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. 1999 Oct;77(4):1858–1870. doi: 10.1016/S0006-3495(99)77029-3

Brownian dynamics simulation of DNA condensation.

P E Sottas 1, E Larquet 1, A Stasiak 1, J Dubochet 1
PMCID: PMC1300469  PMID: 10512808

Abstract

DNA condensation observed in vitro with the addition of polyvalent counterions is due to intermolecular attractive forces. We introduce a quantitative model of these forces in a Brownian dynamics simulation in addition to a standard mean-field Poisson-Boltzmann repulsion. The comparison of a theoretical value of the effective diameter calculated from the second virial coefficient in cylindrical geometry with some experimental results allows a quantitative evaluation of the one-parameter attractive potential. We show afterward that with a sufficient concentration of divalent salt (typically approximately 20 mM MgCl(2)), supercoiled DNA adopts a collapsed form where opposing segments of interwound regions present zones of lateral contact. However, under the same conditions the same plasmid without torsional stress does not collapse. The condensed molecules present coexisting open and collapsed plectonemic regions. Furthermore, simulations show that circular DNA in 50% methanol solutions with 20 mM MgCl(2) aggregates without the requirement of torsional energy. This confirms known experimental results. Finally, a simulated DNA molecule confined in a box of variable size also presents some local collapsed zones in 20 mM MgCl(2) above a critical concentration of the DNA. Conformational entropy reduction obtained either by supercoiling or by confinement seems thus to play a crucial role in all forms of condensation of DNA.

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Selected References

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  1. Bednar J., Furrer P., Stasiak A., Dubochet J., Egelman E. H., Bates A. D. The twist, writhe and overall shape of supercoiled DNA change during counterion-induced transition from a loosely to a tightly interwound superhelix. Possible implications for DNA structure in vivo. J Mol Biol. 1994 Jan 21;235(3):825–847. doi: 10.1006/jmbi.1994.1042. [DOI] [PubMed] [Google Scholar]
  2. Bloomfield V. A. DNA condensation by multivalent cations. Biopolymers. 1997;44(3):269–282. doi: 10.1002/(SICI)1097-0282(1997)44:3<269::AID-BIP6>3.0.CO;2-T. [DOI] [PubMed] [Google Scholar]
  3. Bloomfield V. A. DNA condensation. Curr Opin Struct Biol. 1996 Jun;6(3):334–341. doi: 10.1016/s0959-440x(96)80052-2. [DOI] [PubMed] [Google Scholar]
  4. Bloomfield V. A., Wilson R. W., Rau D. C. Polyelectrolyte effects in DNA condensation by polyamines. Biophys Chem. 1980 Jun;11(3-4):339–343. doi: 10.1016/0301-4622(80)87006-2. [DOI] [PubMed] [Google Scholar]
  5. Brenner S. L., McQuarrie D. A. Force balances in systems of cylindrical polyelectrolytes. Biophys J. 1973 Apr;13(4):301–331. doi: 10.1016/S0006-3495(73)85987-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Duguid J., Bloomfield V. A., Benevides J., Thomas G. J., Jr Raman spectroscopy of DNA-metal complexes. I. Interactions and conformational effects of the divalent cations: Mg, Ca, Sr, Ba, Mn, Co, Ni, Cu, Pd, and Cd. Biophys J. 1993 Nov;65(5):1916–1928. doi: 10.1016/S0006-3495(93)81263-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Felgner P. L., Ringold G. M. Cationic liposome-mediated transfection. Nature. 1989 Jan 26;337(6205):387–388. doi: 10.1038/337387a0. [DOI] [PubMed] [Google Scholar]
  8. Gavryushov S., Zielenkiewicz P. Electrostatic potential of B-DNA: effect of interionic correlations. Biophys J. 1998 Dec;75(6):2732–2742. doi: 10.1016/S0006-3495(98)77717-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Hammermann M., Brun N., Klenin K. V., May R., Tóth K., Langowski J. Salt-dependent DNA superhelix diameter studied by small angle neutron scattering measurements and Monte Carlo simulations. Biophys J. 1998 Dec;75(6):3057–3063. doi: 10.1016/S0006-3495(98)77746-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Hammermann M., Steinmaier C., Merlitz H., Kapp U., Waldeck W., Chirico G., Langowski J. Salt effects on the structure and internal dynamics of superhelical DNAs studied by light scattering and Brownian dynamics. Biophys J. 1997 Nov;73(5):2674–2687. doi: 10.1016/S0006-3495(97)78296-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Jian H., Schlick T., Vologodskii A. Internal motion of supercoiled DNA: brownian dynamics simulations of site juxtaposition. J Mol Biol. 1998 Nov 27;284(2):287–296. doi: 10.1006/jmbi.1998.2170. [DOI] [PubMed] [Google Scholar]
  12. Klenin K., Merlitz H., Langowski J. A Brownian dynamics program for the simulation of linear and circular DNA and other wormlike chain polyelectrolytes. Biophys J. 1998 Feb;74(2 Pt 1):780–788. doi: 10.1016/S0006-3495(98)74003-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Li A. Z., Huang H., Re X., Qi L. J., Marx K. A. A gel electrophoresis study of the competitive effects of monovalent counterion on the extent of divalent counterions binding to DNA. Biophys J. 1998 Feb;74(2 Pt 1):964–973. doi: 10.1016/S0006-3495(98)74019-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Ma C., Bloomfield V. A. Condensation of supercoiled DNA induced by MnCl2. Biophys J. 1994 Oct;67(4):1678–1681. doi: 10.1016/S0006-3495(94)80641-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Marko JF, Siggia ED. Statistical mechanics of supercoiled DNA. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1995 Sep;52(3):2912–2938. doi: 10.1103/physreve.52.2912. [DOI] [PubMed] [Google Scholar]
  16. Merlitz H., Rippe K., Klenin K. V., Langowski J. Looping dynamics of linear DNA molecules and the effect of DNA curvature: a study by Brownian dynamics simulation. Biophys J. 1998 Feb;74(2 Pt 1):773–779. doi: 10.1016/S0006-3495(98)74002-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Porschke D. Dynamics of DNA condensation. Biochemistry. 1984 Oct 9;23(21):4821–4828. doi: 10.1021/bi00316a002. [DOI] [PubMed] [Google Scholar]
  18. Post C. B., Zimm B. H. Light-scattering study of DNA condensation: competition between collapse and aggregation. Biopolymers. 1982 Nov;21(11):2139–2160. doi: 10.1002/bip.360211105. [DOI] [PubMed] [Google Scholar]
  19. Rau D. C., Parsegian V. A. Direct measurement of the intermolecular forces between counterion-condensed DNA double helices. Evidence for long range attractive hydration forces. Biophys J. 1992 Jan;61(1):246–259. doi: 10.1016/S0006-3495(92)81831-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Record M. T., Jr, Lohman M. L., De Haseth P. Ion effects on ligand-nucleic acid interactions. J Mol Biol. 1976 Oct 25;107(2):145–158. doi: 10.1016/s0022-2836(76)80023-x. [DOI] [PubMed] [Google Scholar]
  21. Rybenkov V. V., Cozzarelli N. R., Vologodskii A. V. Probability of DNA knotting and the effective diameter of the DNA double helix. Proc Natl Acad Sci U S A. 1993 Jun 1;90(11):5307–5311. doi: 10.1073/pnas.90.11.5307. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Rybenkov V. V., Vologodskii A. V., Cozzarelli N. R. The effect of ionic conditions on DNA helical repeat, effective diameter and free energy of supercoiling. Nucleic Acids Res. 1997 Apr 1;25(7):1412–1418. doi: 10.1093/nar/25.7.1412. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Rybenkov V. V., Vologodskii A. V., Cozzarelli N. R. The effect of ionic conditions on the conformations of supercoiled DNA. I. Sedimentation analysis. J Mol Biol. 1997 Mar 28;267(2):299–311. doi: 10.1006/jmbi.1996.0876. [DOI] [PubMed] [Google Scholar]
  24. Rybenkov V. V., Vologodskii A. V., Cozzarelli N. R. The effect of ionic conditions on the conformations of supercoiled DNA. II. Equilibrium catenation. J Mol Biol. 1997 Mar 28;267(2):312–323. doi: 10.1006/jmbi.1996.0877. [DOI] [PubMed] [Google Scholar]
  25. Schellman J. A., Parthasarathy N. X-ray diffraction studies on cation-collapsed DNA. J Mol Biol. 1984 May 25;175(3):313–329. doi: 10.1016/0022-2836(84)90351-6. [DOI] [PubMed] [Google Scholar]
  26. Schlick T., Li B., Olson W. K. The influence of salt on the structure and energetics of supercoiled DNA. Biophys J. 1994 Dec;67(6):2146–2166. doi: 10.1016/S0006-3495(94)80732-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Shaw S. Y., Wang J. C. Knotting of a DNA chain during ring closure. Science. 1993 Apr 23;260(5107):533–536. doi: 10.1126/science.8475384. [DOI] [PubMed] [Google Scholar]
  28. Skerjanc J., Strauss U. P. Interactions of polyelectrolytes with simple electrolytes. 3. The binding of magnesium ion by deoxyribonucleic acid. J Am Chem Soc. 1968 Jun 5;90(12):3081–3085. doi: 10.1021/ja01014a017. [DOI] [PubMed] [Google Scholar]
  29. Sprous D., Harvey S. C. Action at a distance in supercoiled DNA: effects of sequence on slither, branching, and intramolecular concentration. Biophys J. 1996 Apr;70(4):1893–1908. doi: 10.1016/S0006-3495(96)79754-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Stigter D. Interactions of highly charged colloidal cylinders with applications to double-stranded. Biopolymers. 1977 Jul;16(7):1435–1448. doi: 10.1002/bip.1977.360160705. [DOI] [PubMed] [Google Scholar]
  31. Vologodskii A. V., Cozzarelli N. R. Conformational and thermodynamic properties of supercoiled DNA. Annu Rev Biophys Biomol Struct. 1994;23:609–643. doi: 10.1146/annurev.bb.23.060194.003141. [DOI] [PubMed] [Google Scholar]
  32. Vologodskii A., Cozzarelli N. Modeling of long-range electrostatic interactions in DNA. Biopolymers. 1995 Mar;35(3):289–296. doi: 10.1002/bip.360350304. [DOI] [PubMed] [Google Scholar]

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