Advertisement

Randomly charged polymers

  • Mehran Kardar
  • Yacov Kantor
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 492)

Abstract

Polyampholytes (PAs) are polymers with a random sequence of positive and negative charges along their backbone. We have studied systematically the dependence of internal energy and shape of the PA on its excess charge by combining analytic arguments, Monte Carlo simulations, and exact enumeration of all configurations of short chains. The results indicate that the overall excess charge, Q, is the main determinant of the size of the PA. A polymer composed of a mixture of N positive and negative charges ±qo, is compact for Q<Q cqoN, and expanded otherwise. The transition between the two states at low temperatures is reminiscent of the Rayleigh shape instability of a charged drop. A uniform excess charge causes the breakup of a fluid drop; we show that a uniformly charged polymer stretches out to a necklace shape. The inhomogeneities in charge distort the shape away from an ordered necklace. The freezing transition of a PA, and its relevance to proteins is also discussed.

Keywords

Monte Carlo Simulation Coulomb Interaction Compact Globule Excess Charge Charged Drop 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P.G. de Gennes, Scaling Concepts in Polymer Physics, Cornell Univ. Press, Ithaca (1979).Google Scholar
  2. [2]
    M. Mezard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond, World Scientific, Singapore (1987).zbMATHGoogle Scholar
  3. [3]
    D.L. Stein, Proc. Natl. Acad. Sci. USA 82, 3670 (1985)CrossRefADSGoogle Scholar
  4. [3a]
    J.D. Bryngelson and P.G. Wolynes, Proc. Natl. Acad. Sci. USA 84, 7524 (1987)CrossRefADSGoogle Scholar
  5. [3b]
    H.S. Chan and K.A. Dill, Physics Today 46(2), 24 (1993)CrossRefGoogle Scholar
  6. [3c]
    T. Garel and H. Orland, Europhys. Lett. 6, 307 (1988)ADSCrossRefGoogle Scholar
  7. [3d]
    E.I. Shakhnovich and A.M. Gutin, Europhys. Lett. 8 327 (1989)ADSCrossRefGoogle Scholar
  8. [3e]
    M. Karplus and E.I. Shakhnovich, in Protein Folding, ed by T.E. Creighton, ch.4, p. 127, (Freeman & Co, New York, 1992).Google Scholar
  9. [5]
    D. Dressler and H. Potter, Discovering Enzymes, (Scientific American Library, NY, 1990).Google Scholar
  10. [6]
    J. Copart and F. Candau, Macromolecules 26, 1333 (1993)CrossRefADSGoogle Scholar
  11. [6a]
    M. Scouri, J.P. Munch, S.F. Candau, S. Neyret, and F. Candau, Macromol. 27, 69 (1994).CrossRefADSGoogle Scholar
  12. [7]
    X.-H. Yu, A. Tanaka, K. Tanaka, and T. Tanaka, J. Chem. Phys. 97, 7805 (1992); Yu X.-H., Ph. D. thesis, MIT (1993)CrossRefADSGoogle Scholar
  13. [7a]
    A. E. English, S. Mafe, J.A. Manzanares, X.-H. Yu, A. Yu. Grosberg, and T. Tanaka, J. Chem. Phys 104, 8713 (1996).CrossRefADSGoogle Scholar
  14. [8]
    Y. Kantor and M. Kardar, Europhys. Lett. 14, 421 (1991).ADSCrossRefGoogle Scholar
  15. [9]
    Y. Kantor, H. Li, and M. Kardar, Phys. Rev. Lett. 69, 61 (1992)CrossRefADSGoogle Scholar
  16. [9a]
    Y. Kantor, M. Kardar, and H. Li, Phys. Rev. E49, 1383 (1994).ADSGoogle Scholar
  17. [10]
    Y. Kantor and M. Kardar, Europhys. Lett. 27, 643 (1994)CrossRefADSGoogle Scholar
  18. [10a]
    Y. Kantor and M. Kardar, Phys. Rev. E51, 1299 (1995).ADSGoogle Scholar
  19. [11]
    Y. Kantor and M. Kardar, Phys. Rev. E52, 835 (1995).ADSGoogle Scholar
  20. [12]
    P.G. Higgs and J.-F. Joanny, J. Chem. Phys. 94, 1543 (1991)CrossRefADSGoogle Scholar
  21. [12a]
    J. Wittmer, A. Johner and J.F. Joanny, Europhys. Lett. 24, 263 (1993).ADSCrossRefGoogle Scholar
  22. [13]
    Lord Rayleigh, Phil. Mag. 14, 184 (1882).Google Scholar
  23. [14]
    G. Taylor, Proc. R. Soc. London A280 383 (1964).ADSGoogle Scholar
  24. [15]
    J.M. Blatt and V.F. Weisskopf, Theoretical Nuclear Physics, ch. 7, p. 303, Willey, New York (1952)zbMATHGoogle Scholar
  25. [15a]
    R.D. Evans, The Atomic Nucleus, ch. 11, p. 387, McGraw-Hill, New York (1955).zbMATHGoogle Scholar
  26. [16]
    N. Bohr and J. A. Wheeler, Phys. Rev. 56, 426 (1939).zbMATHCrossRefADSGoogle Scholar
  27. [17]
    E. Feenberg, Phys. Rev. 55, 504 (1939).zbMATHCrossRefADSGoogle Scholar
  28. [18]
    F. Weizsacker, Naturwiss. 27, 133 (1939).CrossRefADSGoogle Scholar
  29. [19]
    A.V. Dobrynin, S.P. Obukhov, and M. Rubinstein, preprint (1995).Google Scholar
  30. [20]
    N. Lee and S.P. Obukhov, work in progress (1996); see http://www.phys.ufl.edu/∼nlee/research.html.Google Scholar
  31. [21]
    Y. Kantor and D. Ertaş, J. Phys. A27, L907 (1994).Google Scholar
  32. [22]
    B. Derrida, Phys. Rev. Lett. 45, 79 (1980).CrossRefADSMathSciNetGoogle Scholar
  33. [23]
    V.S. Pande, A.Yu. Grosberg, C. Joerg, M. Kardar, and T. Tanaka, preprint (1996).Google Scholar
  34. [24]
    V.S. Pande, A.Yu. Grosberg, and T. Tanaka, Proc. Nat. Acad. Sci. USA 91, 12976 (1994).CrossRefADSGoogle Scholar
  35. [25]
    M. Annaka and T. Tanaka, Nature 355, 430 (1992).CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Mehran Kardar
    • 1
  • Yacov Kantor
    • 2
  1. 1.Department of PhysicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.School of Physics and AstronomyTel Aviv UniversityTel AvivIsrael

Personalised recommendations