Towards the prediction of order parameters from molecular dynamics simulations in proteins

Journal of Chemical Physics

Volumn 136, Issue 16, 2012, Pages

  Perilla, Juan R ^a   Woolf, Thomas B ^a  

^a JOHNS HOPKINS UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX ENERGY LANDSCAPES; CONFORMATIONAL CHANGE; DESCRIPTORS; DIMENSIONALITY REDUCTION; INTERMEDIATE STATE; MOLECULAR DYNAMICS CALCULATION; MOLECULAR DYNAMICS SIMULATIONS; MOLECULAR UNDERSTANDING; NONLINEAR TIME SERIES; ORDER PARAMETER; PROTEIN FUNCTIONS; PROTEIN STRUCTURES;

PROTEINS;

MOLECULAR DYNAMICS;

PROTEIN;

ARTICLE; CHEMISTRY; MOLECULAR DYNAMICS; PROTEIN CONFORMATION;

MOLECULAR DYNAMICS SIMULATION; PROTEIN CONFORMATION; PROTEINS;

EID: 84860497586     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3702447     Document Type: Article

References (91)

1. B. J. Berne, Molecular Dynamics and Monte Carlo Simulations of Rare Events (Academic, 1985).
2. P. A. Kollman, Free-energy calculations: Applications to chemical and biochemical phenomena., Chem. Rev. 93, 2395-2417 (1993). 10.1021/cr00023a004
3. C. Bartels and M. Karplus, Probability distributions for complex systems: Adaptive umbrella sampling of the potential energy., J. Phys. Chem. B 102, 865-880 (1998). 10.1021/jp972280j
4. J. D. Chodera, W. C. Swope, J. W. Pitera, C. Seok, and K. A. Dill, Use of the weighted histogram analysis method for the analysis of simulated and parallel tempering simulations., J. Chem. Theory Comput. 3, 26-41 (2007). 10.1021/ct0502864
5. S. Kumar, J. M. Rosenberg, D. Bouzida, R. H. Swendsen, and P. A. Kollman, The weighted histogram analysis method for free-energy calculations on biomolecules. i. the method., J. Comput. Chem. 13, 1011-1021 (1992). 10.1002/jcc.540130812
6. M. R. Shirts and J. D. Chodera, Statistically optimal analysis of samples from multiple equilibrium states., J. Chem. Phys. 129, 124105 (2008). 10.1063/1.2978177
7. X. Kong and C. L. Brooks, Lambda-dynamics: A new approach to free energy calculations., J. Chem. Phys. 105, 2414 (1996). 10.1063/1.472109
8. B. Roux, T. Allen, S. Berneche, and W. Im, Theoretical and computational models of biological ion channels., Q. Rev. Biophys. 37, 15-103 (2004). 10.1017/S0033583504003968
9. N. Echols, D. Milburn, and M. Gerstein, Molmovdb: Analysis and visualization of conformational change and structural flexibility., Nucleic. Acids Res. 31, 478-482 (2003). 10.1093/nar/gkg104
10. V. Alexandrov, U. Lehnert, N. Echols, D. Milburn, D. Engelman, and M. Gerstein, Normal modes for predicting protein motions: A comprehensive database assessment and associated web tool., Protein Sci. 14, 633-643 (2005). 10.1110/ps.04882105
11. B. Brooks and M. Karplus, Harmonic dynamics of proteins: Normal modes and fluctuations in bovine pancreatic trypsin inhibitor., Proc. Natl. Acad. Sci. U.S.A. 80, 6571-6575 (1983). 10.1073/pnas.80.21.6571
12. F. Tama and Y.-H Sanejouand, Conformational change of proteins arising from normal mode calculations., Protein Eng. 14, 1-6 (2001). 10.1093/protein/14.1.1
13. N. Go, T. Noguti, and T. Nishikawa, Dynamics of a small globular protein in terms of low-frequency vibrational modes., Proc. Natl. Acad. Sci. U.S.A. 80, 3696-3700 (1983). 10.1073/pnas.80.12.3696
14. L. Skjaerven, S. M. Hollup, and N. Reuter, Normal mode analysis for proteins., J. Mol. Struct.: THEOCHEM 898, 42-48 (2009). 10.1016/j.theochem.2008. 09.024
15. H. Wako, M. Kato, and S. Endo, Promode: A database of normal mode analyses on protein molecules with a full-atom model., Bioinformatics 20, 2035-2043 (2004). 10.1093/bioinformatics/bth197
16. W. Zheng and S. Doniach, A comparative study of motor-protein motions by using a simple elastic-network model., Proc. Natl. Acad. Sci. U.S.A. 100 (23), 13253-13258 (2003). 10.1073/pnas.2235686100
17. C. Chennubhotla and I. Bahar, Signal propagation in proteins and relation to equilibrium fluctuations., PLOS Comput. Biol. 3, 1716-1726 (2007).
18. A. Amadei, A. B. M. Linssen, and H. J. C. Berendsen, Essential dynamics of proteins., Proteins: Struct., Funct., and Bioinf. 17, 412-425 (1993). 10.1002/prot.340170408
19. B. L. de Groot, D. M. F. van Aalten, A. Amadei, and H. J. C. Berendsen, The consistency of large concerted motions in proteins in molecular dynamics simulations., Biophys. J. 71, 1707-1713 (1996). 10.1016/S0006-3495(96)79372-4
20. A. E. Garcia, Large-amplitude nonlinear motions in proteins., Phys. Rev. Lett. 68 (17), 2696-2699 (1992). 10.1103/PhysRevLett.68.2696
21. S. Hayward, A. Kitao, and N. Go, Harmonicity and anharmonicity in protein dynamics: A normal mode analysis and principal component analysis., Proteins: Struct., Funct., and Genet. 23, 177-186 (1995). 10.1002/prot.340230207
22. D. M. F. van Aalten, A. Amadei, A. B. M. Linssen, V. G. H. Eijsink, G. Vriend, and H. J. C. Berendsen, The essential dynamics of thermolysin: Confirmation of the hinge-bending motion and comparison of simulations in vacuum and water., Proteins: Struct., Funct., and Bioinf. 22, 45 (1995). 10.1002/prot.340220107
23. J. S. Hub and B. L. de Groot, Detection of functional modes in protein dynamics., PLOS Comput. Biol. 5 (8), e1000480 (2009). 10.1371/journal.pcbi. 1000480
24. O. F. Lange and H. Grubmller, Full correlation analysis of conformational protein dynamics., Proteins: Struct., Funct., and Bioinf. 70 (4), 1294-1312 (2008). 10.1002/prot.21618
25. A. Ramanathan, A. J. Savol, C. J. Langmead, P. K. Agarwal, and C. S. Chennubhotla, Discovering conformational sub-states relevant to protein function., PLoS ONE 6 (1), e15827 (2011). 10.1371/journal.pone.0015827
26. A. J. Savol, V. M. Burger, P. K. Agarwal, A. Ramanathan, and C. S. Chennubhotla, QAARM: quasi-anharmonic autoregressive model reveals molecular recognition pathways in ubiquitin., Bioinformatics 27 (13), i52-i60 (2011). 10.1093/bioinformatics/btr248
27. R. Crehuet and M. J. Field, A temperature-dependent nudged-elastic-band algorithm., J. Chem. Phys. 118 (21), 9563-9571 (2003). 10.1063/1.1571817
28. P. Eastman, N. G. Jensen, and S. Doniach, Simulation of protein folding by reaction path annealing., J. Chem. Phys. 114 (8), 3823-3841 (2001). 10.1063/1.1342162
29. H. Huang, E. Ozkirimli, and C. B. Post, Comparison of three perturbation molecular dynamics methods for modeling conformational transitions., J. Chem. Theory Comput. 5 (5), 1304-1314 (2009). 10.1021/ct9000153
30. S. Huo and J. E. Straub, The MaxFlux algorithm for calculating variationally optimized reaction paths for conformational transitions in many body systems at finite temperature., J. Chem. Phys. 107 (13), 5000-5006 (1997). 10.1063/1.474863
31. M. K. Kim, G. S. Chirikjian, and R. L. Jernigan, Elastic models of conformational transitions in macromolecules., J. Mol. Graphics Modell. 21 (2), 151-160 (2002). 10.1016/S1093-3263(02)00143-2
32. L. R. Pratt, A statistical method for identifying transition states in high dimensional problems., J. Chem. Phys. 85 (9), 5045-5048 (1986). 10.1063/1.451695
33. W. Ren, E. Vanden-Eijnden, P. Maragakis, and W. E, Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide., J. Chem. Phys. 123 (13), 134109 (2005). 10.1063/1.2013256
34. B. W. Zhang, D. Jasnow, and D. M. Zuckerman, Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin., Proc. Natl. Acad. Sci. U.S.A. 104 (46), 18043-18048 (2007). 10.1073/pnas.0706349104
35. W. Zheng, B. R. Brooks, and G. Hummer, Protein conformational transitions explored by mixed elastic network models., Proteins 69 (1), 43-57 (2007). 10.1002/prot.21465
36. W. Zheng and B. R. Brooks, Normal-modes-based prediction of protein conformational changes guided by distance constraints., Biophys. J. 88 (5), 3109-3117 (2005). 10.1529/biophysj.104.058453
37. P. G. Bolhuis, C. Dellago, and D. Chandler, Reaction coordinates of biomolecular isomerization., Proc. Natl. Acad. Sci. U.S.A. 97 (11), 5877-82, 5 (2000). 10.1073/pnas.100127697
38. C. Dellago, P. G. Bolhuis, F. S. Csajka, and D. Chandler, Transition path sampling and the calculation of rate constants., J. Chem. Phys. 108 (5), 1964-1977 (1998). 10.1063/1.475562
39. P. Maragakis and M. Karplus, Large amplitude conformational change in proteins explored with a plastic network model: Adenylate kinase., J. Mol. Biol. 352 (4), 807-822, 9 (2005). 10.1016/j.jmb.2005.07.031
40. A. van der Vaart and M. Karplus, Simulation of conformational transitions by the restricted perturbation-targeted molecular dynamics method., J. Chem. Phys. 122 (11), 114903 (2005). 10.1063/1.1861885
41. O. Beckstein, E. J. Denning, J. R. Perilla, and T. B. Woolf, Zipping and unzipping of adenylate kinase: atomistic insights into the ensemble of openclosed transitions., J Mol. Biol. 394 (1), 160-176 (2009). 10.1016/j.jmb.2009.09.009
42. E. J. Denning and T. B. Woolf, Cooperative nature of gating transitions in K channels as seen from dynamic importance sampling calculations., Proteins: Struct., Funct., and Bioinf. 78 (5), 1105-1119 (2010). 10.1002/prot.22632
43. H. Jang and T. B. B. Woolf, Multiple pathways in conformational transitions of the alanine dipeptide: An application of dynamic importance sampling., J. Comput. Chem. 27 (11), 1136-1141 (2006). 10.1002/jcc.20444
44. J. R. Perilla, O. Beckstein, E. J. Denning, and T. B. Woolf, Computing ensembles of transitions from stable states: Dynamic importance sampling., J. Comput. Chem. 32 (2), 196-209 (2011). 10.1002/jcc.21564
45. T. Shimamura, S. Weyand, O. Beckstein, N. G. Rutherford, J. M. Hadden, D. Sharples, M. S. P. Sansom, S. Iwata, P. J. F. Henderson, and A. D. Cameron, Molecular basis of alternating access membrane transport by the sodium-hydantoin transporter Mhp1., Science 328 (5977), 470-473 (2010). 10.1126/science.1186303
46. P. J. Stansfeld and M. S. P. Sansom, Molecular simulation approaches to membrane proteins., Structure (London) 19 (11), 1562-1572 (2011). 10.1016/j.str.2011.10.002
47. T. Woolf, Path corrected functionals of stochastic trajectories: towards relative free energy and reaction coordinate calculations., Chem. Phys. Lett. 289 (5-6), 433-441 (1998). 10.1016/S0009-2614(98)00427-8
48. D. M. Zuckerman and T. B. Woolf, Dynamic reaction paths and rates through importance-sampled stochastic dynamics., J. Chem. Phys. 111 (21), 9475-9484 (1999). 10.1063/1.480278
49. D. M. Zuckerman and T. B. Woolf, Efficient dynamic importance sampling of rare events in one dimension., Phys. Rev. E 63 (1), 016702 (2000). 10.1103/PhysRevE.63.016702
50. D. M. Zuckerman and T. B. Woolf, Transition events in butane simulations: Similarities across models., J. Chem. Phys. 116 (6), 2586-2591 (2002). 10.1063/1.1433501
51. W. Wagner, Unbiased Monte Carlo evaluation of certain functional integrals., J. Comput. Phys. 71 (1), 21-33 (1987). 10.1016/0021-9991(87)90017-9
52. I. Andricioaei and M. Karplus, On the calculation of entropy from covariance matrices of the atomic fluctuations., J. Chem. Phys. 115, 6289-6292 (2001). 10.1063/1.1401821
53. M. A. Balsera, W. Wriggers, Y. Oono, and K. Schulten, Principal component analysis and long time protein dynamics., J. Phys. Chem. 100 (7), 2567-2572 (1996). 10.1021/jp9536920
54. T. Horiuchi and N. Go, Projection of Monte Carlo and molecular dynamics trajectories onto the normal mode axes: Human lysozyme., Proteins: Struct., Funct., and Bioinf. 10 (2), 106-116 (1991). 10.1002/prot.340100204
55. T. Ichiye and M. Karplus, Collective motions in proteins: A covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations., Proteins: Struct., Funct., and Bioinf. 11, 205-217 (1991). 10.1002/prot.340110305
56. M. Karplus and J. Kushick, Method for estimating the configurational entropy of macromolecules., Macromolecules 14, 325-332 (1981). 10.1021/ma50003a019
57. J. Schlitter, Estimation of absolute and relative entropies of macromolecules using the covariance matrix., Chem. Phys. Lett. 215 (6), 617-621 (1993). 10.1016/0009-2614(93)89366-P
58. K. Henzler-Wildman and D. Kern, Dynamic personalities of proteins., Nature (London) 450 (7172), 964-972 (2007). 10.1038/nature06522
59. M. Lei, J. Velos, A. Gardino, A. Kivenson, M. Karplus, and D. Kern, Segmented transition pathway of the signaling protein nitrogen regulatory protein C., J. Mol. Biol. 392 (3), 823-836 (2009). 10.1016/j.jmb.2009.06.065
60. C. Peng, L. Zhang, and T. H-Gordon, Instantaneous normal modes as an unforced reaction coordinate for protein conformational transitions., Biophys. J. 98 (10), 2356-2364 (2010). 10.1016/j.bpj.2010.01.044
61. H. Kamberaj and A. van der Vaart, Extracting the causality of correlated motions from molecular dynamics simulations., Biophys. J. 97 (6), 1747-1755 (2009). 10.1016/j.bpj.2009.07.019
62. F. M. Reza, An Introduction to Information Theory (Dover, 1994).
63. C. E. Shannon, A mathematical theory of communication., MD Comput. Comp. Med. Pract. 27 (4), 306-317 (1948).
64. S. Kullback and R. A. Leibler, On information and sufficiency., Ann. Math. Stat. 22 (1), 79-86 (1951). 10.1214/aoms/1177729694
65. T. Schreiber, Measuring information transfer., Phys. Rev. Lett. 85 (2), 461-464 (2000). 10.1103/PhysRevLett.85.461
66. B. Gourévitch and J. J. Eggermont, Evaluating information transfer between auditory cortical neurons., J. Neurophysiol. 97 (3), 2533-2543 (2007). 10.1152/jn.01106.2006
67. R. Marschinski and H. Kantz, Analysing the information flow between financial time series. An improved estimator for transfer entropy., Eur. Phys. J. B 30 (2), 275-281 (2002). 10.1140/epjb/e2002-00379-2
68. J. J. Borrok, L. L. Kiessling, and K. T. Forest, Conformational changes of glucose/galactose-binding protein illuminated by open, unliganded, and ultra-high-resolution ligand-bound structures., Protein Sci. 16 (6), 1032-1041 (2007). 10.1110/ps.062707807
69. M. Lungarella, A. Pitti, and Y. Kuniyoshi, Information transfer at multiple scales., Phys. Rev. E 76 (5), 056117 (2007). 10.1103/PhysRevE.76.056117
70. M. Staniek and K. Lehnertz, Symbolic transfer entropy., Phys. Rev. Lett. 100 (15), 158101 (2008). 10.1103/PhysRevLett.100.158101
71. J. Lin, E. Keogh, S. Lonardi, and B. Chiu, A symbolic representation of time series, with implications for streaming algorithms., in Proceedings of the 8th ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery DMKD 03 (ACM, 2003), p. 2.
72. B. R. Brooks, C. L. Brooks, A. D. Mackerell, L. Nilsson, R. J. Petrella, B. Roux, Y. Won, G. Archontis, C. Bartels, S. Boresch, A. Caflisch, L. Caves, Q. Cui, A. R. Dinner, M. Feig, S. Fischer, J. Gao, M. Hodoscek, W. Im, K. Kuczera, T. Lazaridis, J. Ma, V. Ovchinnikov, E. Paci, R. W. Pastor, C. B. Post, J. Z. Pu, M. Schaefer, B. Tidor, R. M. Venable, H. L. Woodcock, X. Wu, W. Yang, D. M. York, and M. Karplus, CHARMM: The biomolecular simulation program., J. Comput. Chem. 30 (10), 1545-1614 (2009). 10.1002/jcc.21287
73. M. Schaefer, C. Bartels, and M. Karplus, Solution conformations and thermodynamics of structured peptides: molecular dynamics simulation with an implicit solvation model., J. Mol. Biol. 284 (3), 835-848 (1998). 10.1006/jmbi.1998.2172
74. C. A Hastings, S.-Y. Lee, Ho. S. Cho, D. Yan, S. Kustu, and D. E. Wemmer, High-resolution solution structure of the beryllofluoride-activated NtrC receiver domain., Biochemistry 42 (30), 9081-9090 (2003). 10.1021/bi0273866
75. D. Kern, B. F. Volkman, P. Luginbühl, M. J. Nohaile, S. Kustu, and D. E. Wemmer, Structure of a transiently phosphorylated switch in bacterial signal transduction., Nature (London) 402 (6764), 894-898 (1999). 10.1038/47273
76. B. F. Volkman, D. Lipson, D. E. Wemmer, and D. Kern, Two-state allosteric behavior in a single-domain signaling protein., Science 291 (5512), 2429-2433 (2001). 10.1126/science.291.5512.2429
77. J. C. Phillips, R. Braun, W. Wang, J. Gumbart, E. Tajkhorshid, E. Villa, C. Chipot, R. D. Skeel, L. Kale, and K. Schulten, Scalable molecular dynamics with NAMD., J. Comp. Chem. 26 (16), 1781-1802 (2005). 10.1002/jcc.20289
78. A. Jain, R. Hegger, and G. Stock, Hidden complexity of protein free-energy landscapes revealed by principal component analysis by parts., J. Phys. Chem. Lett. 1, 2769-2773 (2010). 10.1021/jz101069e
79. C. Snow, G. Qi, and H. Steven, Essential dynamics sampling study of adenylate kinase: Comparison to citrate synthase and implications for the hinge and shear mechanisms of domain motions., Proteins: Struct., Funct., and Bioinf. 67, 325-337 (2009). 10.1002/prot.21280
80. N. Kantarci-Carsibasi, T. Haliloglu, and P. Doruker, Conformational transition pathways explored by Monte Carlo simulation integrated with collective modes., Biophys. J. 95, 5862-5873 (2008). 10.1529/biophysj.107.128447
81. G. Miloshevsky and P. Jordan, Open-state conformation of the KcsA K channel: Monte Carlo normal mode following simulations., Structure 15 (12), 1654-1662 (2007). 10.1016/j.str.2007.09.022
82. Z. Zhang, Y. Shi, and H. Liu, Molecular dynamics simulations of peptides and proteins with amplified collective motions., Biophys. J. 84, 3583-3593 (2003). 10.1016/S0006-3495(03)75090-5
83. O. Miyashita, J. N. Onuchic, and P. G. Wolynes, Nonlinear elasticity, proteinquakes, and the energy landscapes of functional transitions in proteins., Proc. Natl. Acad. Sci. U.S.A. 100, 12570-12575 (2003). 10.1073/pnas.2135471100
84. G. R. Bowman and V. S. Pande, Protein folded states are kinetic hubs., Proc. Natl. Acad. Sci. U.S.A. 107, 10890-10895 (2010). 10.1073/pnas.1003962107
85. M. Lei, M. I. Zavodsky, L. A. Kuhn, and M. F. Thorpe, Sampling protein conformations and pathways., J. Comput. Chem. 25, 1133-1148 (2004). 10.1002/jcc.20041
86. J. M. Bofill and J. M. Anglada, Finding transition states using reduced potential-energy surfaces., Theor. Chem. Acc. 105 (6), 463-472 (2001). 10.1007/s002140000252
87. C. J. Cerjan and W. H. Miller, On finding transition states., J. Chem. Phys. 75 (6), 2800-2806 (1981). 10.1063/1.442352
88. R. Elber and D. Shalloway, Temperature dependent reaction coordinates., J. Chem. Phys. 112 (13), 5539-5545 (2000). 10.1063/1.481131
89. M. A. Rohrdanz, W. Zheng, M. Maggioni, and C. Clementi, Determination of reaction coordinates via locally scaled diffusion map., J. Chem. Phys. 134, 124116 (2011). 10.1063/1.3569857
90. W. Humphrey, A. Dalke, and K. Schulten, VMD: Visual molecular dynamics., J. Mol. Graphics 14, 33-38 (1996). 10.1016/0263-7855(96)00018-5
91. A. D. MacKerell, Jr., M. Feig, C. L. Brooks III, Extending the treatment of backbone energetics in protein force fields: Limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations., J. Comput. Chem. 25, 1400-1415 (2004). 10.1002/jcc.20065