Skip to main content
Log in

Poland–Scheraga Models and the DNA Denaturation Transition

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Poland–Scheraga models were introduced to describe the DNA denaturation transition. We give a rigorous and refined discussion of a family of these models. We derive possible scaling functions in the neighborhood of the phase transition point and review common examples. We introduce a self-avoiding Poland–Scheraga model displaying a first order phase transition in two and three dimensions. We also discuss exactly solvable directed examples. This complements recent suggestions as to how the Poland–Scheraga class might be extended in order to display a first order transition, which is observed experimentally.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. M. Baiesi, E. Carlon, Y. Kafri, D. Mukamel, E. Orlandini, and A. L. Stella, Inter-strand distance distribution of DNA near melting, Phys. Rev. E 67:21911–21917 (2002); cond-mat/0211236.

    Google Scholar 

  2. M. Baiesi, E. Carlon, E. Orlandini, and A. L. Stella, A simple model of DNA denaturation and mutually avoiding walk statistics, Eur. Phys. J. B 29:129–134 (2002); cond-mat/0207122.

    Google Scholar 

  3. M. Baiesi, E. Carlon, and A. L. Stella, Scaling in DNA unzipping models: denaturated loops and end-segments as branches of a block copolymer network, Phys. Rev. E 66:21804–21812 (2002); cond-mat/0205125.

    Google Scholar 

  4. R. D. Blake et al., Statistical mechanical simulation of polymeric DNA melting with MELTSIM, Bioinformatics 15:370–375 (1999).

    Google Scholar 

  5. R. Blossey and C. Carlon, Reparametrizing loop entropy weights: Effect on DNA melting curves, preprint (2002); cond-mat/0212457.

  6. M. Bousquet-Mèlou and A. J. Guttmann, Enumeration of three-dimensional convex polygons, Ann. Comb. 1:27–53 (1997).

    Google Scholar 

  7. R. Brak, A. L. Owczarek, and T. Prellberg, Exact scaling behavior of partially convex vesicles, J. Stat. Phys. 76:1101–1128 (1994).

    Google Scholar 

  8. E. Carlon, E. Orlandini, and A. L. Stella, The roles of stiffness and excluded volume in DNA denaturation, Phys. Rev. Lett. 88:198101–198104 (2002); cond-mat/0108308.

    Google Scholar 

  9. M. S. Causo, B. Coluzzi, and P. Grassberger, Simple model for the DNA denaturation transition, Phys. Rev. E 62:3958–3973 (2000).

    Google Scholar 

  10. M. E. Fisher, Effect of excluded volume on phase transitions in biopolymers, J. Chem. Phys. 45:1469–1473 (1966).

    Google Scholar 

  11. M. E. Fisher, Walks, walls, wetting, and melting, J. Stat. Phys. 34:667–729 (1984).

    Google Scholar 

  12. P. Flajolet and R. Sedgewick, Analytic combinatorics: Functional equations, rational and algebraic functions, INRIA preprint 4103 (2001).

  13. T. Garel and H. Orland, On the role of mismatches in DNA denaturation, Saclay preprint T03/045 (2003); cond-mat/0304080.

  14. A. J. Guttmann, Asymptotic analysis of power-series expansions, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds., Vol. 13 (Academic, New York, 1989), pp. 1–234.

    Google Scholar 

  15. A. J. Guttmann and T. Prellberg, Staircase polygons, elliptic integrals, Heun functions, and lattice Green functions, Phys. Rev. E 47:R2233–R2236 (1993).

    Google Scholar 

  16. A. Hanke and R. Metzler, Comment on “Why is the DNA denaturation transition first order?” Phys. Rev. Lett. 90:159801(2003); cond-mat/0110164.

    Google Scholar 

  17. A. Hanke and R. Metzler, Entropy loss in long-distance DNA looping, preprint (2002); cond-mat/0211468.

  18. E. J. Janse van Rensburg, The Statistical Mechanics of Interacting Walks, Polygons, Animals, and Vesicles (Oxford University Press, New York, 2000).

    Google Scholar 

  19. I. Jensen, A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice, J. Phys. A: Math. Gen. 36:5731–5745 (2003); cond-mat/0301468.

    Google Scholar 

  20. Y. Kafri, D. Mukamel, and L. Peliti, Why is the DNA denaturation transition first order?, Phys. Rev. Lett. 85:4988–4992 (2000); cond-mat/0007141.

    Google Scholar 

  21. Y. Kafri, D. Mukamel, and L. Peliti, Melting and unzipping of DNA, Eur. Phys. J. B 27:135–146 (2001); cond-mat/0108323.

    Google Scholar 

  22. Y. Kafri, D. Mukamel, and L. Peliti, Reply to comment by Hanke and Metzler, preprint (2001); cond-mat/0112179, cond-mat/0302589.

  23. Y. Kafri, D. Mukamel, and L. Peliti, Denaturation and unzipping of DNA: Statistical mechanics of interacting loops, Physica A 306:39–50 (2002).

    Google Scholar 

  24. E. B. Kolomeisky and J. P. Straley, Universality classes for line-depinning transitions, Phys. Rev. B 46:12664–12674 (1992).

    Google Scholar 

  25. R. Lipowsky, Typical and exceptional shape fluctuations of interacting strings, Europhys. Lett. 15:703–708 (1991).

    Google Scholar 

  26. D. Marenduzzo, A. Trovato, and A. Maritan, Phase diagram of force-induced DNA unzipping in exactly solvable models, Phys. Rev. E 64:031901–031912 (2001); cond-mat/0101207.

    Google Scholar 

  27. D. Marenduzzo, S. M. Bhattacharjee, A. Maritan, E. Orlandini, and F. Seno, Dynamical scaling of the DNA unzipping transition, Phys. Rev. Lett. 88:28102–28105 (2002); cond-mat/0103142.

    Google Scholar 

  28. N. Madras and G. Slade, The Self-Avoiding Walk (Birkhäuser, Boston, 1993).

    Google Scholar 

  29. M. Peyrard and A. R. Bishop, Statistical mechanics of a nonlinear model for DNA denaturation, Phys. Rev. Lett. 62:2755–2758 (1989).

    Google Scholar 

  30. D. Poland and H. A. Scheraga, Phase transitions in one dimension and the helix-coil transition in polyamino acids, J. Chem. Phys. 45:1456–1463 (1966).

    Google Scholar 

  31. D. Poland and H. A. Scheraga, Occurrence of a phase transition in nucleic acid models, J. Chem. Phys. 45:1464–1469 (1966).

    Google Scholar 

  32. T. Prellberg and R. Brak, Critical exponents from nonlinear functional equations for partially directed cluster models, J. Stat. Phys. 78:701–730 (1995).

    Google Scholar 

  33. D. W. Sumners and S. G. Whittington, Knots in self-avoiding walks, J. Phys. A 21:1689–1694 (1988).

    Google Scholar 

  34. N. Theodorakopoulos, T. Dauxois, and M. Peyrard, Order of the phase transition in models of DNA thermal denaturation, Phys. Rev. Lett. 85:6–9 (2000); cond-mat/0004487.

    Google Scholar 

  35. R. M. Wartell and A. S. Benight, Thermal denaturation of DNA molecules: A comparison of theory with experiment, Phys. Rep. 126:67–107 (1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Richard, C., Guttmann, A.J. Poland–Scheraga Models and the DNA Denaturation Transition. Journal of Statistical Physics 115, 925–947 (2004). https://doi.org/10.1023/B:JOSS.0000022370.48118.8b

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JOSS.0000022370.48118.8b

Navigation