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The Algebra of Gene Assembly in Ciliates

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Discrete and Topological Models in Molecular Biology

Part of the book series: Natural Computing Series ((NCS))

Abstract

The formal theory of intramolecular gene assembly in ciliates is fitted into the well-established theories of Euler circuits in 4-regular graphs, principal pivot transformations, and delta-matroids.

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References

  1. M. Aigner, The Penrose polynomial of graphs and matroids, in Surveys in Combinatorics, vol 288, ed. by J.W.P. Hirschfeld. London Mathematical Society Lecture Note Series (Cambridge University Press, Cambridge, 2001), pp. 11–46. doi:10.1017/CBO9780511721328.004

    Google Scholar 

  2. M. Aigner, H. van der Holst, Interlace polynomials. Linear Algebra Appl. 377, 11–30 (2004). doi:10.1016/j.laa.2003.06.010

    Article  MATH  Google Scholar 

  3. A. Angeleska, N. Jonoska, M. Saito, DNA recombination through assembly graphs. Discret. Appl. Math. 157(14), 3020–3037 (2009). doi:10.1016/j.dam.2009.06.011

    Article  MATH  MathSciNet  Google Scholar 

  4. R. Arratia, B. Bollobás, G. Sorkin, The interlace polynomial of a graph. J. Comb. Theory B 92(2), 199–233 (2004). doi:10.1016/j.jctb.2004.03.003

    Article  MATH  Google Scholar 

  5. A. Bouchet, Isotropic systems. Eur. J. Comb. 8, 231–244 (1987). doi:10.1016/S0195-6698(87)80027-6

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Bouchet, Representability of Δ-matroids, in Proceedings of the 6th Hungarian Colloquium of Combinatorics, Colloquia Mathematica Societatis János Bolyai, Eger, vol. 52 (North-Holland, 1987), pp. 167–182

    Google Scholar 

  7. A. Bouchet, Graphic presentations of isotropic systems. J. Comb. Theory B 45(1), 58–76 (1988). doi:10.1016/0095-8956(88)90055-X

    Article  MATH  MathSciNet  Google Scholar 

  8. A. Bouchet, Tutte-Martin polynomials and orienting vectors of isotropic systems. Graphs Comb. 7(3), 235–252 (1991). doi:10.1007/BF01787630

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Bouchet, A. Duchamp, Representability of Δ-matroids over GF(2). Linear Algebra Appl. 146, 67–78 (1991). doi:10.1016/0024-3795(91)90020-W

    Article  MATH  MathSciNet  Google Scholar 

  10. R. Brijder, H. Hoogeboom, The fibers and range of reduction graphs in ciliates. Acta Inform. 45, 383–402 (2008). doi:10.1007/s00236-008-0074-3

    Article  MATH  MathSciNet  Google Scholar 

  11. R. Brijder, H. Hoogeboom, Interlace polynomials for delta-matroids (2010). [arXiv:1010.4678]

    Google Scholar 

  12. R. Brijder, H. Hoogeboom, The group structure of pivot and loop complementation on graphs and set systems. Eur. J. Comb. 32, 1353–1367 (2011). doi:10.1016/j.ejc.2011.03.002

    Article  MATH  MathSciNet  Google Scholar 

  13. R. Brijder, H. Hoogeboom, Nullity invariance for pivot and the interlace polynomial. Linear Algebra Appl. 435, 277–288 (2011). doi:10.1016/j.laa.2011.01.024

    Article  MATH  MathSciNet  Google Scholar 

  14. R. Brijder, H. Hoogeboom, Bicycle matroids and the Penrose polynomial for delta-matroids (2012). [arXiv:1210.7718]

    Google Scholar 

  15. R. Brijder, H. Hoogeboom, Binary symmetric matrix inversion through local complementation. Fundam. Inform. 116(1–4), 15–23 (2012). doi:10.3233/FI-2012-664

    MATH  MathSciNet  Google Scholar 

  16. R. Brijder, M. Daley, T. Harju, N. Jonoska, I. Petre, G. Rozenberg, Computational nature of gene assembly in ciliates, in Handbook of Natural Computing, ed. by G. Rozenberg, T. Bäck, J. Kok, vol. 3 (Springer, Berlin/London, 2012), pp. 1233–1280. doi:10.1007/978-3-540- 92910-9_37

    Google Scholar 

  17. R. Brijder, T. Harju, H. Hoogeboom, Pivots, determinants, and perfect matchings of graphs. Theor. Comput. Sci. 454, 64–71 (2012). doi:10.1016/j.tcs.2012.02.031

    Article  MATH  MathSciNet  Google Scholar 

  18. R. Cottle, J.S. Pang, R. Stone, The Linear Complementarity Problem (Academic, San Diego, 1992)

    MATH  Google Scholar 

  19. A. Ehrenfeucht, I. Petre, D. Prescott, G. Rozenberg, Circularity and other invariants of gene assembly in ciliates, in Words, Semigroups, and Transductions, ed. by M. Ito et al. (World Scientific, Singapore, 2001), pp. 81–97. doi:10.1142/9789812810908_0007

    Google Scholar 

  20. A. Ehrenfeucht, T. Harju, I. Petre, G. Rozenberg, Characterizing the micronuclear gene patterns in ciliates. Theory Comput. Syst. 35, 501–519 (2002). doi:10.1007/s00224-002-1043-9

    Article  MATH  MathSciNet  Google Scholar 

  21. A. Ehrenfeucht, I. Petre, D. Prescott, G. Rozenberg, String and graph reduction systems for gene assembly in ciliates. Math. Struct. Comput. Sci. 12, 113–134 (2002). doi:10.1017/ S0960129501003516

    Article  MATH  MathSciNet  Google Scholar 

  22. A. Ehrenfeucht, T. Harju, I. Petre, D. Prescott, G. Rozenberg, Formal systems for gene assembly in ciliates. Theor. Comput. Sci. 292, 199–219 (2003). doi:10.1016/S0304-3975(01)00223-7

    Article  MATH  MathSciNet  Google Scholar 

  23. A. Ehrenfeucht, T. Harju, I. Petre, D. Prescott, G. Rozenberg, Computation in Living Cells – Gene Assembly in Ciliates (Springer, Berlin/New York, 2004)

    Book  MATH  Google Scholar 

  24. J. Ellis-Monaghan, C. Merino, Graph polynomials and their applications I: the Tutte polynomial, in Structural Analysis of Complex Networks, ed. by M. Dehmer (Birkhäuser, Boston, 2011), pp. 219–255. doi:10.1007/978-0-8176-4789-6_9

    Chapter  Google Scholar 

  25. J. Ellis-Monaghan, C. Merino, Graph polynomials and their applications II: Interrelations and interpretations, in Structural Analysis of Complex Networks, ed. by M. Dehmer (Birkhäuser, Boston, 2011), pp. 257–292. doi:10.1007/978-0-8176-4789-6_10

    Chapter  Google Scholar 

  26. J. Geelen, A generalization of Tutte’s characterization of totally unimodular matrices. J. Comb. Theory B 70, 101–117 (1997). doi:10.1006/jctb.1997.1751

    Article  MATH  MathSciNet  Google Scholar 

  27. F. Genest, Graphes eulériens et complémentarité locale. Ph.D. thesis, Université de Montréal, 2002. Available online: arXiv:math/0701421v1

    Google Scholar 

  28. R. Glantz, M. Pelillo, Graph polynomials from principal pivoting. Discret. Math. 306(24), 3253–3266 (2006). doi:10.1016/j.disc.2006.06.003

    Article  MATH  MathSciNet  Google Scholar 

  29. T. Harju, C. Li, I. Petre, G. Rozenberg, Parallelism in gene assembly. Nat. Comput. 5(2), 203–223 (2006). doi:10.1007/s11047-005-4462-0

    Article  MATH  MathSciNet  Google Scholar 

  30. F. Jaeger, On transition polynomials of 4-regular graphs, in Cycles and Rays, ed. by G. Hahn, G. Sabidussi, R. Woodrow. NATO ASI Series, vol. 301 (Kluwer, Dordrecht, 1990), pp. 123–150. doi:10.1007/978-94-009-0517-7_12

    Google Scholar 

  31. A. Kotzig, Eulerian lines in finite 4-valent graphs and their transformations, in Theory of Graphs, Proceedings of the Colloquium, Tihany, 1966 (Academic, New York, 1968), pp. 219–230

    Google Scholar 

  32. P. Martin, Enumérations eulériennes dans les multigraphes et invariants de Tutte-Grothendieck. Ph.D. thesis, Institut d’Informatique et de Mathématiques Appliquées de Grenoble (IMAG), 1977. Available online: http://tel.archives-ouvertes.fr/tel-00287330_v1/

  33. S. Oum, Rank-width and vertex-minors. J. Comb. Theory B 95(1), 79–100 (2005). doi:10.1016/ j.jctb.2005.03.003

    Article  MATH  MathSciNet  Google Scholar 

  34. T. Parsons, Applications of principal pivoting, in Proceedings of the Princeton Symposium on Mathematical Programming, ed. by H. Kuhn (Princeton University Press, Princeton, 1970), pp. 567–581

    Google Scholar 

  35. R. Penrose, Applications of negative dimensional tensors, in Combinatorial Mathematics and Its Applications, Oxford, ed. by D. Welsh (Academic, 1971), pp. 211–244

    Google Scholar 

  36. P. Pevzner, Computational Molecular Biology: An Algorithmic Approach (The MIT Press, Cambridge, MA/ London, 2000)

    Google Scholar 

  37. D. Prescott, Genome gymnastics: unique modes of DNA evolution and processing in ciliates. Nat. Rev. 1, 191–199 (2000). doi:10.1038/35042057

    Article  Google Scholar 

  38. D. Prescott, A. Greslin, Scrambled Actin I gene in the micronucleus of Oxytricha nova. Dev. Genet. 13, 66–74 (1992). doi:10.1002/dvg.1020130111

    Article  Google Scholar 

  39. D. Prescott, A. Ehrenfeucht, G. Rozenberg, Molecular operations for DNA processing in hypotrichous ciliates. Eur. J. Protistol. 37, 241–260 (2001). doi:10.1078/0932-4739-00807

    Article  Google Scholar 

  40. J. Schur, Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind. Journal für die reine und angewandte Mathematik 147, 205–232 (1917). http://resolver.sub.uni-goettingen.de/purl?PPN243919689_0147

    Google Scholar 

  41. L. Traldi, L. Zulli, A bracket polynomial for graphs, I. J. Knot Theory Ramif. 18(12), 1681–1709 (2009). doi:10.1142/S021821650900766X

    Article  MATH  MathSciNet  Google Scholar 

  42. M. Tsatsomeros, Principal pivot transforms: properties and applications. Linear Algebra Appl. 307(1–3), 151–165 (2000). doi:10.1016/S0024-3795(99)00281-5

    Article  MATH  MathSciNet  Google Scholar 

  43. A. Tucker, A combinatorial equivalence of matrices, in Combinatorial Analysis, Proceedings of Symposia in Applied Mathematics, vol. X, Columbia University, 24–26 April 1958 (American Mathematical Society, 1960), pp. 129–140. doi:10.1090/psapm/010

    Google Scholar 

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Author information

Authors and Affiliations

  1. Hasselt University, Diepenbeek, Belgium

    Robert Brijder

  2. Transnational University of Limburg, Diepenbeek, Belgium

    Robert Brijder

  3. Leiden Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands

    Hendrik Jan Hoogeboom

Authors
  1. Robert Brijder
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  2. Hendrik Jan Hoogeboom
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Correspondence to Hendrik Jan Hoogeboom .

Editor information

Editors and Affiliations

  1. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Nataša Jonoska

  2. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Masahico Saito

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Brijder, R., Hoogeboom, H.J. (2014). The Algebra of Gene Assembly in Ciliates. In: Jonoska, N., Saito, M. (eds) Discrete and Topological Models in Molecular Biology. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40193-0_13

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  • DOI: https://doi.org/10.1007/978-3-642-40193-0_13

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