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Introduction to DNA Topology

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Discrete and Topological Models in Molecular Biology

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

Abstract

In this expository chapter we give an elementary introduction to DNA and to proteins that can knot and link circular DNA, with a special focus on recombination. We also describe the Ernst and Sumners tangle model of the action of proteins on circular DNA.

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Notes

  1. 1.

    The rational numbers plus infinity.

References

  1. C. Adams, The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots (American Mathematical Society, Providence, RI, 2004)

    Google Scholar 

  2. A. Akopian, S. Gourlay, H. James, S.D. Colloms, Communication between accessory factors and the Cre recombinase at hybrid psi-loxP sites. J. Mol. Biol. 357(5), 1394–1408 (2006)

    Article  Google Scholar 

  3. P. Argos, A. Landy, K. Abremski, J.B. Egan, E. Haggard-Ljungquist, R.H. Hoess, M.L. Kahn, B. Kalionis, S.V.L. Narayana, L.S. Pierson, N. Sternberg, J.M. Leong, The integrase family of site-specific recombinases: regional similarities and global diversity. EMBO J. 5(2), 433–440 (1986)

    Google Scholar 

  4. A.D. Bates, A. Maxwell, DNA Topology. In Focus (IRL Press at Oxford University Press, Oxford/New York, 1993)

    Google Scholar 

  5. M. Better, C. Lu, R.C. Williams, H. Echols, Site-specific DNA condensation and pairing mediated by the int protein of bacteriophage lambda. Proc. Natl. Acad. Sci. U S A 79(19), 5837–5841 (1982)

    Article  Google Scholar 

  6. T. Biswas, H. Aihara, M. Radman-Livaja, D. Filman, A. Landy, T. Ellenberger, A structural basis for allosteric control of DNA recombination by lambda integrase. Nature 435(7045), 1059–1066 (2005)

    Article  Google Scholar 

  7. G.W. Blakely, A.O. Davidson, D.J. Sherratt, Sequential strand exchange by XerC and XerD during site-specific recombination at dif. J. Biol. Chem. 275(14), 9930–9936 (2000)

    Article  Google Scholar 

  8. M. Bregu, D.J. Sherratt, S.D. Colloms, Accessory factors determine the order of strand exchange in Xer recombination at psi. EMBO J. 21(14), 3888–3897 (2002)

    Article  Google Scholar 

  9. D. Buck, K. Baker, The classification of rational subtangle replacements between rational tangles. Algebra. Geome Topol. 13, 1413–1463 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  10. D. Buck, M. Mauricio, Connect sum of lens spaces surgeries: application to Hin recombination. Math. Proc. Camb. Philos. Soc. 150(3), 505–525 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  11. G.R. Buck, E.L. Zechiedrich, DNA disentangling by type-2 topoisomerases. J. Mol. Biol. 340(5), 933–939 (2004)

    Article  Google Scholar 

  12. C. Calladine, H. Drew, B. Luisi, A. Travers, Understanding DNA: The Molecule and How it Works (Elsevier, San Diego, CA, 2004)

    Google Scholar 

  13. S.M. Chen, F. Heffron, W.J. Chazin, Two-dimensional 1H NMR studies of 32-base-pair synthetic immobile Holliday junctions: complete assignments of the labile protons and identification of the base-pairing scheme. Biochemistry 32(1), 319–326 (1993)

    Article  Google Scholar 

  14. S.M. Chen, W.J. Chazin, Two-dimensional 1H NMR studies of immobile holliday junctions: nonlabile proton assignments and identification of crossover isomers. Biochemistry 33(38), 11453–11459 (1994)

    Article  Google Scholar 

  15. Y. Chen, U. Narendra, E.L. Iype, M.M. Cox, A.P. Rice, Crystal structure of a Flp recombinase-Holliday junction complex: assembly of an active oligomer by helix swapping. Mol. Cell 6(4), 885–897 (2000)

    Google Scholar 

  16. R.M. Clegg, A.I. Murchie, D.M. Lilley, The solution structure of the four-way DNA junction at low-salt conditions: a fluorescence resonance energy transfer analysis. Biophys. J. 66(1), 99–109 (1994)

    Article  Google Scholar 

  17. J.H. Conway, An enumeration of knots and links, and some of their algebraic properties, in Computational Problems in Abstract Algebra (Proceedings of a Conference Held at Oxford, 1967) (Pergamon, Oxford, 1970), pp. 329–358

    Google Scholar 

  18. J.P. Cooper, P.J. Hagerman, Gel electrophoretic analysis of the geometry of a DNA four-way junction. J. Mol. Biol. 198(4), 711–719 (1987)

    Article  Google Scholar 

  19. J.P. Cooper, P.J. Hagerman, Geometry of a branched DNA structure in solution. Proc. Natl. Acad. Sci. U S A 86(19), 7336–7340 (1989)

    Article  Google Scholar 

  20. J.P. Cooper, P.J. Hagerman, Analysis of fluorescence energy transfer in duplex and branched DNA molecules. Biochemistry 29(39), 9261–9268 (1990)

    Article  Google Scholar 

  21. N.J. Crisona, R.L. Weinberg, B.J. Peter, D.W. Sumners, N.R. Cozzarelli, The topological mechanism of phage lambda integrase. J. Mol. Biol. 289(4), 747–775 (1999)

    Article  Google Scholar 

  22. M. Culler, C.M. Gordon, J. Luecke, P.B. Shalen, Dehn surgery on knots. Bull. Am. Math. Soc. (N.S.) 13(1), 43–45 (1985)

    Google Scholar 

  23. I.K. Darcy, Biological distances on DNA knots and links: applications to Xer recombination. J. Knot Theory Ramif. 10(2), 269–294 (2001). Knots in Hellas ’98, Vol. 2 (Delphi)

    Google Scholar 

  24. I.K. Darcy, Solving unoriented tangle equations involving 4-plats. J. Knot Theory Ramifi. 14(8), 993–1005 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  25. I.K. Darcy, R.G. Scharein, TopoICE-R: 3D visualization modeling the topology of DNA recombination. Bioinformatics 22(14), 1790–1791 (2006)

    Article  Google Scholar 

  26. I.K. Darcy, A. Bhutra, J. Chang, N. Druivenga, C. McKinney, R.K. Medikonduri, S. Mills, J. Navarra Madsen, A. Ponnusamy, J. Sweet, T. Thompson, Coloring the Mu transpososome. BMC Bioinform. 7, 435 (2006)

    Article  Google Scholar 

  27. I.K. Darcy, R.G. Scharein, A. Stasiak, 3D visualization software to analyze topological outcomes of topoisomerase reactions. Nucleic Acids Res. 36(11), 3515–3521 (2008)

    Article  Google Scholar 

  28. I.K. Darcy, J. Luecke, M. Vazquez, Tangle analysis of difference topology experiments: applications to a Mu protein-DNA complex. Algebra. Geome Topol. 9(4), 2247–2309 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  29. I.K. Darcy, K. Ishihara, R.K. Medikonduri, K. Shimokawa, Rational tangle surgery and Xer recombination on catenanes. Algebra. Geome Topol. 12(2), 1183–1210 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  30. F.B. Dean, A. Stasiak, T. Koller, N.R. Cozzarelli, Duplex DNA knots produced by Escherichia coli topoisomerase I. Structure and requirements for formation. J. Biol. Chem. 260(8), 4975–4983 (1985)

    Google Scholar 

  31. B.F. Eichman, M. Ortiz-Lombardia, J. Aymami, M. Coll, P.S. Ho, The inherent properties of DNA four-way junctions: comparing the crystal structures of Holliday junctions. J. Mol. Biol. 320(5), 1037–1051 (2002)

    Article  Google Scholar 

  32. C. Ernst, Tangle equations. J. Knot Theory Ramifi. 5(2), 145–159 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  33. C. Ernst, Tangle equations. II. J. Knot Theory Ramifi. 6(1), 1–11 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  34. C. Ernst, D.W. Sumners, A calculus for rational tangles: applications to DNA recombination. Math. Proc. Camb. Philos. Soc. 108(3), 489–515 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  35. R.E. Franklin, R.G. Gosling, Evidence for 2-chain helix in crystalline structure of sodium deoxyribonucleate. Nature 172(4369), 156–157 (1953)

    Article  Google Scholar 

  36. R.E. Franklin, R.G. Gosling, Molecular configuration in sodium thymonucleate. Nature 171(4356), 740–741 (1953)

    Article  Google Scholar 

  37. M. Gellert, H. Nash, Communication between segments of DNA during site-specific recombination. Nature 325(6103), 401–404 (1987)

    Article  Google Scholar 

  38. K. Ghosh, G.D. Van Duyne, Cre-loxP biochemistry. Methods 28(3), 374–383 (2002)

    Google Scholar 

  39. D.N. Gopaul, F. Guo, G.D. Van Duyne, Structure of the Holliday junction intermediate in Cre-loxP site-specific recombination. EMBO J. 17(14), 4175–4187 (1998)

    Article  Google Scholar 

  40. S.C. Gourlay, S.D. Colloms, Control of Cre recombination by regulatory elements from Xer recombination systems. Mol. Microbiol. 52(1), 53–65 (2004)

    Article  Google Scholar 

  41. I. Grainge, M. Bregu, M. Vazquez, V. Sivanathan, S.C. Ip, D.J. Sherratt, Unlinking chromosome catenanes in vivo by site-specific recombination. EMBO J. 26(19), 4228–4238 (2007)

    Article  Google Scholar 

  42. N.D. Grindley, K.L. Whiteson, P.A. Rice, Mechanisms of site-specific recombination. Ann. Rev. Biochem. 75, 567–605 (2006)

    Article  Google Scholar 

  43. F. Guo, D.N. Gopaul, G.D. van Duyne, Structure of Cre recombinase complexed with DNA in a site-specific recombination synapse. Nature 389(6646), 40–46 (1997)

    Article  Google Scholar 

  44. A.H. Hardin, S.K. Sarkar, Y. Seol, G.F. Liou, N. Osheroff, K.C. Neuman, Direct measurement of DNA bending by type IIA topoisomerases: implications for non-equilibrium topology simplification. Nucleic Acids Res. 39(13), 5729–5743 (2011)

    Article  Google Scholar 

  45. R.M. Harshey, M. Jayaram, The mu transpososome through a topological lens. Crit. Rev. Biochem. Mol. Biol. 41(6), 387–405 (2006)

    Article  Google Scholar 

  46. W.D. Heyer, Biochemistry of eukaryotic homologous recombination, in Molecular Genetics of Recombination, ed. by A. Aguilera, R. Rothstein (Springer, Heidelberg, 2007), pp. 95–133

    Chapter  Google Scholar 

  47. M. Hirasawa, K. Shimokawa, Dehn surgeries on strongly invertible knots which yield lens spaces. Proc. Am. Math. Soc. 128(11), 3445–3451 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  48. R. Holliday, A mechanism for gene conversion in fungi. Genet. Res. Camb. 5, 282–304 (1964)

    Article  Google Scholar 

  49. K.E. Huffman, S.D. Levene, DNA-sequence asymmetry directs the alignment of recombination sites in the Flp synaptic complex. J. Mol. Biol. 286, 1–13 (1999)

    Article  Google Scholar 

  50. A. Hughes, Primary DNA molecular structure (2005). Connexions web site, Available at: http://cnx.org/content/m11411/1.8/

  51. N.R. Kallenbach, R.I. Ma, N.C. Seeman, An immobile nucleic acid junction constructed from oligonucleotides. Nature 305, 829–831 (1983)

    Article  Google Scholar 

  52. E. Kilbride, M.R. Boocock, W.M. Stark, Topological selectivity of a hybrid site-specific recombination system with elements from Tn3 res/resolvase and bacteriophage P1 loxP/Cre. J. Mol. Biol. 289(5), 1219–1230 (1999)

    Article  Google Scholar 

  53. E.A. Kilbride, M.E. Burke, M.R. Boocock, W.M. Stark, Determinants of product topology in a hybrid Cre-Tn3 resolvase site-specific recombination system. J. Mol. Biol. 355(2), 185–195 (2006)

    Article  Google Scholar 

  54. S. Kim, A 4-string tangle analysis of DNA-protein complexes based on difference topology. ProQuest LLC, Ann Arbor, 2009. Ph.D. thesis, The University of Iowa

    Google Scholar 

  55. S. Kim, A generalized 4-string solution tangle of DNA-protein complexes. J. Korean Soc. Ind. Appl. Math. 15(3), 161–175 (2011)

    MathSciNet  Google Scholar 

  56. S. Kim, I.K. Darcy, Topological analysis of DNA-protein complexes, in Mathematics of DNA Structure, Function and Interactions. IMA Volumes in Mathematics and its Applications, vol. 150 (Springer, New York, 2009), pp. 177–194

    Google Scholar 

  57. K. Kimura, V.V. Rybenkov, N.J. Crisona, T. Hirano, N.R. Cozzarelli, 13S condensin actively reconfigures DNA by introducing global positive writhe: implications for chromosome condensation. Cell 98(2), 239–248 (1999)

    Article  Google Scholar 

  58. S.C. Kowalczykowski, D.A. Dixon, A.K. Eggleston, S.D. Lauder, W.M. Rehrauer, Biochemistry of homologous recombination in Escherichia coli. Microbiol. Rev. 58(3), 401–465 (1994)

    Google Scholar 

  59. C. Lesterlin, C. Pages, N. Dubarry, S. Dasgupta, F. Cornet, Asymmetry of chromosome Replichores renders the DNA translocase activity of FtsK essential for cell division and cell shape maintenance in Escherichia coli. PLoS Genet. 4(12), e1000288 (2008)

    Google Scholar 

  60. Z. Liu, L. Zechiedrich, H.S. Chan, Action at hooked or twisted hooked DNA juxtapositions rationalizes unlinking preference of type-2 topoisomerases. J. Mol. Biol. 400(5), 963–982 (2010)

    Article  Google Scholar 

  61. P.K. Mandal, S. Venkadesh, N. Gautham, Structure of d(cgggtacccg)4 as a four-way Holliday junction. Acta. Crystallogr. Sect. F Struct. Biol. Cryst. Commun. 67(Pt 12), 1506–1510 (2011)

    Article  Google Scholar 

  62. M. Ortiz-Lombardia, A. Gonzalez, R. Eritja, J. Aymami, F. Azorin, M. Coll, Crystal structure of a DNA holliday junction. Nat. Struct. Biol. 6(10), 913–917 (1999)

    Article  Google Scholar 

  63. S. Pathania, M. Jayaram, R. Harshey, Path of DNA within the Mu transpososome: transposase interaction bridging two Mu ends and the enhancer trap five DNA supercoils. Cell 109, 425–436 (2002)

    Article  Google Scholar 

  64. Z.M. Petrushenko, C.H. Lai, R. Rai, V.V. Rybenkov, DNA reshaping by MukB. Right-handed knotting, left-handed supercoiling. J. Biol. Chem. 281(8), 4606–4615 (2006)

    Google Scholar 

  65. C. Price, A biological application for the oriented skein relation. ProQuest LLC, Ann Arbor, 2012. Ph.D. thesis, The University of Iowa

    Google Scholar 

  66. G.D. Recchia, M. Aroyo, D. Wolf, G. Blakely, D. Sherratt, FtsK-dependent and -independent pathways of Xer site-specific recombination. EMBO J. 18(20), 5724–5734 (1999)

    Article  Google Scholar 

  67. E. Richet, P. Abcarian, H.A. Nash, Synapsis of attachment sites during lambda integrative recombination involves capture of a naked DNA by a protein-DNA complex. Cell 52(1), 9–17 (1988)

    Article  Google Scholar 

  68. E.D. Ross, R.B. Den, P.R. Hardwidge, L.J. Marter, Improved quantitation of DNA curvature using ligation ladders. Nucleic Acids Res. 27(21), 4135–4142 (1999)

    Article  Google Scholar 

  69. V.V. Rybenkov, C. Ullsperger, A.V. Vologodskii, N.R. Cozzarelli, Simplification of DNA topology below equilibrium values by type II topoisomerases. Science 277(5326), 690–693 (1997)

    Article  Google Scholar 

  70. Y. Saka, M. Vazquez, Tanglesolve: topological analysis of site-specific recombination. Bioinformatics 18(7), 1011–1012 (2002)

    Article  Google Scholar 

  71. G.J. Sarkis, L.L. Murley, A.E. Leschziner, M.R. Boocock, W.M. Stark, N.D. Grindley, A model for the gamma delta resolvase synaptic complex. Mol. Cell 8(3), 623–631 (2001)

    Article  Google Scholar 

  72. R.G. Scharein, Interactive topological drawing. ProQuest LLC, Ann Arbor, 1998. Ph.D. thesis, The University of British Columbia

    Google Scholar 

  73. A.M. Segall, H.A. Nash, Architectural flexibility in lambda site-specific recombination: three alternate conformations channel the attL site into three distinct pathways. Genes Cells 1(5), 453–463 (1996)

    Article  Google Scholar 

  74. H. Senechal, J. Delesques, G. Szatmari, Escherichia coli ArgR mutants defective in cer/Xer recombination, but not in DNA binding. FEMS Microbiol. Lett. 305(2), 162–169 (2010)

    Article  Google Scholar 

  75. Y. Seol, A.H. Hardin, M.P. Strub, G. Charvin, K.C. Neuman, Comparison of DNA decatenation by Escherichia coli topoisomerase IV and topoisomerase III: implications for non-equilibrium topology simplification. Nucleic Acids Res. 41, 4640–4649 (2013)

    Article  Google Scholar 

  76. K. Shimokawa, K. Ishihara, M. Vazquez, Tangle analysis of DNA unlinking by the Xer/FtsK system. Bussei Kenkyu 92, 89–92 (2009)

    Google Scholar 

  77. L.S. Shlyakhtenko, V.N. Potaman, R.R. Sinden, Y.L. Lyubchenko, Structure and dynamics of supercoil-stabilized DNA cruciforms. J. Mol. Biol. 280(1), 61–72 (1998)

    Article  Google Scholar 

  78. C. Sissi, M. Palumbo, In front of and behind the replication fork: bacterial type iia topoisomerases. Cell Mol. Life Sci. 67(12), 2001–2024 (2010)

    Article  Google Scholar 

  79. W.M. Stark, D.J. Sherratt, M.R. Boocock, Site-specific recombination by Tn3 resolvase: topological changes in the forward and reverse reactions. Cell 58(4), 779–790 (1989)

    Article  Google Scholar 

  80. D.W. Sumners, C. Ernst, S.J. Spengler, N.R. Cozzarelli, Analysis of the mechanism of DNA recombination using tangles. Q. Rev. Biophys. 28(3), 253–313 (1995)

    Article  Google Scholar 

  81. P. Tait, On knots. Trans. R. Soc. Edinb. 28, 145–190 (1877)

    MATH  Google Scholar 

  82. M. Vazquez, D.W. Sumners, Tangle analysis of Gin site-specific recombination. Math. Proc. Camb. Philos. Soc. 136(3), 565–582 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  83. M. Vazquez, S.D. Colloms, D.W. Sumners, Tangle analysis of Xer recombination reveals only three solutions, all consistent with a single three-dimensional topological pathway. J. Mol. Biol. 346(2), 493–504 (2005)

    Article  Google Scholar 

  84. A.A. Vetcher, A.Y. Lushnikov, J. Navarra-Madsen, R.G. Scharein, Y.L. Lyubchenko, I.K. Darcy, S.D. Levenc, DNA topology and geometry in Flp and Cre recombination. J. Mol. Biol. 357(4), 1089–1104 (2006)

    Article  Google Scholar 

  85. A.A. Vetcher, A.E. McEwen, R. Abujarour, A. Hanke, S.D. Levene, Gel mobilities of linking-number topoisomers and their dependence on DNA helical repeat and elasticity. Biophys. Chem. 148(1–3), 104–111 (2010)

    Article  Google Scholar 

  86. A. Vologodskii, Theoretical models of DNA topology simplification by type IIA DNA topoisomerases. Nucleic Acids Res. 37(10), 3125–3133 (2009)

    Article  Google Scholar 

  87. J.C. Wang, Cellular roles of DNA topoisomerases: a molecular perspective. Nat. Rev. Mol. Cell Biol. 3(6), 430–440 (2002)

    Article  Google Scholar 

  88. J.C. Wang, Untangling the Double Helix: DNA Entanglement and the Action of the DNA Topoisomerases (Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, 2009)

    Google Scholar 

  89. S.A. Wasserman, N.R. Cozzarelli, Supercoiled DNA-directed knotting by T4 topoisomerase. J. Biol. Chem. 266(30), 20567–20573 (1991)

    Google Scholar 

  90. J.D. Watson, F.H. Crick, Molecular structure of nucleic acids; a structure for deoxyribose nucleic acid. Nature 171(4356), 737–738 (1953)

    Article  Google Scholar 

  91. G. Witz, A. Stasiak, DNA supercoiling and its role in DNA decatenation and unknotting. Nucleic Acids Res. 38(7), 2119–2133 (2010)

    Article  Google Scholar 

  92. C. Wyman, R. Kanaar, Homologous recombination: down to the wire. Curr. Biol. 14(15), R629–R631 (2004)

    Article  Google Scholar 

  93. C. Wyman, D. Ristic, R. Kanaar, Homologous recombination-mediated double-strand break repair. DNA Repair 3(8–9), 827–833 (2004)

    Article  Google Scholar 

  94. K. Yamada, M. Ariyoshi, K. Morikawa, Three-dimensional structural views of branch migration and resolution in DNA homologous recombination. Curr. Opin. Struct. Biol. 14(2), 130–137 (2004)

    Article  Google Scholar 

  95. W. Zheng, C. Galloy, B. Hallet, M. Vazquez, The tangle model for site-specific recombination: a computer interface and the TnpI-IRS recombination system, in Knot Theory for Scientific Objects-Proceedings of the International Workshop on Knot Theory for Scientific Objects held in Osaka (Japan), March 8–10, 2006, vol 1 ed. by Akio Kawauchi. OCAMI Studies (Osaka Municipal universities Press, Sakai, 2007), pp. 251–271, http://www.omup.jp/modules/tinyd1/index.php?id=25&easiestml_lang=en

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Acknowledgements

This research was supported in part by a grant from the joint Division of Mathematical Sciences (DMS) and National Institute of General Medical Sciences (NIGMS) Initiative to Support Research in the Area of Mathematical Biology (grant number NSF 0800285 to I.K.D. and NSF DMS-0800929 to S.D.L). We wish to thank Massa Shoura for providing Figs. 1b, 8, and 9.

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Authors and Affiliations

  1. Department of Mathematics and Program in Applied Mathematical and Computational Sciences, University of Iowa, 14 MLH, Iowa City, IA, 52242, USA

    Isabel K. Darcy

  2. Departments of Bioengineering, Molecular and Cell Biology, and Physics, University of Texas at Dallas, 800 West Campbell Road, Richardson, TX, 75080, USA

    Stephen D. Levene

  3. Hypnagogic Software, Vancouver, BC, Canada

    Robert G. Scharein

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  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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Darcy, I.K., Levene, S.D., Scharein, R.G. (2014). Introduction to DNA Topology. 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_15

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