Skip to main content
SpringerLink
Log in

Network model of a protein globule

  • Original Paper
  • Published:
Journal of Biological Physics Aims and scope Submit manuscript

Abstract

Phase transition of a protein globule is considered in the frameworks of (i) the generalized mean-field theory for the order parameter, characterizing the extent of the deviation of a protein three-dimensional structure from its native state and (ii) the network model that treats a protein globule as a small-world network with a significant percent of long-range links between amino acid residues. Temperature dependencies of the introduced order parameter are defined and phase-transition temperatures are found on the basis of the function defining the distribution of links’ numbers for protein residues. An important role of long-range links, promoting considerable rise of thermal protein stability, is demonstrated by the example of a correlation between protein melting temperature and a fraction of disulfide bonds.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Barabási, A.L., Oltvai, Z.N.: Network biology: understanding the cell’s functional organization. Nat. Rev. Genet. 5, 101–113 (2004)

    Article  Google Scholar 

  2. Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 5, 167–256 (2003)

    Article  ADS  Google Scholar 

  3. Atilgan, C., Okan, O.B., Atilgan, A.R.: Network-based models as tools hinting at non-evident protein functionality. Ann. Rev. Biophys. 41, 205–225 (2012)

    Article  Google Scholar 

  4. Miyazawa, S., Jernigan, R.L.: Residue–residue potentials with a favorable contact pair term and an unfavorable high packing density term, for simulation and threading. J. Mol. Biol. 256, 623–644 (1996)

    Article  Google Scholar 

  5. Bagler, G., Sinha, S.: Assortative mixing in protein contact networks and protein folding kinetics. Bioinformatics 23, 1760–1767 (2007)

    Article  Google Scholar 

  6. Atilgan, A.R., Akan, P., Baysal, C.: Small-world communication of residues and significance for protein dynamics. Biophys. J. 86, 85–91 (2004)

    Article  Google Scholar 

  7. Vendruscolo, M., Dokholyan, N.V., Paci, E., Karplus, M.: Small-world view of the amino acids that play a key role in protein folding. Phys. Rev. 65, 061910 (2002)

    Google Scholar 

  8. Gaci, O., Balev, S.: Motif prediction in amino acid interaction networks, vol. l. In: Proc. World Congress on Eng. and Comp. Sci, San Francisco, USA (2009)

  9. Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature (London) 393, 440–442 (1998)

    Article  ADS  Google Scholar 

  10. Milgram, S.: The small-world problem. Psychol. Today 1, 61–67 (1967)

    Google Scholar 

  11. Jiao, X., Chang, S.: Scoring function based on weighted residue network. Int. J. Mol. Sci. 12, 8773–8786 (2011)

    Article  Google Scholar 

  12. Plaxco, K.W., Simons, K.T., Baker, D.: Contact order, transition state placement and the refolding rates of single domain proteins. J. Mol. Biol. 277, 985–994 (1998)

    Article  Google Scholar 

  13. Ivankov, D.N., Garbuzynskiy, S.O., Alm, E., Plaxco, K.W., Baker, D., Finkelstein, A.V.: Contact order revisited: influence of protein size on the folding rate. Protein Sci. 12, 2057–062 (2003)

    Article  Google Scholar 

  14. Finkelstein, A.V., Ivankov, D.N., Garbuzynskiy, S.O., Galzitskaya, O.V.: Understanding the folding rates and folding nuclei of globular proteins. Curr. Protein Pept. Sci. 8, 521–536 (2007)

    Article  Google Scholar 

  15. Herrero, C.P.: Ising model in small-world networks. Phys. Rev. E 65, 66110 (2002)

    Article  ADS  Google Scholar 

  16. Grosberg, A.Y., Khokhlov, A.R.: Statistical Physics of Macromolecules. Springer (1994)

  17. Landau, L.D., Lifshitz, E.M.: Statistical Physics. Butterworth-Heinemann (1980)

  18. Kittel, C.: Introduction to Solid State Physics. Wiley (2004)

  19. Chandrasekhar, S.: Liquid Crystals. Cambridge Univ. Press (1994)

  20. Birstein, T.M., Ptitsy, O.B.: Conformation of Macromolecules. Nauka, Moscow (in Russian) (1964)

    Google Scholar 

  21. Mallick, P., Boutz, D.R., Eisenberg, D., Yeates, T.O.: Genomic evidence that the intracellular proteins of archaeal microbes contain disulfide bonds. Proc. Natl. Acad. Sci. 99, 96799684 (2002)

    Google Scholar 

  22. Jorda, J., Yeates, T.O.: Widespread disulfide bonding in proteins from thermophilic Archaea. Hindawi Publ. Corp, Archaea, vol. 2011, 9 p. Article ID 409156. doi:10.1155/2011/409156

  23. Meilikhov, E.Z., Farzetdinova, R.M.: Generalized mean-field theory for Ising spins in small-world networks. Phys. Rev. E 71, 046111 (2005)

    Article  ADS  Google Scholar 

  24. Berman, H., Henrick, K., Nakamura, H.: Announcing the worldwide Protein Data Bank. Nat. Struct. Biol. 10, 980 (2003)

    Article  Google Scholar 

  25. Huang, J., Kawashima, S.I., Kanehisa, M.: New amino acid indices based on residue network topology. Gen. Inf. 18, 152–161 (2007)

    Google Scholar 

  26. Romero, P., Obradovic, Z., Kissinger, C., Villafrance, J.E., Dunker, A.K.: Identifying disordered regions in proteins from amino acid sequence. In: Proceedings of the International Conference on Neural Networks, pp. 91–95 (1997)

  27. Scopes, R.K.: Protein Purification: Principles and Practice, 3rd edn., pp. 98–100. Springer (1994)

  28. Privalov, P.L., Dragan, A.I.: Microcalorimetry of biological macromolecules. Biophys. Chem. 126, 16–24 (2007)

    Article  Google Scholar 

  29. Volkenshtein, M.V.: Biophysics. Mir, Moscow (1983)

    Google Scholar 

  30. Nanoscale Materials in Chemistry, 2nd edn. Klabunde, K.J., Richards, R.M. (eds.). Wiley (2009)

  31. Zhou, Y., Vitkup, D., Karplus, M.: Native proteins are surface-molten solids: application of the Lindemann criterion for the solid versus liquid state. J. Mol. Biol. 285, 1371–1375 (1999)

    Article  Google Scholar 

  32. Privalov, P.L.: Stability of proteins. Proteins which do not present a single cooperative system. Adv. Protein Chem. 35, 1–104 (1982)

    Article  Google Scholar 

  33. Lopes, J.V., Pogorelov, Y.G., Lopes dos Santos, J.B.M., Toral, R.: Exact solution of Ising model on a small-world network. Phys. Rev. E 70, 026112 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  34. Peierls, R.: On Ising model of ferro magnetis. Proc. Camb. Philol. Soc. 32, 477–481 (1936)

    Article  MATH  ADS  Google Scholar 

  35. Grifths, R.B.: Peierls proof of spontaneous magnetization in a two-dimensional Ising ferromagnet. Phys. Rev. 136, A437–A439 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  36. Meilikhov, E.Z., Farzetdinova, R.M.: Curie temperature for small-world Ising systems of different dimensions. J. Magn. Magn. Mater. 300, 254–256 (2006)

    Article  ADS  Google Scholar 

  37. Birgelson, J.D., Wolynes, P.G.: Spin glasses and the statistical mechanics of protein folding. Proc. Natl. Acad. Sci. U. S. A. 84, 7524–7528 (1987)

    Article  ADS  Google Scholar 

  38. Birgelson, J.D., Wolynes, P.G.: Intermediates and barrier crossing in random energy model with application to protein folding. J. Phys. Chem. 93, 6902–6915 (1989)

    Article  Google Scholar 

Download references

Acknowledgement

This work has been supported by Grants ## 12-02-00550, 11-02-00363a of the Russian Foundation of Basic Researches.

Author information

Authors and Affiliations

  1. Kurchatov Institute, 123182, Moscow, Russia

    E. Z. Meilikhov & R. M. Farzetdinova

Authors
  1. E. Z. Meilikhov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. M. Farzetdinova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Z. Meilikhov.

Appendix

Appendix

Table 1 Melting temperatures T m of some proteins with the total number N R of their residues, the number N S of disulfide bonds and the effective fraction p = N S /N R of those bonds*
Full size table

Rights and permissions

Reprints and permissions

About this article

Cite this article

Meilikhov, E.Z., Farzetdinova, R.M. Network model of a protein globule. J Biol Phys 39, 673–685 (2013). https://doi.org/10.1007/s10867-013-9326-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10867-013-9326-8

Keywords

Search

Navigation