Skip to main content
SpringerLink
Log in

Nonlinear Dynamics of DNA

  • Conference paper
  • First Online:
Nonlinear Science at the Dawn of the 21st Century

Part of the book series: Lecture Notes in Physics ((LNP,volume 542))

Abstract

The main features of nonlinear dynamics of DNA as a new field of nonlinear science named nonlinear biomolecular dynamics are briefly described

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Scott, A.C., Solitons in biological molecules. Comments Mol. Cell. Biol. 3, 5–57, 1985.

    Google Scholar 

  2. Zhou G.-F., Zhang Ch.-T., A short review on the nonlinear motion in DNA. Phys. Scripta 43, 347–352, 1991.

    Article  ADS  Google Scholar 

  3. Yakushevich L.V., Nonlinear dynamics of biopolymers: theoretical models, experimental data. Quart. Rev. Biophys. 26, 201–223, 1993.

    Article  Google Scholar 

  4. Gaeta G., Reiss C., Peyrard M., Dauxois T., Simple models of nonlinear DNA dynamics. Rev. Nuovo Cimento 17, 1–48, 1994.

    Article  Google Scholar 

  5. Nonlinear Excitations in Biomolecules. Ed. M. Peyrard. Springer, Berlin, 1995.

    Google Scholar 

  6. Davydov A.S., Solitons in Bioenergetics. Naukova Dumka

    Google Scholar 

  7. Yakushevich L.V., Methods of Theoretical Physics and Their Applications to Biopolymer Sciences. Nova Science Publishers, New York, 1996.

    Google Scholar 

  8. Yakushevich L.V., Nonlinear Physics of DNA, John Wiley and Sons, Chichester, New York, Weinheim, Brisbane, Singapore, Toronto, 1998

    MATH  Google Scholar 

  9. Scott A.C., Chu F.Y., McLaughlin D.W., The soliton: a new concept in applied science. Proc. IEEE 61, 1443–1483, 1973.

    Google Scholar 

  10. Solitons in Action. Eds. K. Lonngren, A. Scott. Academic Press, New York, 1978.

    MATH  Google Scholar 

  11. Solitons. Eds. R.K. Bullough, P.J. Caudrey. Springer-Verlag, Berlin, 1980.

    MATH  Google Scholar 

  12. Structure and Dynamics: Nucleic Acids and Proteins. Eds. E. Clementi, R.H. Sarma. Adenine Press, New York, 1993.

    Google Scholar 

  13. Structure and Motion: Membranes, Nucleic Acids and Proteins. Eds. E. Clementi, G. Corongiu, M.H. Sarma, R.H. Sarma. Adenine Press, New York, 1985.

    Google Scholar 

  14. McCommon J.A., Harvey S.C., Dynamics of Proteins and Nucleic Acids. Cambridge University Press, Cambridge, 1987.

    Google Scholar 

  15. Davydov A.S., Solitons in molecular systems. Physica Scripta 20, 387–394, 1979.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. Englander S.W., Kallenbach N.R., Heeger A.J., Krumhansl J.A., Litwin A., Nature of the open state in long polynucleotide double helices: possibility of soliton excitations. Proc. Natl. Acad. Sci. USA 77, 7222–7226, 1980.

    Google Scholar 

  17. Yomosa S., Soliton excitations in deoxyribonucleic acid (DNA) double helices. Phys. Rev. A 27, 2120–2125, 1983.

    Article  ADS  MathSciNet  Google Scholar 

  18. Yomosa S., Solitary excitations in deoxyribonucleic acid (DNA) double helices. Phys. Rev. A 30, 474–480, 1984.

    Article  ADS  Google Scholar 

  19. Takeno S., Homma S., Topological solitons and modulated structure of bases in DNA double helices. Prog. Theor. Phys. 70, 308–311, 1983.

    Article  ADS  Google Scholar 

  20. Homma S., Takeno S., A coupled base-rotator model for structure and dynamics of DNA. Prog. Theor. Phys. 72, 679–693, 1984.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. Krumhansl J.A., Alexander D.M., Nonlinear dynamics and conformational excitations in biomolecular materials. In: Structure and Dynamics: Nucleic Acids and Proteins. Eds. E. Clementi, R.H. Sarma. Adenine Press, New York, 1983, pp. 61–80.

    Google Scholar 

  22. Krumhansl J.A., Wysin G.M., Alexander D.M., Garcia A., Lomdahl P.S., Layne S.P., Further theoretical studies of nonlinear conformational motions in double-helix DNA. In: Structure and Motion: Membranes, Nucleic Acids and Proteins. Eds. E. Clementi, G. Corongiu, M.H. Sarma, R.H. Sarma. Adenine Press, New York, 1985, pp. 407–415.

    Google Scholar 

  23. Fedyanin V.K., Yakushevich L.V., Scattering of neutrons and light by DNA solitons. Stud. biophys. 103, 171–178, 1984.

    Google Scholar 

  24. Fedyanin V.K., Gochev I., Lisy V., Nonlinear dynamics of bases in continual model of DNA double helices. Stud. biophys. 116, 59–64, 1986.

    Google Scholar 

  25. Fedyanin V.K., Lisy V., Soliton conformational excitations in DNA. Stud. biophys. 116, 65–71, 1986.

    Google Scholar 

  26. Yakushevich L.V., The effects of damping, external fields and inhomogeneity on the nonlinear dynamics of biopolymers. Stud. biophys. 121, 201–207, 1987.

    Google Scholar 

  27. Yakushevich L.V., Nonlinear DNA dynamics: a new model. Phys. Lett. A 136, 413–417, 1989.

    Article  ADS  Google Scholar 

  28. Yakushevich L.V., Investigation of a system of nonlinear equations simulating DNA torsional dynamics. Stud. biophys. 140, 163–170, 1991.

    Google Scholar 

  29. Zhang Ch.-T., Soliton excitations in deoxyribonucleic acid (DNA) double helices. Phys. Rev. A 35, 886–891, 1987.

    Article  ADS  MathSciNet  Google Scholar 

  30. Prohofsky E.W., Solitons hiding in DNA and their possible significance in RNA transcription. Phys. Rev. A 38, 1538–1541, 1988.

    Article  ADS  Google Scholar 

  31. Muto V., Holding J., Christiansen P.L., Scott A.C., Solitons in DNA. J. Biomol. Struct. Dyn. 5, 873–894, 1988.

    Google Scholar 

  32. Muto V., Scott A.S., Christiansen P.L., Thermally generated solitons in a Toda lattice model of DNA. Phys. Lett. A 136, 33–36, 1989.

    Article  ADS  Google Scholar 

  33. Muto V., Lomdahl P.S., Christiansen P.L., Two-dimensional discrete model for DNA dynamics: longitudinal wave propagation and denaturation. Phys. Rev. A 42, 7452–7458, 1990.

    Article  ADS  Google Scholar 

  34. Van Zandt L.L., DNA soliton realistic parameters. Phys. Rev. A 40, 6134–6137, 1989.

    Article  ADS  Google Scholar 

  35. Peyrard M., Bishop A.R., Statistical mechanics of a nonlinear model for DNA denaturation. Phys. Rev. Lett. 62, 2755–2758, 1989.

    Article  ADS  Google Scholar 

  36. Dauxois T., Peyrard M., Willis C.R., Localized breather-like solutions in a discrete Klein-Gordon model and application to DNA. Phys. D 57, 267–282, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  37. Dauxois T., Dynamics of breathers modes in a nonlinear helicoidal model of DNA. Phys. Lett. A 159, 390–395, 1991.

    Article  ADS  Google Scholar 

  38. Gaeta G., On a model of DNA torsion dynamics. Phys. Lett. A 143, 227–232, 1990.

    Article  ADS  MathSciNet  Google Scholar 

  39. Gaeta G., Solitons in planar and helicoidal Yakushevich model of DNA dynamics. Phys. Lett. A 168, 383–389, 1992.

    Article  ADS  Google Scholar 

  40. Salerno M., Discrete model for DNA-promotor dynamics. Phys. Rev. A 44, 5292–5297, 1991.

    Article  ADS  MathSciNet  Google Scholar 

  41. Bogolubskaya A.A., Bogolubsky I.L., Two-component localized solutions in a nonlinear DNA model. Phys. Lett. A 192, 239–246, 1994.

    Article  ADS  Google Scholar 

  42. Hai W., Kink couples in deoxyribonucleic acid (DNA) double helices. Phys. Lett. A 186, 309–316, 1994.

    Article  ADS  Google Scholar 

  43. Gonzalez J.A., Martin-Landrove M., Solitons in a nonlinear DNA model. Phys. Lett. A 191, 409–415, 1994.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  44. Webb S.J., Booth A.D., Absorption of microwave by microorganisms. Nature 222, 1199–1200, 1969.

    Article  ADS  Google Scholar 

  45. Swicord M.L., Davis C.C., Microwave absorption of DNA between 8 and 12 GHz. Biopolymers 21, 2453–2460, 1982.

    Article  Google Scholar 

  46. Swicord M.L., Davis C.C., An optical method of investigating the microwave absorption characteristics of DNA and other biomolecules in solution. Bioelectromagnetics 4, 21–42, 1983.

    Article  Google Scholar 

  47. Edwards G.S., Davis C.C., Saffer J.D., Swicord M.L., Resonant absorption of selected DNA molecules. Phys. Rev. Lett. 53, 1284–1287, 1984.

    Article  ADS  Google Scholar 

  48. Zhang Ch.T., Harmonic and subharmonic resonances of microwave absorption in DNA. Phys. Rev. A 40, 2148–2153, 1989.

    Article  ADS  Google Scholar 

  49. Baverstock K.F., Cundal R.D., Are solitons responsible for energy transfer in oriented DNA?. Int. J. Radiat. Biol. 55, 152–153, 1989.

    Google Scholar 

  50. Selvin P.R., Cook D.N., Pon N.G., Bauer W.R., Klein M.P., Hearst J.E., Torsional rigidity of positively and negatively supercoiled DNA. Science 255, 82–85, 1992.

    Article  ADS  Google Scholar 

  51. Xiao J.-X., Lin J.-T., Zhang G.-X., The influence of longitudinal vibration on soliton excitation in DNA double helices. J. Phys. A: Math. Gen. 20, 2425–2432, 1987.

    Article  ADS  MathSciNet  Google Scholar 

  52. Volkov S.N., Conformational transition. Dynamics and mechanism of longrange effects in DNA. J. Theor. Biol. 143, 485–496, 1990.

    Article  Google Scholar 

  53. Yakushevich L.V., Nonlinear vector model of the internal DNA dynamics. In: Mathematical Models of Non-linear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media. Eds. Uvarova L.A., Arinshtein A.E., and Latyshev A.V. Plenum Publishing Corporation, New York, (to appear).

    Google Scholar 

  54. Dauxois M., Peyrard M., Bishop A.R., Entropy-driven DNA denaturation. Phys. Rev. E 47, R44–R47, 1993.

    Article  ADS  Google Scholar 

  55. Krumhansl J.A., Schrieffer J.R., Dynamics and statistical mechanics of a one-dimensional model hamiltonian for structural phase transitions. Phys. Rev. B 11, 3535–3545, 1975.

    Article  ADS  Google Scholar 

  56. Nakanishi M., Tsuboi M., Saijo Y., Nagamure T., Stopped-flow ultraviolet spectroscopy for hydrogen-exchange studies of nucleic acids. FEBS Lett. 81, 61–64, 1977.

    Article  Google Scholar 

  57. Nakanishi M., Tsuboi M., Two channels of hydrogen exchange in a doublehelical nucleic acid. J. Mol. Biol. 124, 61–77, 1978.

    Article  Google Scholar 

  58. Mandal C., Kallenbach N.R., Englander S.W. Base-pair opening and closing reactions in the double helix. J. Mol. Biol. 135, 391–411, 1979.

    Article  Google Scholar 

  59. Frank-Kamenetskii M.D., Fluctuational motility of DNA. Mol. Biol. 17, 639–652, 1983 (In Russian).

    Google Scholar 

  60. Frank-Kamenetskii M.D., How the double helix breathes. Nature 328,17–18, 1987.

    Article  ADS  Google Scholar 

  61. Gabriel G., Grant E.H., Tata R., Brown P.R., Gestblom B., Noreland E., Microwave absorption in aqueous solutions of DNA. Nature 328, 145–146, 1987.

    Article  ADS  Google Scholar 

  62. Maleev V.Ya., Kashpur V.A., Glibitsky G.M., Krasnitskaya A.A., Veretelnik Ye.V., Absorption of DNA solutions in the 9-12 GHz frequency range. Biopolim. Kletka 2, 35–38, 1986.

    Google Scholar 

  63. Foster K.R., Epstein B.R., Galt M.A., Resonances in the dielectric absorption of DNA ? Biophys. J. 52, 421–425, 1987.

    Article  ADS  Google Scholar 

  64. Garibov R.A., Ostrovskii A.V., Does the microwave radiation change the dynamical behavior of macromolecules? Uspekhi Sovrem. Biol. 110, 306–320, 1990 (In Russian).

    Google Scholar 

  65. Davis M.E., Van Zandt L.L., Microwave response of DNA in solution. Theory. Phys. Rev. 37 A, 888–899, 1988.

    ADS  Google Scholar 

  66. Van Zandt L.L., Resonant microwave absorption by dissolved DNA. Phys. Rev. Lett. 57, 2085–2087, 1986.

    Article  ADS  Google Scholar 

  67. Van Zandt L.L., Davis M.E., Theory of anomalous resonant absorption of DNA at microwave frequencies. J. Biomol. Struct. Dyn. 3, 1045–1053, 1986.

    Google Scholar 

  68. Muto V., Scott A.C., Christiansen P.L., Microwave and thermal generation of solitons in DNA. J. de Phys. 50, C3, 217–222, 1989.

    Google Scholar 

  69. Baverstock K.F., Cundall R.B., Solitons and energy transfer in DNA. Nature, 332, N3, 312–313, 1988.

    Article  ADS  Google Scholar 

  70. Baverstock K.F., Cundall R.B., Long-range energy transfer in DNA. Radiation Physics and Chemistry, 32, 553–556, 1988.

    Google Scholar 

  71. Arroyo C.M., Carmichael A.J., Swenberg C.E., Myers L.S., Neutron induced free radicals in oriented DNA. Int. J. Radiat. Biol. 50, 789–793, 1986.

    Article  Google Scholar 

  72. Miller J.H., Wilson W.E., Swenberg C.E., Myers L.S., Charlton D.E., Stochastic model for free radical yields in oriented DNA exposed to density ionizing radiation at 77 K. Int. J. Radiat. Biol. 53, 901–907, 1988.

    Article  Google Scholar 

  73. Edholm O., Nilsson L., Berg O., Ehrenberg M., Claesens F., Grässlund A., Jönsson B., Taleman O., Biomolecular dynamics. A report from a workshop in Gysinge, Sweden, October 4–7, 1982. Quart. Rev. Biophys. 17, 125–151, 1984.

    Google Scholar 

  74. Khan A., Bhaumic D., Dutta-Roy B., The possible role of solitonic process during A to B conformational changes in DNA. Bull. Math. Biol. 47, 783–789, 1985.

    MATH  Google Scholar 

  75. Sobell H.M., Kink-antikink bound states in DNA structure. In: Biological Macromolecules and Assemblies. Eds. F.A. Jurnak, A. McPherson. John Wiley and Sons, New York, 1984, pp. 172–234.

    Google Scholar 

  76. Volkov S.N., Conformational transition. Dynamics and mechanism of longrange effects in DNA. J. Theor. Biol. 143, 485–496, 1990.

    Article  Google Scholar 

  77. Jensen P., Jaric M.V., Bannemann K.H., Soliton-like processes during rightleft transition in DNA. Phys. Lett. 95 A, 204–208, 1983.

    Article  Google Scholar 

  78. Volkov S.N., Nonlinear waves and conformational mobility of DNA. Preprint ITP-84-52P, Inst. Theor. Phys., Kiev.

    Google Scholar 

  79. Pohl F.M., Jovin T.M., Baehr W., Holbrook J.J., Ethidium bromide as a cooperative effector of a DNA structure. Proc. Natl. Acad. Sci. USA 69, 3805–3809, 1972.

    Google Scholar 

  80. Kolata G.B., Bacterial genetics: action at a distance on DNA. Science 198, 41–42, 1977.

    Article  ADS  MathSciNet  Google Scholar 

  81. Hogan M., Dattagupta N., Crothers D.M., Transmission of allosteric effects in DNA. Nature 278, 521–524, 1979.

    Article  ADS  Google Scholar 

  82. Crothers D.M., Fried M., Transmission of long-range effects in DNA. Cold Spring Harbor Symposia on Quantitative Biology 47, 263–269, 1983.

    Google Scholar 

  83. Wells R.D., Goodman T.C., Hillen W., Horn G.T., Klein R.D., Larson J.E., Mller U.R., Nevendorf S.R., Panayatatos N., Stirdivant S.M., DNA structure and gene: Progress in Nucleic Acid Research and Molecular Biology. Academic Press, New York, Vol. 24, 1980, pp. 167–267.

    Google Scholar 

  84. Yakushevich L.V., Non-linear DNA dynamics and problems of gene regulation. Nanobiology 1, 343–350, 1992.

    Google Scholar 

  85. Polozov R.V., Yakushevich L.V., Nonlinear waves in DNA and regulation of transcription. J. Theor. Biol. 130, 423–430, 1988.

    Article  Google Scholar 

  86. Salerno M., Dynamical properties of DNA promoters. Phys. Lett. A 167, 49–53, 1992.

    Article  ADS  MathSciNet  Google Scholar 

  87. Salerno M., Kivshar Yu. S. DNA promoters and nonlinear dynamics. Phys. Lett. A 193, 263–266, 1994.

    Article  ADS  Google Scholar 

  88. Salerno M., Nonlinear dynamics of plasmid pB R322 promoters. In: Nonlinear Excitations in Biomolecules. Ed. Peyrard M., Springer, 1995, pp. 147–153.

    Google Scholar 

  89. Fritzsche H., “New structural and dynamic aspects of DNA as revealed by nuclear magnetic resonance”. Comm. Mol. Biophys. 1, 325–336, 1982.

    MathSciNet  Google Scholar 

  90. Keepers J. W., James Th. L., Models for DNA backbone motions: an interpretation of NMR relaxation experiments. J. Am. Chem. Soc. 104, 929–939, 1982.

    Article  Google Scholar 

  91. McClure W. R., Mechanism and control of transcription in procaryotes. Ann. Rev. Biochem. 54, 171–204, 1985. revealed by nuclear magnetic resonance. Comm. Mol. Biophys. 1, 325-336, 1982.

    Article  Google Scholar 

Download references

Authors
  1. L.V. Yakushevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematical Modelling, The Technical University of Denmark, Building 321, 2800, Kgs. Lyngby, Denmark

    P. L. Christiansen , M. P. Sørensen  & A. C. Scott ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yakushevich, L. (2000). Nonlinear Dynamics of DNA. In: Christiansen, P.L., Sørensen, M.P., Scott, A.C. (eds) Nonlinear Science at the Dawn of the 21st Century. Lecture Notes in Physics, vol 542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46629-0_19

Download citation

  • DOI: https://doi.org/10.1007/3-540-46629-0_19

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66918-0

  • Online ISBN: 978-3-540-46629-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation