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DNA and differential geometry

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References

  1. Bauer, W. R., Crick, F. H. C., White, J. H.: Supercoiled DNA.Scient. Am. 243, 118–133 (July, 1980)

    Google Scholar 

  2. Brown, P. O., Cozzarelli, N. R.: A sign inversion mechanism for enzymatic supercoiling of DNA.Science 206, 1081–1083 (30. Nov. 1979)

    Article  Google Scholar 

  3. Calugareanu, G.: Sur les classes ďisotopie des noeuds tridimensonnels et leurs invariants.Czechoslovak Math. J. 11, 588–625 (1961)

    MathSciNet  Google Scholar 

  4. Crick, F. H. C.: Linking numbers and nucleosomes.Proc. Natl. Acad. Sci. USA 73, 2639–2643 (1976)

    Article  MathSciNet  Google Scholar 

  5. Cozzarelli, N. R.: DNA gyrase and the supercoiling of DNA.Science 207, 953–960 (29. February 1980)

    Article  Google Scholar 

  6. Frank-Kamenetskii, M. D., Lukashin, A. V., Vologodski, A. V.: Statistical mechanics and topology of polymer chains.Nature 258, 298–402 (1975)

    Article  Google Scholar 

  7. Fuller, F. B.: The writhing number of a space curve.Proc. Natl. Acad. Sci. USA 68, 815–819 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  8. Fuller, F. B.: Decomposition of the linking number of a closed ribbon: A problem from molecular biology.Proc. Natl. Acad. Sci. USA 75, 3557 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hsieh, T.-S., Brutlag, D.: ATP-dependent DNA topoisomerase from D. melanogaster reversibly catenates duplex DNA rings.Cell 21, 115–125 (1980)

    Article  Google Scholar 

  10. Klotz, G., Kleinschmidt, A. K., Goebel, W.: Counting super- helical turns in electron micrographs of large plasmids.Ninth International Congress on Electron Microscopy, Toronto 1978, 2, 196–197

    Google Scholar 

  11. Liu, L. F., Wang, J. C.: On the degree of unwinding of the DNA helix by ethidium. II. Studies by electron microscopy.Biochim. etBiophys. Acta 395, 405–412 (1975)

    Article  Google Scholar 

  12. Pohl, W. F.: Some integral formulas for space curves and their generalization.Amer. J. of Math. 90, 1321–1345 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  13. Pohl, W. F.: The self-linking number of a closed space curve.J. of Math. and Mech. 17, 975–986 (1968)

    MATH  MathSciNet  Google Scholar 

  14. Pohl, W. F.: The probability of linking of random closed curves. To appear in Geometry Symposium, Utrecht. On the occasion of N. A. Kuiper’s 60th birthday.Lecture Notes in Mathematics. Springer, Berlin Heidelberg New York

  15. Pohl, W. F., Roberts, G. W.: Topological considerations in the theory of replication of DNA.J. Math. Biology 6, 383–402 (1978)

    Article  MathSciNet  Google Scholar 

  16. Rodley, G. A., Scobie, R. S., Bates, R. H. T., Lewitt, R. M.: A possible conformation for double-stranded polynucleotides.Proc. Natl. Acad. Sci. USA 73, 2959–2963 (1976)

    Article  Google Scholar 

  17. Sasisekharan, V., Pattabiraman, N., Gupta, G.: Some implications of an alternative structure for DNA.Proc. Natl. Acad. Sci. USA 75, 4092–4096 (1978)

    Article  Google Scholar 

  18. Stettler, V. H., Weber, H., Koller, T., Weissmann, C.: Preparation and characterization of form V DNA, the duplex DNA resulting from association of complementary circular single- stranded DNA.J. Molec. Biology 131, 21–40 (1979)

    Article  Google Scholar 

  19. Wang, A. H.-J., Quigley, G. J., Kolpak, F. J., Crawford, J. L., Van Boom, J. H., Van der Marel, G., Rich, A.: Molecular structure of a left-handed double helical DNA fragment at atomic resolution.Nature 282, 680–686 (1979)

    Article  Google Scholar 

  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. Biology 43, 25–39 (1969)

    Article  Google Scholar 

  21. 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)

    Article  Google Scholar 

  22. Wang, J. C.: Helical repeat of DNA in solution.Proc. Natl. Acad. Sci. USA 76, 200–203 (1979)

    Article  Google Scholar 

  23. White, J. H.: Self-linking and the Gauss integral in higher dimensions.Amer. J. of Math. 91, 693–728 (1969)

    Article  MATH  Google Scholar 

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  1. Department of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA

    William F. Pohl

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Pohl, W.F. DNA and differential geometry. The Mathematical Intelligencer 3, 20–27 (1980). https://doi.org/10.1007/BF03023391

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