Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 6, Number 6, 2011
Biomathematics Education
|
|
---|---|---|
Page(s) | 108 - 135 | |
Section | Discrete Modeling | |
DOI | https://doi.org/10.1051/mmnp/20116607 | |
Published online | 05 October 2011 |
- S. Elrod, W. Stansfield. Schaum’s Outline of Genetics, Fifth Edition. McGraw-Hill, New York, 2010. [Google Scholar]
- R. Brooker, E. Widmaier, L. Graham, P. Stiling. Biology, Second Edition. McGraw-Hill, New York, 2010. [Google Scholar]
- 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. [Google Scholar]
- P. Karp. Cell and Molecular Biology: Concepts and Experiments, Fifth Edition. Wiley, New York, 2007. [Google Scholar]
- W. H. Elliott, D. C. Elliott. Biochemistry and Molecular Biology, Fourth Edition. Oxford University Press, Oxford, U.K., 2009. [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- N. R. Cozzarelli, J. C. Wang. DNA Topology and Its Biological Effects. Cold Spring Harbor Monograph Series 20, 1990. [Google Scholar]
- G. Balliano, P. Milla. Topology of DNA: When manipulation supports the lack of “space-filling" imagination. Biochemical Education, 25 (1997), 209–210. [CrossRef] [Google Scholar]
- J. R. Jungck, H. Gaff, A. E. Weisstein. Mathematical manipulative models: In defense of “Beanbag Biology". CBE Life Sci Educ. 9 (2010), 201–211. [Google Scholar]
- 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. [CrossRef] [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- “kitefrog". Möbius Strip: New Discoveries. 2011 (2008). [Google Scholar]
- 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. [Google Scholar]
- A. D. Bates, A. Maxwell. DNA Topology. Oxford University Press, New York, 2005. [Google Scholar]
- T. C. Boles, J. H. White, N. R. Cozzarelli. Structure of plectonemically supercoiled DNA. J. Mol. Biol. 213 (1990), 931–951. [CrossRef] [PubMed] [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- H. Willenbrock, D. W. Ussery. Chromatin architecture and gene expression in Escherichia coli. Genome Biol. 5 (2004), 252. [Google Scholar]
- J. H. White. Self-linking and the Gauss integral in higher dimensions. American Journal of Mathematics. 91 (1969), 693–728. [Google Scholar]
- W. R. Bauer, F. H. Crick, J. H. White. Supercoiled DNA. Sci. Am. 243 (1980), 100–113. [PubMed] [Google Scholar]
- T. T. Eckdahl. Investigating DNA supercoiling. The American Biology Teacher. 61 (1999), 214–216. [CrossRef] [Google Scholar]
- 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. [Google Scholar]
- G. Witz, A. Stasiak. DNA supercoiling and its role in DNA decatenation and unknotting. Nucl. Acids Res. 38 (2010), 2119–2133. [CrossRef] [Google Scholar]
- M. D. F. Kamenetskii. Unraveling DNA: The most important molecule of life, John Wiley & Sons, 1997. [Google Scholar]
- A. Sossinsky, G. Weiss. Knots: Mathematics with a twist. Harvard University Press, 2002. [Google Scholar]
- 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. USA 98 (2001), 8219–8226. [CrossRef] [Google Scholar]
- L. H. Kauffman, S. Lambropoulou. On the classification of rational tangles. Advances in Applied Mathematics. 33 (2004), 199–237. [CrossRef] [MathSciNet] [Google Scholar]
- C. Adams. The Knot book: An elementary introduction to the mathematical theory of knots. W.H. Freeman, 1994. [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- 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. [Google Scholar]
- 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. USA 82 (1985), 3124–3128. [CrossRef] [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- J. L. Nitiss. Targeting DNA topoisomerase II in cancer chemotherapy. Nat Rev Cancer. 9 (2009), 338–350. [CrossRef] [PubMed] [Google Scholar]
- K. D. Corbett, J. M. Berger. Structure, molecular mechanisms, and evolutionary relationships in DNA topoisomerases. Annu. Rev. Biophys. Biomol. Struct. 33 (2004), 95–118. [CrossRef] [PubMed] [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- J. M. Berger, S. J. Gamblin, S. C. Harrison, J. C. Wang. Structure and mechanism of DNA topoisomerase II. Nature. 379 (1996), 225–232. [CrossRef] [PubMed] [Google Scholar]
- C. A. Austin, L. M. Fisher. DNA topoisomerases: enzymes that change the shape of DNA. Sci. Prog. 74 (1990), 147–161. [PubMed] [Google Scholar]
- J. J. Champoux. DNA topoisomerases: structure, function, and mechanism. Annu. Rev. Biochem. 70 (2001), 369–413. [CrossRef] [PubMed] [Google Scholar]
- J. Roca. The mechanisms of DNA topoisomerases. Trends Biochem. Sci. 20 (1995), 156–160. [CrossRef] [PubMed] [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- P. H. von Hippel, E. Delagoutte. Macromolecular complexes that unwind nucleic acids. Bioessays. 25 (2003), 1168–1177. [CrossRef] [PubMed] [Google Scholar]
- A. Worcel, S. Strogatz, D. Riley. Structure of chromatin and the linking number of DNA. Proc. Natl. Acad. Sci. USA 78 (1981), 1461–1465. [CrossRef] [PubMed] [Google Scholar]
- L. A. A. Nicholl, D. S. T. Nicholl. Modelling the Eukaryotic chromosome: A stepped approach. Journal of Biological Education. 21 (1987), 99–103. [CrossRef] [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- 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. [Google Scholar]
- M. Buenemann, P. Lenz. A geometrical model for DNA organization in bacteria. PLoS ONE. 5 (2010), e13806. [Google Scholar]
- T. A. Shapiro, P.T. Englund. The structure and replication of kinetoplast DNA. Annu. Rev. Microbiol. 49 (1995), 117–143. [CrossRef] [PubMed] [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- G. W. Hatfield, C. J. Benham. DNA topology-mediated control of global gene expression in Escherichia coli. Annu. Rev. Genet. 36 (2002), 175–203. [CrossRef] [PubMed] [Google Scholar]
- A. Vologodskii, N. R. Cozzarelli. Effect of supercoiling on the juxtaposition and relative orientation of DNA sites. Biophys. J. 70 (1996), 2548–2556. [CrossRef] [PubMed] [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- A. Vologodskii. Theoretical models of DNA topology simplification by type IIA DNA topoisomerases. Nucleic Acids Res. 37 (2009), 3125–3133. [CrossRef] [PubMed] [Google Scholar]
- K. C. Neuman. Single-molecule measurements of DNA topology and topoisomerases. J. Biol. Chem. 285 (2010), 18967–18971. [Google Scholar]
- N. Sonnenschein, M Geertz, G. Muskhelishvili, M. Hütt. Analog regulation of metabolic demand. MBC Systems Biology 5 (2011), 40-52. [Google Scholar]
- R. Messer, P. Staffin. Topology now! Math Assoc. of America, 2006. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.