Statistical Mechanical Theory of Protein Folding in Water Environment

  • Alexander V.  YakubovichEmail author
  • Andrey V.  Solov’yov
  • Walter Greiner
Part of the FIAS Interdisciplinary Science Series book series (FIAS)


We present a statistical mechanics formalism for the theoretical description of the process of protein folding\(\leftrightarrow \)unfolding transition in water environment. The formalism is based on the construction of the partition function of a protein obeying two-stage-like folding kinetics. Using the statistical mechanics model of solvation of hydrophobic hydrocarbons we obtain the partition function of infinitely diluted solution of proteins in water environment. The calculated dependencies of the protein heat capacities upon temperature are compared with the corresponding results of experimental measurements for staphylococcal nuclease.


Partition Function Potential Energy Surface Electrostatic Field Conformational State Solvation Shell 
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.



A.Y. thanks Stiftung Polytechnische Gesellschaft Frankfurt am Main for financial support.


  1. 1.
    V. Muñoz, Conformational dynamics and ensembles in protein folding. Annu. Rev. Biophys. Biomol. Struct. 36, 395–412 (2007)CrossRefGoogle Scholar
  2. 2.
    K.A. Dill, S.B. Ozkan, M.S. Shell, T.R. Weikl, The protein folding problem. Annu. Rev. Biophys. 37, 289–316 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    J.N. Onuchic, P.G. Wolynes, Theory of protein folding. Curr. Op. Struct. Biol. 14, 70–75 (2004)CrossRefGoogle Scholar
  4. 4.
    E. Shakhnovich, Protein folding thermodynamics and dynamics: Where physics, chemistry, and biology meet. Chem. Rev. 106, 1559–1588 (2006)CrossRefGoogle Scholar
  5. 5.
    N.V. Prabhu, K.A. Sharp, Protein-solvent interactions. Chem. Rev. 106, 1616–1623 (2006)CrossRefGoogle Scholar
  6. 6.
    A. Yakubovich, I. Solov’yov, A. Solov’yov, W. Greiner, Ab initio theory of helix\(\leftrightarrow \)coil phase transition. Eur. Phys. J. D. 46, 215–225, (2007)(arXiv:0704.3079v1 [])Google Scholar
  7. 7.
    A. Yakubovich, I. Solov’yov, A. Solov’yov, W. Greiner, Ab initio description of phase transitions in finite bio-nano-systems. Europhys. News 38, 10 (2007)Google Scholar
  8. 8.
    I. Solov’yov, A. Yakubovich, A. Solov’yov, W. Greiner, \(\alpha \)-helix\(\leftrightarrow \)random coil phase transition: analysis of ab initio theory predictions. Eur. Phys. J. D. 46, 227–240 (2008) (arXiv:0704.3085v1 [])Google Scholar
  9. 9.
    A. Yakubovich, I. Solov’yov, A. Solov’yov, W. Greiner, Phase transition in polypeptides: a step towards the understanding of protein folding. Eur. Phys. J. D 40, 363–367 (2006)Google Scholar
  10. 10.
    A. Yakubovich, I. Solov’yov, A. Solov’yov, W. Greiner, Conformational changes in glycine tri- and hexapeptide. Eur. Phys. J. D 39, 23–34 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    A. Yakubovich, I. Solov’yov, A. Solov’yov, W. Greiner, Conformations of glycine polypeptides. Khimicheskaya Fizika (Chemical Physics) (in Russian) 25, 11–23 (2006)Google Scholar
  12. 12.
    I. Solov’yov, A. Yakubovich, A. Solov’yov, W. Greiner, On the fragmentation of biomolecules: fragmentation of alanine dipeptide along the polypeptide chain. J. Exp. Theor. Phys. 103, 463–471 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    I. Solov’yov, A. Yakubovich, A. Solov’yov, W. Greiner, Ab initio study of alanine polypeptide chain twisting. Phys. Rev. E 73, 021916 (2006)ADSCrossRefGoogle Scholar
  14. 14.
    I. Solov’yov, A. Yakubovich, A. Solov’yov, W. Greiner, Potential energy surface for alanine polypeptide chains. J. Exp. Theor. Phys. 102, 314–326 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    B. Noetling, D.A. Agard, How general is the nucleation condensation mechanism? Proteins 73, 754–764 (2008)CrossRefGoogle Scholar
  16. 16.
    S. Kumar, C.-J. Tsai, R. Nussinov, Maximal stabilities of reversible two-state proteins. Biochemistry 41, 5359–5374 (2002)Google Scholar
  17. 17.
    J. H. Griffith, H. Scheraga, Statistical thrmodynamics of aqueous solutions. i. water structure, solutions with non-polar solutes, and hydrophobic ineractions. J. Mol. Struc. 682, 97–113 (2004)Google Scholar
  18. 18.
    A. Bakk, J.S. Høye, A. Hansen, Apolar and polar solvation thermodynamics related to the protein unfolding process. Biophys. J. 82, 713–719 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    Y. Griko, P. Privalov, J. Aturtevant, S. Venyaminov, Cold denaturation of staphyloccocal nuclease. Proc. Natl. Acad. Sci. U.S.A 85, 3343–3347 (1988)ADSCrossRefGoogle Scholar
  20. 20.
    P. Privalov, Thermodynamics of protein folding. J. Chem. Thermodyn. 29, 447–474 (1997)CrossRefGoogle Scholar
  21. 21.
    S. He, H.A. Scheraga, Macromolecular conformational dynamics in torsion angle space. J. Chem. Phys. 108, 271–286 (1998)ADSCrossRefGoogle Scholar
  22. 22.
    S. He, H.A. Scheraga, Brownian dynamics simulations of protein folding. J. Chem. Phys. 108, 287–300 (1998)ADSCrossRefGoogle Scholar
  23. 23.
    W. Scott, W. van Gunsteren, The GROMOS Software Package for Biomolecular Simulations, in Methods and Techniques in Computational Chemistry: METECC-95, ed. by E. Clementi, G. Corongiu (STEF, Cagliari, 1995), pp. 397–434Google Scholar
  24. 24.
    W. Cornell, P. Cieplak, C. Bayly et al., A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc. 117, 5179–5197 (1995)Google Scholar
  25. 25.
    A. MacKerell, D. Bashford, R. Bellott et al., All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B 102, 3586–3616 (1998)CrossRefGoogle Scholar
  26. 26.
    S. Krimm, J. Bandekar, Vibrational analysis of peptides, polypeptides, and proteins v. normal vibrations of \(\beta \)-turns. Biopolymers 19, 1–29 (1980)CrossRefGoogle Scholar
  27. 27.
    M. Cubrovic, O. Obolensky, A. Solov’yov, Semistiff polymer model of unfolded proteins and its application to nmr residual dipolar couplings. Eur. Phys. J. D. 51, 41–49 (2009)ADSCrossRefGoogle Scholar
  28. 28.
    A. Finkelstein, O. Ptitsyn, Protein Physics: A Course of Lectures (Elsevier Books, Oxford, 2002)Google Scholar
  29. 29.
    G. Makhatadze, P. Privalov, Contribution to hydration to protein folding thermodynamics. I. The enthalpy of hydration. J. Mol. Biol. 232, 639–659 (1993)Google Scholar
  30. 30.
    W. Humphrey, A. Dalke, K. Schulten, Vmd - visual molecular dynamics. J. Molec. Graphics 14, 33–38 (1996)CrossRefGoogle Scholar
  31. 31.
    F.A. Cotton, E.E. Hazen Jr, M.J. Legg, Staphylococcal nuclease: Proposed mechanism of action based on structure of enzyme-thymidine 3’,5’-bisphosphate-calcium ion complex at 1.5-a resolution. Proc. Natl. Acad. Sci. U.S.A 76, 2551–2555 (1979)ADSCrossRefGoogle Scholar
  32. 32.
    Protein data bank, (2009)
  33. 33.
    J.C. Phillips, R. Braun, W. Wang et al., Scalable molecular dynamics with NAMD. J. Comp. Chem. 26, 1781–1802 (2005)CrossRefGoogle Scholar
  34. 34.
    R. Wade, M.H. Mazor, J.A. McCammon, F. Quiocho, A molecular dynamics study of thermodynamic and structural aspects of the hydration of cavities in proteins. Biopolymers 31, 919–931 (1991)CrossRefGoogle Scholar
  35. 35.
    J. Mazur, R.L. Jernican, Distance-dependent dielectric constants and their application to double-helical DNA. Biopolymers 31, 1615–1629 (1991)CrossRefGoogle Scholar
  36. 36.
    J.H. Griffith, H. Scheraga, Statistical thermodynamics of aqueous solutions ii.alkali halides at infinite dilution. J. Mol. Struc. 711, 33–48 (2004)Google Scholar
  37. 37.
    H.-X. Zhou, Residual charge interactions in unfolded staphylococcal nuclease can be explained by the gaussian-chain model. Biophys. J. 83, 2981–2986 (2002)ADSCrossRefGoogle Scholar
  38. 38.
    J.P. Collman, R. Boulatov, C.J. Sunderland, L. Fu, Functional analogues of cytochrome c oxidase, myoglobin, and hemoglobin. Chem. Rev. 104, 561–588 (2004)CrossRefGoogle Scholar
  39. 39.
    D. Shortle, M.S. Ackerman, Persistence of native-like topology in a denatured protein in 8 m urea. Science 293, 487–489 (2001)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Alexander V.  Yakubovich
    • 1
    • 2
    Email author
  • Andrey V.  Solov’yov
    • 1
  • Walter Greiner
    • 1
  1. 1.Frankfurt Institute for Advanced StudiesGoethe UniversityFrankfurt am MainGermany
  2. 2.Author A.Y. on leave from A.F. Ioffe Physical Technical InstituteSaint-PetersburgRussia

Personalised recommendations