Skip to main content
Log in

Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract

We study the conformational dynamics within homopolymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength \( \varepsilon\) and the globule size N G is observed. We find two distinct dynamical regimes: a liquid-like regime (for \( \varepsilon\) < \( \varepsilon_{{\rm s}}^{}\) with fast internal dynamics and a solid-like regime (for \( \varepsilon\) > \( \varepsilon_{{\rm s}}^{}\) with slow internal dynamics. The cohesion strength \( \varepsilon_{{\rm s}}^{}\) of this freezing transition depends on N G . Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with \( \varepsilon\) and scales extensive in N G . This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.

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. J. Chuang, Y. Kantor, M. Kardar, Phys. Rev. E 65, 011802 (2001)

    Article  ADS  Google Scholar 

  2. R. Bundschuh, U. Gerland, Phys. Rev. Lett. 95, 208104 (2005)

    Article  ADS  Google Scholar 

  3. K. Luo, T. Ala-Nissila, S.C. Ying, R. Metzler, Europhys. Lett. 88, 68006 (2009)

    Article  ADS  Google Scholar 

  4. N. Gunari, A.C. Balazs, G.C. Walker, J. Am. Chem. Soc. 129, 10046 (2007)

    Article  Google Scholar 

  5. M. Rief, M. Gautel, F. Oesterhelt, J.M. Fernandez, H.E. Gaub, Science 276, 1109 (1997)

    Article  Google Scholar 

  6. D.B. Staple, S.H. Payne, A.L.C. Reddin, H.J. Kreuzer, Phys. Rev. Lett. 101, 248301 (2008)

    Article  ADS  Google Scholar 

  7. M. Mandal, R.R. Breaker, Nat. Rev. Mol. Cell Biol. 5, 451 (2004)

    Article  Google Scholar 

  8. P.G. de Gennes, J. Chem. Phys. 55, 572 (1971)

    Article  ADS  Google Scholar 

  9. G.S. Jas, W.A. Eaton, J. Hofrichter, J. Phys. Chem. B 105, 261 (2001)

    Article  Google Scholar 

  10. S.A. Pabit, H. Roder, S.J. Hagen, Biochemistry 43, 12532 (2004)

    Article  Google Scholar 

  11. F. Graeter, P. Heider, R. Zangi, B.J. Berne, J. Am. Chem. Soc. 130, 11578 (2008)

    Article  Google Scholar 

  12. D.E. Sagnella, J.E. Straub, D. Thirumalai, J. Chem. Phys. 113, 7702 (2000)

    Article  ADS  Google Scholar 

  13. A.Y. Grosberg, S.K. Nechaev, E.I. Shakhnovich, J. Phys. (Paris) 49, 2095 (1988)

    Google Scholar 

  14. A. Grosberg, Y. Rabin, S. Havlin, A. Neer, Europhys. Lett. 23, 373 (1993)

    Article  ADS  Google Scholar 

  15. 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 et al., Science 326, 289 (2009)

    Article  ADS  Google Scholar 

  16. M.G. Poirier, A. Nemani, P. Gupta, S. Eroglu, J.F. Marko, Phys. Rev. Lett. 86, 360 (2001)

    Article  ADS  Google Scholar 

  17. T. Frisch, A. Verga, Phys. Rev. E 65, 041801 (2002)

    Article  ADS  Google Scholar 

  18. N.A. Denesyuk, J.D. Weeks, Phys. Rev. Lett. 102, 108101 (2009)

    Article  ADS  Google Scholar 

  19. C.F. Abrams, N.K. Lee, S.P. Obukhov, Europhys. Lett. 59, 391 (2002)

    Article  ADS  Google Scholar 

  20. A. Serr, C. Sendner, F. Mü, Europhys. Lett. 92, 38002 (2010)

    Article  ADS  Google Scholar 

  21. F. Celestini, T. Frisch, X. Oyharcabal, Phys. Rev. E 70, 012801 (2004)

    Article  ADS  Google Scholar 

  22. J. Chuang, A.Y. Grosberg, T. Tanaka, J. Chem. Phys. 112, 6434 (2000)

    Article  ADS  Google Scholar 

  23. V. Barsegov, G. Morrison, D. Thirumalai, Phys. Rev. Lett. 100, 248102 (2008)

    Article  ADS  Google Scholar 

  24. B.S. Khatri, M. Kawakami, K. Byrne, D.A. Smith, T.C.B. McLeish, Biophys. J. 92, 1825 (2007)

    Article  ADS  Google Scholar 

  25. Y. von Hansen, F. Sedlmeier, M. Hinczewski, R.R. Netz, Phys. Rev. E 84, 051501 (2011)

    Article  ADS  Google Scholar 

  26. A.E. Filippov, J. Klafter, M. Urbakh, Phys. Rev. Lett. 92, 135503 (2004)

    Article  ADS  Google Scholar 

  27. Y. Murayama, H. Wada, M. Sano, Europhys. Lett. 79, 58001 (2007)

    Article  ADS  Google Scholar 

  28. A.V. Finkelstein, O.V. Galzitskaya, Phys. Life Rev. 1, 23 (2004)

    Article  ADS  Google Scholar 

  29. R. Gerber, A. Tahiri-Alaoui, P.J. Hore, W. James, J. Biol. Chem. 282, 6300 (2007)

    Article  Google Scholar 

  30. R. Zwanzig, Proc. Natl. Acad. Sci. U.S.A. 85, 2029 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  31. C. Hyeon, D. Thirumalai, Proc. Natl. Acad. Sci. U.S.A. 100, 10249 (2003)

    Article  ADS  Google Scholar 

  32. A. Alexander-Katz, H. Wada, R.R. Netz, Phys. Rev. Lett. 103, 028102 (2009)

    Article  ADS  Google Scholar 

  33. M. Hinczewski, Y. von Hansen, J. Dzubiella, R.R. Netz, J. Chem. Phys. 132, 245103 (2010)

    Article  ADS  Google Scholar 

  34. R.B. Best, G. Hummer, Proc. Natl. Acad. Sci. U.S.A. 107, 1088 (2010)

    Article  ADS  Google Scholar 

  35. D.K. Klimov, D. Thirumalai, Proc. Natl. Acad. Sci. U.S.A. 96, 6166 (1999)

    Article  ADS  Google Scholar 

  36. N. Yoshinaga, K. Yoshikawa, T. Ohta, Eur. Phys. J. E 17, 485 (2005)

    Article  Google Scholar 

  37. G. Morrison, C. Hyeon, N.M. Toan, B.Y. Ha, D. Thirumalai, Macromolecules 40, 7343 (2007)

    Article  ADS  Google Scholar 

  38. O. Braun, U. Seifert, Europhys. Lett. 68, 746 (2004)

    Article  ADS  Google Scholar 

  39. R. Metzler, W. Reisner, R. Riehn, R. Austin, J.O. Tegenfeldt, I.M. Sokolov, Europhys. Lett. 76, 696 (2006)

    Article  ADS  Google Scholar 

  40. A. Vologodskii, Biophys. J. 90, 1594 (2006)

    Article  ADS  Google Scholar 

  41. L. Huang, D.E. Makarov, J. Phys. Chem. A 111, 10338 (2007)

    Article  Google Scholar 

  42. C.E. Sing, T.R. Einert, R.R. Netz, A. Alexander-Katz, Phys. Rev. E 83, 040801(R) (2011)

    Article  ADS  Google Scholar 

  43. D.F. Parsons, D.R.M. Williams, Phys. Rev. E 74, 041804 (2006)

    Article  ADS  Google Scholar 

  44. D.F. Parsons, D.R.M. Williams, J. Chem. Phys. 124, 221103 (2006)

    Article  ADS  Google Scholar 

  45. W. Paul, T. Strauch, F. Rampf, K. Binder, Phys. Rev. E 75, 060801 (2007)

    Article  ADS  Google Scholar 

  46. F. Rampf, W. Paul, K. Binder, Europhys. Lett. 70, 628 (2005)

    Article  ADS  Google Scholar 

  47. Y. Zhou, C.K. Hall, M. Karplus, Phys. Rev. Lett. 77, 2822 (1996)

    Article  ADS  Google Scholar 

  48. M.P. Taylor, W. Paul, K. Binder, J. Chem. Phys. 131, 114907 (2009)

    Article  ADS  Google Scholar 

  49. V.G. Rostiashvili, G. Migliorini, T.A. Vilgis, Phys. Rev. E 64, 051112 (2001)

    Article  ADS  Google Scholar 

  50. H. Liang, H. Chen, J. Chem. Phys. 113, 4469 (2000)

    Article  ADS  Google Scholar 

  51. J. Torres, P. Nealey, J. de Pablo, Phys. Rev. Lett. 85, 3221 (2000)

    Article  ADS  Google Scholar 

  52. T.S. Jain, J.J. de Pablo, Macromolecules 35, 2167 (2002)

    Article  ADS  Google Scholar 

  53. F. Varnik, J. Baschnagel, K. Binder, Phys. Rev. E 65, 021507 (2002)

    Article  ADS  Google Scholar 

  54. J. Baschnagel, F. Varnik, J. Phys.: Condens. Matter 17, R851 (2005)

    Article  ADS  Google Scholar 

  55. M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, 1999)

  56. W.T. Coffey, The Langevin Equation (World Scientific, 2005)

  57. D.L. Ermak, J.A. McCammon, J. Chem. Phys. 69, 1352 (1978)

    Article  ADS  Google Scholar 

  58. J.C.M. Gebhardt, T. Bornschlögl, M. Rief, Proc. Natl. Acad. Sci. U.S.A. 107, 2013 (2010)

    Article  ADS  Google Scholar 

  59. M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids (Oxford University Press, 1989)

  60. A. Alexander-Katz, M.F. Schneider, S.W. Schneider, A. Wixforth, R.R. Netz, Phys. Rev. Lett. 97, 138101 (2006)

    Article  ADS  Google Scholar 

  61. D. Vitkup, D. Ringe, G.A. Petsko, M. Karplus, Nat. Struct. Biol. 7, 34 (2000)

    Article  Google Scholar 

  62. M. Abramowitz, I.A. Stegun (Editors), Handbook of Mathematical Functions, tenth edn. (U.S. Department of Commerce, 2002)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to T. R. Einert.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Einert, T.R., Sing, C.E., Alexander-Katz, A. et al. Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations. Eur. Phys. J. E 34, 130 (2011). https://doi.org/10.1140/epje/i2011-11130-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2011-11130-8

Keywords

Navigation