DNA and differential geometry. (English) Zbl 0447.92013

Pohl, William F.

Math. Intell. 3, 20-27 (1980).

MSC:

92D10	Genetics and epigenetics
53C99	Global differential geometry

Keywords:

spatial structure of DNA

Citations:

Zbl 0193.509

References:

[1]	Bauer, W. R., Crick, F. H. C., White, J. H.: Supercoiled DNA.Scient. Am. 243, 118–133 (July, 1980)
[2]	Brown, P. O., Cozzarelli, N. R.: A sign inversion mechanism for enzymatic supercoiling of DNA.Science 206, 1081–1083 (30. Nov. 1979)
[3]	Calugareanu, G.: Sur les classes ďisotopie des noeuds tridimensonnels et leurs invariants.Czechoslovak Math. J. 11, 588–625 (1961) · Zbl 0118.16005
[4]	Crick, F. H. C.: Linking numbers and nucleosomes.Proc. Natl. Acad. Sci. USA 73, 2639–2643 (1976)
[5]	Cozzarelli, N. R.: DNA gyrase and the supercoiling of DNA.Science 207, 953–960 (29. February 1980)
[6]	Frank-Kamenetskii, M. D., Lukashin, A. V., Vologodski, A. V.: Statistical mechanics and topology of polymer chains.Nature 258, 298–402 (1975)
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[9]	Hsieh, T.-S., Brutlag, D.: ATP-dependent DNA topoisomerase from D. melanogaster reversibly catenates duplex DNA rings.Cell 21, 115–125 (1980)
[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
[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)
[12]	Pohl, W. F.: Some integral formulas for space curves and their generalization.Amer. J. of Math. 90, 1321–1345 (1968) · Zbl 0181.50303
[13]	Pohl, W. F.: The self-linking number of a closed space curve.J. of Math. and Mech. 17, 975–986 (1968) · Zbl 0164.54005
[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)
[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)
[17]	Sasisekharan, V., Pattabiraman, N., Gupta, G.: Some implications of an alternative structure for DNA.Proc. Natl. Acad. Sci. USA 75, 4092–4096 (1978)
[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)
[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)
[20]	Wang, J. C.: Variation of the average rotation angle of the DNA helix and the superhelical turns of covalently closed cyclic {\(\lambda\)} DNA.J. Mol. Biology 43, 25–39 (1969)
[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)
[22]	Wang, J. C.: Helical repeat of DNA in solution.Proc. Natl. Acad. Sci. USA 76, 200–203 (1979)
[23]	White, J. H.: Self-linking and the Gauss integral in higher dimensions.Amer. J. of Math. 91, 693–728 (1969) · Zbl 0193.50903