Thermodynamics and Kinetics of Protein Folding: A Mean Field Theory
K. K. Liang (梁國淦), M. Hayashi (林輪年), Y. J. Shiu (許瑛珍), Y. Mo (莫燕),
J. S. Shao (邵久書), Y. J. Yan (嚴以京), and S. H. Lin (林聖賢)
Institute of Atomic and Molecular Science, Academia Sinica, Taipei, Taiwan
The kinetic Ising model in the mean field approximation is applied to study the equilibrium and
kinetic behaviors of protein folding-unfolding. In our model, we regard a protein as a topological
collection of interacting peptide bonds (or other protein unites). According to this model,
thermodynamics and kinetics of protein folding-unfolding are rated to the elementary process of
folding←→unfolding of such interacting units. We shall show that even for the so-called
two-state case of protein folding-unfolding, the kinetic behaviors are predicted to be in general
non-exponential and that universal curves exist separately for the thermodynamic behaviors and
kinetics behaviors of protein folding-unfolding. Our model can treat the effect of temperature and
denaturant concentration on the thermodynamics and kinetics of protein folding-unfolding and
provide the Chevron plot. It can also be used to calculate the force-extension curve in the atomic
force microscopic studies of protein folding-unfolding. Satisfactory demonstrations are presented
for treating experimental observations on the thermodynamical and kinetic responses of protein
folding-unfolding to the changes in temperature and denaturant concentration and for exhibiting
universal plots of protein.
References
1 C. B. Anfinsen, Science, 1973, 181, 223.; 2 R. L. Baldwin and G. D. Rose, Trends Biochem. Sci.,
1999, 24, 77; R. L. BaldwinG. D. Rose Trends Biochem. Sci.19992426.; 3 S. Akiyama, S.
Takahashi, K. Ishimori and I. Morishima, Nature Struct. Biol., 2000, 7, 514.; 4 T. Sivaraman, T. K.
S. Kumar, Y. T. Tu, W. Wang, W. Y. Lin, H. M. Chen and C. Yu, Biochem. Biophys. Res.
Commun., 1999, 260, 284.; 5 V. R. Agashe, M. C. R. Shastry and J. B. Udganokar, Nature, 1999,
377, 754.; 6 R. Zwanzig, Proc. Natl. Acad. Sci. USA, 1995, 92, 9801.; 7 R. Zwanzig, Proc. Natl.
Acad. Sci. USA, 1997, 94, 148.; 8 R. Doyle, K. Simons, H. Qian and D. Baker, Proteins Struct.
Funct. Genet., 1997, 29, 282.; 9 K. Iguchi, Int. J. Mod. Phys. B, 2002, 16, 1807.; 10 P. Bruscolini
and A. Pelizzola, Phys. Rev. Lett., 2002, 88art. no. 258101.; 11 V. Munõz, P. A. Thompson, J.
Hofrichter and W. A. Eaton, Nature, 1997, 390, 196.; 12 V. Munõz and W. A. Eaton, Proc. Natl.
Acad. Sci. USA, 1999, 96, 11 311.; 13 E. Alm and D. Baker, Proc. Natl. Acad. Sci. USA, 1999, 96,
11 305.; 14 O. V. Galzitskaya and A. V. Finkelstein, Proc. Natl. Acad. Sci USA, 1999, 96, 11 299.;
15 D. Baker, Nature, 2000, 405, 39.; 16 A. Flammini, J. R. Banavar and A. Maritan, Europhys. Lett.,
2002, 58, 623.; 17 M. Carrion-Vazquez, A. F. Oberhauser, T. F. Fisher, P. E. Marszalek, H. Li and J.
M. Fernandez, Prog. Biophys. Molec. Biol., 2000, 74, 63.; 18 A. Engel, H. E. Gaub and D. J.
Muller, Curr. Biol., 1999, 9, R133–R136.; 19 H. P. Erickson, Science, 1997, 276, 1090.; 20 M. S.
Kellermayer, S. B. Smith, H. L. Granzier and C. Bustamante, Science, 1997, 276, 1112.; 21 X.
Zhuang, T. Ho, H. D. Kim, T. Centner, S. Labeit and S. Chu, Proc. Natl. Acad. Sci., USA, 2000, 97,
14 241.; 22 A. Boeglin, X.-G. Zhang and S. H. Lin, Physica A, 1986, 137, 439.; 23 T. Kikuchi,
Biophys. Chem., 1997, 65, 109.; 24 T. Kikuchi, Biophys. Chem., 2000, 85, 93.; 25 T. L. Hill,
Introduction to Statistical Thermodynamics Dover, New York, 1986.; 26 S. H. Lin, R. G. Alden, R.
Islampour, H. Ma and A. A. Villaeys, Density Matrix Method and Femtosecond Processes World
Scientific, 1991.; 27 W. Colo’n, G. A. Elo‥ ve, L. P. Wakem, F. Shweman and H. Roder,
Biochemistry, 1996, 35, 5538.; 28 P. A. Thompson, V. Munoz, G. S. Jas, E. R. Henry, W. A. Eaton
and J. Hofrichter, J. Phys. Chem.B, 2000, 104, 378.; 29 B. Gillespie and K. W. Plaxco, Proc. Natl.
Acad. Sci. USA, 2000, 97, 12 014.; 30 H. Eyring, D. Henderson, B. J. Stover and E. M. Eyring,
Statistical Mechanics and Dynamics Wiley-Interscience, 1964.; 31 A. F. Oberhauser, P. K. Hansma,
M. Carrion-Vazquez and J. M. Fernandez, Proc. Natl. Acad. Sci., USA, 2001, 98, 468.; 32 H.
Eyring, S. H. Lin and S. M. Lin Basic Chemical Kinetics Wiley-Interscience, New York, 1981, pp.
438–448.