Abstract
Beyond the “traditional” functions such as gene storage, transport and protein synthesis, recent discoveries reveal that RNAs have important “new” biological functions including the RNA silence and gene regulation of riboswitch. Such functions of noncoding RNAs are strongly coupled to the RNA structures and proper structure change, which naturally leads to the RNA folding problem including structure prediction and folding kinetics. Due to the polyanionic nature of RNAs, RNA folding structure, stability and kinetics are strongly coupled to the ion condition of solution. The main focus of this chapter is to review the recent progress in the three major aspects in RNA folding problem: structure prediction, folding kinetics and ion electrostatics. This chapter will introduce both the recent experimental and theoretical progress, while emphasize the theoretical modelling on the three aspects in RNA folding.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bloomfield VA, Crothers DM, Tinoco IJ (2000) Nucleic acids: structure, properties and functions. University Science Books, Sausalito
Walter NG, Woodson SA, Batey RT (eds) (2009) Non-coding RNA. Non-protein coding RNAs. Springer, Berlin
Cruz JA, Westhof E (2009) The dynamic landscapes of RNA architecture. Cell 136:604–609
Zuker M, Stiegler P (1981) Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res 9:133–148
Hofacker IL, Fontana W, Stadler PF, Bonhoeffer S, Tacker M, Schuster P (1994) Fast folding and comparison of RNA secondary structures. Monatsh Chem 125:167–188
Ding Y, Lawrence CE (2003) A statistical sampling algorithm for RNA secondary structure prediction. Nucleic Acids Res 31:7280–7301
Do CB, Woods DA, Batzoglou S (2006) CONTRAfold: RNA secondary structure prediction without physics-based models. Bioinformatics 23:90–98
Mathews DH, Turner DH (2006) Prediction of RNA secondary structure by free energy minimization. Curr Opin Struct Biol 16:270–278
Massire C, Westhof E (1998) MANIP: an interactive tool for modelling RNA. J Mol Graph Model 16(197–205):255–257
Zwieb C, Mueller F (1997) Three-dimensional comparative modeling of RNA. Nucleic Acids Symp Ser 36:69–71
Jossinet F, Westhof E (2005) Sequence to Structure (S2S): display, manipulate and interconnect RNA data from sequence to structure. Bioinformatics 21:3320–3321
Jossinet F, Ludwig TE, Westhof E (2010) Assemble: an interactive graphical tool to analyze and build RNA architectures at the 2D and 3D levels. Bioinformatics 26:2057–2059
Martinez HM, Maizel JV, Shapiro BA (2008) RNA2D3D: a program for generating, viewing, and comparing 3-dimensional models of RNA. J Biomol Struct Dyn 25:669–683
Rother M, Rother K, Puton T, Bujnicki JM (2011) ModeRNA: a tool for comparative modeling of RNA 3D structure. Nucleic Acids Res 1–16
Flores SC, Wan YQ, Russell R, Altman RB (2010) Predicting RNA structure by multiple template homology modeling. Pac Symp Biocomput 15:216–227
Paliy M, Melnik R, Shapiro BA (2010) Coarse-graining RNA nanostructures for molecular dynamics simulations. Phys Biol 7:036001
Tan RKZ, Petrov AS, Harvey SC (2006) YUP: molecular simulation program for coarse-grained and multiscaled models. J Chem Theory Comput 2:529–540
Jonikas MA, Radmer RJ, Laederach A, Das R, Pearlman S, Herschlag D, Altman RB (2009) Coarse-grained modeling of large RNA molecules with knowledge-based potentials and structural filters. RNA 15:189–199
Jonikas MA, Radmer RJ, Altman RB (2009) Knowledge-based instantiation of full atomic detail into coarse-grain RNA 3D structural models. Bioinformatics 25:3259–3266
Taxilaga-Zetina O, Pliego-Pastrana P, Carbajal-Tinoco MD (2010) Three-dimensional structures of RNA obtained by means of knowledge-based interaction potentials. Phys Rev E 81:041914
Cao S, Chen SJ (2011) Physics-based de novo prediction of RNA 3D structures. J Phys Chem B 115:4216–4226
Cao S, Chen SJ (2006) Predicting RNA pseudoknot folding thermodynamics. Nucleic Acids Res 34:2634–2652
Cao S, Chen SJ (2005) Predicting RNA folding thermodynamics with a reduced chain representation model. RNA 11:1184–1897
Ding F, Sharma S, Chalasani P, Demidov VV, Broude NE, Dokholyan NV (2008) Ab initio RNA folding by discrete molecular dynamics: from structure prediction to folding mechanisms. RNA 14:1164–1173
Sharma S, Ding F, Dokholyan NV (2008) iFoldRNA: three-dimensional RNA structure prediction and folding. Bioinformatics 24:1951–1952
Ding F, Lavender CA, Weeks KM, Dokholyan NV (2012) Three-dimensional RNA structure refinement by hydroxyl radical probing. Nat Methods 9:603–608
Xia Z, Gardner DP, Gutell RR, Ren P (2010) Coarse-grained model for simulation of RNA three-dimensional structures. J Phys Chem B 114:13497–13506
Pasquali S, Derreumaux P (2010) HiRE-RNA: a high resolution coarse-grained model for RNA. J Phys Chem B 114:11957–11966
Zhang J, Dundas J, Lin M, Chen M, Wang W, Liang J (2009) Prediction of geometrically feasible three-dimensional structures of pseudoknotted RNA through free energy estimation. RNA 15:2248–2263
Zhang J, BianYQ Wang W (2012) RNA fragment modeling with a nucleobase discrete-state model. Phys Rev E 85:021909
Das R, Baker D (2007) Automated de novo prediction of native-like RNA tertiary structures. Proc Natl Acad Sci 104:14664–14669
Das R, Karanicolas J, Baker D (2010) Atomic accuracy in predicting and designing noncanonical RNA structure. Nat Methods 7:291–294
Bida JP, Maher LJ III (2012) Improved prediction of RNA tertiary structure with insights into native state dynamics. RNA 18:385–393
Parisien M, Major F (2008) The MC-Fold and MC-Sym pipeline infers RNA structure from sequence data. Nature 452:51–55
Lemieux S, Major F (2006) Automated extraction and classification of RNA tertiary structure cyclic motifs. Nucleic Acids Res 34:2340–2346
Zhao YJ, Gong Z, Xiao Y (2011) Improvement of the hierarchical approach for predicting RNA tertiary structure. J Biomol Struct Dyn 28:815–826
Gong Z, Zhao Y, Xiao Y (2010) RNA stability under different combinations of amber force fields and solvation models. J Biomol Struct Dyn 28(3):431–441
Seetin MJ, Mathews DH (2011) Automated RNA tertiary structure prediction from secondary structure and low-resolution restraints. J Comput Chem 32:2232–2244
Baumstark T, Schroder AR, Riesner D (1997) Viroid processing: switch from cleavage to ligation is driven by a change from a tetraloop to a loop E conformation. EMBO J 16:599–610
Perrotta AT, Been MD (1998) A toggle duplex in hepatitis delta virus self-cleaving RNA that stabilizes an inactive and a salt-dependent pro-active ribozyme conformation. J Mol Biol 279:361–373
Schultes EA, Bartel DP (2000) One sequence, two ribozymes: implications for the emergence of new ribozyme folds. Science 289:448–452
Kruger K, Grabowski P, Zaug AJ, Sands J, Gottschling DE, Cech TR (1982) Self-splicing RNA: autoexcision and autocyclization of the ribosomal RNA intervening sequence of Tetrahymena. Cell 31:147–157
Bartel DP, Szostak JW (1993) Isolation of new ribozymes from a large pool of random sequences. Science 261:1411–1418
Joyce GF (1989) Amplication, mutation and selection of catalytic RNA. Gene 82:83–87
Ellington AE, Szostak JW (1990) In vitro selection of RNA molecules that bind specific ligands. Nature 346:818–822
Tuerk C, Gold L (1990) Systematic evolution of ligands by exponential enrichment: RNA ligands to bacteriophage T4 DNA polymerase. Science 249:505–510
Mironov AS, Gusarov I, Rafikov R, Lopez LE, Shatalin K, Kreneva RA, Perumov DA, Nudler E (2002) Sensing small molecules by nascent RNA: a mechanism to control transcription in bacteria. Cell 111:747–756
Nahvi A, Sudarsan N, Ebert MS, Zou X, Brown KL, Breaker RR (2002) Genetic control by metabolite binding mRNA. Chem Biol 9:1043–1049
Winkler WC, Breaker RR (2003) Genetic control by metabolite-binding riboswitches. Chem Bio Chem 4:1024–1032
Bartel DP (2004) MicroRNAs: genomics, biogenesis, mechanism and function. Cell 116:281–297
Nudler E, Mironov AS (2004) The riboswitch control of bacterial metabolism. Trends Biochem Sci 29:11–17
He L, Hannon GJ (2004) MicroRNAs: small RNAs with a big role in gene regulation. Nature Rev Genet 5:522–531
Winkler WC, Nahvi A, Roth A, Collins JA, Breaker RR (2004) Control of gene expression by a natural metabolite-responsive ribozyme. Nature 428:281–286
Gerdes K, Wagner EGH (2007) RNA antitoxins. Curr Opin Microbiol 10:117
Nagel JHA, Gultyaev AP, Gerdes K, Pleij CWA (1999) Metastable structures and refolding kinetics in hok mRNA of plasmid R1. RNA 5:1408–1419
Groeneveld H, Thimon K, Duin J (1995) Translational control of maturation-protein synthesis in phage MS2: a role for the kinetics of RNA folding? RNA 1:79–88
Porschke D (1977) Elementary steps of base recognition and helix-coil transitions in nucleic acids. Mol Biol Biochem Biophys 24:191–218
Craig ME, Crothers DM, Doty P (1971) Relaxation kinetics of dimer formation by self complementary oligonucleotides. J Mol Biol 62:383–401
Crothers DM, Cole PE, Hilbers CW, Shulman RG (1974) The molecular mechanism of thermal unfolding of Escherichia coli formylmethionine transfer RNA. J Mol Biol 87:63–88
Micura R, Hobartner C (2003) On secondary structure rearrangements and equilibria of small RNAs. Chem Biochem 4:984–990
Furtig B, Buck J, Manoharan V, Bermel W, Jaschke A, Wenter P, Pitsch S, Schwalbe H (2007) Time-resolved NMR studies of RNA folding. Biopolymers 86:360–383
Harlepp S, Marchal T, Robert J, Leger J, Xayaphoummine A, Isambert H, Chatenay D (2003) Probing complex RNA structures by mechanical force. Eur Phys J E-Soft Matter 12:605–615
Jean JM, Hall KB (2001) 2-Aminopurine fluorescence quenching and lifetimes: role of base stacking. Proc Natl Acad Sci USA 98:37–41
Liphardt J, Onoa B, Smith SB, Tinoco IJ, Bustamante C (2001) Reversible unfolding of single RNA molecules by mechanical force. Science 292:733–737
Bonnet G, Krichevsky O, Libchaber A (1998) Kinetics of conformational fluctuations in DNA hairpin-loops. Proc Natl Acad Sci USA 95:8602–8606
Ansari A, Kunznetsov SV, Shen Y (2001) Configurational diffusion down a folding funnel describes the dynamics of DNA hairpins. Proc Natl Acad Sci USA 98:7771–7776
Wallace MI, Ying L, Balasubramanian S, Klenerman D (2001) Non-arrhenius kinetics for the loop closure of a DNA hairpin. Proc Natl Acad Sci USA 98:5584–5589
Bai Y, Das R, Millett IS, Herschlag D, Doniach S (2005) Probing counterion modulated repulsion and attraction between nucleic acid duplexes in solution. Proc Natl Acad Sci USA 102:1035–1040
Chu VB, Herschlag D (2008) Unwinding RNA’s secrets: advances in the biology, physics, and modeling of complex RNAs. Curr Opin Struct Biol 18:305–314
Draper DE (2008) RNA folding: thermodynamic and molecular descriptions of the roles of ions. Biophys J 95:5489–5495
Chen SJ (2008) RNA folding: conformational statistics, folding kinetics, and ion electrostatics. Annu Rev Biophys 37:197–214
Tan ZJ, Chen SJ (2011) Importance of diffuse ions binding to RNA. Met Ions Life Sci 9:101–124
Bowman JC, Lenz TK, Hud NV, Williams LD (2012) Cations in charge: magnesium ions in RNA folding and catalysis. Curr Opin Struct Biol 22:262–272
Cruz JA et al (2012) RNA-puzzles: A CASP-like evaluation of RNA three-dimensional structure prediction. RNA 18:610–625
Shapiro BA, Yingling YG, Kasprzak W, Bindewald E (2007) Bridging the gap in RNA structure prediction. Curr Opn Struct Biol 17:157–165
Hajdin CE, Ding F, Dokholyan NV, Weeks KM (2010) On the significance of an RNA tertiary structure prediction. RNA 16:1340–1349
Laing C, Schlick T (2011) Computational approaches to RNA structure prediction, analysis, and design. Curr Opin Struct Biol 21:1–13
Laing C, Schlick T (2010) Computational approaches to 3D modeling of RNA. J Phys Condens Matter 22:283101
Rother K, Rother M, Boniecki M, Puton T, Bujnicki JM (2011) RNA and protein 3D structure modeling: similarities and differences. J Mol Model 17:2325–2336
Levitt M (1969) Detailed molecular model for transfer ribonucleic acid. Nature 224:759–763
Chothia C, Gerstein M (1997) How far can sequences diverge? Nature 385:579–581
Anfinsen CB (1973) Principles that govern the folding of protein chains. Science 181:223–230
Baker D, Sali A (2001) Protein structure prediction and structural genomics. Science 294:93–96
Zhang Y, Skolnick J (2004) Automated structure prediction of weakly homologous proteins on a genomic scale. Proc Natl Acad Sci USA 101:7594–7599
Simons KT, Kooperberg C, Huang E (1997) Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and bayesian scoring functions. J Mol Biol 268:209–225
Zhang WB, Chen SJ (2002) RNA hairpin-folding kinetics. Proc Natl Acad Sci USA 99:1931–1936
Zhang WB, Chen SJ (2003) Master equation approach to finding the rate-limiting steps in biopolymer folding. J Chem Phys 118:3413
Konishi Y, Ooi T, Scheraga HA (1982) Regeneration of ribonuclease a from the reduced protein rate-limiting steps. Biochemistry 21:4734–4740
Zhang WB, Chen SJ (2003) Analyzing the biopolymer folding rates and pathways using kinetic cluster method. J Chem Phys 119:8716–8729
Flamm C, Fontana W, Hofacker IL, Schuster P (2000) RNA folding at elementary step resolution. RNA 6:325–338
Isambert H, Siggia ED (2000) Modeling RNA folding paths with pseudoknots: application to hepatitis d-virus ribozyme. Proc Natl Acad Sci USA 97:6515–6520
Danilova LV, Pervouchine DD, Favorov AV, Mironov AA (2006) RNA kinetics: a web server that models secondary structure kinetics of an elongating RNA. J Bioinf Comp Biol 4:589–596
Martinez HM (1984) An RNA folding rule. Nucleic Acids Res 12:323–335
Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22:403–434
Schmitz M, Steger G (1996) Discription of RNA folding by simulated annealing. J Mol Biol 255:254–266
Gultyaev AP, Batenburg FH, Pleij CW (1995) The computer-simulation of RNA folding pathways using a genetic algorithm. J Mol Biol 250:37–51
Mironov A, Kister A (1985) A kinetic approach to the prediction of RNA secondary structures. J Biomol Struct Dyn 2:953–962
Mironov AA, Lebedev VF (1993) A kinetic model of RNA folding. Biosystems 30:49–56
Isambert H, Siggia ED (2000) Modeling RNA folding paths with pseudoknots: application to hepatitis delta virus ribozyme. Proc Natl Acad Sci USA 97:6515–6520
Danilova LV, Pervoud DD, Favorov AA, Mironov AA (2006) RNAKinetics: a web server that models secondary structure kinetics of an elongating RNA. J Bioinform Comput Biol 4:589–596
Ndifon W (2005) A complex adaptive systems approach to the kinetic folding of RNA. Biosystems 82:257–265
Zhao PN, Zhang WB, Chen SJ (2010) Predicting secondary structural folding kinetics for nucleic acids. Biophys J 98:1617–1625
Tang X, Thomas S, Tapia L, Giedroc DP, Amato NM (2008) Simulating RNA folding kinetics on approximated energy landscapes. J Mol Biol 381:1055–1067
Hofacker IL, Flamm C, Heine C, Wolfinger MT, Scheuermann G, Stadler PF (2010) BarMap: RNA folding on dynamic energy landscapes. RNA 16:1308–1316
Geis M, Flamm C, Wolfinger MT, Tanzer A, Hofacker IL, Middendorf M, Mandl C, Stadler PF, Thurner C (2008) Enhancement of transactivation activity of Rta of Epstein-Barr virus by RanBPM. J Mol Biol 379:242–261
Flamm C, Hofacker IL, Stadler PF, Wolfinger MT (2002) Barrier trees of degenerate landscapes. Z Phys Chem 216:155–173
Wolfinger MT, Svrcek-Seiler WA, Flamm C, Hofacker IL, Stadler PF (2004) Efficient computation of RNA folding dynamics. J Phys A Math Gen 37:4731–4741
Tang X, Kirkpatrick B, Thomas S, Song G, Amato NM (2005) Using motion planning to study RNA folding kinetics. J Comp Biol 12:862–881
Zhang WB, Chen SJ (2006) Exploring the complex folding kinetics of RNA hairpins: I. general folding kinetics analysis. Biophys J 90:765–777
Tacker M, Fontana W, Stadler PF, Schuster P (1994) Statistics of RNA melting kinetics. Eur Biophys J 23:29
Suvernev AA, Frantsuzov PA (1995) Statistical description of nucleic acid secondary structure folding. J Biomol Struct Dyn 13:135–144
Jacob C, Breton N, Daegelen P, Peccoud J (1997) Probability distribution of the chemical states of a closed system and thermodynamic law of mass action from kinetics: the RNA example. J Chem Phys 107:2913
Isambert H, Siggia ED (2000) Modeling RNA folding paths with pseudoknots: application to hepatitis delta virus ribozyme. Proc Natl Acad Sci USA 97:6515–6520
Xia TB, SantaLucia J, Turner DH (1998) Thermodynamic parameters for an expanded nearest-neighbor model for formation of RNA duplexes with Watson–Crick base pairs. Biochemistry 37:14719–14735
Mathews DH, Sabina J, Zuker M, Turner DH (1999) Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. J Mol Biol 288:911–940
Morgan SR, Higgs PG (1998) Barrier heights between ground states in a model of RNA secondary structure. J Phys A Math Gen 31:3153–3170
Henkin TM, Yanofsky C (2002) Regulation by transcription attenuation in bacteria: how RNA provides instructions for transcription termination/antitermination decisions. BioEssays 24:700–707
Merino E, Yanofsky C (2005) Transcription attenuation: a highly conserved regulatory strategy used by bacteria. Trends Genet 21:260–264
Franch T, Gultyaev AP, Gerder K (1997) Programmed cell death by hok/sok of plasmid R1: processing at the hok mRNA 3′-end triggers structural rearrangements that allow translation and antisense RNA binding. J Mol Biol 273:38–51
Heilman-Miller SL, Woodson SA (2003) Effect of transcription on folding of the Tetrahymena ribozyme. RNA 9:722–733
Brehm SL, Cech TR (1983) The fate of an intervening sequence RNA: excision and cyclization of the Tetrahymena ribosomal RNA intervening sequence in vivo. Biochemistry 22:2390–2397
Zhang F, Ramsay ES, Woodson SA (1995) In vivo facilitation of Tetrahymena group I intron splicing in Escherichia coli pre-ribosomal RNA. RNA 1:284–292
Treiber DK, Williamson JR (2001) Beyond kinetic traps in RNA folding. Curr Opin Struct Biol 11:309–314
Woodson SA (2002) Folding mechanisms of group I ribozymes: role of stability and contact order. Biochem Soc Trans 30:1166–1169
Zhang LB, Bao P, Michael JL, Zhang Y (2009) Slow formation of a pseudoknot structure is rate limiting in the productive co-transcriptional folding of the self-splicing Candida intron. RNA 15:1986–1992
Pan T, Artsimovitch I, Fang X, Landick R, Sosnick TR (1999) Folding of a large ribozyme during transcription and the effect of the elongation factor NusA. Proc Natl Acad Sci USA 96:9545–9550
Zhao PN, Zhang WB, Chen SJ (2011) Cotranscriptional folding kinetics of ribonucleic acid secondary structures. J Chem Phys 135:245101
Das R, Mills TT, Kwok LW, Maskel GS, Millett IS, Doniach S, Finkelstein KD, Herschlag D, Pollack L (2003) Counterion distribution around DNA probed by solution X-ray scattering. Phys Rev Lett 90:188103
Andresen K, Qiu X, Pabit SA, Lamb JS, Park HY, Kwok LW, Pollack L (2008) Mono- and trivalent ions around DNA: a small-angle scattering study of competition and interactions. Biophys J 95:287–295
Pabit SA, Qiu X, Lamb JS, Li L, Meisburger SP, Pollack L (2009) Both helix topology and counterion distribution contribute to the more effective charge screening in dsRNA compared with dsDNA. Nucleic Acids Res 37:3887–3896
Kirmizialtin S, Pabit SA, Meisburger SP, Pollack L, Elber R (2012) RNA and its ionic cloud: solution scattering experiments and atomically detailed simulations. Biophys J 102:819–828
Bai Y, Greenfeld M, Travers KJ, Chu VB, Lipfert J, Doniach S, Herschlag D (2007) Quantitative and comprehensive decomposition of the ion atmosphere around nucleic acids. J Am Chem Soc 129:14981–14988
Krakauer H (1971) The binding of Mg++ ions to polyadenylate, polyuridylate, and their complexes. Biopolymers 10:2459–2490
Clement RM, Sturm J, Daune MP (1973) Interaction of metallic cations with DNA VI. Specific binding of Mg2+ and Mn2+. Biopolymers 12:405–421
Soto M, Misra V, Draper DE (2007) Tertiary structure of an RNA pseudoknot is stabilized by “diffuse” Mg2+ ions. Biochemistry 46:2973–2983
Grilley D, Misra V, Caliskan G, Draper DE (2007) Importance of partially unfolded conformations for Mg2+-induced folding of RNA tertiary structure: structural models and free energies of Mg2+ interactions. Biochemistry 46:10266–10278
Rialdi G, Levy J, Biltonen R (1972) Thermodynamic studies of transfer ribonucleic acids. I. Magnesium binding to yeast phenylalanine transfer ribonucleic acid. Biochemistry 11:2472–2479
Romer R, Hach R (1975) tRNA conformation and magnesium binding. A study of a yeast phenylalanine-specific tRNA by a fluorescent indicator and differential melting curves. Eur J Biochem 55:271–284
Stellwagen E, Dong Q, Stellwagen NC (2007) Quantitative analysis of monovalent counterion binding to random-sequence, double-stranded DNA using the replacement ion method. Biochemistry 46:2050–2058
Smith SB, Cui YJ, Bustamante C (1996) Overstretching B-DNA: The elastic response of individual double-stranded and single-stranded DNA molecules. Science 271:795–799
Murphy MC, Rasnik I, Cheng W, Lohman TM, Ha T (2004) Probing single-stranded DNA conformational flexibility using fluorescence spectroscopy. Biophys J 86:2530–2537
Tinland B, Pluen A, Sturm J, Weill G (1997) Persistende length of single-stranded DNA. Macromolecules 30:5763–5765
McIntosh DB, Saleh O (2011) Slat species-dependent electrostatic effects on ssDNA elasticity. Macromolecules 44:2328–2333
Sim AYL, Lipfert J, Herschlag D, Doniach S (2012) Salt dependence of the radius of gyration and flexibility of single-stranded DNA in solution probed by small-angle x-ray scattering. Phys Rev E 86:021901
Chen H, Meisburger SP, Pabit SA, Sutton JL, Webb WW, Pollack L (2012) Ionic strength-dependent persistence lengths of single-stranded RNA and DNA. Proc Natl Acad Sci USA 109:799–804
Bizarro CV, Alemany A, Ritort F (2012) Non-specific binding of Na+ and Mg2+ to RNA determined by force spectroscopy methods. Nucleic Acids Res 40:6922–6935
Tan ZJ, Chen SJ (2006) Electrostatic free energy landscape for nucleic acid helix assembly. Nucleic Acids Res 34:6629–6639
Williams P, Longfellow CE, Freier SM, Kierzek R, Turner DH (1989) Laser temperature-jump, spectroscopic, and thermodynamic study of salt effects on duplex formation by dGCATGC. Biochemistry 28:4283–4291
Nakano S, Fujimoto M, Hara H, Sugimoto N (1999) Nucleic acid duplex stability: influence of base composition on cation effects. Nucleic Acids Res 27:2957–2965
Serra MJ, Baird JD, Dale T, Fey BL, Retatagos K, Westhof E (2002) Effects of magnesium ions on the stabilization of RNA oligomers of defined structures. RNA 8:307–323
Owczarzy R, Moreira BG, You Y, Behlke MA, Walder JA (2008) Predicting stability of DNA duplexes in solutions containing magnesium and monovalent cations. Biochemistry 47:5336–5353
Kuznetsov SV, Ren CC, Woodson SA, Ansari A (2008) Loop dependence of the stability and dynamics of nucleic acid hairpins. Nucleic Acids Res 36:1098–1112
Vieregg J, Cheng W, Bustamante C, Tinoco I Jr (2007) Measurement of the effect of monovalent cations on RNA hairpin stability. J Am Chem Soc 129:14966–14973
Tan ZJ, Chen SJ (2006) Nucleic acid helix stability: effects of salt concentration, cation valency and size, and chain length. Biophys J 90:1175–1190
Tan ZJ, Chen SJ (2007) RNA helix stability in mixed Na+/Mg2+ solution. Biophys J 92:3615–3632
Tan ZJ, Chen SJ (2008) Salt dependence of nucleic acid hairpin stability. Biophys J 95:738–752
Nixon PL, Giedroc DP (1998) Equilibrium unfolding (folding) pathway of a model H-type pseudoknotted RNA: the role of magnesium ions in stability. Biochemistry 37:16116–16129
Stellwagen E, Muse JM, Stellwagen NC (2011) Monovalent cation size and DNA conformational stability. Biochemistry 50:3084–3094
Anthony PC, Sim AY, Chu VB, Doniach S, Block SM, Herschlag D (2012) Electrostatics of nucleic acid folding under conformational constraint. J Am Chem Soc 134:4607–4614
SantaLucia JJ (1998) A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics. Proc Natl Acad Sci USA 95:1460–1465
Zuker M (2003) Mfold web server for nucleic acid folding and hybridization prediction. Nucleic Acids Res 31:3406–3415
Chen SJ, Dill KA (2000) RNA folding energy landscapes. Proc Natl Acad Sci USA 97:646–651
SantaLucia J, Hicks D (2004) The thermodynamics of DNA structural motifs. Annu Rev Biophys Biomol Struct 33:415–440
Zhang WB, Chen SJ (2006) Exploring the complex folding kinetics of RNA hairpins: II. Effect of sequence, length, and misfolded states. Biophys J 90:778–787
Theimer A, Giedroc DP (2000) Contribution of the intercalated adenosine at the helical junction to the stability of the gag-pro frameshifting pseudoknot from mouse mammary tumor virus. RNA 6:409–421
Koculi E, Hyeon C, Thirumalai D, Woodson SA (2007) Charge density of divalent metal cations determines RNA stability. J Am Chem Soc 129:2676–2682
Takamoto K, He Q, Morris S, Chance MR, Brenowitz M (2002) Monovalent cations mediate formation of native tertiary structure of the Tetrahymena thermophila ribozyme. Nature Struct Biol 9:928–933
Moghaddam S, Caliskan G, Chauhan S, Hyeon C, Briber RM, Thirumalai D, Woodson SA (2009) Metal ion dependence of cooperative collapse transitions in RNA. J Mol Biol 393:753–764
Heilman-Miller SL, Thirumalai D, Woodson SA (2001) Role of counterion condensation in folding of the Tetrahymena ribozyme. I. Equilibrium stabilization by cations. J Mol Biol 306:1157–1166
Lambert D, Leipply D, Shiman R, Draper DE (2009) The influence of monovalent cation size on the stability of RNA tertiary structures. J Mol Biol 390:791–804
Walter NG, Burke JM, Millar DP (1999) Stability of hairpin ribozyme tertiary structure is governed by the interdomain junction. Nature Struct Biol 6:544–549
Pljevaljcic G, Millar DP, Deniz AA (2004) Freely diffusing single hairpin ribozymes provide insights into the role of secondary structure and partially folded states in RNA folding. Biophys J 87:457–467
Leipply D, Draper DE (2011) Evidence for a thermodynamically distinct Mg2+ ion associated with formation of an RNA tertiary structure. J Am Chem Soc 133:13397–13405
Weixlbaumer A, Werner A, Flamm C, Westhof E, Schroeder R (2004) Determination of thermodynamic parameters for HIV DIS type loop-loop kissing complexes. Nucleic Acids Res 32:5126–5133
Lorenz C, Piganeau N, Schroeder R (2006) Stabilities of HIV-1 DIS type RNA loop-loop interactions in vitro and in vivo. Nucleic Acids Res 34:334–342
Vander Meulen KA, Butcher SE (2012) Characterization of the kinetic and thermodynamic landscape of RNA folding using a novel application of isothermal titration calorimetry. Nucleic Acids Res 40:2140–2151
Tan ZJ, Chen SJ (2010) Predicting ion binding properties for RNA tertiary structures. Biophys J 99:1565–1576
Tan ZJ, Chen SJ (2011) Salt contribution to RNA tertiary structure folding stability. Biophys J 101:176–187
Tan ZJ, Chen SJ (2012) Ion-mediated RNA structural collapse: effect of spatial confinement. Biophys J 103:827–836
Rau DC, Parsegian VA (1992) Direct measurement of the intermolecular forces between counterion-condensed DNA double helices. Evidence for long range attractive hydration forces. Biophys J 61:246–259
Rau DC, Parsegian VA (1992) Direct measurement of temperature-dependent solvation forces between DNA double helices. Biophys J 61:260–271
Bai Y, Chu VB, Lipfert J, Pande VS, Herschlag D, Doniach S (2008) Critical assessment of nucleic acid electrostatics via experimental and computational investigation of an unfolded state ensemble. J Am Chem Soc 130:12334–12341
Qiu X, Andresen K, Kwok LW, Lamb JS, Park HY, Pollack L (2007) Inter-DNA attraction mediated by divalent counterions. Phys Rev Lett 99:038104
Qiu X, Parsegian VA, Rau DC (2010) Divalent counterion-induced condensation of triple-strand DNA. Proc Natl Acad Sci USA 107:21482–21486
Li L, Pabit SA, Meisburger SP, Pollack L (2011) Double-stranded RNA resists condensation. Phys Rev Lett 106:108101
Tan ZJ, Chen SJ (2009) Predicting electrostatic force in RNA folding. Methods Enzymol 469:465–487
Manning GS (1978) The molecular theory of polyelectrolyte solutions with applications to the electrostatic properties of polynucleotides. Q Rev Biophys 11:179–246
Schurr MJ (2009) Polyanion models of nucleic acid-metal ion interactions. In: Hud NV (ed) Nucleic acid-metal ion interactions. Royal Society of Chemistry, London, pp 307–344
Ray J, Manning GS (2000) Formation of loose clusters in polyelectrolyte solutions. Macromolecules 33:2901–2908
Lyubartsev P, Nordenskiold L (1995) Monte Carlo simulation study of ion distribution and osmotic pressure in hexagonally oriented DNA. J Phys Chem 99:10373–10382
Dai L, Mu Y, Nordenskiöld L, van der Maarel JR (2008) Molecular dynamics simulation of multivalent-ion mediated attraction between DNA molecules. Phys Rev Lett 100:118301
Gilson MK, Sharp KA, Honig B (1987) Calculating the electrostatic potential of molecules in solution: method and error assessment. J Comput Chem 9:327–335
Boschitsch H, Fenley MO (2007) A new outer boundary formulation and energy corrections for the nonlinear Poisson-Boltzmann equation. J Comput Chem 28:909–921
Baker NA, Sept D, Joseph S, Holst MJ, McCammon JA (2000) Electrostatics of nanosystems: application to microtubules and the ribosome. Proc Natl Acad Sci USA 98:10037–10041
Zhou YC, Feig M, Wei GW (2008) Highly accurate biomolecular electrostatics in continuum dielectric environments. J Comput Chem 29:87–97
Lu B, Cheng X, Huang J, McCammon JA (2010) AFMPB: an adaptive fast multipole Poisson-Boltzmann solver for calculating electrostatics in biomolecular systems. Comput Phys Commun 181:1150–1160
Misra VK, Shiman R, Draper DE (2003) A thermodynamic framework for the magnesium-dependent folding of RNA. Biopolymers 69:118–136
Tan ZJ, Chen SJ (2005) Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte. J Chem Phys 122:044903
Chu VB, Bai Y, Lipfert J, Herschlag D, Doniach S (2007) Evaluation of ion binding to DNA duplexes using a size-modified Poisson-Boltzmann theory. Biophys J 93:3202–3209
Kirmizialtin S, Silalahi AR, Elber R, Fenley MO (2012) The ionic atmosphere around A-RNA: Poisson-Boltzmann and molecular dynamics simulations. Biophys J 102:829–838
Gavryushov S (2008) Electrostatics of B-DNA in NaCl and CaCl2 solutions: ion size, interionic correlation, and solvent dielectric saturation effects. J Phys Chem B 112:8955–8965
Grochowski P, Trylska J (2008) Continuum molecular electrostatics, salt effects and counterion binding. A review of the Poisson-Boltzmann theory and its modifications. Biopolymers 89:93–113
Forsman J (2004) A simple correlation-corrected Poisson-Boltzmann theory. J Phys Chem B 108:9236–9245
Vlachy V (1999) Ionic effect beyond Poisson-Boltzmann theory. Annu Rev Phys Chem 50:145–165
Wang K, Yu YX, Gao GH (2008) Density functional study on the structural and thermodynamic properties of aqueous DNA-electrolyte solution in the framework of cell model. J Chem Phys 128:185101
Chen YG, Weeks JD (2006) Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions. Proc Natl Acad Sci USA 103:7560–7565
Tan ZJ, Chen SJ (2006) Ion-mediated nucleic acid helix-helix interactions. Biophys J 91:518–536
Tan ZJ, Chen SJ (2008) Electrostatic free energy landscapes for DNA helix bending. Biophys J 94:3137–3149
Chen G, Tan ZJ, Chen SJ (2010) Salt-dependent folding energy landscape of RNA three-way junction. Biophys J 98:111–120
Chen G, Chen SJ (2011) Quantitative analysis of the ion-dependent folding stability of DNA triplexes. Phys Biol 8:066006
He Z, Chen SJ (2012) Predicting ion-nucleic acid interactions by energy landscape-guided sampling. J Chem Theo Compt 8:2095–2102
Cate JH, Gooding AR, Podell E, Zhou K, Golden BL, Kundrot CE, Cech TR, Doudna JA (1996) Crystal structure of a group I ribozyme domain: principles of RNA packing. Science 273:1678–1685
Zhou HX, Rivas G, Minton AP (2008) Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences. Annu Rev Biophys 37:375–397
Lambert D, Leipply D, Draper DE (2010) The osmolyte TMAO stabilizes native RNA tertiary structures in the absence of Mg2+: evidence for a large barrier to folding from phosphate dehydration. J Mol Biol 404:138–157
Pincus DL, Hyeon C, Thirumalai D (2008) Effects of trimethylamine N-oxide (TMAO) and crowding agents on the stability of RNA hairpins. J Am Chem Soc 130:7364–7372
Kilburn D, Roh JH, Guo L, Briber RM, Woodson SA (2010) Molecular crowding stabilizes folded RNA structure by the excluded volume effect. J Am Chem Soc 132:8690–8696
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Shanghai Jiaotong University Press, Shanghai and Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Tan, Z., Zhang, W., Shi, Y., Wang, F. (2015). RNA Folding: Structure Prediction, Folding Kinetics and Ion Electrostatics. In: Wei, D., Xu, Q., Zhao, T., Dai, H. (eds) Advance in Structural Bioinformatics. Advances in Experimental Medicine and Biology, vol 827. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9245-5_11
Download citation
DOI: https://doi.org/10.1007/978-94-017-9245-5_11
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-017-9244-8
Online ISBN: 978-94-017-9245-5
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)