Lifting the curtain: Using topology to probe the hidden action of enzymes

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Volumn 34, Issue , 1996, Pages 51-76

  Sumners, De Witt ^a  

^a NONE

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EID: 0013166073     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (57)

1. Adams, C., 1994, The Knot Book: An Elementary Introduction to Mathematical Theory of Knots, New York: W.H. Freeman.
2. Kauffman, L.H., 1987, On Knots, Princeton, N.J.: Princeton University Press.
3. Livingston, C., 1994, Knot Theory, Carus Mathematical Monograph, Vol. 24, Washington, D.C.: Mathematical Association of America.
4. Rolfsen, D., 1990, Knots and Links, Berkeley, Calif.: Publish or Perish, Inc. Each of these mathematics books has an easygoing, reader-friendly style and numerous pictures, a very important commodity when one is trying to understand knot theory. Application of Geometry and Topology to Biology
5. Bauer, W.R., F.H.C. Crick, and J.H. White, 1980, "Supercoiled DNA," Scientific American 243, 100-113. This paper is a very nice introduction to the description and measurement of DNA supercoiling.
6. Sumners, D.W., 1987, "The role of knot theory in DNA research," pp. 297-318 in Geometry and Topology, C. McCrory and T. Shifrin (eds.), New York: Marcel Dekker.
7. Sumners, D.W., 1990, "Untangling DNA," The Mathematical Intelligencer 12, 71-80. These papers are expository articles written for a mathematical audience. The first gives an overview of knot theory and DNA, and the second describes the tangle model.
8. Sumners, D.W. (ed.), 1994, New Scientific Applications of Geometry and Topology. Proceedings of Symposia in Applied Mathematics, Vol. 45, Providence, R.I.: American Mathematical Society. This volume contains six expository papers outlining new applications of geometry and topology in molecular biology, chemistry, polymers, and physics. Three of the papers concern DNA applications.
9. Walba, D.M., 1985, "Topological stereochemistry," Tetrahedron 41, 3161-3212. This paper is written by a chemist and describes topological ideas in synthetic chemistry and molecular biology. It is a good place to witness the translation of technical terms of science to mathematical concepts, and vice versa.
10. Wang. J.C., 1982. "DNA topoisomerases," Scientific American 247, 94-109. This paper describes how topoisomerases act to control DNA geometry and topology in various life processes in the cell.
11. Wasserman, S.A., and N.R. Cozzarelli, 1986. "Biochemical topology: Applications to DNA recombination and replication." Science 232, 951-960. This paper describes the topological approach to enzymology protocol and reviews the results of various experiments on topoisomerases and recombinases.
12. White, J.H., 1989, "An introduction to the geometry and topology of DNA structure." pp. 225-253 in Mathematical Methods for DNA Sequences, M.S. Waterman (ed.), Boca Raton, Fla.: CRC Press. This is a very nice introductory mathematical treatment of linking number, twist, and writhe, with DNA applications.
13. Abremski, K., B. Frommer, and R.H. Hoess, 1986, "Linking-number changes in the DNA substrate during Cre-mediated loxP site-specific recombination," Journal of Molecular Biology 192, 17-26.
14. Benjamin, H.W., and N.R. Cozzarelli, 1990, "Geometric arrangements of Tn3 resolvase sites," J. Biol. Chem. 265, 6441-6447.
15. Burde, G., and H. Zieschang, 1985, Knots, New York: W. De Gruyter.
16. Conway, J.H., 1970, "An enumeration of knots and links and some of their related properties," pp. 329-358 in Computational Problems in Abstract Algebra; Proceedings of a Conference at Oxford 1967, Oxford: Pergamon Press.
17. Cozzarelli, N.R., 1992, "The biological roles of DNA topology," in New Scientific Applications of Geometry and Topology, Proceedings of Symposia in Applied Mathematics, D.W. Sumners (ed.), Providence, R.I.: American Mathematical Society.
18. Cozzarelli, N.R., M.A. Krasnow, S.P. Gerrard, and J.H. White, 1984, "A topological treatment of recombination and topoisomerases," Cold Spring Harbor Symp. Quant. Biol. 49, 383-400.
19. Crowell, R.H., and R.H. Fox, 1977, Introduction to Knot Theory. Graduate Texts in Mathematics 57, New York: Springer-Verlag.
20. Culler, M.C., C.M. Gordon, J. Luecke, and P.B. Shalen, 1987, "Dehn surgery on knots," Ann. Math. 125, 237-300.
21. Dean, F.B., A. Stasiak, T. Koller, and N.R. Cozzarelli, 1985, "Duplex DNA knots produced by Escherichia coli topoisomerase I," J. Biol. Chem. 260, 4975-4983.
22. Droge, P., and N.R. Cozzarelli, 1989, "Recombination of knotted substrates by Tn3 resolvase," Proceedings of the National Academy of Sciences USA 86, 6062-6066.
23. Englund, P.T., S.L. Hajduk, and J.C. Marini, 1982, "The molecular biology of trypanosomes," Annu. Rev. Biochem. 51, 695-726.
24. Ernst, C., and D.W. Sumners, 1987, "The growth of the number of prime knots," Math. Proc. Cambridge Philos. Soc. 102, 303-315.
25. Ernst, C., and D.W. Sumners, 1990, "A calculus for rational tangles: Applications to DNA recombination," Math. Proc. Cambridge Philos. Soc. 108, 489-515.
26. Griffith, J.D., and H.A. Nash, 1985, "Genetic rearrangement of DNA induces knots with a unique topology: Implications for the mechanism of synapsis and crossing-over," Proceedings of the National Academy of Sciences USA 82, 3124-3128.
27. Heichman, K.A., and R.C. Johnson, 1990, "The Hin invertasome: Protein-mediated joining of distant recombination sites at the enhancer," Science 249, 511-517.
28. Kanaar, R., P. van de Putte, and N.R. Cozzarelli, 1988, "Gin-mediated DNA inversion: Product structure and the mechanism of strand exchange," Proceedings of the National Academy of Sciences USA 85, 752-756.
29. Kanaar, R., A. Klippel, E. Shekhtman, J.M. Dungan, R. Kahmann, and N.R. Cozzarelli, 1990, "Processive recombination by the phage Mu gin system: Implications for mechanisms of DNA exchange, DNA site alignment, and enhancer action," Cell 62, 353-366.
30. Kauffman, L.H., 1987, On Knots, Princeton, N.J.: Princeton University Press.
31. Kim, S., and A. Landy, 1992, "Lambda Int protein bridges between higher order complexes at two distant chromosomal loci attL and attR," Science 256, 198-203.
32. Krasnow, M.A., A. Stasiak, S.J. Spengler, F. Dean, T. Koller, and N.R. Cozzarelli, 1983, "Determination of the absolute handedness of knots and catenanes of DNA," Nature 304, 559-560.
33. 3," J. London Math. Soc. 30, 512-520.
34. Langer, J., and D.A. Singer, 1985, "Curve straightening and a minimax argument for closed elastic curves," Topology 24, 75-88.
35. Lickerish, W.B.R., 1981, "Prime knots and tangles," Trans. Am. Math. Soc. 267, 321-332.
36. Lickorish, W.B.R., 1988, "Polynomials for links," Bull. London Math. Soc. 20, 558-588.
37. Marini, J.C., K.G. Miller, and P.T. Englund, 1980, "Decatenation of kinetoplast DNA by topoisomerases," J. Biol. Chem. 255, 4976-4979.
38. Pollock, T.J., and H.A. Nash, 1983, "Knotting of DNA caused by genetic rearrangement: Evidence for a nucleosome-like structure in site-specific recombination of bacteriophage lambda," Journal of Molecular Biology 170, 1-18.
39. Rauch, C.A., P.T. Englund, S.J. Spengler, N.R. Cozzarelli, and J.H. White, 1994, "Kinetoplast DNA: Structure and replication," (in preparation).
40. Rolfsen, D., 1990, Knots and Links, Berkeley, Calif: Publish or Perish, Inc.
41. Ryan, K.A., T.A. Shapiro, C.A. Rauch, J.D. Griffith, and P.T. Englund, 1988, "A knotted free minicircle in kinetoplast DNA," Proceedings of the National Academy of Sciences USA 85, 5844-5848.
42. Sherratt, D., P. Dyson, M. Boocock, L. Brown, D. Summers, G. Stewart, and P. Chan, 1984, "Site-specific recombination in transposition and plasmid stability," Cold Spring Harbor Symp. Quant. Biol. 49, 227-233.
43. Shishido, K., N. Komiyama, and S. Ikawa, 1987, "Increased production of a knotted form of plasmid pBR322 DNA in Escherichia coli DNA topoisomerase mutants," Journal of Molecular Biology 195, 215-218.
44. Spengler, S.J., A. Stasiak, and N.R. Cozzarelli, 1984, "Quantitative analysis of the contributions of enzyme and DNA to the structure of lambda integrative recombinants," Cold Spring Harbor Symp. Quant. Biol. 49, 745-749.
45. Spengler, S.J., A. Stasiak, and N.R. Cozzarelli, 1985, "The stereostructure of knots and catenanes produced by phage lambda integrative recombination: Implications for mechanism and DNA structure," Cell 42, 325-334.
46. Stark, W.M.. D.J. Sherratt, and M.R. Boocock, 1989. "Site-specific recombination by Tn3 resolvase: Topological changes in the forward and reverse reactions." Cell 58, 779-790.
47. Sumners, D.W., 1987a, "Knots, macromolecules and chemical dynamics," pp. 297-318 in Graph Theory and Topology in Chemistry, King and Rouvray (eds.), New York: Elsevier.
48. Sumners, D.W., 1987b, "The role of knot theory in DNA research," pp. 297-318 in Geometry and Topology, C. McCrory and T. Shifrin (eds.), New York: Marcel Dekker.
49. Sumners, D.W., 1990, "Untangling DNA," The Mathematical Intelligencer 12, 71-80.
50. Sumners, D.W., 1992 "Knot theory and DNA," in New Scientific Applications of Geometry and Topology, Proceedings of Symposia in Applied Mathematics, Vol. 45, D.W. Sumners (ed.), Providence, R.I.: American Mathematical Society.
51. Sumners, D.W., C.E. Ernst, N.R. Cozzarelli, and S.J. Spengler, 1994, "The tangle model for enzyme mechanism," (in preparation).
52. Wang, J.C., 1982, "DNA topoisomerases," Scientific American 247, 94-109.
53. Wang, J.C., 1985, "DNA topoisomerases," Annu. Rev. Biochem. 54, 665-697.
54. Wasserman, S.A., and N.R. Cozzarelli, 1985, "Determination of the stereostructure of the product of Tn3 resolvase by a general method," Proceedings of the National Academy of Sciences USA 82, 1079-1083.
55. Wasserman, S.A., J.M. Dungan, and N.R. Cozzarelli, 1985, "Discovery of a predicted DNA knot substantiates a model for site-specific recombination," Science 229, 171-174.
56. Wasserman, S.A., and N.R. Cozzarelli, 1986, "Biochemical topology: Applications to DNA recombination and replication," Science 232, 951-960.
57. White, J.H., K.C. Millett, and N.R. Cozzarelli, 1987, "Description of the topological entanglement of DNA catenanes and knots by a powerful method involving strand passage and recombination," Journal of Molecular Biology 197, 585-603.