A coarse-grained model with implicit salt for RNAs: Predicting 3D structure, stability and salt effect

Journal of Chemical Physics

Volumn 141, Issue 10, 2014, Pages

  Shi, Ya Zhou ^a   Wang, Feng Hua ^a   Wu, Yuan Yan ^a   Tan, Zhi Jie ^a  

^a WUHAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

FORECASTING; RNA; SIMULATED ANNEALING; TEMPERATURE; THERMODYNAMICS;

3-DIMENSIONAL; 3D STRUCTURE; COARSE GRAINED MODELS; COARSE-GRAINED FORCE FIELDS; COMPUTATIONAL MODEL; MEAN DEVIATION; PSEUDO-KNOTS; SIMULATED ANNEALING ALGORITHMS;

NUCLEIC ACIDS;

INORGANIC SALT; RNA;

CHEMICAL STRUCTURE; CHEMISTRY; CONFORMATION; MONTE CARLO METHOD; RNA STABILITY; THERMODYNAMICS;

MODELS, MOLECULAR; MONTE CARLO METHOD; NUCLEIC ACID CONFORMATION; RNA; RNA STABILITY; SALTS; THERMODYNAMICS;

EID: 84926325302     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4894752     Document Type: Article

References (123)

1. F. Crick, " Central dogma of molecular biology," Nature (London) 227, 561-563 (1970). 10.1038/227561a0
2. E. A. Doherty and J. A. Doudnan, " Ribozyme structures and mechanisms," Annu. Rev. Biophys. Biomol. Struct. 30, 457-475 (2001). 10.1146/annurev.biophys.30.1.457
3. G. J. Hannon, " RNA interference," Nature (London) 418, 244-251 (2002). 10.1038/418244a
4. J. Chen and W. Zhang, " Kinetic analysis of the effects of target structures on siRNA efficiency," J. Chem. Phys. 137, 225102 (2012). 10.1063/1.4769821
5. T. E. Edwards, D. J. Klein, and A. R. Ferre-d'Amare, " Riboswitches: Small-molecule recognition by gene regulatory RNAs," Curr. Opin. Chem. Biol. 17, 273-279 (2007). 10.1016/j.sbi.2007.05.004
6. I. Tinoco Jr. and C. Bustamante, " How RNA folds," J. Mol. Biol. 293, 271-281 (1999). 10.1006/jmbi.1999.3001
7. P. T. X. Li, J. Vieregg, and I. Tinoco Jr., " How RNA unfolds and refolds," Annu. Rev. Biochem. 77, 77-100 (2008). 10.1146/annurev.biochem.77.061206.174353
8. A. M. Mustoe, C. L. Brooks, and H. M. Al-Hashimi, " Hierarchy of RNA functional dynamics," Annu. Rev. Biochem. 83, 441-466 (2014). 10.1146/annurev-biochem-060713-035524
9. K. B. Hall, " Spectroscopic probes of RNA structures and dynamics," Methods Mol. Biol. 875, 67-84 (2012). 10.1007/978-1-61779-806-1-4
10. W. Zhang, and S. J. Chen, " RNA hairpin-folding kinetics," Proc. Natl. Acad. Sci. U.S.A. 99, 1931-1936 (2002). 10.1073/pnas.032443099
11. P. Zhao, W. Zhang, and S. J. Chen, " Predicting secondary structural folding kinetics for nucleic acids," Biophys. J. 98, 1617-1625 (2010). 10.1016/j.bpj.2009.12.4319
12. S. A. Woodson, " Metal ions and RNA folding: A highly charged topic with a dynamic future," Curr. Opin. Struct. Biol. 9, 104-109 (2005). 10.1016/j.cbpa.2005.02.004
13. D. E. Draper, " Folding of RNA tertiary structure: Linkages between backbone phosphates, ions, and water," Biopolymers 99, 1105-1113 (2013). 10.1002/bip.22249
14. K. B. Hall, " RNA does the folding dance of twist, turn, stack," Proc. Natl. Acad. Sci. U.S.A. 110, 16706-16707 (2013). 10.1073/pnas.1316029110
15. J. Lipfert, S. Doniach, R. Das, and D. Herschlag, " Understanding nucleic acid-ion interactions," Annu. Rev. Biochem. 83, 813-841 (2014). 10.1146/annurev-biochem-060409-092720
16. A. Kundagrami, and M. Muthukumar, " Theory of competitive counterion adsorption on flexible polyelectrolytes: Divalent salts," J. Chem. Phys. 128, 244901 (2008). 10.1063/1.2940199
17. M. Muthukumar, " Theory of counter-ion condensation on flexible polyelectrolytes: Adsorption mechanism," J. Chem. Phys. 120, 9343 (2004). 10.1063/1.1701839
18. S. A. Pabit, J. L. Sutton, H. Chen, and L. Pollack, " Role of ion valence in the submillisecond collapse and folding of a small RNA domain," Biochemistry 52, 1539-1546 (2013). 10.1021/bi3016636
19. Z. J. Tan, and S. J. Chen, " Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte," J. Chem. Phys. 122, 044903 (2005). 10.1063/1.1842059
20. Z. J. Tan, and S. J. Chen, " Predicting ion binding properties for RNA tertiary structures," Biophys. J. 99, 1565-1576 (2010). 10.1016/j.bpj.2010.06.029
21. B. A. Shapiro, Y. G. Yingling, W. Kasprzak, and E. Bindewald, " Bridging the gap in RNA structure prediction," Curr. Opin. Struct. Biol. 17, 157-165 (2007). 10.1016/j.sbi.2007.03.001
22. S. J. Chen, " RNA folding: Conformational statistics, folding kinetics, and ion electrostatics," Annu. Rev. Biophys. 37, 197-214 (2008). 10.1146/annurev.biophys.37.032807.125957
23. M. Levitt, " Detailed molecular model for transfer ribonucleic acid," Nature (London) 224, 759-763 (1969). 10.1038/224759a0
24. F. Michel and E. Westhof, " Modelling of the three-dimensional architecture of group I catalytic introns based on comparative sequence analysis," J. Mol. Biol. 216, 585-610 (1990). 10.1016/0022-2836(90)90386-Z
25. M. E. Harris, J. M. Nolan, A. Malhotra, J. W. Brown, S. C. Harvey, and N. R. Pace, " Use of photoaffinity crosslinking and molecular modeling to analyze the global architecture of ribonuclease P RNA," Embo. J. 13, 3953-3963 (1994)
26. S. M. Stagg, J. A. Mears, and S. C. Harvey," A structural model for the assembly of the 30S subunit of the ribosome," J. Mol. Biol. 328, 49-61 (2003). 10.1016/S0022-2836(03)00174-8
27. M. Gruebele and D. Thirumalai," Perspective: Reaches of chemical physics in biology," J. Chem. Phys. 139, 121701 (2013). 10.1063/1.4820139
28. K. Rother, M. Rother, M. Boniecki, T. Puton, and J. M. Bujnicki, " RNA and protein 3D structure modeling: Similarities and differences," J. Mol. Model 17, 2325-2336 (2011). 10.1007/s00894-010-0951-x
29. C. Laing and T. Schlick, " Computional approaches to RNA structure prediction, analysis, and design," Curr. Opin. Struct. Biol. 21, 306-318 (2011). 10.1016/j.sbi.2011.03.015
30. C. Laing and T. Schlick, " Computatonal approaches to 3D modeling of RNA," J. Phys.: Condens. Matter. 22, 283101 (2010). 10.1088/0953-8984/22/28/283101
31. J. A. Cruz, M. F. Blanchet, M. Boniecki, J. M. Bujnicki, S. J. Chen, S. Cao, R. Das, F. Ding, N. V. Dokholyan, S. C. Flores, L. Huang, C. A. Lavender, V. Lisi, F. Major, K. Mikolajczak, D. J. Patel, A. Philips, T. Puton, J. Santalucia, F. Sijenyi, T. Hermann, K. Rother, M. Rother, A. Serganov, M. Skorupski, T. Soltysinski, P. Sripakdeevong, I. Tuszynska, K. M. Weeks, C. Waldsich, M. Wildauer, N. B. Leontis, and E. Westhof, " RNA-Puzzles: A CASP-like evalution of RNA three-dimensional structure prediction," RNA 18, 610-625 (2012). 10.1261/rna.031054.111
32. C. E. Hajdin, F. Ding, N. V. Dokholyan, and K. M. Weeks, " On the significance of an RNA tertiary structure prediction," RNA 16, 1340-1349 (2010). 10.1261/rna.1837410
33. Y. Z. Shi, Y. Y. Wu, F. H. Wang, and Z. J. Tan," RNA structure prediction: Progress and perspective," Chin. Phys. B 23, 078701 (2014). 10.1088/1674-1056/23/7/078701
34. K. J. Riley and L. J. Maher," p53-RNA interactions: New clues in an old mystery," RNA 13, 1825-1833 (2007). 10.1261/rna.673407
35. C. Massire and E. Westhof, " MANIP: An interactive tool for modelling RNA," J. Mol. Graph. Model. 16, 197-205 (1998). 10.1016/S1093-3263(98)80004-1
36. F. Jossinet and E. Westhof, " Sequence to Structure (S2S): Display, manipulate and interconnect RNA data from sequence to structure," Bioinformatics 21, 3320-3321 (2005). 10.1093/bioinformatics/bti504
37. F. Jossinet, T. E. Ludwig, and E. Westhof, " Assemble: An interactive graphical tool to analyze and build RNA architectures at 2D and 3D levels," Bioinformatics 26, 2057-2059 (2010). 10.1093/bioinformatics/btq321
38. H. M. Martinez, J. V. Maizel Jr., and B. A. Shapiro, " RNA 2D3D: A program for generating, viewing, and comparing 3-dimensional models of RNA," J. Biomol. Struct. Dyn. 25, 669-683 (2008). 10.1080/07391102.2008.10531240
39. C. Zwieb and F. Muller, " Three-dimensional comparative modeling of RNA," Nucleic Acids Symp. Ser. 36, 69-71 (1997)
40. T. J. Macke and D. A. Case, " Modeling unusual nucleic acid structures," in Molecular Modeling of Nucleic Acids, ACS Symposium Series Vol. 682 (American Chemical Society, 1998), pp. 379-393
41. M. Rother, K. Rother, T. Puton, and J. M. Bujnicki, " ModeRNA: A tool for comparative modeling of RNA 3D structure," Nucleic Acids Res. 39, 4007-4022 (2011). 10.1093/nar/gkq1320
42. S. C. Flores and R. B. Altman, " Turning limited experimental information into 3D models of RNA," RNA 16, 1769-1778 (2010). 10.1261/rna.2112110
43. F. Sijenyi, P. Saro, Z. Ouyang, K. Damm-Ganamet, M. Wood, J. Jiang, and J. SantaLucia Jr., " The RNA dolding problems: Different levels of RNA structure prediction," in RNA 3D Structure Analysis and Prediction, Nucleic Acids and Molecular Biology Series, edited by N. Leontis and E. Westhof (Springer, 2011)
44. M. Popenda, M. Szachniuk, M. Antczak, K. J. Purzycka, P. Lukasiak, N. Bartol, J. Blazewicz, and R. W. Adamiak, " Automated 3D structure composition for large RNAs," Nucleic Acids Res. 40, e112 (2012). 10.1093/nar/gks339
45. M. Parisien and F. Major, " The MC-Fold and MC-Sym pipeline infers RNA structure from sequence data," Nature (London) 452, 51-55 (2008). 10.1038/nature06684
46. R. Das and D. Baker, " Automated de novo prediction of native-like RNA tertiary structures," Proc. Natl. Acad. Sci. U.S.A. 104, 14664-14669 (2007). 10.1073/pnas.0703836104
47. R. Das, J. Karanicolas, and D. Baker, " Atomic accuracy in predicting and designing noncanonical RNA structure," Nat. Methods 7, 291-294 (2010). 10.1038/nmeth.1433
48. J. P. Bida and L. J. Maher III, " Improved prediction of RNA tertiary structure with insights into native state dynamics," RNA 18, 385-393 (2012). 10.1261/rna.027201.111
49. J. Frellsen, I. Moltke, M. Thiim, K. V. Mardia, and J. Ferkinghoff-Borg, " A probabilistic model of RNA conformational space," PLoS Comput. Biol. 5, e1000406 (2009). 10.1371/journal.pcbi.1000406
50. A. Y. Sim, M. Levitt, and P. Minary, " Modeling and design by hierarchical natural moves," Proc. Natl. Acad. Sci. U.S.A. 109, 2890-2895 (2012). 10.1073/pnas.1119918109
51. Y. Zhao, Y. Huang, Z. Gong, Y. Wang, J. Man, and Y. Xiao, " Automated and fast building of three-dimensional RNA structures," Sci. Rep. 2, 734 (2012). 10.1038/srep00734
52. J. Zhang, Y. Bian, H. Lin, and W. Wang, " RNA fragment modeling with a nucleobase discrete-state model," Phys. Rev. E 85, 021909 (2012). 10.1103/PhysRevE.85.021909
53. Y. Zhao, Z. Gong, and Y. Xiao, " Improvements of the hierarchical approach for predicting RNA tertiary structure," J. Biomol. Struct. Dyn. 28, 815-826 (2011). 10.1080/07391102.2011.10508609
54. Y. Huang, S. Liu, D. Guo, L. Li, and Y. Xiao," A novel protocol for three-dimensional structure prediction of RNA-protein complexes," Sci. Rep. 3, 1887 (2013). 10.1038/srep01887
55. R. K. Z. Tan, A. S. Petrov, and S. C. Harvey, " YUP: A molecular simulation program for coarse-grained and multiscaled models," J. Chem. Theory Comput. 2, 529-540 (2006). 10.1021/ct050323r
56. M. A. Jonikas, R. J. Radmer, A. Laederach, R. Das, S. Pearlman, D. Herschlag, and R. B. Altman, " Coarse-grained modeling of large RNA molecules with knowledge-based potentials and structural filters," RNA 15, 189-199 (2009). 10.1261/rna.1270809
57. O. Taxilaga-Zetina, P. Pliego-Pastrana, and M. D. Carbajal-Tinoco, " Three-dimensional structures of RNA obtained by means of knowledge-based interaction potentials," Phys. Rev. E 81, 041914 (2010). 10.1103/PhysRevE.81.041914
58. F. Ding, S. Sharma, P. Chalasani, V. V. Demidov, N. E. Broude, and N. V. Dokholyan, " Ab initio RNA folding by discrete molecular dynamics: From structure prediction to folding mechanisms," RNA 14, 1164-1173 (2008). 10.1261/rna.894608
59. S. Sharma, F. Ding, and N. V. Dokholyan, " iFoldRNA: Three-dimensional RNA structure prediction and folding," Bioinformatics 24, 1951-1952 (2008). 10.1093/bioinformatics/btn328
60. S. Cao and S. J. Chen, " Predicting RNA folding thermodynamics with a reduced chain representation model," RNA 11, 1884-1897 (2005). 10.1261/rna.2109105
61. S. Cao and S. J. Chen, " Physics-based de novo prediction of RNA 3D structures," J. Phys. Chem. B 115, 4216-4226 (2011). 10.1021/jp112059y
62. S. Pasquali and P. Derreumaux, " HiRE: A high resolution coarse-grained energy model for RNA," J. Phys. Chem. B 114, 11957-11966 (2010). 10.1021/jp102497y
63. T. Cragnolini, P. Derreumaux, and S. Pasquali," Coarse-grained simulations of RNA and DNA duplexes," J. Phys. Chem. B 117, 8047-8060 (2013). 10.1021/jp400786b
64. Z. Xia, D. P. Gardner, R. R. Gutell, and P. Ren, " Coarse-grained model for simulation RNA three-dimensional structures," J. Phys. Chem. B 114, 13497-13506 (2010). 10.1021/jp104926t
65. Z. Xia, D. R. Bell, Y. Shi, and P. Ren, " RNA 3D structure prediction by using a coarse-grained model and experimental data," J. Phys. Chem. B 117, 3135-3144 (2013). 10.1021/jp400751w
66. P. Sulc, F. Romano, T. E. Ouldridge, J. P. K. Doye, and A. A. Louis, " A nucleotide-level coarse-grained model of RNA," J. Chem. Phys. 140, 235102 (2014). 10.1063/1.4881424
67. N. Hori and S. Takada, " Coarse-grained structure-based model for RNA-protein complexes developed by fluctuation matching," J. Chem. Theory Comput. 8, 3384-3394 (2012). 10.1021/ct300361j
68. T. E. Cheatham III, and M. A. Young, " Molecular dynamics simulation of nucleic acids: Successes, limitations, and promise," Biopolymers 56, 232-256 (2000). 10.1002/1097-0282(2000)56:4<232::AID-BIP10037>3.0.CO;2-H
69. M. Paliy, R. Melnik, and B. A. Shapiro, " Coarse-grained RNA nanostructures for molecular dynamics simulations," Phys. Biol. 7, 036001 (2010). 10.1088/1478-3975/7/3/036001
70. N. E. Buchete, J. E. Straub, and D. Thirumalai, " Anisotropic coarse-grained statistical potentials improve the ability to identify nativelike protein structures," J. Chem. Phys. 118, 7658 (2003). 10.1063/1.1561616
71. A. E. Giessen and J. E. Straub, " Coarse-grained model of coil-to-helix kinetics demonstrates the importance of multiple nucleation sites in helix folding," J. Chem. Theory Comput. 2, 674-684 (2006). 10.1021/ct0503318
72. J. J. de Pablo, " Coarse-grained simulations of macromolecules: From DNA to nanocomposites," Annu. Rev. Phys. Chem. 62, 555 (2011). 10.1146/annurev-physchem-032210-103458
73. M. G. Saunders and G. A. Voth, " Coarse-graining methods for computational biology," Annu. Rev. Biophys. 42, 73-93 (2013). 10.1146/annurev-biophys-083012-130348
74. W. G. Noid, " Perspective: Coarse-grained models for biomolecular systems," J. Chem. Phys. 139, 090901 (2013). 10.1063/1.4818908
75. N. Denesyuk and D. Thirumalai, " Coarse-grained model for predicting RNA folding thermodynamics," J. Phys. Chem. B 117, 4901-4911 (2013). 10.1021/jp401087x
76. C. Hyeon and D. Thirumalai, " Mechanical unfolding of RNA hairpins," Proc. Natl. Acad. Sci. U.S.A. 102, 6789-6794 (2005). 10.1073/pnas.0408314102
77. E. Humphris-Narayanan, and A. M. Pyle," Discrete RNA Libraries from pseudo-torsional space," J. Mol. Biol. 421, 6-26 (2012). 10.1016/j.jmb.2012.03.002
78. F. H. Wang, Y. Y. Wu, and Z. J. Tan, " Salt contribution to the flexibility of single-stranded nucleic acid of finite length," Biopolymers 99, 370-381 (2013). 10.1002/bip.22189
79. +]'s and the description of the 46 RNAs used in this work and predicted results
80. Z. J. Tan and S. J. Chen, " Nucleic acid helix stability: Effects of salt concentration, cation valence and size, and chain length," Biophys. J. 90, 1175-1190 (2006). 10.1529/biophysj.105.070904
81. G. S. Manning, " The molecular theory of polyelectrolyte solutions with applications to the electrostatic properties of polynucleotides," Q. Rev. Biophys. 11, 179-246 (1978). 10.1017/S0033583500002031
82. C. M. Gherghe, C. W. Leonard, F. Ding, N. V. Dokholyan, and K. M. Week, " Native-like RNA tertiary structures using a sequence-encoded cleavage agent and refinement by discrete molecular dynamics," J. Am. Chem. Soc. 131, 2541-2546 (2009). 10.1021/ja805460e
83. T. Xia, J. SantaLucia Jr., M. E. Burkand, R. Kierzek, S. J. Schroeder, X. Jiao, C. Cox, and D. H. Turner, " Thermodynamic parameters for an expanded nearest-neighbor model for formation of RNA duplexes with Watson-Crick base pairs," Biochemistry 37, 14719-14735 (1998). 10.1021/bi9809425
84. D. H. Mathews, J. Sabina, M. Zuker, and D. H. Turner, " Expended sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure," J. Mol. Biol. 288, 911-940 (1999). 10.1006/jmbi.1999.2700
85. F. Leonarski, F. Trovato, V. Tozzini, A. Les, and J. Trylska, " Evolutionary algorithm in the optimization of a coarse-grained force field," J. Chem. Theory Comput. 9, 4874-4889 (2013). 10.1021/ct4005036
86. J. Berrauer, X. Huang, A. Y. Sim, and M. Levitt, " Fully differentiable coarse-grained and all-atom knowledge-based potentials for RNA structure evaluation," RNA 17, 1066-1075 (2011). 10.1261/rna.2543711
87. S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, " Optimization by simulated annealing," Science 220, 671-680 (1983). 10.1126/science.220.4598.671
88. M. Schmitz and G. Steger, " Discription of RNA folding by simulated annealing," J. Mol. Biol. 255, 254-266 (1996). 10.1006/jmbi.1996.0021
89. N. Madras and A. D. Sokal, " The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk," J. Stat. Phys. 50, 109-186 (1988). 10.1007/BF01022990
90. M. Parisien, J. A. Cruz, E. Westhof, and F. Major, " New metrics for comparing and assessing discrepancies between RNA 3D structures and models," RNA 15, 1875-1885 (2009). 10.1261/rna.1700409
91. W. Humphrey, A. Dalke, and K. Schulten, " VMD: Visual molecular dynamics," J. Mol. Graph. 14, 33-8, 27-8 (1996). 10.1016/0263-7855(96)00018-5
92. D. W. Staple and S. E. Butcher, " Pseudoknots: RNA structures with diverse functions," PLoS Biol. 3, e213 (2005). 10.1371/journal.pbio.0030213
93. S. Cao and S. J. Chen, " Predicting RNA pseudoknot folding thermodynamics," Nucleic Acids Res. 34, 2634-2652 (2006). 10.1093/nar/gkl346
94. S. Chauhan and S. A. Woodson," Tertiary interactions determine the accuracy of RNA folding," J. Am. Chem. Soc. 130, 1296-1303 (2008). 10.1021/ja076166i
95. J. Zhang, J. Dundas, M. Lin, M. Chen, W. Wang, and J. Liang, " Prediction of geometrically feasible three-dimensional structures of pseudoknotted RNA through free energy estimation," RNA 15, 2248-2263 (2009). 10.1261/rna.1723609
96. Y. Zhang, J. Zhang, and W. Wang, " Atomistic analysis of pseudoknotted RNA unfolding," J. Am. Chem. Soc. 133, 6882-6885 (2011). 10.1021/ja1109425
97. X. Xu and S. J. Chen, " Kinetic mechanism of conformational switch between bistable RNA hairpins," J. Am. Chem. Soc. 134, 12499-12507 (2012). 10.1021/ja3013819
98. M. J. Serra, M. H. Lyttle, T. J. Axenson, C. A. Schadt, and D. H. Turner, " RNA hairpin loop stability depends on closing base pair," Nucleic Acids Res. 21, 3845-3849 (1993). 10.1093/nar/21.16.3845
99. M. J. Serra, W. T. Barnes, K. Betschart, M. J. Gutierrez, K. J. Sprouse, C. K. Riley, L. Stewart, and R. E. Temel, " Improved parameters for the prediction of RNA hairpin stability," Biochemistry 36, 4844-4851 (1997). 10.1021/bi962608j
100. C. J. Vecenie and M. J. Serra, " Stability of RNA hairpin loops closed by AU base pairs," Biochemistry 43, 11813-11817 (2004). 10.1021/bi049954i
101. C. J. Vecenie, C. V. Morrow, A. Zyra, and M. J. Serra, " Sequence dependence of the stability of RNA hairpin molecules with six nucleotide loops," Biochemistry 45, 1400-1407 (2006). 10.1021/bi051750u
102. D. R. Groebe and O. C. Uhlenbeck, " Characterization of RNA hairpin loop stability," Nucleic Acids Res. 16, 11725-11735 (1988). 10.1093/nar/16.24.11725
103. D. J. Williams and K. B. Hall, " Thermodynamic comparison of salt dependence of natural RNA hairpins and RNA hairpins with non-nucleotide spacers," Biochemistry 35, 14665-14670 (1996). 10.1021/bi961654g
104. Z. J. Tan and S. J. Chen, " Salt dependence of nucleic acid hairpin stability," Biophys. J. 95, 738-752 (2008). 10.1529/biophysj.108.131524
105. A. M. Soto, V. Misra, and D. E. Draper, " Tertiary structure of an RNA pseudoknot is stabilized by "diffuse" Mg2+ ions," Biochemistry 46, 2973-2983 (2007). 10.1021/bi0616753
106. P. L. Nixon and D. P. Giedroc, " Energetics of a strongly pH dependent RNA tertiary structure in a frameshifting pseudoknot," J. Mol. Biol. 296, 659-671 (2000). 10.1006/jmbi.1999.3464
107. Z. J. Tan and S. J. Chen, " Salt contribution to RNA tertiary structure folding stability," Biophys. J. 101, 176-187 (2011). 10.1016/j.bpj.2011.05.050
108. Z. J. Tan and S. J. Chen, " Ion-mediated RNA structural collapse: Effect of spatial confinement," Biophys. J. 103, 827-836 (2012). 10.1016/j.bpj.2012.06.048
109. +-induced changes in the HIV-1 TAR conformational dynamics using NMR residual dipolar couplings: New insights into the role of counterions and electrostatic interactions in adaptive recognition," Biochemistry 46, 6525-6535 (2007). 10.1021/bi700335n
110. R. Lavery, M. Moakher, J. H. Maddocks, D. Petkeviciute, and K. Zakrzewska, " Conformational analysis of nucleic acids revisited: Curves+," Nucleic Acids Res. 37, 5917-5929 (2009). 10.1093/nar/gkp608
111. W. Stephenson, S. Keller, R. Santiago, J. E. Albrecht, P. N. Asare-Okai, S. A. Tenenbaum, M. Zuker, and P. T. X. Li, " Combining temperature and force to study folding of an RNA hairpin," Phys. Chem. Chem. Phys. 16, 906-917 (2014). 10.1039/c3cp52042k
112. S. Biyun, S. S. Cho, and D. Thirumalai, " Folding of human telomerase RNA pseudoknot using ion-jump and temperature-quench simulations," J. Am. Chem. Soc. 133, 20634-20643 (2011). 10.1021/ja2092823
113. Z. J. Tan and S. J. Chen," Importance of diffuse metal ion binding to RNA," Met. Ions Life Sci. 9, 101-124 (2011). 10.1039/9781849732512-00101
114. M. Parisien and F. Major," Determining RNA three-dimensional structures using low-resolution data," J. Struct. Biol. 179, 252-260 (2012). 10.1016/j.jsb.2011.12.024
115. R. Das, M. Kudaravalli, M. Jonikas, A. Laederach, R. Fong, J. P. Schwans, D. Baker, J. A. Piccirilli, R. B. Altman, and D. Herschlag, " Structural inference of native and partially folded RNA by high-throughput contact mapping," Proc. Natl. Acad. Sci. U.S.A. 105, 4144-4149 (2008). 10.1073/pnas.0709032105
116. S. E. Butcher and A. M. Pyle, " The molecular interactions that stabilize RNA tertiary structure: RNA motifs, patterns, and networks," Acc. Chem. Res. 44, 1302-1311 (2011). 10.1021/ar200098t
117. M. H. Bailor, A. M. Mustoe, C. L. Brooks, and H. M. Al-Hashimi, " Topological constraints: Using RNA secondary structure to model 3D conformation, folding pathways, and dynamic adaptation," Curr. Opin. Struct. Biol. 21, 296-305 (2011). 10.1016/j.sbi.2011.03.009
118. M. J. Seetin and D. H. Mathews, " Automated RNA tertiary structure prediction from secondary structure and low-resolution restraints," J. Comput. Chem. 32, 2232-2244 (2011). 10.1002/jcc.21806
119. K. A. Wilkinson, E. J. Merino, and K. M. Weeks, " Selective 2′-hydroxyl acylation analyzed by primer extension (SHAPE): Quantitative RNA structure analysis at single nucleotide resolution," Nat. Protoc. 1, 1610-1616 (2006). 10.1038/nprot.2006.249
120. C. Laing, S. Jung, N. Kim, S. Elmetwaly, M. Zahran, and T. Schlick, " Predicting helical topologies in RNA junctions as tree graphs," PLoS One 8, e71947 (2013). 10.1371/journal.pone.0071947
121. F. Ding, C. A. Lavender, K. M. Weeks, and N. V. Dokholyan, " Three-dimensional RNA structure refinement by hydroxyl radical probing," Nat. Methods 9, 603-608 (2012). 10.1038/nmeth.1976
122. Z. J. Tan, and S. J. Chen, " RNA helix stability in mixed Na+/Mg2 +solution," Biophys. J. 92, 3615-3632 (2007). 10.1529/biophysj.106.100388
123. M. A. Jonikas, R. J. Radmer, and R. B. Altman, " Knowledge-based instantiation of full atomic detail into coarse-grain RNA 3D structural models," Bioinformatics 25, 3259-3266 (2009). 10.1093/bioinformatics/btp576