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Bulletin of Mathematical Biology

, Volume 67, Issue 4, pp 701–718 | Cite as

Nonlinear waves in double-stranded DNA

  • Natalia L. Komarova
  • Avy Soffera
Article

Abstract

We propose a nonlinear model derived from first principles, to describe bubble dynamics of DNA. Our model equations include a term derived from the dissipative effect of intermolecular vibrational modes. Such modes are excited by the propagating bubble, and we term this ‘curvature dissipation’. The equations that we derive allow for stable pinned localized kinks which form the bubble. We perform the stability analysis and specify the energy requirements for the motion of the localized solutions. Our findings are consistent with properties of DNA dynamics, and can be used in models for denaturation bubbles, RNA and DNA transcription, nucleotide excision repair and meiotic recombination.

Keywords

Mathematical Biology Localize Solution Soliton Solution Nucleotide Excision Repair Meiotic Recombination 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Alberts, B. et al., 2002. Molecular Biology of the Cell. Taylor & Francis, Inc.Google Scholar
  2. Altan-Bonnet, G., Libchaber, A., Krichevsky, O., 2003. Bubble dynamics in double-stranded DNA. Phys. Rev. Lett. 90, 138101.Google Scholar
  3. Ashkin, A., 1997. Optical trapping and manipulation of neutral particles using lasers. Proc. Natl. Acad. Sci. 94, 4853–4860.CrossRefGoogle Scholar
  4. Aubry, S., 1997. Breathers in nonlinear lattices: existence, linear stability and quantization. Physica D 103, 201–250.MathSciNetCrossRefGoogle Scholar
  5. Barbi, M., Cocco, S., Peyrard, M., 1999a. Helicoidal model for DNA openings. Phys. Lett. A 253, 358–369.CrossRefGoogle Scholar
  6. Barbi, M., Cocco, S., Peyrard, M., Ruffo, S., 1999b. A twist opening model for DNA. J. Biol. Phys. 24, 358–369.CrossRefGoogle Scholar
  7. Barbi, M., Lepri, S., Peyrard, M., Theodorakopoulos, N., 2003. Thermal denaturation of a helicoidal DNA model. Phys. Rev. E 68, 061909–061923.Google Scholar
  8. Beard, D., Schlick, T., 2000a. Inertial stochastic dynamics. I. Long-time-step methods for Langevin dynamics. J. Chem. Phys. 112(17), 7313–7322.CrossRefGoogle Scholar
  9. Beard, D., Schlick, T., 2000b. Inertial stochastic dynamics. II. Influence of inertia on slow kinetic processes of supercoiled DNA. J. Chem. Phys. 112(17), 7323–7338.CrossRefGoogle Scholar
  10. Bensimon, D., Simon, A.J., Croquette, V., Bensimon, A., 1995. Stretching DNA with a receding meniscus: experiments and models. Phys. Rev. Lett. 74, 4754–4757.CrossRefGoogle Scholar
  11. Bernet, J., Zakrzewska, K., Lavery, R., 1997. Modelling base pair opening: the role of helical twist. J. Mol. Struct. (Theochem) 398–399, 473–482.CrossRefGoogle Scholar
  12. Beveridge, D.L., Dixit, S.B., Barreiro, G., Thayer, K.M., 2004. Molecular dynamics simulations of DNA curvature and flexibility: helix phasing and premelting. Biopolymers 73(3), 380–403.CrossRefGoogle Scholar
  13. Bhattacharjee, S.M., Seno, F., 2003. Helicase on DNA: a phase coexistence based mechanism. J. Phys. A 36, L181–L187.CrossRefGoogle Scholar
  14. Bianco, P.R., Kowalczykowski, S.C., 2000. Translocation step size and mechanism of the RecBC DNA helicase. Nature 405, 368–372.CrossRefGoogle Scholar
  15. Bogolubskaya, A.A., Bogolubsky, I.L., 1994. Two-component localized solutions in a nonlinear DNA model. Phys. Lett. A 192, 239–246.CrossRefGoogle Scholar
  16. Boland, T., Ratner, B.D., 1995. Direct measurement of hydrogen bonding in DNA nucleotide bases by atomic force microscopy. Proc. Natl. Acad. Sci. 92, 5297–5301.CrossRefGoogle Scholar
  17. Briki, F., Ramstein, J., Lavery, R., Genest, D., 1991. Evidence for the stochastic nature of base pair opening in DNA: a Brownian dynamics simulation. J. Am. Chem. Soc. 113, 2490–2493.CrossRefGoogle Scholar
  18. Bussiek, M., Klenin, K., Langowski, J., 2002. Kinetics of site-site interactions in supercoiled DNA with bent sequences. J. Mol. Biol. 322(4), 707–718.CrossRefGoogle Scholar
  19. Campa, A., 2001. Bubble propagation in a helicoidal molecular chain. Phys. Rev. E 63, 021901–021910.Google Scholar
  20. Dauxois, T., Peyrard, M., Willis, C.R., 1992. Localized breather-like solution in a discrete Klein-Gordon model and application to DNA. Physica D 57, 267–282.MathSciNetCrossRefzbMATHGoogle Scholar
  21. Englander, S.W., Kallenbach, N.R., Heeger, A.J., Krumhansl, J.A., Litwin, S., 1980. Nature of the open state in long polynucleotide double helices: possibility of soliton excitations. Proc. Natl. Acad. Sci. 77, 7222–7226.CrossRefGoogle Scholar
  22. Evans, E., Fellows, J., Coffer, A., Wood, R.D., 1997. Open complex formation around a lesion during nucleotide excision repair provides a structure for cleavage by human XPG protein. EMBO J. 16, 625–638.CrossRefGoogle Scholar
  23. Fedyanin, V.K., Gochev, I., Lisy, V., 1986. Nonlinear dynamics of bases in continual model of DNA double helices. Stud. Biophys. 116, 59–64.Google Scholar
  24. Fischer, B.M., Walther, M., Jepsen, P.U., 2002. Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy. Phys. Med. Biol. 47, 3807–3814.CrossRefGoogle Scholar
  25. Gelles, J., Landick, R., 1998. RNA polymerase as a molecular motor. Cell 93, 13–16.CrossRefGoogle Scholar
  26. Gerland, U., Bundschuh, R., Hwa, T., 2001. Force-induced denaturation of RNA. Biophys. J. 81, 1324–1332.CrossRefGoogle Scholar
  27. Giudice, E., Varnai, P., Lavery, R., 2003. Base pair opening within B-DNA: free energy pathways for GC and AT pairs from umbrella sampling simulations. Nucleic Acids Res. 31(5), 1434–1443.CrossRefGoogle Scholar
  28. Goldstein, R.E., Goriely, A., Wolgemuth, C.W., 2000. Bistable helices. Phys. Rev. Lett. 84(7), 1631–1634.CrossRefGoogle Scholar
  29. Hansma, H.G., 1996. Atomic force microscopy of biomolecules. J. Vasc. Sci. Technol. B 14, 1390–1394.CrossRefGoogle Scholar
  30. Joos, B., Duesbery, M.S., 1997. Dislocation kink migration energies and the Frenkel-Kontorova model. Phys. Rev. B 55, 11161–11166.Google Scholar
  31. Kafri, Y., Mukamel, D., Peliti, L., 2000. Why is the DNA denaturation transition first order? Phys. Rev. Lett. 85, 4988–4991.CrossRefGoogle Scholar
  32. Kamien, R.D., Lubensky, T.V., Nelson, P., O’Hern, C.S., 1997. Direct determination of DNA twist-stretch coupling. Europhys. Lett. 38, 237–242.MathSciNetCrossRefGoogle Scholar
  33. Koch, S.J., Wang, M.D., 2003. Dynamic force spectroscopy of protein-DNA interactions by unzipping DNA. Phys. Rev. Lett. 91, 028103.Google Scholar
  34. Lankas, F., Sponer, J., Langowski, J., Cheatham 3rd, T.E., 2004. DNA deformability at the base pair level. J. Am. Chem. Soc. 126(13), 4124–4125.CrossRefGoogle Scholar
  35. Lee, S.A., Anderson, A., Smith, W., Griffey, R.H., Mohan, V., 2000. Temperature-dependent Raman and infrared spectra of nucleosides Part I—adenosine. J. Raman Spectrosc. 31, 891–896.CrossRefGoogle Scholar
  36. Lee, S.A., Li, J., Anderson, A., Smith, W., Griffey, R.H., Mohan, V., 2001. Temperature-dependent Raman and infrared spectra of nucleosides: II, cytidine. J. Raman Spectrosc. 32, 795–802.CrossRefGoogle Scholar
  37. Lighthill, M.J., 1975. Mathematical Biofluid Dynamics. Society for Industrial and Applied Mathematics, Philadelphia.Google Scholar
  38. McConnell, K.J, Beveridge, D.L., 2000. DNA structure: what’s in charge? J. Mol. Biol. 304(5), 803–820.CrossRefGoogle Scholar
  39. McConnell, K.J., Beveridge, D.L., 2001. Molecular dynamics simulations of B-DNA: sequence effects on Atract-induced bending and flexibility. J. Mol. Biol. 314(1), 23–40.CrossRefGoogle Scholar
  40. Muto, V., Lomdahl, P.S., Christiansen, P.L., 1990. Two-dimensional discrete model for DNA dynamics: longitudinal wave propagation and denaturation. Phys. Rev. A 42, 7452–7458.CrossRefGoogle Scholar
  41. Mu, D., Wakasugi, M., Hsu, D.S., Sancar, A., 1997. Characterization of reaction intermediates of human excision repair nuclease. J. Biol. Chem. 272, 28971–28979.Google Scholar
  42. Olson, W., 2004. Private communication.Google Scholar
  43. Peyrard, M., Bishop, A.R., 1989. Statistical mechanics of a nonlinear model for DNA denaturation. Phys. Rev. Lett. 62, 2755–2758.CrossRefGoogle Scholar
  44. Poglitsch, C.L., Meredith, G.D., Gnatt, A.L., Jensen, G.J., Chang, W.H., Fu, J., Kornberg, R.D., 1999. Electron crystal structure of an RNA polymerase II transcription elongation complex. Cell 98, 791–798.CrossRefGoogle Scholar
  45. Porath, D., Cuniberti, G., Di Felice, R., 2004. Charge transport in DNA-based devices. cond-mat/0403640.Google Scholar
  46. Ramachandran, G., Schlick, T., 1995. Solvent effects on supercoiled DNA explored by Langevin dynamics simulations. Phys. Rev. E 51, 6188–6203.CrossRefGoogle Scholar
  47. Ramstein, J., Lavery, R., 1988. Energetic coupling between DNA bending and base pair opening. Proc. Natl. Acad. Sci. USA 85, 7231–7235.CrossRefGoogle Scholar
  48. Schlick, T., 1995. Modeling superhelical DNA: recent analytical and dynamical approaches. Theory and Simulation, Honig, B. (Ed.), Curr. Opin. Struct. Biol. 5(2).Google Scholar
  49. Schlick, T., 2001. Time-trimming tricks for dynamic simulations: splitting force updates to reduce computational work. Structure 9, R45–R53.CrossRefGoogle Scholar
  50. Smith, S.B., Cui, Y., Bustamante, C., 1996. Overstretching B-DNA: the elastic response of individual double stranded and single stranded DNA molecules. Science 271, 795–799.Google Scholar
  51. Soffer, A., 2001. Dissipation through dispersion. CRM Proc. Lecture Notes 27, 175–184.Google Scholar
  52. Theodorakopoulos, N., Dauxois, T., Peyrard, M., 2000. Order of the phase transition in models of DNA thermal denaturation. Phys. Rev. Lett. 85, 6–9.CrossRefGoogle Scholar
  53. Wang, M.D., Schnitzer, M.J., Yin, H., Landick, R., Gelles, J., Block, S.M., 1998. Force and velocity measured for single molecules of RNA polymerase. Science 282, 902–907.CrossRefGoogle Scholar
  54. Wiggins, C.H., Goldstein, R.E., 1998. Flexive and propulsive dynamics of elastica at low Reynolds number. Phys. Rev. Lett. 80(17), 3879–82.CrossRefGoogle Scholar
  55. Willis, C., El-Batanouny, M., Stancioff, P., 1986. Sine-Gordon kinks on a discrete lattice. I. Hamiltonian formalism. Phys. Rev. B 33, 1904–1911.CrossRefGoogle Scholar
  56. Yakushevich, L.V., 1989. Nonlinear DNA dynamics: a new model. Phys. Lett. A 136, 413–417.CrossRefGoogle Scholar
  57. Yang, L., Beard, W.A., Wilson, S.H., Roux, B., Broyde, S., Schlick, T., 2002. Local deformations revealed by dynamics simulations of DNA polymerase with DNA mismatches at the primer terminus. J. Mol. Biol. 321, 459–478.CrossRefGoogle Scholar
  58. Zou, Y., Houten, B.V., 1999. Strand opening by the UvrA(2)B complex allows dynamic recognition of DNA damage. EMBO J. 18, 4889–4901.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2005

Authors and Affiliations

  1. 1.Department of MathematicsRutgers UniversityPiscatawayUSA
  2. 2.Institute for Advanced StudyPrincetonUSA

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