The formation of a cation-stabilized guanine quadruplex (G-DNA) stem is an exceptionally slow process involving complex kinetics that has not yet been characterized at atomic resolution. Here, we investigate the formation of a parallel stranded G-DNA stem consisting of four strands of d(GGGG) using molecular dynamics simulations with explicit inclusion of counterions and solvent. Due to the limitations imposed by the nanosecond timescale of the simulations, rather than watching for the spontaneous formation of G-DNA, our approach probes the stability of possible supramolecular intermediates (including two-, three-, and four-stranded assemblies with out-of-register base pairing between guanines) on the formation pathway. The simulations suggest that "cross-like" two-stranded assemblies may serve as nucleation centers in the initial formation of parallel stranded G-DNA quadruplexes, proceeding through a series of rearrangements involving trapping of cations, association of additional strands, and progressive slippage of strands toward the full stem. To supplement the analysis, approximate free energies of the models are obtained with explicit consideration of the integral cations. The approach applied here serves as a prototype for qualitatively investigating other G-DNA molecules using molecular dynamics simulation and free-energy analysis.

National Center for Biomolecular Research Masaryk University 612 37 Brno Czech Republic

Zobrazit více v PubMed

Andricioaei, I., and M. Karplus. 2001. On the calculation of the entropy from covariance matrices on the atomic fluctuations. J. Chem. Phys. 115:6289–6292.

Aqvist, J. 1990. Ion-water interaction potentials derived from free energy perturbation simulations. J. Phys. Chem. 94:8021–8024.

Arimondo, P. B., J. F. Riou, J. L. Mergny, J. Tazi, J. S. Sun, T. Garestier, and C. Helene. 2000. Interaction of human DNA topoisomerase I with G-quartet structures. Nucleic Acids Res. 28:4832–4838. PubMed PMC

Arnott, S., and D. W. Hukins. 1972. Optimised parameters for A-DNA and B-DNA. Biochem. Biophys. Res. Commun. 47:1504–1509. PubMed

Arthanari, H., and P. H. Bolton. 1999. Porphyrins can catalyze the interconversion of DNA quadruplex structural types. Anticancer Drug Des. 14:317–326. PubMed

Bearss, D. J., L. H. Hurley, and D. D. Von Hoff. 2000. Telomere maintenance mechanisms as a target for drug development. Oncogene. 19:6632–6641. PubMed

BenNaim, A. 1987. Solvation Thermodynamics. Plenum Press, New York.

Berendsen, H. J. C., J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak. 1984. Molecular dynamics with coupling to an external bath. J. Comput. Phys. 81:3684–3690.

Beveridge, D. L., and K. J. McConnell. 2000. Nucleic acids: theory and computer simulation, Y2K. Cur. Op. Struct. Biol. 10:182–196. PubMed

Bouaziz, S., A. Kettani, and D. J. Patel. 1998. A K cation-induced conformational switch within a loop spanning segment of a DNA quadruplex containing G-G-G-C repeats. J. Mol. Biol. 282:637–652. PubMed

Cheatham 3rd, T. E., P. Cieplak, and P. A. Kollman. 1999. A modified version of the Cornell et al. force field with improved sugar pucker phases and helical repeat. J. Biomol. Struct. Dyn. 16:845–862. PubMed

Cheatham 3rd, T. E., and P. A. Kollman. 2000. Molecular dynamics simulation of nucleic acids. Annu. Rev. Phys. Chem. 51:435–471. PubMed

Cheatham 3rd, T. E., and M. A. Young. 2001. Molecular dynamics simulations of nucleic acids: Successes, limitations and promise. Biopol. (Nuc. Acid Sci.). 56:232–256. PubMed

Chiu, S.-W., M. Clark, S. Subramaniam, and E. Jakobsson. 2000. Collective motion artifacts arising in long-duration molecular dynamics simulations. J. Comput. Chem. 21:121–131.

Chowdhury, S., and M. Bansal. 2000. Effect of coordinated ions on structure and flexibility of parallel G-quadruplexes: a molecular dynamics study. J. Biomol. Struct. Dyn. 18:11–28. PubMed

Chowdhury, S., and M. Bansal. 2001a. G-quadruplex structure can be stable with only some coordination sites being occupied by cations: a six-nanosecond molecular dynamics study. J. Phys. Chem. B. 105:7572–7578.

Chowdhury, S., and M. Bansal. 2001b. A nanosecond molecular dynamics study of antiparallel d(G)(7) quadruplex structures: effect of the coordinated cations. J. Biomol. Struct. Dyn. 18:647–669. PubMed

Cornell, W. D., P. Cieplak, C. I. Bayly, I. R. Gould, K. M. Merz, D. M. Ferguson, D. C. Spellmeyer, T. Fox, J. W. Caldwell, and P. A. Kollman. 1995. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc. 117:5179–5197.

Cubero, E., A. Avino, B. G. de la Torre, M. Frieden, R. Eritja, F. J. Luque, C. Gonzalez, and M. Orozco. 2002. Hoogsteen-based parallel-stranded duplexes of DNA. Effect of 8-amino-purine derivatives. J. Am. Chem. Soc. 124:3133–3142. PubMed

Cubero, E., F. J. Luque, and M. Orozco. 2001. Theoretical studies of d(A:T)-based parallel-stranded DNA duplexes. J. Am. Chem. Soc. 123:12018–12025. PubMed

Essmann, U., L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen. 1995. A smooth particle mesh Ewald method. J. Chem. Phys. 103:8577–8593.

Fang, G., and T. R. Cech. 1993. The β-subunit of Oxytricha telomere-binding protein promotes G-quartet formation by telomeric DNA. Cell. 74:875–885. PubMed

Feig, M., and B. M. Pettitt. 1998. Structural equilibrium of DNA represented with different force fields. Biophys. J. 75:134–149. PubMed PMC

Ferrin, T. E., C. C. Huang, L. E. Jarvis, and R. Langridge. 1988. The MIDAS display system. J. Mol. Graph. 6:13–27.

Friedman, H. L., and C. V. Krishnan. 1973. Thermodynamics of ion hydration. In Water. A Comprehensive Treatise: Aqueous Solutions of Simple Electrolytes. F. Franks, editor. Plenum Press, New York. 1–93.

Froloff, N., A. Windemuth, and B. Honig. 1997. On the calculation of binding free energies using continuum methods: Application to MHC class I protein-peptide interactions. Protein Sci. 6:1293–1301. PubMed PMC

Gilbert, D. E., and J. Feigon. 1999. Multistranded DNA structures. Cur. Op. Struct. Biol. 9:305–314. PubMed

Gilson, M. K., J. A. Given, B. L. Bush, and J. A. McCammon. 1997. The statistical-thermodynamic basis for computation of binding affinities: a critical review. Biophys. J. 72:1047–1069. PubMed PMC

Gilson, M. K., K. A. Sharp, and B. H. Honig. 1987. Calculating the electrostatic potential of molecules in solution: method and error assessment. J. Comput. Chem. 9:327–335.

Gu, J. D., and J. Leszczynski. 2000. Structures and properties of the planar G·C·G·C tetrads: Ab initio HF and DFT studies. J. Phys. Chem. A. 104:7353–7358.

Guittat, L., P. Alberti, J. L. Mergny, J. F. Riou, M. P. Teulade-Fichou, and P. Mailliet. 2001. Telomerase inhibitors: possible consequences in cancer therapy. M S-Medecine Sciences. 17:1076–1081.

Haider, S., G. N. Parkinson, and S. Neidle. 2002. Crystal structure of the potassium form of an Oxytricha nova G-quadruplex. J. Mol. Biol. 320:189–200. PubMed

Hammond-Kosack, M. C., M. W. Kilpatrick, and K. Docherty. 1993. The human insulin gene-linked polymorphic region adopts a G-quartet structure in chromatin assembled in vitro. J. Mol. Endo. 10:121–126. PubMed

Han, H. Y., C. L. Cliff, and L. H. Hurley. 1999. Accelerated assembly of G-quadruplex structures by a small molecule. Biochemistry. 38:6981–6986. PubMed

Han, H. Y., and L. H. Hurley. 2000. G-quadruplex DNA: a potential target for anti-cancer drug design. Trends Pharmacol. Sci. 21:136–142. PubMed

Han, H. Y., D. R. Langley, A. Rangan, and L. H. Hurley. 2001. Selective interactions of cationic porphyrins with G-quadruplex structures. J. Am. Chem. Soc. 123:8902–8913. PubMed

Hansson, T., J. Marelius, and J. Aqvist. 1998. Ligand binding affinity prediction by linear interaction energy methods. J. Comp.-Aided Mol. Des. 12:27–35. PubMed

Hardin, C. C., M. J. Corregan, D. V. Lieberman, and B. A. Brown 2nd. 1997. Allosteric interactions between DNA strands and monovalent cations in DNA quadruplex assembly: thermodynamic evidence for three linked association pathways. Biochemistry. 36:15428–15450. PubMed

Hardin, C. C., E. Henderson, T. Watson, and J. K. Prosser. 1991. Monovalent cation induced structural transitions in telomeric DNAs: G-DNA folding intermediates. Biochemistry. 30:4460–4472. PubMed

Hardin, C. C., A. G. Perry, and K. White. 2000. Thermodynamic and kinetic characterization of the dissociation and assembly of quadruplex nucleic acids. Biopolymers. 56:147–194. PubMed

Harris, S. A., E. Gavathiotis, M. S. Searle, M. Orozco, and C. A. Laughton. 2001. Cooperativity in drug-DNA recognition: a molecular dynamics study. J. Am. Chem. Soc. 123:12658–12663. PubMed

Harvey, S. C., R. K.-Z. Tan, and T. E. Cheatham 3rd. 1998. The flying ice cube: velocity rescaling in molecular dynamics simulations leads to violation of equipartition. J. Comput. Chem. 19:726–740.

Henderson, E., C. C. Hardin, S. K. Walk, I. J. Tinoco, and E. H. Blackburn. 1987. Telomeric DNA oligonucleotides form novel intramolecular structures containing guanine-guanine base pairs. Cell. 51:899–908. PubMed

Hermans, J., and L. Wang. 1997. Inclusion of loss of translational and rotational freedom in theoretical estimates of free energies of binding. Application to a complex of benzene and mutant T4 lysozyme. J. Am. Chem. Soc. 119:2707–2714.

Hobza, P., M. Kabelac, J. Sponer, P. Mejzlik, and J. Vondrasek. 1997. Performance of empirical potentials (AMBER, CFF95, CVFF, CHARMM, OPLS, POLTEV), semiempirical quantum chemical methods (AM1, MNDO/M, PM3), and ab initio Hartree-Fock method for interaction of DNA bases: comparison with nonempirical beyond Hartree-Fock results. J. Comput. Chem. 18:1136–1150.

Hobza, P., and J. Sponer. 1999. Structure, energetics, and dynamics of the nucleic acid base pairs: nonempirical ab initio calculations. Chem. Rev. 99:3247–3276. PubMed

Horvath, M. P., and S. C. Schultz. 2001. DNA G-quartets in a 1.86 Å resolution structure of an Oxytricha nova telomeric protein-DNA complex. J. Mol. Biol. 310:367–377. PubMed

Hud, N. V., P. Schultze, V. Sklenar, and J. Feigon. 1999. Binding sites and dynamics of ammonium ions in a telomere repeat DNA quadruplex. J. Mol. Biol. 285:233–243. PubMed

Hud, N. V., F. W. Smith, F. A. L. Anet, and J. Feigon. 1996. The selectivity for K+ versus Na+ in DNA quadruplexes is dominated by relative free energies of hydration: a thermodynamic analysis by 1H NMR. Biochemistry. 35:15383–15390. PubMed

Hummer, G., L. R. Pratt, and A. E. Garcia. 1996. Free energy of ionic hydration. J. Phys. Chem. 100:1206–1215.

Hurley, L. H., R. T. Wheelhouse, D. Sun, S. M. Kerwin, M. Salazar, D. Y. Fedoroff, F. X. Han, H. Han, E. Izbicka, and D. D. von Hoff. 2000a. G-quadruplexes as targets for drug design. Pharmacol. Ther. 85:141–158. PubMed

Hurley, L. H., R. T. Wheelhouse, D. Sun, S. M. Kerwin, M. Salazar, O. Y. Fedoroff, F. X. Han, H. Y. Han, E. Izbicka, and D. D. Von Hoff. 2000b. G-quadruplexes as targets for drug design. Pharmacol. Ther. 85:141–158. PubMed

Izbicka, E., R. T. Wheelhouse, E. Raymond, K. K. Davidson, R. A. Lawrence, D. Y. Sun, B. E. Windle, L. H. Hurley, and D. D. Von Hoff. 1999. Effects of cationic porphyrins as G-quadruplex interactive agents in human tumor cells. Cancer Res. 59:639–644. PubMed

Jayaram, B., D. Sprous, M. A. Young, and D. L. Beveridge. 1998. Free energy analysis of the conformational preferences of A and B forms of DNA in solution. J. Am. Chem. Soc. 120:10629–10633.

Jorgensen, W. L., J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein. 1983. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 79:926–935.

Karplus, M., and J. N. Kushick. 1981. Method for estimating the configurational entropy of macromolecules. Macromol. 14:325–332.

Kettani, A., S. Bouaziz, A. Gorin, H. Zhao, R. A. Jones, and D. J. Patel. 1998. Solution structure of a Na cation stabilized DNA quadruplex containing G-G-G-G and G-C-G-C tetrads formed by G-G-G-C repeats observed in adeno-associated viral DNA. J. Mol. Biol. 282:619–636. PubMed

Kollman, P. A., I. Massova, C. Reyes, B. Kuhn, S. Huo, L. Chong, M. Lee, T. Lee, Y. Duan, W. Wang, O. Donini, P. Cieplak, J. Srinivasan, D. A. Case, and T. E. Cheatham 3rd. 2000. Calculating structures and free energies of complex molecules: Combining molecular mechanics and continuum models. Acc. Chem. Res. 33:889–897. PubMed

Koradi, R., M. Billeter, and K. Wuthrich. 1996. MOLMOL: a program for display and analysis of macromolecular structures. J. Mol. Graph. 14:51–55, 29–32. PubMed

Krestov, G. A. 1991. Thermodynamics of Solvation. Ellis Horwood, New York.

Lane, A. N., and T. C. Jenkins. 2001. Structures and properties of multi-stranded nucleic acids. Current Organic Chemistry. 5:845–869.

Laughlan, G., A. I. H. Murchie, D. G. Norman, M. H. Moore, P. C. E. Moody, D. M. J. Lilley, and B. Luisi. 1994. The high-resolution crystal-structure of a parallel-stranded guanine tetraplex. Science. 265:520–524. PubMed

Lazaridis, T., A. Masunov, and F. Gandolfo. 2002. Contributions to the binding free energy of ligands to avidin and streptavidin. Proteins. 47:194–208. PubMed

Luo, R., and M. K. Gilson. 2000. Synthetic adenine receptors: direct calculation of binding affinity and entropy. J. Am. Chem. Soc. 122:2934–2937.

Macaya, R. F., P. Schulze, F. W. Smith, J. A. Roe, and J. Feigon. 1993. Thrombin-binding DNA aptamer forms a unimolecular quadruplex structure in solution. Proc. Natl. Acad. Sci. USA. 90:3745–3749. PubMed PMC

Marcus, Y. 1994. A simple empirical model describing the thermodynamics of hydration of ions of widely varying charges, sizes, and shapes. Biophys. Chem. 51:111–127.

Marelius, J., T. Hansson, and J. Aqvist. 1998. Calculation of ligand binding free energies from molecular dynamics simulations. Int. J. Quant. Chem. 69:77–88.

McQuarrie, D. A. 1976. Statistical Mechanics. Harper and Row, New York.

Mergny, J. L., L. Lacroix, M. P. Teulade-Fichou, C. Hounsou, L. Guittat, M. Hoarau, P. B. Arimondo, J. P. Vigneron, J. M. Lehn, J. F. Riou, T. Garestier, and C. Helene. 2001. Telomerase inhibitors based on quadruplex ligands selected by a fluorescence assay. Proc. Natl. Acad. Sci. USA. 98:3062–3067. PubMed PMC

Mergny, J. L., P. Mailliet, F. Lavelle, J. F. Riou, A. Laoui, and C. Helene. 1999. The development of telomerase inhibitors: the G-quartet approach. Anticancer Drug Des. 14:327–339. PubMed

Meyer, M., M. Brandl, and J. Suhnel. 2001a. Are guanine tetrads stabilized by bifurcated hydrogen bonds? J. Phys. Chem. A. 105:8223–8225.

Meyer, M., T. Steinke, M. Brandl, and J. Suhnel. 2001b. Density functional study of guanine and uracil quartets and of guanine quartet/metal ion complexes. J. Comput. Chem. 22:109–124.

Misra, V. K., and B. Honig. 1996. The electrostatic contribution to the B to Z transition of DNA. Biochemistry. 35:1115–1124. PubMed

Misra, V. K., K. A. Sharp, R. A. Friedman, and B. Honig. 1994. Salt effects on ligand-DNA binding. Minor groove binding antibiotics. J. Mol. Biol. 238:245–263. PubMed

Nadel, Y., P. Weisman-Shomer, and M. Fry. 1995. The fragile X syndrome single strand d(CGG)n nucleotide repeats readily fold back to form unimolecular hairpin structures. J. Biol. Chem. 270:28970–28977. PubMed

Neidle, S., R. J. Harrison, A. P. Reszka, and M. A. Read. 2000. Structure-activity relationships among guanine-quadruplex telomerase inhibitors. Pharmacol. Ther. 85:133–139. PubMed

Nicholls, A., and B. Honig. 1991. A rapid finite difference algorithm, utilizing successive over-relaxation to solve the Poisson-Boltzmann equation. J. Comput. Chem. 12:435–445.

Page, M. I., and W. P. Jencks. 1971. Entropic contributions to rate accelerations in enzymic and intramolecular reactions and the chelate effect. Proc. Natl. Acad. Sci. USA. 68:1678–1683. PubMed PMC

Parkinson, G. N., M. P. Lee, and S. Neidle. 2002. Crystal structure of parallel quadruplexes from human telomeric DNA. Nature. 417:876–880. PubMed

Pearlman, D. A., D. A. Case, J. W. Caldwell, W. S. Ross, T. E. Cheatham, S. Debolt, D. Ferguson, G. Seibel, and P. Kollman. 1995. AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structure and energetic properties of molecules. Comp. Phys. Commun. 91:1–41.

Phillips, K., Z. Dauter, A. I. H. Murchie, D. M. J. Lilley, and B. Luisi. 1997. The crystal structure of a parallel-stranded guanine tetraplex at 0.95 Å resolution. J. Mol. Biol. 273:171–182. PubMed

Read, M., R. J. Harrison, B. Romagnoli, F. A. Tanious, S. H. Gowan, A. P. Reszka, W. D. Wilson, L. R. Kelland, and S. Neidle. 2001. Structure-based design of selective and potent G quadruplex-mediated telomerase inhibitors. Proc. Natl. Acad. Sci. USA. 98:4844–4849. PubMed PMC

Read, M. A., A. A. Wood, J. R. Harrison, S. M. Gowan, L. R. Kelland, H. S. Dosanjh, and S. Neidle. 1999. Molecular modeling studies on G-quadruplex complexes of telomerase inhibitors: structure-activity relationships. J. Med. Chem. 42:4538–4546. PubMed

Ryckaert, J. P., G. Ciccotti, and H. J. C. Berendsen. 1977. Numerical integration of the Cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes. J. Comput. Phys. 23:327–341.

Saenger, W. 1984. Principles of Nucleic Acid Structure. C. E. Cantor, editor. Springer-Verlag, New York.

Sanner, M. F., A. J. Olson, and J.-C. Spehner. 1996. Reduced surface: an efficient way to compute molecular surfaces. Biopolymers. 38:305–320. PubMed

Schafer, H., A. E. Mark, and W. F. van Gunsteren. 2000. Absolute entropies from molecular dynamics simulation trajectories. J. Chem. Phys. 113:7809–7817.

Schaffitzel, C., I. Berger, J. Postberg, J. Hanes, H. J. Lipps, and A. Pluckthun. 2001. In vitro generated antibodies specific for telomeric guanine-quadruplex DNA react with Stylonychia lemnae macronuclei. Proc. Natl. Acad. Sci. USA. 98:8572–8577. PubMed PMC

Schlitter, J. 1993. Estimation of absolute and relative entropies of macromolecules using the covariance matrix. Chem. Phys. Lett. 215:617–621.

Schwarzl, S. M., T. B. Tschopp, J. C. Smith, and S. Fischer. 2002. Can the calculation of ligand binding free energies be improved with continuum solvent electrostatics and an ideal-gas entropy correction? J. Comput. Chem. 23:1143–1149. PubMed

Sharp, K. A., and B. Honig. 1990. Electrostatic interactions in macromolecules: theory and applications. Annu. Rev. Biophys. Biophys. Chem. 19:301–332. PubMed

Shields, G. C., C. A. Laughton, and M. Orozco. 1997. Molecular dynamics simulations of the d(TAT) triplex helix. J. Am. Chem. Soc. 119:7463–7469.

Shields, G. C., C. A. Laughton, and M. Orozco. 1998. Molecular dynamics simulation of a PNA-DNA-PNA triple helix in aqueous solution. J. Am. Chem. Soc. 120:5895–5904.

Simonsson, T., P. Pecinka, and M. Kubista. 1998. DNA tetraplex formation in the control region of c-myc. Nucleic Acids Res. 26:1167–1172. PubMed PMC

Smith, F. W., and J. Feigon. 1992. Quadruplex structure of Oxytricha telomeric DNA oligonucleotides. Nature. 356:164–168. PubMed

Smith, F. W., and J. Feigon. 1993. Strand orientation in the DNA quadruplex formed from the Oxytricha telomere repeat nucleotide d(G4T4G4-quadruplex) in solution. Biochemistry. 32:8682–8692. PubMed

Spackova, N., I. Berger, M. Egli, and J. Sponer. 1998. Molecular dynamics of a hemiprotonated intercalated four-stranded i-DNA: Stable trajectories on a nanosecond time scale. J. Am. Chem. Soc. 120:6147–6151.

Spackova, N., I. Berger, and J. Sponer. 1999. Nanosecond molecular dynamics simulations of parallel and antiparallel guanine quadruplex DNA molecules. J. Am. Chem. Soc. 121:5519–5534.

Spackova, N., I. Berger, and J. Sponer. 2000. Nanosecond molecular dynamics of zipper-like DNA duplex structures containing sheared G-A mismatch pairs. J. Am. Chem. Soc. 122:7564–7572.

Spackova, N., I. Berger, and J. Sponer. 2001. Structural dynamics and cation interactions of DNA quadruplex molecules containing mixed guanine/cytosine quartets revealed by large-scale MD simulations. J. Am. Chem. Soc. 123:3295–3307. PubMed

Spackova, N., T. E. Cheatham 3rd, F. Ryjacek, F. Lankas, L. van Meervelt, P. Hobza, and J. Sponer. 2003. Molecular dynamics simulations and thermodynamics analysis of DNA-drug complexes. I. Minor groove binding between 4′,6-diamidino-2-phenylindole (DAPI) and DNA duplexes in solution. J. Am. Chem. Soc. 125:1759–1769. PubMed

Sponer, J., J. Florian, J. Leszczynski, and P. Hobza. 1996. Nonplanar DNA base pairs. J. Biomol. Struct. Dyn. 13:827–833. PubMed

Sponer, J., and P. Hobza. 1994. G-C base pair in parallel-stranded DNA—a novel type of base pairing: an ab initio quantum chemical study. J. Biomol. Struct. Dyn. 12:671–680. PubMed

Sponer, J., J. Leszczynski, and P. Hobza. 1996. Structures and energies of hydrogen-bonded DNA base pairs. A nonempirical study with inclusion of electron correlation. J. Phys. Chem. 100:1965–1974.

Sprous, D., M. A. Young, and D. L. Beveridge. 1998. Molecular dynamics studies of the conformational preferences of a DNA double helix in water and an ethanol/water mixture: theoretical considerations of the A⇔B transition. J. Phys. Chem. B. 102:4658–4667.

Srinivasan, J., T. E. Cheatham 3rd, P. Cieplak, P. A. Kollman, and D. A. Case. 1998. Continuum solvent studies of the stability of DNA, RNA and phosphoramidate helices. J. Am. Chem. Soc. 120:9401–9409.

Stefl, R., N. Spackova, I. Berger, J. Koca, and J. Sponer. 2001a. Molecular dynamics of DNA quadruplex molecules containing inosine, 6-thioguanine, and 6-thiopurine. Biophys. J. 80:455–468. PubMed PMC

Stefl, R., L. Trantirek, M. Vorlickova, J. Koca, V. Sklenar, and J. Kypr. 2001b. A-like guanine-guanine stacking in the aqueous DNA duplex of d(GGGGCCCC). J. Mol. Biol. 307:513–524. PubMed

Strahan, G. D., M. A. Keniry, and R. H. Shafer. 1998. NMR structure refinement and dynamics of the K+-[d(G3T4G3)]2 quadruplex via particle mesh Ewald molecular dynamics simulations. Biophys. J. 75:968–981. PubMed PMC

Sun, D., and L. H. Hurley. 2001. Targeting telomeres and telomerase. Methods Enzymol. 340:573–592. PubMed

Tidor, B., and M. Karplus. 1994. The contribution of vibrational entropy to molecular association. J. Mol. Biol. 238:405–414. PubMed

Trantirek, L., R. Stefl, M. Vorlickova, J. Koca, V. Sklenar, and J. Kypr. 2000. An A-type double helix of DNA having B-type puckering of the deoxyribose rings. J. Mol. Biol. 297:907–922. PubMed

Tsui, V., and D. A. Case. 2001. Calculations of the absolute free energies of binding between RNA and metal ions using molecular dynamics simulations and continuum electrostatics. J. Phys. Chem. B. 105:11314–11325.

Vitha, M. F., and P. W. Carr. 2000. The chemical meaning of the standard free energy of transfer: use of van der Waals' equation of state to unravel the interplay between free volume, volume entropy, and the role of standard states. J. Phys. Chem. B. 104:5343–5349.

Vorobjev, Y. N., J. C. Almagro, and J. Hermans. 1998. Discrimination between native and intentionally misfolded conformations of proteins: ES/IS, a new method for calculating conformational free energy that uses both dynamics simulations with an explicit solvent and an implicit solvent continuum model. Proteins. 32:399–413. PubMed

Wang, A. H., G. J. Quigley, F. J. Kolpak, J. L. Crawford, J. H. van Boom, G. van der Marel, and A. Rich. 1979. Molecular structure of a left-handed double helical DNA fragment at atomic resolution. Nature. 283:743–745. PubMed

Wang, Y., and D. J. Patel. 1993. Solution structure of the human telomeric repeat d[AG3(T2AG3)3] G-tetraplex. Structure. 1:263–282. PubMed

Yu, Y. B., P. L. Privalov, and R. S. Hodges. 2001. Contribution of translational and rotational motions to molecular association in aqueous solution. Biophys. J. 81:1632–1642. PubMed PMC

Computer Folding of Parallel DNA G-Quadruplex: Hitchhiker's Guide to the Conformational Space

Mechanical Stability and Unfolding Pathways of Parallel Tetrameric G-Quadruplexes Probed by Pulling Simulations

Complexity of Guanine Quadruplex Unfolding Pathways Revealed by Atomistic Pulling Simulations

Parallel G-triplexes and G-hairpins as potential transitory ensembles in the folding of parallel-stranded DNA G-Quadruplexes

Structural dynamics of propeller loop: towards folding of RNA G-quadruplex

Exploring the Dynamics of Propeller Loops in Human Telomeric DNA Quadruplexes Using Atomistic Simulations

Hairpins participating in folding of human telomeric sequence quadruplexes studied by standard and T-REMD simulations

Extended molecular dynamics of a c-kit promoter quadruplex

Structural dynamics of possible late-stage intermediates in folding of quadruplex DNA studied by molecular simulations

Molecular dynamics simulations of G-DNA and perspectives on the simulation of nucleic acid structures

Dynamics of the base of ribosomal A-site finger revealed by molecular dynamics simulations and Cryo-EM

Molecular dynamics simulations and their application to four-stranded DNA

Hinge-like motions in RNA kink-turns: the role of the second a-minor motif and nominally unpaired bases

Molecular dynamics simulations of Guanine quadruplex loops: advances and force field limitations