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Algebraic and Topological Models for DNA Recombinant Processes

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3340))

Abstract

We propose algebraic and topological techniques that could be employed for studying recombinant DNA processes. We show that sequence of splices performed by the operation hi-excision/reinsertion on one DNA molecule can be modeled by the elements of a semidirect product of n-copies of the cyclic group of order 2 and the symmetric group S n . We associate a surface in space-time (subspace of ℝ3 ×[0,1]) with a sequence of splicings on circular molecules and present examples of applications of this model.

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References

  1. Carter, J.S., Saito, M.: Knotted surfaces and their diagrams, the American Mathematical Society (1998)

    Google Scholar 

  2. Darcy, I.K.: Biological distances on DNA knots and links: applications to XER recombination. In: Knots in Hellas 1998, vol.2 (Delphi). J. Knot Theory Ramifications, vol. 10(2), pp. 269–294 (2001)

    Google Scholar 

  3. Ehrenfeucht, A., Harju, T., Petre, I., Prescot, D.M., Rozenberg, G.: Computation in living cells-gene assembly in ciliates. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  4. Flapan, E.: When topology meets chemistry. In: A topological look at molecular chirality. Outlooks. Mathematical Association of America, Washington, DC. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  5. Freyd, P.J., Yetter, D.N.: Braided compact closed categories with applications to low-dimensional topology. Adv. Math. 77(2), 156–182 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  6. Garside, F.: The braid group and other groups. Quart. J. Math. Oxford 20(2), 235–254 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  7. Garzon, M., Jonoska, N., Karl, S.A.: Bounded Complexity of DNA Computing. BioSystems 52, 63–72 (1999)

    Article  Google Scholar 

  8. Head, T., Paun, Gh., Pixton, D.: Language theory and molecular genetics. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of formal languages, Vol.II, pp. 295–358. Springer, Heidelberg (1997)

    Google Scholar 

  9. Hosokawa, F., Kawauchi, A., Nakanishi, Y., Sakuma, M.: Note on critical points of surfaces in 4-space. Kobe J. Math. 1(20), 151–152 (1984)

    MATH  MathSciNet  Google Scholar 

  10. Joyal, A., Street, R.: Braided tensor categories. Adv. Math. 102(1), 20–78 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kawauchi, A.: A survey of knot theory. In: Translated and revised from the 1990 Japanese original by the author, Birkhäuser Verlag, Basel (1996)

    Google Scholar 

  12. Kawauchi, A.: On the integral homology of infinite cyclic coverings of links. Kobe J. Math. 4(1), 31–41 (1987)

    MATH  MathSciNet  Google Scholar 

  13. Kronheimer, P.B., Mrowka, T.S.: Gauge theory for embedded surfaces, I. Topology 32, 773–826 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  14. Landweber, L.F., Kari, L.: The evolution of cellular computing: nature’s solution to a computational problem. BioSystems 52, 3–13 (1999)

    Article  Google Scholar 

  15. Landweber, L.F., Kari, L.: Universal molecular computation in ciliates. In: Landweber, L., Winfree, E. (eds.) Evolution as Computation. Springer, Heidelberg (1999)

    Google Scholar 

  16. Magnus, W., Karrass, A., Solitar, D.: Combinatorial group theory. Presentations of groups in terms of generators and relations. Second revised edition. Dover Publications, Inc., New York (1976)

    MATH  Google Scholar 

  17. Mac Lane, S.: Categories for the working mathematician. In: Graduate Texts in Mathematics. Second edition, vol. 5, Springer-Verlag, New York (1998)

    Google Scholar 

  18. Munkres, J.R.: Topology, 2nd edn. Prentice-Hall, Englewood Cliffs (2000) (first edition 1975)

    MATH  Google Scholar 

  19. Ozsvath, P., Szabo, Z.: Knot Floer homology and the four-ball genus, Geom. Topol. 7, 615–639 (2003)

    MATH  MathSciNet  Google Scholar 

  20. Paun, Gh., Rozenberg, G., Salomaa, A.: DNA Computing, new computing paradigms. Springer, Heidelberg (1998)

    MATH  Google Scholar 

  21. Rasmussen, J.A.: Khovanov homology and the slice genus, Preprint, available at: http://xxx.lanl.gov/abs/math.GT0402131

  22. Rolfsen, D.: Knots and links. Mathematics Lecture Series, vol. 7. Perish, Inc., Berkeley (1976)

    MATH  Google Scholar 

  23. Roseman, D.: Twisting and turning in four dimensions, a video made at Geometry Center (1993)

    Google Scholar 

  24. Sumners, D.W.: Untangling DNA. Math. Intelligencer 12(3), 71–80 (1990)

    Article  MATH  MathSciNet  Google Scholar 

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Jonoska, N., Saito, M. (2004). Algebraic and Topological Models for DNA Recombinant Processes. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds) Developments in Language Theory. DLT 2004. Lecture Notes in Computer Science, vol 3340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30550-7_5

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  • DOI: https://doi.org/10.1007/978-3-540-30550-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24014-3

  • Online ISBN: 978-3-540-30550-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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