Journal of Mathematical Biology

, Volume 6, Issue 4, pp 383–402 | Cite as

Topological consideration in the theory of replication of DNA

  • William F. Pohl
  • George W. Roberts


An obvious difficulty of the Watson-Crick model of DNA is that the intertwining of the strands would seem to hinder their separation during replication. The nature of the difficulty is here made precise and is called the alignment problem. It is shown that the swivelase theory, found in current textbooks and thought to overcome the difficulty, does not in fact do so. The various conceivable solutions of the alignment problem are considered and rejected, leading to the conclusion that chromosomal DNA is not double-helical. An alternative model of DNA is discussed. In addition a topological classification of DNA denaturation processes is given, and an alternative interpretation of the gel electrophoresis experiments on circular duplex DNA is suggested.

Key words

Replication of DNA Watson-Crick model Double-helical structure 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alberts, B., Sternglanz, R.: Recent excitement in the DNA replication problem. Nature269, 655–661 (1977)CrossRefGoogle Scholar
  2. 2.
    Bauer, W., Vinograd, J.: The interaction of closed circular DNA with intercalative dyes. I. The superhelix density of SV40 DNA in the presence and absence of dye. J. Mol. Biol.33, 141–171 (1968)CrossRefGoogle Scholar
  3. 3.
    Cairns, J.: The bacterial chromosome. Scientific American, Jan. 1966Google Scholar
  4. 4.
    Crick, F. H. C.: Linking numbers and nucleosomes. Proc. Natl. Acad. Sci. USA73, 2639–2643 (1976)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Depew, R. E., Wang, J. C.: Conformal flucturations of DNA helix. Proc. Natl. Acad. Sci. USA72, 4275–4279 (1975)CrossRefGoogle Scholar
  6. 6.
    Frank-Kamenetskii, M. D., Lukashin, A. V., Vologodski, A. V.: Statistical mechanics and topology of polymer chains. Nature258, 398–402 (1975)CrossRefGoogle Scholar
  7. 7.
    Freifelder, D.: Physical Biochemistry. San Francisco: Freeman, 1976Google Scholar
  8. 8.
    Fuller, F. B.: The writhing number of a space curve. Proc. Natl. Acad. Sci. USA68, 815–819 (1971)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Germond, J. E., Hirt, B., Oudet, P., Gross-Bellard, M., Chambon, P.: Folding of the DNA double helix in chromatin-like structures from Simian Virus 40. Proc. Natl. Acad. Sci. USA72, 1843–1847 (1975)CrossRefGoogle Scholar
  10. 10.
    Hayes, W.: The Genetics of Bacteria and their Viruses. Oxford and Edinburgh: Blackwell, 1968Google Scholar
  11. 11.
    Keller, W.: Determination of the number of superhelical turns in simian virus 40 DNA by gel electrophoresis. Proc. Natl. Acad. Sci. USA72, 4876–4880 (1975)CrossRefGoogle Scholar
  12. 12.
    Kornberg, A.: DNA Synthesis. San Francisco: Freeman, 1974Google Scholar
  13. 13.
    Lehninger, A. L.: Biochemistry (2nd edition). New York: Worth, 1975Google Scholar
  14. 14.
    Liu, L. F., Depew, R. E., Wang, J. C.: Knotted single-stranded DNA rings: A novel topological isomer of circular single-stranded DNA formed by treatment withEscherichia coli ω protein. J. Mol. Biol.106, 439–452 (1976)CrossRefGoogle Scholar
  15. 15.
    Liu, L. F., Wang, J. C.: On the degree of unwinding of the DNA helix by ethidium II. Studies by electron microscopy. Biochim. et Biophys. Acta395, 405–412 (1975)Google Scholar
  16. 16.
    Parker, D. L., Glaser, D. A.: Effect of growth conditions on DNA-membrane attachment inEscherichia coli. Proc. Natl. Acad. Sci. USA72, 2446–2450 (1975)CrossRefGoogle Scholar
  17. 17.
    Pohl, W. F.: The self-linking number of a closed space curve. Journal of Mathematics and Mechanics17, 975–986 (1968)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Pulleyblank, D. E., Shure, M., Tang, D., Vinograd, J., Vosberg, H.-P.: Action of nicking-closing enzyme on supercoiled and nonsupercoiled closed circular DNA: Formation of a Boltzmann distribution of topological isomers. Proc. Natl. Acad. Sci. USA72, 4280–4284 (1975)CrossRefGoogle Scholar
  19. 19.
    Rodley, G. A., Scobie, R. S., Bates, R. H. T., Lewitt, R. M.: A possible conformation for double-stranded polynucleotides. Proc. Natl. Acad. Sci. USA73, 2959–2963 (1976)CrossRefGoogle Scholar
  20. 20.
    Wang, J. C.: Variation of the average rotation angle of the DNA helix and the superhelical turns of covalently closed cyclic λ DNA. J. Mol. Biol.43, 25–39 (1969)CrossRefGoogle Scholar
  21. 21.
    Wang, J. C.: Degree of superhelicity of covalently closed cyclic DNA's fromEscherichia coli. J. Mol. Biol.43, 263–272 (1969)CrossRefGoogle Scholar
  22. 22.
    Wang, J. C.: Interaction between DNA and anEscherichia coli protein ω. J. Mol. Biol.55, 523–533 (1971)CrossRefGoogle Scholar
  23. 23.
    Wang, J. C.: The degree of unwinding of the DNA helix by ethidium I. Titration of twisted PM2 DNA molecules in alkaline cesium chloride density gradients. J. Mol. Biol.89, 783–801 (1974)CrossRefGoogle Scholar
  24. 24.
    Wang, J. C., Liu, L.: DNA topoisomerases: enzymes which catalyse the concerted breaking and rejoining of DNA backbone bonds. (To appear)Google Scholar
  25. 25.
    Watson, J. D.: Molecular Biology of the Gene (3rd edition). Menlo Park, Calif.: Benjamin, 1976Google Scholar
  26. 26.
    White, J. H.: Self-linking and the Gauss integral in higher dimensions. American Journal of Mathematics91, 693–728 (1969)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • William F. Pohl
    • 1
  • George W. Roberts
    • 2
  1. 1.Department of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of PhilosophyDuke UniversityDurhamUSA

Personalised recommendations