Efficient maximum likelihood parameterization of continuous-time Markov processes

Journal of Chemical Physics

Volumn 143, Issue 3, 2015, Pages

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

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS TIME SYSTEMS; MARKOV PROCESSES; MAXIMUM LIKELIHOOD ESTIMATION; MOLECULAR DYNAMICS;

CONFIDENCE INTERVAL; CONTINUOUS TIME MARKOV PROCESS; DYNAMICAL PROCESS; FINITE STATE SPACES; FINITE TIME INTERVALS; MAXIMUM LIKELIHOOD ESTIMATOR; MOLECULAR DYNAMICS SIMULATIONS; PHYSICAL CONSTRAINTS;

MAXIMUM LIKELIHOOD;

MARKOV CHAIN; MOLECULAR DYNAMICS; PROTEIN FOLDING; STATISTICAL MODEL; TIME FACTOR; UNCERTAINTY;

LIKELIHOOD FUNCTIONS; MARKOV CHAINS; MOLECULAR DYNAMICS SIMULATION; PROTEIN FOLDING; TIME FACTORS; UNCERTAINTY;

EID: 84937468342     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4926516     Document Type: Article

References (64)

1. B. Singer and S. Spilerman, Am. J. Sociol. 82, 1 (1976). 10.1086/226269
2. H. Madsen, H. Spliid, and P. Thyregod, J. Clim. Appl. Meteorol. 24, 629 (1985). 10.1175/1520-0450(1985)024<0629:MMIDAC>2.0.CO;2
3. C. M. Turner, R. Startz, and C. R. Nelson, J. Financ. Econ. 25, 3 (1989). 10.1016/0304-405X(89)90094-9
4. V. N. Minin and M. A. Suchard, J. Math. Biol. 56, 391 (2008). 10.1007/s00285-007-0120-8
5. R. A. Jarrow, D. Lando, and S. M. Turnbull, Rev. Financ. Stud. 10, 481 (1997). 10.1093/rfs/10.2.481
6. S. Spilerman, Am. J. Sociol. 78, 599 (1972). 10.1086/225366
7. M. Kimura, J. Mol. Evol. 16, 111 (1980). 10.1007/BF01731581
8. D. F. Anderson and T. G. Kurtz, Design and Analysis of Biomolecular Circuits (Springer, 2011), pp. 3-42.
9. A. Ikai and C. Tanford, Nature 230, 100 (1971). 10.1038/230100a0
10. R. Zwanzig, Proc. Natl. Acad. Sci. U. S. A. 94, 148 (1997). 10.1073/pnas.94.1.148
11. I. E. Sánchez and T. Kiefhaber, J. Mol. Biol. 325, 367 (2003). 10.1016/S0022-2836(02)01230-5
12. H. S. Chan and K. A. Dill, Proteins: Struct., Funct., Bioinf. 30, 2 (1998). 10.1002/(SICI)1097-0134(19980101)30:1<2::AID-PROT2>3.0.CO;2-R
13. M. Pirchi, G. Ziv, I. Riven, S. S. Cohen, N. Zohar, Y. Barak, and G. Haran, Nat. Commun. 2, 493 (2011). 10.1038/ncomms1504
14. 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
15. 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
16. M. Senne, B. Trendelkamp-Schroer, A. S. Mey, C. Schütte, and F. Noé, J. Chem. Theory Comput. 8, 2223 (2012). 10.1021/ct300274u
17. R. Banerjee and R. I. Cukier, J. Phys. Chem. B 118, 2883 (2014). 10.1021/jp412130d
18. D. Shukla, C. X. Hernández, J. K. Weber, and V. S. Pande, Acc. Chem. Res. 48, 414 (2015). 10.1021/ar5002999
19. F. Noé and S. Fischer, Curr. Opin. Struct. Biol. 18, 154 (2008). 10.1016/j.sbi.2008.01.008
20. J. D. Chodera and F. F. Noé, Curr. Opin. Stuct. Biol 25, 135 (2014). 10.1016/j.sbi.2014.04.002
21. P. Metzner, E. Dittmer, T. Jahnke, and C. Schütte, J. Comput. Phys. 227, 353 (2007). 10.1016/j.jcp.2007.07.032
22. I. Holmes and G. Rubin, J. Mol. Biol. 317, 753 (2002). 10.1006/jmbi.2002.5405
23. M. Bladt and M. Sørensen, J. R. Stat. Soc., Ser. B 67, 395 (2005). 10.1111/j.1467-9868.2005.00508.x
24. J. F. C. Kingman, Probab. Theory Relat. Fields 1, 14 (1962). 10.1007/BF00531768
25. E. Davies, Electron. J. Probab. 15, 1474 (2010). 10.1214/EJP.v15-733
26. J. Adams and J. Doll, Surf. Sci. 103, 472 (1981). 10.1016/0039-6028(81)90278-8
27. A. F. Voter and J. D. Doll, J. Chem. Phys. 82, 80 (1985). 10.1063/1.448739
28. H. Mori, Prog. Theor. Phys. 33, 423 (1965). 10.1143/PTP.33.423
29. R. Zwanzig, Phys. Rev. 124, 983 (1961). 10.1103/PhysRev.124.983
30. D. Crommelin and E. Vanden-Eijnden, J. Comput. Phys. 217, 782 (2006). 10.1016/j.jcp.2006.01.045
31. D. Crommelin and E. Vanden-Eijnden, Multiscale Model. Simul. 7, 1751 (2009). 10.1137/080735977
32. R. B. Israel, J. S. Rosenthal, and J. Z. Wei, Math. Finance 11, 245 (2001). 10.1111/1467-9965.00114
33. J. D. Kalbfleisch and J. F. Lawless, J. Am. Stat. Assoc. 80, 863 (1985). 10.1080/01621459.1985.10478195
34. S. Asmussen, O. Nerman, and M. Olsson, Scand. J. Stat. 23, 419 (1996), available at www.jstor.org/stable/4616418.
35. A. Hobolth and J. L. Jensen, Stat. Appl. Genet. Mol. Biol. 4, 1 (2005). 10.2202/1544-6115.1127
36. R. I. Jennrich and P. B. Bright, Technometrics 18, 385 (1976). 10.1080/00401706.1976.10489469
37. R. Byrd, P. Lu, J. Nocedal, and C. Zhu, SIAM J. Sci. Comput. 16, 1190 (1995). 10.1137/0916069
38. C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, ACM Trans. Math. Software 23, 550 (1997). 10.1145/279232.279236
39. 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
40. A. Al-Mohy and N. Higham, SIAM J. Sci. Comput. 34, C153 (2012). 10.1137/110852553
41. D. Bakry, I. Gentil, and M. Ledoux, Analysis and Geometry of Markov Diffusion Operators, Grundlehren der mathematischen Wissenschaften Vol. 348 (Springer International Publishing, 2014).
42. W. H. Vandevender and K. H. Haskell, SIGNUM Newsl. 17, 16 (1982). 10.1145/1057594.1057595
43. B. Gough, GNU Scientific Library Reference Manual (Network Theory Ltd., 2009).
44. E. Jones, T. Oliphant, P. Peterson et al., "SciPy: Open source scientific tools for Python," 2001.
45. Linear Statistical Inference and its Applications, edited by C. R. Rao (John Wiley & Sons, Inc., 1973).
46. D. V. Murthy and R. T. Haftka, Int. J. Numer. Methods Eng. 26, 293 (1988). 10.1002/nme.1620260202
47. R. T. McGibbon, C. R. Schwantes, and V. S. Pande, J. Phys. Chem. B 118, 6475 (2014). 10.1021/jp411822r
48. A.-L. Barabási and R. Albert, Science 286, 509 (1999). 10.1126/science.286.5439.509
49. 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, Science 330, 341 (2010). 10.1126/science.1187409
50. F. Liu, D. Du, A. A. Fuller, J. E. Davoren, P. Wipf, J. W. Kelly, and M. Gruebele, Proc. Natl. Acad. Sci. U. S. A. 105, 2369 (2008). 10.1073/pnas.0711908105
51. 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," preprint bioRxiv (2014). 10.1101/008896
52. C. R. Schwantes and V. S. Pande, J. Chem. Theory Comput. 9, 2000 (2013). 10.1021/ct300878a
53. G. Pérez-Hernández, F. Paul, T. Giorgino, G. De Fabritiis, and F. Noé, J. Chem. Phys. 139, 015102 (2013). 10.1063/1.4811489
54. S. Lloyd, IEEE Trans. Inf. Theory 28, 129 (1982). 10.1109/TIT.1982.1056489
55. D. Arthur and S. Vassilvitskii, in Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SIAM, 2007), pp. 1027-1035.
56. P. Deuflhard, W. Huisinga, A. Fischer, and C. Schütte, Linear Algebra Appl. 315, 39 (2000). 10.1016/S0024-3795(00)00095-1
57. M. Sarich, F. Noé, and C. Schütte, Multiscale Model. Simul. 8, 1154 (2010). 10.1137/090764049
58. W. C. Swope, J. W. Pitera, and F. Suits, J. Phys. Chem. B 108, 6571 (2004). 10.1021/jp037421y
59. G. R. Bowman, X. Huang, and V. S. Pande, Methods 49, 197 (2009). 10.1016/j.ymeth.2009.04.013
60. D. Chandler, J. Chem. Phys. 68, 2959 (1978). 10.1063/1.436049
61. D. Chandler, in Classical and Quantum Dynamics in Condensed Phase Simulations, edited by B. J. Berne, G. Ciccotti, and D. J. Coker (World Scientific, Singapore, 1998), pp. 3-23.
62. Both our algorithm and Holmes-Rubin estimator were implemented the Cython language and compiled to C++. Our implementation of the Holmes-Rubin estimator is available at https://github.com/rmcgibbo/holmes-rubin.
63. R. M. Neal, in Handbook of Markov Chain Monte Carlo, edited by S. Brooks, A. Gelman, G. L. Jones, and X.-L. Meng (Chapman & Hall / CRC, 2011), pp. 113-162.
64. B. Trendelkamp-Schroer and F. Noé, J. Chem. Phys. 138, 164113 (2013). 10.1063/1.4801325