Using stochastic models calibrated from nanosecond nonequilibrium simulations to approximate mesoscale information

Journal of Chemical Physics

Volumn 130, Issue 14, 2009, Pages

  Calderon, Christopher P ^a   Janosi, Lorant ^b   Kosztin, Ioan ^b  

^a Rice University   (United States)

^b UNIVERSITY OF MISSOURI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX SYSTEMS; CONFIDENCE BANDS; DIFFUSION COEFFICIENTS; GRAMICIDIN A; HIGH-DIMENSIONAL SYSTEMS; INITIAL CONFIGURATIONS; MAXIMUM-LIKELIHOOD; MESO-SCALE; MOLECULAR DYNAMICS SIMULATIONS; NON EQUILIBRIUM TRAJECTORIES; NON-EQUILIBRIUM SIMULATIONS; PHYSICAL SIGNIFICANCES; POTASSIUM IONS; POTENTIAL OF MEAN FORCES; REACTION COORDINATES; SINGLE MOLECULES; STOCHASTIC DIFFERENTIAL EQUATIONS; THERMAL FLUCTUATIONS; TYPE METHODS;

DIFFERENTIAL EQUATIONS; DYNAMICS; MAXIMUM LIKELIHOOD ESTIMATION; MODELS; MOLECULAR DYNAMICS; RANDOM PROCESSES; REACTION KINETICS; STOCHASTIC CONTROL SYSTEMS; TIME SERIES;

STOCHASTIC MODELS;

GRAMICIDIN; POTASSIUM;

ARTICLE; BACILLUS; BIOLOGY; CHEMICAL MODEL; CHEMISTRY; COMPUTER SIMULATION; DIFFUSION; ION TRANSPORT; METABOLISM; METHODOLOGY; STATISTICS; THERMODYNAMICS;

BACILLUS; COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; DIFFUSION; GRAMICIDIN; ION TRANSPORT; MODELS, CHEMICAL; POTASSIUM; STOCHASTIC PROCESSES; THERMODYNAMICS;

EID: 65249151354     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3106225     Document Type: Article

References (93)

1. M. Carrion-Vazquez, A. Oberhauser, T. Fisher, P. Marszalek, H. Li, and J. Fernandez, Prog. Biophys. Mol. Biol. 0079-6107 10.1016/S0079-6107(00)00017-1 74, 63 (2000).
2. C. Bustamante, Z. Bryant, and S. Smith, Nature (London) 0028-0836 10.1038/nature01405 421, 423 (2003).
3. D. Collin, F. Ritort, C. Jarzynski, S. Smith, I. Tinoco, Jr., and C. Bustamante, Nature (London) 0028-0836 10.1038/nature04061 437, 231 (2005).
4. S. Liu, G. Bokinsky, N. Walter, and X. Zhuang, Proc. Natl. Acad. Sci. U.S.A. 104, 12634 (2007). 0027-8424
5. M. Sotomayor and K. Schulten, Science 0036-8075 10.1126/science.1137591 316, 1144 (2007).
6. C. Calderon, J. Martinez, R. Carroll, and D. Sorensen, http://www.caam.rice.edu/tech-reports/2008-abstracts.html#TR08-17, 2008.
7. C. Calderon, J. Chem. Phys. 0021-9606 10.1063/1.2567098 126, 084106 (2007).
8. C. Calderon and R. Chelli, J. Chem. Phys. 0021-9606 10.1063/1.2903439 128, 145103 (2008).
9. C. Jarzynski, Phys. Rev. E 1063-651X 10.1103/PhysRevE.56.5018 56, 5018 (1997).
10. M. Balsera, S. Stepaniants, S. Izrailev, Y. Oono, and K. Schulten, Biophys. J. 73, 1281 (1997). 0006-3495
11. G. E. Crooks, J. Stat. Phys. 0022-4715 10.1023/A:1023208217925 90, 1481 (1998).
12. D. E. Makarov, P. K. Hansma, and H. Metiu, J. Chem. Phys. 0021-9606 10.1063/1.1369622 114, 9663 (2001).
13. G. Hummer and A. Szabo, Proc. Natl. Acad. Sci. U.S.A. 0027-8424 10.1073/pnas.071034098 98, 3658 (2001).
14. S. Park and K. Schulten, J. Chem. Phys. 0021-9606 10.1063/1.1651473 120, 5946 (2004).
15. I. Kosztin, B. Barz, and L. Janosi, J. Chem. Phys. 0021-9606 10.1063/1.2166379 124, 064106 (2006).
16. M. W. Forney, L. Janosi, and I. Kosztin, Phys. Rev. E 1063-651X 10.1103/PhysRevE.78.051913 78, 051913 (2008).
17. D. Minh and A. Adib, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.100. 180602 100, 180602 (2008).
18. R. Chelli, S. Marsili, and P. Procacci, Phys. Rev. E 1063-651X 10.1103/PhysRevE.77.031104 77, 031104 (2008).
19. C. Calderon, N. Harris, C. Kiang, and D. Cox, J. Phys. Chem. B 113, 138 (2009). 1520-6106
20. C. Calderon, W. Chen, N. Harris, K. Lin, and C. Kiang, J. Phys.: Condens. Matter 21, 034114 (2009). 0953-8984
21. J. Jimenez and T. Ozaki, J. Time Ser. Anal. 0143-9782 10.1111/j.1467-9892.2005.00454.x 27, 77 (2006).
22. Y. Hong and H. Li, Rev. Financ. Stud. 18, 37 (2005). 1465-7368
23. M. Brandt and P. Santa-Clara, J. Financ. Econ. 0304-405X 10.1016/S0304-405X(01)00093-9 63, 161 (2002).
24. Y. At-Sahalia, Ann. Stat. 0090-5364 10.1214/009053607000000622 36, 906 (2008).
25. In Sec. we provide a brief illustration and discussion demonstrating these two viewpoints.
26. S. Paramore, G. Ayton, and G. Voth, J. Chem. Phys. 0021-9606 10.1063/1.2463306 126, 051102 (2007).
27. C. Calderon and K. Arora, J. Chem. Theory Comput. 5, 47 (2009). 1549-9618
28. T. Allen, O. Andersen, and B. Roux, Biophys. J. 0006-3495 10.1529/biophysj.105.077073 90, 3447 (2006).
29. T. Bastug, A. Gray-Weale, S. Patra, and S. Kuyucak, Biophys. J. 0006-3495 10.1529/biophysj.105.073205 90, 2285 (2006).
30. A. Mamonov, M. Kurnikova, and R. Coalson, Biophys. Chem. 0301-4622 10.1016/j.bpc.2006.03.019 124, 268 (2006).
31. T. Bastug and S. Kuyucak, Chem. Phys. Lett. 436, 383 (2007). 0009-2614
32. T. Allen, O. Andersen, and B. Roux, Proc. Natl. Acad. Sci. U.S.A. 0027-8424 10.1073/pnas.2635314100 101, 117 (2003).
33. B. Roux, T. Allen, S. Berneche, and W. Im, Q. Rev. Biophys. 0033-5835 10.1017/S0033583504003968 37, 15 (2004).
34. T. Bastug, S. Patra, and S. Kuyucak, Chem. Phys. Lipids 0009-3084 10.1016/j.chemphyslip.2006.02.012 141, 197 (2006).
35. T. Bastug and S. Kuyucak, J. Chem. Phys. 0021-9606 10.1063/1.2710267 126, 105103 (2007).
36. G. Miloshevsky and P. Jordan, Biophys. J. 0006-3495 10.1529/biophysj.103. 037853 86, 92 (2004).
37. T. Bastug, P. C. Chen, S. M. Patra, and S. Kuyucak, J. Chem. Phys. 0021-9606 10.1063/1.2904461 128, 155104 (2008).
38. G. Crooks, Phys. Rev. E 1063-651X 10.1103/PhysRevE.61.2361 61, 2361 (2000).
39. R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford Univeristy Press, New York, 2001).
40. D. Sigg, H. Qian, and F. Bezanilla, Biophys. J. 76, 782 (1999). 0006-3495
41. J. Gullingsrud, R. Braun, and K. Schulten, J. Comput. Phys. 0021-9991 10.1006/jcph.1999.6218 151, 190 (1999).
42. D. Kopelevich, A. Panagiotopoulos, and I. Kevrekidis, J. Chem. Phys. 0021-9606 10.1063/1.1839174 122, 044908 (2005).
43. G. Hummer, New J. Phys. 1367-2630 10.1088/1367-2630/7/1/001 7, 34 (2005).
44. All stochastic integrals here denote Itô integrals.
45. D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications (Academic, New York, 2002).
46. N. D. Socci, J. N. Onuchic, and P. G. Wolynes, J. Chem. Phys. 0021-9606 10.1063/1.471317 104, 5860 (1996).
47. P. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer-Verlag, Berlin, 1992).
48. See EPAPS Document No. E-JCPSA6-130-007914 for Item 1) A PDF containing additional figures; Item 2) MATLAB scripts illustrating MLE with known transition density. For more information on EPAPS, see http://www.aip.org/ pubservs/epaps.html.
49. P. Li and D. Makarov, J. Chem. Phys. 0021-9606 10.1063/1.1615233 119, 9260 (2003).
50. A. Chorin, A. Kast, and R. Kupferman, Proc. Natl. Acad. Sci. U.S.A. 0027-8424 10.1073/pnas.95.8.4094 95, 4094 (1998).
51. R. Kupferman and A. Stuart, Physica D 0167-2789 10.1016/j.physd.2004.04. 011 199, 279 (2004).
52. A. Ma, A. Nag, and A. R. Dinner, J. Chem. Phys. 0021-9606 10.1063/1.2183768 124, 144911 (2006).
53. We use the term "configuration" to refer to all particle coordinate and velocities and the term "conformation" to refer to protein's positional degrees of freedom throughout.
54. WR is similar, but instead the reverse velocity v pull R (constant magnitude but opposite sign of v pull F) is used.
55. M. Shirts, B. E., G. Hooker, and V. Pande, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.91.140601 91, 140601 (2003).
56. J. Gore, F. Ritort, and C. Bustamante, Proc. Natl. Acad. Sci. U.S.A. 109, 12564 (2003). 0027-8424
57. Y. At-Sahalia and R. Kimmel, NBER Technical Working Paper No. 0286, 2002 (available at http://ideas.repec.org/p/nbr/nberte/0286.html).
58. S. Chen and T. C. Y., " Parameter estimation and bias correction for diffusion processes.," J. Econometr., in press.
59. S. Kou and X. Xie, Phys. Rev. Lett. 93, 180603 (2004). 0031-9007
60. B. Roux and M. Karplus, J. Phys. Chem. 0022-3654 10.1021/j100165a049 95, 4856 (1991).
61. S. Crouzy, T. B. Woolf, and B. Roux, Biophys. J. 67, 1370 (1994). 0006-3495
62. Here we define Wd W-U (z) slightly differently (only method 2 uses this definition).
63. G. Evensen and P. van Leeuwen, Mon. Weather Rev. 128, 1852 (2000).
64. C. Calderon, Multiscale Model. Simul. 1540-3459 10.1137/050643647 6, 656 (2007).
65. L. E. Townsley, W. A. Tucker, S. Sham, and J. F. Hinton, Biochemistry 0006-2960 10.1021/bi010942w 40, 11676 (2001).
66. W. Humphrey, A. Dalke, and K. Schulten, J. Mol. Graphics 0263-7855 10.1016/0263-7855(96)00018-5 14, 33 (1996).
67. J. C. Phillips, R. Braun, W. Wang, J. Gumbart, E. Tajkhorshid, E. Villa, C. Chipot, R. D. Skeel, L. Kale, and K. Schulten, J. Comput. Chem. 0192-8651 10.1002/jcc.20289 26, 1781 (2005).
68. A. D. MacKerell, Jr., D. Bashford, M. Bellott, R. L. Dunbrack, Jr., J. D. Evanseck, M. J. Field, S. Fischer, J. Gao, H. Guo, S. Ha, and D. Josep, FASEB J. 6, A143 (1992). 0892-6638
69. A. D. MacKerell, Jr., D. Bashford, M. Bellott, R. L. Dunbrack, Jr., J. D. Evanseck, M. J. Field, S. Fischer, J. Gao, H. Guo, S. Ha, and D. Josep, J. Phys. Chem. B 1089-5647 10.1021/jp973084f 102, 3586 (1998).
70. S. E. Feller, Y. H. Zhang, R. W. Pastor, and B. R. Brooks, J. Chem. Phys. 0021-9606 10.1063/1.470648 103, 4613 (1995).
71. T. Bastug, S. M. Patra, and S. Kuyucak, Chem. Phys. Lett. 0009-2614 10.1016/j.cplett.2006.05.036 425, 320 (2006).
72. T. Darden, D. York, and L. Pedersen, J. Chem. Phys. 0021-9606 10.1063/1.464397 98, 10089 (1993).
73. S. E. Feller, R. W. Pastor, A. Rojnuckarin, S. Bogusz, and B. d R. Brooks, J. Phys. Chem. 0022-3654 10.1021/jp9614658 100, 17011 (1996).
74. B. Roux, O. S. Andersen, and T. W. Allen, J. Chem. Phys. 0021-9606 10.1063/1.2931568 128, 227101 (2008).
75. T. Bastug and S. Kuyucak, J. Chem. Phys. 0021-9606 10.1063/1.2931571 128, 227102 (2008).
76. D. Ruppert, M. Wand, and R. Carroll, Semiparametric Regression (Cambridge University Press, New York, 2003).
77. C. Jarzynski, Phys. Rev. E 1063-651X 10.1103/PhysRevE.73.046105 73, 046105 (2006).
78. D. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, New York, 1992).
79. P. Procacci, S. Marsili, A. Barducci, G. Signorini, and R. Chelli, J. Chem. Phys. 0021-9606 10.1063/1.2360273 125, 164101 (2006).
80. S. Paramore, G. Ayton, and G. Voth, J. Chem. Phys. 14, 105105 (2007). 0021-9606
81. Note that we are not limited to using simple diffusion models as surrogates.
82. Y. At-Sahalia, Econometrica 0012-9682 10.1111/1468-0262.00274 70, 223 (2002).
83. The dissipated work is defined by Wd W (z) -U (z) where the zero point of the PMF is selected to correspond to the initial z value used in the F or R pull. The average of this quantity was computed (results shown in supplementary materials, Fig., Ref.) because method 2 requires this quantity.
84. M. Majumder, N. Chopra, R. Andrews, and B. Hinds, Nature (London) 0028-0836 10.1038/43844a 438, 44 (2005).
85. J. Krishnan, O. Runborg, and I. Kevrekidis, Comput. Chem. Eng. 0098-1354 10.1016/j.compchemeng.2003.08.013 28, 557 (2004).
86. J. Ramsay and B. Silverman, Functional Data Analysis (Springer-Verlag, New York, 2005).
87. M. Rief, H. Clausen-Schaumann, and H. Gaub, Nat. Struct. Biol. 1072-8368 10.1038/7582 6, 346 (1999).
88. C. Ke, M. Humeniuk, H. S-Gracz, and P. Marszalek, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.99.018302 99, 018302 (2007).
89. N. C. Harris, Y. Song, and C. -H. Kiang, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.99.068101 99, 068101 (2007).
90. S. Dixit, M. Singh-Zocchi, J. Hanne, and G. Zocchi, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.94.118101 94, 118101 (2005).
91. M. Vendruscolo and C. Dobson, Science 0036-8075 10.1126/science.1132851 313, 1586 (2006).
92. F. Simmel, Nanomedicine 2, 817 (2007). 1743-5889
93. C. Bustamante, J. Liphardt, and F. Ritort, Phys. Today 0031-9228 58 (7), 43 (2005).