Unraveling the Tangled Complexity of DNA: Combining Mathematical Modeling and Experimental Biology to Understand Replication, Recombination and Repair

S. Robic; J. R. Jungck

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 6, page 108-135
  • ISSN: 0973-5348

Abstract

top
How does DNA, the molecule containing genetic information, change its three-dimensional shape during the complex cellular processes of replication, recombination and repair? This is one of the core questions in molecular biology which cannot be answered without help from mathematical modeling. Basic concepts of topology and geometry can be introduced in undergraduate teaching to help students understand counterintuitive complex structural transformations that occur in every living cell. Topoisomerases, a fascinating class of enzymes involved in replication, recombination and repair, catalyze a change in DNA topology through a series of highly coordinated mechanistic steps. Undergraduate biology and mathematics students can visualize and explore the principles of topoisomerase action by using easily available materials such as Velcro, ribbons, telephone cords, zippers and tubing. These simple toys can be used as powerful teaching tools to engage students in hands-on exploration with the goal of learning about both the mathematics and the biology of DNA structure.

How to cite

top

Robic, S., and Jungck, J. R.. "Unraveling the Tangled Complexity of DNA: Combining Mathematical Modeling and Experimental Biology to Understand Replication, Recombination and Repair." Mathematical Modelling of Natural Phenomena 6.6 (2011): 108-135. <http://eudml.org/doc/222377>.

@article{Robic2011,
abstract = {How does DNA, the molecule containing genetic information, change its three-dimensional shape during the complex cellular processes of replication, recombination and repair? This is one of the core questions in molecular biology which cannot be answered without help from mathematical modeling. Basic concepts of topology and geometry can be introduced in undergraduate teaching to help students understand counterintuitive complex structural transformations that occur in every living cell. Topoisomerases, a fascinating class of enzymes involved in replication, recombination and repair, catalyze a change in DNA topology through a series of highly coordinated mechanistic steps. Undergraduate biology and mathematics students can visualize and explore the principles of topoisomerase action by using easily available materials such as Velcro, ribbons, telephone cords, zippers and tubing. These simple toys can be used as powerful teaching tools to engage students in hands-on exploration with the goal of learning about both the mathematics and the biology of DNA structure. },
author = {Robic, S., Jungck, J. R.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {DNA topology; knot theory; linking number; mathematical manipulatives; supercoiling; undergraduate education; topoisomerases; writhe; twist; DNA replication; recombination and repair},
language = {eng},
month = {10},
number = {6},
pages = {108-135},
publisher = {EDP Sciences},
title = {Unraveling the Tangled Complexity of DNA: Combining Mathematical Modeling and Experimental Biology to Understand Replication, Recombination and Repair},
url = {http://eudml.org/doc/222377},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Robic, S.
AU - Jungck, J. R.
TI - Unraveling the Tangled Complexity of DNA: Combining Mathematical Modeling and Experimental Biology to Understand Replication, Recombination and Repair
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/10//
PB - EDP Sciences
VL - 6
IS - 6
SP - 108
EP - 135
AB - How does DNA, the molecule containing genetic information, change its three-dimensional shape during the complex cellular processes of replication, recombination and repair? This is one of the core questions in molecular biology which cannot be answered without help from mathematical modeling. Basic concepts of topology and geometry can be introduced in undergraduate teaching to help students understand counterintuitive complex structural transformations that occur in every living cell. Topoisomerases, a fascinating class of enzymes involved in replication, recombination and repair, catalyze a change in DNA topology through a series of highly coordinated mechanistic steps. Undergraduate biology and mathematics students can visualize and explore the principles of topoisomerase action by using easily available materials such as Velcro, ribbons, telephone cords, zippers and tubing. These simple toys can be used as powerful teaching tools to engage students in hands-on exploration with the goal of learning about both the mathematics and the biology of DNA structure.
LA - eng
KW - DNA topology; knot theory; linking number; mathematical manipulatives; supercoiling; undergraduate education; topoisomerases; writhe; twist; DNA replication; recombination and repair
UR - http://eudml.org/doc/222377
ER -

References

top
  1. S. Elrod, W. Stansfield. Schaum’s Outline of Genetics, Fifth Edition. McGraw-Hill, New York, 2010.  
  2. R. Brooker, E. Widmaier, L. Graham, P. Stiling. Biology, Second Edition. McGraw-Hill, New York, 2010.  
  3. N. Campbell, N. A. Reece, J. B. Jackson, R. B. Cain, M. L. Urry, L. A. Wasserman, S. A. Minorsky. Biology, Ninth Edition. Benjamin Cummings, San Diego, 2011.  
  4. P. Karp. Cell and Molecular Biology: Concepts and Experiments, Fifth Edition. Wiley, New York, 2007.  
  5. W. H. Elliott, D. C. Elliott. Biochemistry and Molecular Biology, Fourth Edition. Oxford University Press, Oxford, U.K., 2009.  
  6. D. W. Sumners, C. Ernst, S. J. Spengler, N. R. Cozzarelli. Analysis of the mechanism of DNA recombination using tangles. Q. Rev. Biophys.28 (1995), 253–313.  
  7. N. R. Cozzarelli, J. C. Wang. DNA Topology and Its Biological Effects. Cold Spring Harbor Monograph Series 20, 1990.  
  8. G. Balliano, P. Milla. Topology of DNA: When manipulation supports the lack of “space-filling" imagination. Biochemical Education, 25 (1997), 209–210.  
  9. J. R. Jungck, H. Gaff, A. E. Weisstein. Mathematical manipulative models: In defense of “Beanbag Biology". CBE Life Sci Educ.9 (2010), 201–211.  
  10. J. R. Roberts, E. Hagedorn, P. Dillenburg, M. Patrick, T. Herman. Physical models enhance molecular three-dimensional literacy in an introductory biochemistry course*. Biochemistry and Molecular Biology Education, 33 (2005), 105–110.  
  11. T. Herman, J. Morris, S. Colton, A. Batiza, M. Patrick, M. Franzen, D. S. Goodsell. Tactile teaching: exploring protein structure/function using physical models. Biochem. Mol. Biol. Educ.34 (2006), 247–254.  
  12. “kitefrog". Möbius Strip: New Discoveries. 2011 (2008).  
  13. E. Babaev, Intuitive Chemical Topology Concepts (Chapter 5), in: D. Bonchev, R. Rouvray (Eds.), Chemical Topology: Introduction and Fundamentals. Gordon and Breach, 1999, pp. 167–264.  
  14. A. D. Bates, A. Maxwell. DNA Topology. Oxford University Press, New York, 2005.  
  15. T. C. Boles, J. H. White, N. R. Cozzarelli. Structure of plectonemically supercoiled DNA. J. Mol. Biol.213 (1990), 931–951.  
  16. C. D. Hardy, N. J. Crisona, M. D. Stone, N. R. Cozzarelli. Disentangling DNA during replication: a tale of two strands. Philos. Trans. R. Soc. Lond. B. Biol. Sci.359 (2004), 39–47.  
  17. J. M. Fogg, N. Kolmakova, I. Rees, S. Magonov, H. Hansma, J. J. Perona, E. L. Zechiedrich. Exploring writhe in supercoiled minicircle DNA. J. Phys. Condens Matter.18 (2006), S145–S159.  
  18. J. Arsuaga, M. Vazquez, P. McGuirk, S. Trigueros, D. Sumners, J. Roca. DNA knots reveal a chiral organization of DNA in phage capsids. Proc. Natl. Acad. Sci. U. S. A.102 (2005), 9165–9169.  
  19. H. Willenbrock, D. W. Ussery. Chromatin architecture and gene expression in Escherichia coli. Genome Biol. 5 (2004), 252.  
  20. J. H. White. Self-linking and the Gauss integral in higher dimensions. American Journal of Mathematics.91 (1969), 693–728.  
  21. W. R. Bauer, F. H. Crick, J. H. White. Supercoiled DNA. Sci. Am.243 (1980), 100–113.  
  22. T. T. Eckdahl. Investigating DNA supercoiling. The American Biology Teacher.61 (1999), 214–216.  
  23. J. M. Fogg, D. J. Catanese, G. L. Randall, M. C. Swick, L. Zechiedrich. Differences between positively and negatively supercoiled DNA that topoisomerases may distinguish (Chapter), in Mathematics of DNA Structure, Function and Interactions The IMA Volumes in Mathematics and its Applications, 150 (2009), 73–121.  
  24. G. Witz, A. Stasiak. DNA supercoiling and its role in DNA decatenation and unknotting. Nucl. Acids Res.38 (2010), 2119–2133.  
  25. M. D. F. Kamenetskii. Unraveling DNA: The most important molecule of life, John Wiley & Sons, 1997.  
  26. A. Sossinsky, G. Weiss. Knots: Mathematics with a twist. Harvard University Press, 2002.  
  27. L. Postow, N. J. Crisona, B. J. Peter, C. D. Hardy, N. R. Cozzarelli. Topological challenges to DNA replication: Conformations at the fork. Proc. Natl. Acad. Sci. USA98 (2001), 8219–8226.  
  28. L. H. Kauffman, S. Lambropoulou. On the classification of rational tangles. Advances in Applied Mathematics.33 (2004), 199–237.  
  29. C. Adams. The Knot book: An elementary introduction to the mathematical theory of knots. W.H. Freeman, 1994.  
  30. I. K. Darcy, R. G. Scharein, A. Stasiak. 3D visualization software to analyze topological outcomes of topoisomerase reactions. Nucleic Acids Res.36 (2008), 3515–3521.  
  31. P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish, K. Millett, A. Ocneanu. A new polynomial invariant of knots and links. Bull.Amer.Math.Soc.(N.S.).12 (1985), 239–246.  
  32. J. D. Griffith, H. A. Nash. Genetic rearrangement of DNA induces knots with a unique topology: implications for the mechanism of synapsis and crossing-over. Proc. Natl. Acad. Sci. USA82 (1985), 3124–3128.  
  33. S. Trigueros, J. Arsuaga, M. E. Vazquez, D. W. Sumners, J. Roca. Novel display of knotted DNA molecules by two-dimensional gel electrophoresis. Nucleic Acids Res.29 (2001), E67–7.  
  34. J. L. Nitiss. Targeting DNA topoisomerase II in cancer chemotherapy. Nat Rev Cancer.9 (2009), 338–350.  
  35. K. D. Corbett, J. M. Berger. Structure, molecular mechanisms, and evolutionary relationships in DNA topoisomerases. Annu. Rev. Biophys. Biomol. Struct.33 (2004), 95–118.  
  36. P. Forterre, D. Gadelle. Phylogenomics of DNA topoisomerases: their origin and putative roles in the emergence of modern organisms. Nucleic Acids Research.37 (2009), 679–692.  
  37. J. M. Berger, S. J. Gamblin, S. C. Harrison, J. C. Wang. Structure and mechanism of DNA topoisomerase II. Nature.379 (1996), 225–232.  
  38. C. A. Austin, L. M. Fisher. DNA topoisomerases: enzymes that change the shape of DNA. Sci. Prog.74 (1990), 147–161.  
  39. J. J. Champoux. DNA topoisomerases: structure, function, and mechanism. Annu. Rev. Biochem.70 (2001), 369–413.  
  40. J. Roca. The mechanisms of DNA topoisomerases. Trends Biochem. Sci.20 (1995), 156–160.  
  41. F. R. Blattner, G. Plunkett III, C. A. Bloch, N. T. Perna, V. Burland, M. Riley, J. Collado-Vides, J. D. Glasner, C. K. Rode, G. F. Mayhew, J. Gregor, N. W. Davis, H. A. Kirkpatrick, M. A. Goeden, D. J. Rose, B. Mau, Y. Shao. The complete genome sequence of Escherichia coli K-12. Science.277 (1997), 1453–1462.  
  42. P. H. von Hippel, E. Delagoutte. Macromolecular complexes that unwind nucleic acids. Bioessays.25 (2003), 1168–1177.  
  43. A. Worcel, S. Strogatz, D. Riley. Structure of chromatin and the linking number of DNA. Proc. Natl. Acad. Sci. USA78 (1981), 1461–1465.  
  44. L. A. A. Nicholl, D. S. T. Nicholl. Modelling the Eukaryotic chromosome: A stepped approach. Journal of Biological Education.21 (1987), 99–103.  
  45. E. Lieberman-Aiden, N. L. van Berkum, L. Williams, M. Imakaev, T. Ragoczy, A. Telling, I. Amit, B. R. Lajoie, P. J. Sabo, M. O. Dorschner, R. Sandstrom, B. Bernstein, M. A. Bender, M. Groudine, A. Gnirke, J. Stamatoyannopoulos, L. A. Mirny, E. S. Lander, J. Dekker. Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science.326 (2009), 289–293.  
  46. A. Y. Grosberg, S. K. Nechaev, E. I. Shakhnovich. The role of topological constraints in the kinetics of collapse of macromolecules. J.Phys.France.49 (1988), 2095–2100.  
  47. M. Buenemann, P. Lenz. A geometrical model for DNA organization in bacteria. PLoS ONE. 5 (2010), e13806.  
  48. T. A. Shapiro, P.T. Englund. The structure and replication of kinetoplast DNA. Annu. Rev. Microbiol.49 (1995), 117–143.  
  49. J. Chen, C. A. Rauch, J. H. White, P. T. Englund, N. R. Cozzarelli. The Topology of the Kinetoplastic DNA nework. Cell, 80 (1995), 61–69.  
  50. J. Lukes, D. Lys Guilbride, J. Votypka, A. Zikova, R. Benne, P. T. Englund. Kinetoplast DNA network: evolution of an improbable structure. Eukaryotic Cell.1 (2002), 495–502.  
  51. G. W. Hatfield, C. J. Benham. DNA topology-mediated control of global gene expression in Escherichia coli. Annu. Rev. Genet.36 (2002), 175–203.  
  52. A. Vologodskii, N. R. Cozzarelli. Effect of supercoiling on the juxtaposition and relative orientation of DNA sites. Biophys. J.70 (1996), 2548–2556.  
  53. V. V. Rybenkov, C. Ullsperger, A. V. Vologodskii, N. R. Cozzarelli. Simplification of DNA topology below equilibrium values by type II topoisomerases. Science.277 (1997), 690–693.  
  54. A. Vologodskii. Theoretical models of DNA topology simplification by type IIA DNA topoisomerases. Nucleic Acids Res.37 (2009), 3125–3133.  
  55. K. C. Neuman. Single-molecule measurements of DNA topology and topoisomerases. J. Biol. Chem.285 (2010), 18967–18971.  
  56. N. Sonnenschein, M Geertz, G. Muskhelishvili, M. Hütt. Analog regulation of metabolic demand. MBC Systems Biology5 (2011), 40-52.  
  57. R. Messer, P. Staffin. Topology now! Math Assoc. of America, 2006. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.