Thermodynamic Principle Revisited: Theory of Protein Folding
Author(s)
Yi Fang
ABSTRACT
Anfinsen’s thermodynamic hypothesis is reviewed and misunderstandings are clarified. It really should be called the thermodynamic principle of protein folding. Energy landscape is really just the mathematical graph of the Gibbs free energy function G(X;U ,EN), a very high dimensional hyper surface. Without knowing it any picture of the Gibbs free energy landscape has no theoretical base, including the funnel shape claims. New insight given by newly obtained analytic Gibbs free energy function G(X;U ,EN) of protein folding derived via quantum statistical mechanics are discussed. Disputes such as target-based or cause-based; what is the folding force, hydrophobic effect or hydrophilic force? Single molecule or ensemble of molecules to be used for the statistical physics study of protein folding, are discussed. Classical observations of 1970’s and 1980’s about global geometric characteristics of native structures of globular proteins turn out to have grabbed the essence of protein folding, but unfortunately have been largely forgotten.
Anfinsen’s thermodynamic hypothesis is reviewed and misunderstandings are clarified. It really should be called the thermodynamic principle of protein folding. Energy landscape is really just the mathematical graph of the Gibbs free energy function G(X;U ,EN), a very high dimensional hyper surface. Without knowing it any picture of the Gibbs free energy landscape has no theoretical base, including the funnel shape claims. New insight given by newly obtained analytic Gibbs free energy function G(X;U ,EN) of protein folding derived via quantum statistical mechanics are discussed. Disputes such as target-based or cause-based; what is the folding force, hydrophobic effect or hydrophilic force? Single molecule or ensemble of molecules to be used for the statistical physics study of protein folding, are discussed. Classical observations of 1970’s and 1980’s about global geometric characteristics of native structures of globular proteins turn out to have grabbed the essence of protein folding, but unfortunately have been largely forgotten.
Cite this paper
Fang, Y. (2015) Thermodynamic Principle Revisited: Theory of Protein Folding. Advances in Bioscience and Biotechnology, 6, 37-48. doi: 10.4236/abb.2015.61005.
Fang, Y. (2015) Thermodynamic Principle Revisited: Theory of Protein Folding. Advances in Bioscience and Biotechnology, 6, 37-48. doi: 10.4236/abb.2015.61005.
References
[1] Ben-Naim, A. (2011) Pitfalls in Anfinsen’s Thermodynamic Hypothesis. Chemical Physics Letters, 511, 126-128.
http://dx.doi.org/10.1016/j.cplett.2011.05.049 [2] Müller, I. (2010) Miscellania about Entropy, Energy, and Available Free Energy. Symmetry, 2, 916-934.
http://dx.doi.org/10.3390/sym2020916 [3] Anfinsen, C.B. (1973) Principles that Govern the Folding of Protein Chains. Science, 181, 223-230.
http://dx.doi.org/10.1126/science.181.4096.223 [4] Wang, Y., Zhang, H., Li, W. and Scott, R.A. (1995) Discriminating Compact Nonnative Structure from the Native Structure of Globular Proteins. PNAS, 92, 709-713. [5] Kaushik, A. and Gupta, E. (2013) Protein Folding grand Challenge: Hydrophobic vs. Hydrophilic Forces. Journal of Biomolecular Structure and Dynamics, 31, 1011-1012. [6] Ben-Naim, A. (2012) Levinthal’s Question Revisited, and Answered. Journal of Biomolecular Structure and Dynamics, 30, 113-124.
http://dx.doi.org/10.1080/07391102.2012.674286 [7] Lazaridis, T. and Karplus, M. (2003) Thermodynamics of Protein Folding: A Microscopic View. Biophysical Chemistry, 100, 367-395.
http://dx.doi.org/10.1016/S0301-4622(02)00293-4 [8] Ben-Naim, A. (2013) Response to Comments on My Article: Liventhal’s Question Revisited and Answered. Ben-Naim A. (2012) Journal of Biomolecular Structure and Dynamics, 30, 113-124. Journal of Biomolecular Structure and Dynamics, 31, 1028-1033.
http://dx.doi.org/10.1080/07391102.2012.748548 [9] Schafer, N.P., Kim, B.L., Zhang, Q. and Wolynes, P.G. (2013) Learning to Fold Protein Using Energy Landscape Theory. arXiv:1312.7283v1 [q-bio.BM]
http://arxiv.org/pdf/1312.7283.pdf [10] Liu, S.Q., Ji, X.L., Tao, Y., Tan, D.Y., Zhang, K.Q. and Fu, Y.X. (2012) Protein Folding, Binding and Energy Landscape: A Synthesis. In: Kaumaya, P.T.P., Ed., Protein Engineering, Intech, Rijeka, 207-253. [11] Fang, Y. (2015) Why Ben-Naim’s Deepest Pitfall Does Not Exist. To Appear in Open Journal of Biophysics. [12] Fang, Y. (2012) Gibbs Free Energy Formula for Protein Folding. In: Morales-Rodriguez, R., Ed., Thermodynamics—Fundamentals and Its Application in Science, Intech, Rijeka, 47-82.
http://www.intechopen.com/books/thermodynamics-fundamentals-and-its-application-in-science [13] Fang, Y. (2013) Ben-Naim’s Pitfalls: Don Quixote’s Windmill. Open Journal of Biophysics, 3, 13-21. [14] Fang, Y. (2014) The Second Law, Gibbs Free Energy, Geometry, and Protein Folding. Journal of Advances in Physics, 3, 278-285. [15] Fang, Y. (2014) A Gibbs Free Energy Formula for Protein Folding Derived from Quantum Statistics. Science China Physics, Mechanics & Astronomy, 57, 1547-1551.
http://dx.doi.org/10.1007/s11433-013-5288-x [16] Gillet, J. and Ghosh, I. (2013) Concepts on the Protein Folding Problem. Journal of Biomolecular Structure and Dynamics, 31, 1020-1023.
http://dx.doi.org/10.1080/07391102.2012.748546 [17] Bader, R.F.W. (1990) Atoms in Molecules: A Quantum Theory. Clarendon Press, Oxford. [18] Pippard, A.A. (1957) The Elements of Classical Thermodynamics. Cambridge University Press, Cambridge. [19] Richards, F.M. (1977) Areas, Volumes, Packing, and Protein Structure. Annual Review of Biophysics and Bioengineering, 6, 151-176.
http://dx.doi.org/10.1146/annurev.bb.06.060177.001055 [20] Tuñón, I., Silla, E. and Pascual-Ahuir, J.L. (1992) Molecular Surface Area and Hydrophobic Effect. Protein Engineering, Design and Selection, 5, 715-716.
http://dx.doi.org/10.1093/protein/5.8.715 [21] Jackson, R.M. and Sternberg, M.J.E. (1993) Protein Surface Area Defined. Nature, 366, 638.
http://dx.doi.org/10.1038/366638b0 [22] Eisenberg, D. and McLachlan, A.D. (1986) Solvation Energy in Protein Folding and Binding. Nature, 319, 199-203.
http://dx.doi.org/10.1038/319199a0 [23] Fang, Y. and Jing, J. (2008) Implementation of a Mathematical Protein Folding Model. International Journal of Pure and Applied Mathematics, 42, 481-488. [24] Ben-Naim, A. (2013) Comment on a Paper: “Ben-Naim’s ‘Pitfalls’: Don Quixote’s Windmill” by Y. Fang, Open Journal of Biophysics, 2013, 3, 13-21. Open Journal of Biophysics, 3, 275-276. [25] Fang, Y. and Jing, J. (2010) Geometry, Thermodynamics, and Protein. Journal of Theoretical Biology, 262, 383-390.
http://dx.doi.org/10.1016/j.jtbi.2009.09.013 [26] Hubner, I.A. and Shakhnovic, E.I. (2005) Geometric and Physical Considerations for Realistic Protein Models. Physical Review E, 72, Article ID: 022901.
http://dx.doi.org/10.1103/PhysRevE.72.022901 [27] Lee, B. and Richards, F.M. (1971) The Interpretation of Protein Structures: Estimation of Static Accessibility. Journal of Molecular Biology, 55, 379-400.
http://dx.doi.org/10.1016/0022-2836(71)90324-X [28] Janin, J. (1976) Surface Area of Globular Proteins. Journal of Molecular Biology, 105, 13-14.
http://dx.doi.org/10.1016/0022-2836(76)90192-3 [29] Richards, F.M. (1979) Packing Defects, Cavities, Volume Fluctuations, and Access to the Interior of Proteins. Including Some General Comments on Surface Area and Protein Structure. Carlsberg Research Communications, 44, 47-63.
http://dx.doi.org/10.1007/BF02906521 [30] Novotny, J., Bruccoleri, R. and Karplus, M. (1984) An Analysis of Incorrectly Folded Protein Models: Implications for Structure Predictions. Journal of Molecular Biology, 177, 787-818.
http://dx.doi.org/10.1016/0022-2836(84)90049-4 [31] Novotny, J., Rashin, A.A. and Bruccoleri, R. (1986) Criteria that Discriminate between Native Proteins and Incorrectly Folded Models. Proteins, 4, 19-30.
http://dx.doi.org/10.1002/prot.340040105 [32] Fang, Y. (2005) Mathematical Protein Folding Problem. In: Hoffman, D., Ed., Global Theory of Minimal Surfaces. Proceedings of the Clay Mathematical Proceedings, Vol. 2, American Mathematical Society, Clay Mathematics Institute, 611-622.
[1] Ben-Naim, A. (2011) Pitfalls in Anfinsen’s Thermodynamic Hypothesis. Chemical Physics Letters, 511, 126-128.
http://dx.doi.org/10.1016/j.cplett.2011.05.049 [2] Müller, I. (2010) Miscellania about Entropy, Energy, and Available Free Energy. Symmetry, 2, 916-934.
http://dx.doi.org/10.3390/sym2020916 [3] Anfinsen, C.B. (1973) Principles that Govern the Folding of Protein Chains. Science, 181, 223-230.
http://dx.doi.org/10.1126/science.181.4096.223 [4] Wang, Y., Zhang, H., Li, W. and Scott, R.A. (1995) Discriminating Compact Nonnative Structure from the Native Structure of Globular Proteins. PNAS, 92, 709-713. [5] Kaushik, A. and Gupta, E. (2013) Protein Folding grand Challenge: Hydrophobic vs. Hydrophilic Forces. Journal of Biomolecular Structure and Dynamics, 31, 1011-1012. [6] Ben-Naim, A. (2012) Levinthal’s Question Revisited, and Answered. Journal of Biomolecular Structure and Dynamics, 30, 113-124.
http://dx.doi.org/10.1080/07391102.2012.674286 [7] Lazaridis, T. and Karplus, M. (2003) Thermodynamics of Protein Folding: A Microscopic View. Biophysical Chemistry, 100, 367-395.
http://dx.doi.org/10.1016/S0301-4622(02)00293-4 [8] Ben-Naim, A. (2013) Response to Comments on My Article: Liventhal’s Question Revisited and Answered. Ben-Naim A. (2012) Journal of Biomolecular Structure and Dynamics, 30, 113-124. Journal of Biomolecular Structure and Dynamics, 31, 1028-1033.
http://dx.doi.org/10.1080/07391102.2012.748548 [9] Schafer, N.P., Kim, B.L., Zhang, Q. and Wolynes, P.G. (2013) Learning to Fold Protein Using Energy Landscape Theory. arXiv:1312.7283v1 [q-bio.BM]
http://arxiv.org/pdf/1312.7283.pdf [10] Liu, S.Q., Ji, X.L., Tao, Y., Tan, D.Y., Zhang, K.Q. and Fu, Y.X. (2012) Protein Folding, Binding and Energy Landscape: A Synthesis. In: Kaumaya, P.T.P., Ed., Protein Engineering, Intech, Rijeka, 207-253. [11] Fang, Y. (2015) Why Ben-Naim’s Deepest Pitfall Does Not Exist. To Appear in Open Journal of Biophysics. [12] Fang, Y. (2012) Gibbs Free Energy Formula for Protein Folding. In: Morales-Rodriguez, R., Ed., Thermodynamics—Fundamentals and Its Application in Science, Intech, Rijeka, 47-82.
http://www.intechopen.com/books/thermodynamics-fundamentals-and-its-application-in-science [13] Fang, Y. (2013) Ben-Naim’s Pitfalls: Don Quixote’s Windmill. Open Journal of Biophysics, 3, 13-21. [14] Fang, Y. (2014) The Second Law, Gibbs Free Energy, Geometry, and Protein Folding. Journal of Advances in Physics, 3, 278-285. [15] Fang, Y. (2014) A Gibbs Free Energy Formula for Protein Folding Derived from Quantum Statistics. Science China Physics, Mechanics & Astronomy, 57, 1547-1551.
http://dx.doi.org/10.1007/s11433-013-5288-x [16] Gillet, J. and Ghosh, I. (2013) Concepts on the Protein Folding Problem. Journal of Biomolecular Structure and Dynamics, 31, 1020-1023.
http://dx.doi.org/10.1080/07391102.2012.748546 [17] Bader, R.F.W. (1990) Atoms in Molecules: A Quantum Theory. Clarendon Press, Oxford. [18] Pippard, A.A. (1957) The Elements of Classical Thermodynamics. Cambridge University Press, Cambridge. [19] Richards, F.M. (1977) Areas, Volumes, Packing, and Protein Structure. Annual Review of Biophysics and Bioengineering, 6, 151-176.
http://dx.doi.org/10.1146/annurev.bb.06.060177.001055 [20] Tuñón, I., Silla, E. and Pascual-Ahuir, J.L. (1992) Molecular Surface Area and Hydrophobic Effect. Protein Engineering, Design and Selection, 5, 715-716.
http://dx.doi.org/10.1093/protein/5.8.715 [21] Jackson, R.M. and Sternberg, M.J.E. (1993) Protein Surface Area Defined. Nature, 366, 638.
http://dx.doi.org/10.1038/366638b0 [22] Eisenberg, D. and McLachlan, A.D. (1986) Solvation Energy in Protein Folding and Binding. Nature, 319, 199-203.
http://dx.doi.org/10.1038/319199a0 [23] Fang, Y. and Jing, J. (2008) Implementation of a Mathematical Protein Folding Model. International Journal of Pure and Applied Mathematics, 42, 481-488. [24] Ben-Naim, A. (2013) Comment on a Paper: “Ben-Naim’s ‘Pitfalls’: Don Quixote’s Windmill” by Y. Fang, Open Journal of Biophysics, 2013, 3, 13-21. Open Journal of Biophysics, 3, 275-276. [25] Fang, Y. and Jing, J. (2010) Geometry, Thermodynamics, and Protein. Journal of Theoretical Biology, 262, 383-390.
http://dx.doi.org/10.1016/j.jtbi.2009.09.013 [26] Hubner, I.A. and Shakhnovic, E.I. (2005) Geometric and Physical Considerations for Realistic Protein Models. Physical Review E, 72, Article ID: 022901.
http://dx.doi.org/10.1103/PhysRevE.72.022901 [27] Lee, B. and Richards, F.M. (1971) The Interpretation of Protein Structures: Estimation of Static Accessibility. Journal of Molecular Biology, 55, 379-400.
http://dx.doi.org/10.1016/0022-2836(71)90324-X [28] Janin, J. (1976) Surface Area of Globular Proteins. Journal of Molecular Biology, 105, 13-14.
http://dx.doi.org/10.1016/0022-2836(76)90192-3 [29] Richards, F.M. (1979) Packing Defects, Cavities, Volume Fluctuations, and Access to the Interior of Proteins. Including Some General Comments on Surface Area and Protein Structure. Carlsberg Research Communications, 44, 47-63.
http://dx.doi.org/10.1007/BF02906521 [30] Novotny, J., Bruccoleri, R. and Karplus, M. (1984) An Analysis of Incorrectly Folded Protein Models: Implications for Structure Predictions. Journal of Molecular Biology, 177, 787-818.
http://dx.doi.org/10.1016/0022-2836(84)90049-4 [31] Novotny, J., Rashin, A.A. and Bruccoleri, R. (1986) Criteria that Discriminate between Native Proteins and Incorrectly Folded Models. Proteins, 4, 19-30.
http://dx.doi.org/10.1002/prot.340040105 [32] Fang, Y. (2005) Mathematical Protein Folding Problem. In: Hoffman, D., Ed., Global Theory of Minimal Surfaces. Proceedings of the Clay Mathematical Proceedings, Vol. 2, American Mathematical Society, Clay Mathematics Institute, 611-622.