World Scientific
  • Search
  •   
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
×

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at [email protected] for any enquiries.

Application of a skein relation to difference topology experiments

    https://doi.org/10.1142/S0218216519400169Cited by:1 (Source: Crossref)
    This article is part of the issue:

    Difference topology is a technique used to study any protein that can stably bind to DNA. This technique is used to determine the conformation of DNA bound by protein. Motivated by difference topology experiments, we use the skein relation tangle model as a novel technique to study experiments using topoisomerase to study SMC proteins, a family of proteins that stably bind to DNA. The oriented skein relation involves an oriented knot, K+, with a distinguished positive crossing; a knot K, obtained by changing the distinguished positive crossing of K+ to a negative crossing; a knot, KI, resulting from the non-orientation persevering resolution of the distinguished crossing; and a link KD, the orientation preserving resolution of the distinguished crossing. We refer to (K+,K,KD,KI) as the skein quadruple. Topoisomerases are proteins that break one segment of DNA allowing a DNA segment to pass through before resealing the break. Recombinases are proteins that cut two segments of DNA and recombine them in some manner. They can act on direct repeat or inverted repeat sites, resulting in a link or knot, respectively. Thus, the skein quadruple is now viewed as K±= circular DNA substrate, K= product of topoisomerase action, KD= product of recombinase action on directed repeat sites, and KI= product of recombinase action of inverted repeat sites.

    AMSC: 57M25, 57M27

    References

    • 1. J. H. Conway, An enumeration of knots and links, and some of their algebraic properties, Proc. Conf. Computational Problems in Abstract Algebra (Oxford, 1970), pp. 329–358. CrossrefGoogle Scholar
    • 2. I. D. Dazey and D. W. Sumners, A strand passage metric for topoisomerase action, KNOTS’96, Tokyo, 1997, pp. 267–278. Google Scholar
    • 3. I. K. Darcy, Solving unoriented tangle equations involving 4-plats, J. Knot Theory Ramificat. 14 (2005) 993–1005. Link, Web of ScienceGoogle Scholar
    • 4. I. K. Darcy, Solving oriented tangle equations involving 4-plats, J. Knot Theory Ramificat. 14 (2005) 1007–1027. Link, Web of ScienceGoogle Scholar
    • 5. I. K. Darcy et al., Coloring the Mu transpososome, BMC Bioinformat. 7 (2006) 435. Crossref, Web of ScienceGoogle Scholar
    • 6. I. K. Darcy, J. Luecke and M. Vazquez, Tangle analysis of difference topology experiments: Applications to a Mu protein-DNA complex, Algebraic Geometric Topol. 9 (2009) 2247–2309. Crossref, Web of ScienceGoogle Scholar
    • 7. C. Ernst, Tangle equations, J. Knot Theory Ramificat. 5 (1996) 145–159. Link, Web of ScienceGoogle Scholar
    • 8. C. Ernst and D. W. Sumners, A calculus for rational tangles: Applications to DNA recombination, Math. Proc. Cambridge Philosophic. Soc. 108 (1990) 489–515. Crossref, Web of ScienceGoogle Scholar
    • 9. T. Hirano, The ABC of SMC proteins: Two armed ATPases for chromosome condensation, cohesion, and repair, Genes Dev. 16 (2002) 399–414. Crossref, Web of ScienceGoogle Scholar
    • 10. M. Jayaram and R. M. Harshey, The Mu transpososome through a topological lens, Critical Rev. Biochem. Molecular Biol. 41 (2006) 387–405. Crossref, Web of ScienceGoogle Scholar
    • 11. M. Jayaram and R. M. Rasika, Difference topology: Analysis of high-order DNA-protein assemblies. Math. DNA Structure, Function and Interactions. IMA Vol. Math. Appl. 150 (2009) 139–158. Google Scholar
    • 12. S. Kim, A 4-string tangle analysis of DNA-protein complexes based on difference topology, Ph.D. thesis, The University of Iowa (2009). Google Scholar
    • 13. S. Kim and I. K. Darcy, Topological analysis of DNA-protein complexes, Mathematics of DNA Structure, Function and Interactions. IMA Vol. Math. Appl. 150 (2009) 177–194. Google Scholar
    • 14. K. Keiji, V. V. Rybenkov, N. J. Crisona, T. Hirano and N. R. Cozzarelli, 13S condensin actively reconfigures DNA by introducing global positive writhe: Implications for chromosome condensation, Cell 98 (1999) 239–248. Crossref, Web of ScienceGoogle Scholar
    • 15. S. Pathania, M. Jayaram and R. M. Harshey, Path of DNA within the Mu transpososome, Cell 109 (2002) 425–436. Crossref, Web of ScienceGoogle Scholar
    • 16. Z. M. Petrushenko, C. H. Lai, R. Rai and V. V. Rybenkov, DNA Reshaping by MukB Right-handed knotting, Left-handed supercoiling, J. Biol. Chem. 281 (2006) 4606–4615. Crossref, Web of ScienceGoogle Scholar
    • 17. T. Ichiro, The determination of the pairs of two-bridge knots or links with Gordian distance one. Proc. American Mathematical Society 126 (1998) 1565–1571. Crossref, Web of ScienceGoogle Scholar