Skip to main content
SpringerLink
Log in

The Role of Topology in DNA Gel Electrophoresis

  • Chapter
  • First Online:
Topological Interactions in Ring Polymers

Part of the book series: Springer Theses ((Springer Theses))

Abstract

Topology plays a key role in the biophysics of DNA, and is intimately related to its functioning. For instance, transcription of a gene redistributes twist locally to create what is known as supercoiling, while catenanes or knots can prevent cell division, hence they need to be quickly and accurately removed by specialised enzymes known as topoisomerases. But how can one establish experimentally the topological state of a given DNA molecule? By far the most successful and widely used technique for this is gel electrophoresis (Calladine et al. 1997; Bates and Maxwell 2005). This method exploits the empirical observation that the mobility of a charged DNA molecule under an electric field and moving through a gel depends on its size, shape and topology (Bates and Maxwell 2005; Stasiak et al. 1996). Nowadays, gel electrophoresis is a ubiquitous technique (Calladine et al. 1997; Viovy 2000; Dorfman 2010), since it readily allows the separation of polymers with different physical properties and it is systematically used for DNA identification and purification (Calladine et al. 1997).

The Red Queen said: “Now, here, you see, it takes all the running you can do, to keep in the same place”

L. Carroll

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The halving probability p is always taken smaller than the critical (inverse) percolation probability \(1-p_c \simeq 0.75\) (\(p_c\) being the bond percolation probability on a cubic lattice) to avoid the presence of sparse un-connected clusters of un-physically rigid parts of the gel.

  2. 2.

    Here, I neglect the screening due to ions in solution (Maffeo et al. 2010; Stefano et al. 2014). These will be considered in the next section. In any case, the correction due to the presence of ions account only for a pre-factor on the corresponding real-life values of the fields used in the simulations.

  3. 3.

    Differently to the previous Section, the parameters used here are closer to the ones used recently in the literature (Stefano et al. 2014).

References

  • Adams, C.C.: The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots W. H. Freeman and Company, New York (1994)

    MATH  Google Scholar 

  • Alon, U., Mukamel, D.: Gel electrophoresis and diffusion of ring-shaped DNA. Phys. Rev. E 55(2), 1783 (1997)

    Article  ADS  Google Scholar 

  • Arsuaga, J., Vazquez, M., McGuirk, P., Trigueros, S., Sumners, D.W., Roca, J.: DNA knots reveal a chiral organization of DNA in phage capsids. Proc. Natl. Acad. Sci. USA 102(26), 9165 (2005)

    Article  ADS  Google Scholar 

  • Arsuaga, J., Vázquez, M., Trigueros, S., Sumners, D., Roca, J.: Knotting probability of DNA molecules confined in restricted volumes: DNA knotting in phage capsids. Proc. Natl. Acad. Sci. USA 99(8), 5373 (2002)

    Article  ADS  Google Scholar 

  • Baerts, P., Basu, U., Maes, C., Safaverdi, S.: Frenetic origin of negative differential response. Phys. Rev. E 88(5), 052109 (2013)

    Article  ADS  Google Scholar 

  • Baiesi, M., Maes, C., Wynants, B.: Fluctuations and response of nonequilibrium states. Phys. Rev. Lett. 103(1), 010602 (2009)

    Article  ADS  MATH  Google Scholar 

  • Baiesi, M., Maes, C., Wynants, B.: The modified Sutherland-Einstein relation for diffusive non-equilibria. Proc. R. Soc. A 467(2134), 2792 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Baiesi, M., Stella, A.L., Vanderzande, C.: Role of trapping and crowding as sources of negative differential mobility. Phys. Rev. E 92, 042121 (2015)

    Article  ADS  Google Scholar 

  • Barkema, G., Marko, J., Widom, B.: Electrophoresis of charged polymers: simulation and scaling in a lattice model of reptation. Phys. Rev. E 49(6), 5303–5309 (1994)

    Article  ADS  Google Scholar 

  • Bates, A., Maxwell, A.: DNA Topology. Oxford University Press, Oxford (2005)

    Google Scholar 

  • Calladine, C.R., Collis, C.M., Drew, H.R., Mott, M.R.: A study of electrophoretic mobility of DNA in agarose and polyacrylamide gels. J. Mol. Biol. 221(3), 981 (1991)

    Article  Google Scholar 

  • Calladine, C.R., Drew, H., Luisi, F.B., Travers, A.A.: Understanding DNA: The Molecule and How it Works. Elsevier Academic Press, London (1997)

    Google Scholar 

  • Cebrián, J., Kadomatsu-Hermosa, M.J., Castán, A., Martínez, V., Parra, C., Fernández-Nestosa, M.J., Schaerer, C., Martínez-Robles, M.-L., Hernández, P., Krimer, D.B., Stasiak, A., Schvartzman, J.B.: Electrophoretic mobility of supercoiled, catenated and knotted DNA molecules., Nucl. Acids Res. 3112(Ext 4232), 1 (2014)

    Google Scholar 

  • Cole, K.D., Åkerman, B.: The influence of agarose concentration in gels on the electrophoretic trapping of circular DNA. Separ. Sci. Technol. 38(10), 2121 (2003)

    Article  Google Scholar 

  • Di Stefano, M., Tubiana, L., Di Ventra, M., Micheletti, C.: Driving knots on DNA with AC/DC electric fields: topological friction and memory effects. Soft Matter 10, 6491 (2014)

    Article  Google Scholar 

  • Dorfman, K.D.: DNA electrophoresis in microfabricated devices. Rev. Mod. Phys. 82(4), 2903 (2010)

    Article  ADS  Google Scholar 

  • Duke, T.: Tube model of field-inversion electrophoresis. Phys. Rev. Lett. 62(24), 2877 (1989)

    Article  ADS  Google Scholar 

  • Galajda, P., Keymer, J., Chaikin, P., Austin, R.: A wall of funnels concentrates swimming bacteria. J. Bacteriol. 189(23), 8704 (2007)

    Article  Google Scholar 

  • Ghosh, P.K., Hänggi, P., Marchesoni, F., Nori, F.: Giant negative mobility of Janus particles in a corrugated channel. Phys. Rev. E 89(6), 062115 (2014)

    Article  ADS  Google Scholar 

  • Guenet, J.M., Rochas, C.: Agarose sols and gels revisited. Macromol. Symp. 242, 65 (2006)

    Article  Google Scholar 

  • Katritch, V., Bednar, J., Michoud, D., Scharein, R., Dubochet, J., Stasiak, A.: Geometry and physics of knots. Nature 384, 142 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  • Kusner, R., Sullivan, J.: Möbius energies for knots and links, surfaces and submanifolds. Geometric Topology (Proceedings of the 1993 Georgia International Topology Conference) AMS/IP Studies in Advanced Mathematical, pp. 570–604 (1994)

    Google Scholar 

  • Levene, S.D., Zimm, B.H.: Separations of open-circular DNA using pulsed-field electrophoresis. Proc. Natl. Acad. Sci. USA 84(12), 4054 (1987)

    Article  ADS  Google Scholar 

  • Maffeo, C., Schöpflin, R., Brutzer, H., Stehr, R., Aksimentiev, A., Wedemann, G., Seidel, R.: DNA-DNA interactions in tight supercoils are described by a small effective charge density. Phys. Rev. Lett. 105(15), 158101 (2010)

    Article  ADS  Google Scholar 

  • Mickel, S., Arena, V., Bauer, W.: Physical properties and gel electrophoresis behavior of R12-derived plasmid DNAs. Nucl. Acids Res. 4(5), 1465 (1977)

    Article  Google Scholar 

  • Mogilner, A., Rubinstein, B.: The physics of filopodial protrusion. Biophys. J. 89(2), 782 (2005)

    Article  MathSciNet  Google Scholar 

  • Mohan, A., Doyle, P.: Effect of disorder on DNA electrophoresis in a microfluidic array of obstacles. Phys. Rev. E 76(4), 040903 (2007a)

    Article  ADS  Google Scholar 

  • Mohan, A., Doyle, P.S.: Stochastic modeling and simulation of DNA electrophoretic separation in a microfluidic obstacle array. Macromolecules 40(24), 8794 (2007b)

    Article  ADS  Google Scholar 

  • Olavarrieta, L., Martínez-Robles, M.L., Sogo, J.M., Stasiak, A., Hernández, P., Krimer, D.B., Schvartzman, J.B.: Supercoiling, knotting and replication fork reversal in partially replicated plasmids. Nucl. Acids Res. 30(3), 656 (2002)

    Article  Google Scholar 

  • Pernodet, N., Maaloum, M., Tinland, B.: Pore size of agarose gels by atomic force microscopy. Electrophoresis 18, 55 (1997)

    Article  Google Scholar 

  • Piili, J., Marenduzzo, D., Kaski, K., Linna, R.P.: Sedimentation of knotted polymers. Phys. Rev. E 87(1), 012728 (2013)

    Article  ADS  Google Scholar 

  • Rahong, S., Yasui, T., Yanagida, T., Nagashima, K., Kanai, M., Klamchuen, A., Meng, G., He, Y., Zhuge, F., Kaji, N., Kawai, T., Baba, Y.: Ultrafast and wide range analysis of DNA molecules using rigid network structure of solid nanowires. Sci. Rep. 4, 5252 (2014)

    Article  ADS  Google Scholar 

  • Rolfsen, D.: Knots and links. AMS Chelsea Publishing, Providence, Rhode Island (2003)

    MATH  Google Scholar 

  • Rubinstein, M.: Discretized model of entangled-polymer dynamics. Phys. Rev. Lett. 59(17), 1946 (1987)

    Article  ADS  Google Scholar 

  • Stasiak, A., Katritch, V., Bednar, J., Michoud, D., Dubochet, J.: Electrophoretic mobility of DNA knots. Nature 384, 122 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  • Stellwagen, N.C., Stellwagen, E.: Effect of the matrix on DNA electrophoretic mobility. J. Chromatogr. 1216(10), 1917 (2009)

    Article  Google Scholar 

  • Sugiyama, J., Rochas, C., Turquois, T., Taravel, F., Chanzy, H.: Direct imaging of polysaccharide aggregates in frozen aqueous dilute systems. Carbohydr. Polym. 23(4), 261 (1994)

    Article  Google Scholar 

  • Trigueros, S., Arsuaga, J., Vazquez, M.E., Sumners, D., Roca, J.: Novel display of knotted DNA molecules by two-dimensional gel electrophoresis. Nucl. Acids Res. 29(13), E67 (2001)

    Article  Google Scholar 

  • Trigueros, S., Roca, J.: Production of highly knotted DNA by means of cosmid circularization inside phage capsids. BMC Biotechnol. 7, 94 (2007)

    Article  Google Scholar 

  • Viovy, J.: Electrophoresis of DNA and other polyelectrolytes: physical mechanisms. Rev. Mod. Phys. 72(3), 813 (2000)

    Article  ADS  Google Scholar 

  • Viovy, J., Duke, T.: DNA electrophoresis in polymer solutions: Ogston sieving, reptation and constraint release. Electrophoresis 14, 322 (1993)

    Article  Google Scholar 

  • Weber, C., Carlen, M., Dietler, G., Rawdon, E.J., Stasiak, A.: Sedimentation of macroscopic rigid knots and its relation to gel electrophoretic mobility of DNA knots. Sci. Rep. 3, 1091 (2013)

    Article  ADS  Google Scholar 

  • Weber, C., Stasiak, A., De, : Los Rios, P., Dietler, G.: Simulations of electrophoretic collisions of DNA knots with gel obstacles. J. Phys.: Condens. Matter 18(14), S161 (2006a)

    Google Scholar 

  • Weber, C., Stasiak, A., De, : Los Rios, P., Dietler, G.: Numerical simulation of gel electrophoresis of DNA knots in weak and strong electric fields. Biophys. J. 90(9), 3100 (2006b)

    Google Scholar 

  • Whytock, S., Finch, J.: The substructure of agarose gels as prepared for electrophoresis. Biopolymers 31(9), 1025 (1991)

    Article  Google Scholar 

  • Zia, R.K.P., Praestgaard, E.L., Mouritsen, O.G.: Getting more from pushing less: negative specific heat and conductivity in nonequilibrium steady states. Am. J. Phys. 70(4), 384 (2002)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK

    Davide Michieletto

Authors
  1. Davide Michieletto
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Davide Michieletto .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Michieletto, D. (2016). The Role of Topology in DNA Gel Electrophoresis. In: Topological Interactions in Ring Polymers. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-41042-5_6

Download citation

Publish with us

Policies and ethics

Search

Navigation