, and G. Lanckriet, Mach. Learn. 85, 3 (2011). 10.1007/s10994-010-5226-3
74. E. H. Kellogg, O. F. Lange, and D. Baker, J. Phys. Chem. B 116, 11405 (2012). 10.1021/jp3044303
75. E. K. Rains and H. C. Andersen, J. Chem. Phys. 133, 144113 (2010). 10.1063/1.3496438
76. S. Bacallado, J. D. Chodera, and V. Pande, J. Chem. Phys. 131, 045106 (2009). 10.1063/1.3192309
77. G. R. Bowman, J. Chem. Phys. 137, 134111 (2012). 10.1063/1.4755751
78. R. T. McGibbon, B. Ramsundar, M. M. Sultan, G. Kiss, and V. S. Pande, in, (Omnipress, 2014), pp. 1197-1205.
79. R. T. McGibbon, K. A. Beauchamp, C. R. Schwantes, L.-P. Wang, C. X. Hernández, M. P. Harrigan, T. J. Lane, J. M. Swails, and V. S. Pande, "MDTraj: A modern, open library for the analysis of molecular dynamics trajectories," bioRxiv, 2014. 10.1101/008896
80. J. Snoek, H. Larochelle, and R. P. Adams, in Advances in Neural Information Processing Systems, Vol. 25 (Lake Tahoe, USA, 2012) pp. 2951-2959.
81. D. Müllner, J. Stat. Softw. 53, 1 (2013).
82. B. Hess, C. Kutzner, D. van der Spoel, and E. Lindahl, J. Chem. Theory Comput. 4, 435 (2008). 10.1021/ct700301q
83. D.-W. Li and R. Brüschweiler, Angew. Chem. 122, 6930 (2010). 10.1002/ange.201001898
84. W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. 79, 926 (1983). 10.1063/1.445869
85. G. Bussi, D. Donadio, and M. Parrinello, J. Chem. Phys. 126, 014101 (2007). 10.1063/1.2408420
86. M. Parrinello and A. Rahman, J. Appl. Phys. 52, 7182 (1981). 10.1063/1.328693
87. T. Darden, D. York, and L. Pedersen, J. Chem. Phys. 98, 10089 (1993). 10.1063/1.464397