Table of Contents
International Journal of Statistical Mechanics
Volume 2014 (2014), Article ID 439891, 11 pages
http://dx.doi.org/10.1155/2014/439891
Research Article

Exact Solution to the Extended Zwanzig Model for Quasi-Sigmoidal Chemically Induced Denaturation Profiles: Specific Heat and Configurational Entropy

1Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México-Centro Historico, Fray Servando Teresa de Mier 99, 06080 México, DF, Mexico
2Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México-Cuautepec, Avendia la Corona 320 Loma La Palma, 07160 México, DF, Mexico

Received 12 August 2013; Revised 25 November 2013; Accepted 2 December 2013; Published 23 January 2014

Academic Editor: Liao Y. Chen

Copyright © 2014 G. E. Aguilar-Pineda and L. Olivares-Quiroz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. B. Anfinsen, “Principles that govern the folding of protein chains,” Science, vol. 181, no. 4096, pp. 223–230, 1973. View at Google Scholar · View at Scopus
  2. N. K. Nagradova, “Protein folding in the cell: on the mechanisms of its acceleration,” Biochemistry, vol. 69, no. 8, pp. 830–843, 2004. View at Publisher · View at Google Scholar · View at Scopus
  3. R. D. Schaeffer and V. Daggett, “Protein folds and protein folding,” Protein Engineering, Design and Selection, vol. 24, no. 1-2, pp. 11–19, 2011. View at Publisher · View at Google Scholar
  4. A. V. Finkelstein and O. Ptitsyn, Protein Physics: A Course of Lectures, Academic Press, San Diego, Calif, USA, 1st edition, 2002.
  5. K. A. Dill, S. B. Ozkan, M. S. Shell, and T. R. Weikin, “The protein folding problem,” Annual Review of Biophysics, vol. 37, pp. 289–316, 2008. View at Publisher · View at Google Scholar
  6. V. N. Uversky and A. K. Dunker, “Understanding protein non-folding,” Biochimica et Biophysica Acta, vol. 1804, no. 6, pp. 1231–1264, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. J. H. Chen, “Towards the physical basis of how intrinsic disorder mediates protein function,” Archives of Biochemistry and Biophysics, vol. 524, no. 12, pp. 123–131, 2012. View at Publisher · View at Google Scholar
  8. V. N. Uversky, “A decade and a half of protein intrinsic disorder: biology still waits for physics,” Protein Science, vol. 22, no. 6, pp. 693–724, 2013. View at Publisher · View at Google Scholar
  9. O. Hecht, C. Macdonald, and G. R. Moore, “Intrinsically disordered proteins: lessons from colicins,” Biochemical Society Transactions, vol. 40, no. 6, pp. 1534–1538, 2012. View at Publisher · View at Google Scholar
  10. J. Ramprakash, V. Doseeva, A. Galkin et al., “Comparison of the chemical and thermal denaturation of proteins by a two-state transition model,” Analytical Biochemistry, vol. 374, no. 1, pp. 221–230, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. Y. Cao and H. Li, “How do chemical denaturants affect the mechanical folding and unfolding of proteins?” Journal of Molecular Biology, vol. 375, no. 1, pp. 316–324, 2007. View at Publisher · View at Google Scholar
  12. D. R. Canchi and A. E. Garcia, “Cosolvent effects on protein stability,” Annual Review of Physical Chemistry, vol. 64, pp. 273–293, 2013. View at Publisher · View at Google Scholar
  13. J. L. England and G. Haran, “Role of solvation effects in protein denaturation: from thermodynamics to single molecules and back,” Annual Review of Physical Chemistry, vol. 62, pp. 257–277, 2011. View at Publisher · View at Google Scholar
  14. A. Das and C. Mukhopadhyay, “Urea-mediated protein denaturation: a consensus view,” Journal of Physical Chemistry B, vol. 113, no. 38, pp. 12816–12824, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. Z. Yang, P. Xiu, B. Shi, L. Hua, and R. Zhou, “Coherent microscopic picture for urea-induced denaturation of proteins,” Journal of Physical Chemistry B, vol. 116, no. 30, pp. 8856–8862, 2012. View at Publisher · View at Google Scholar
  16. E. Fisicaro, C. Compari, and A. Braibanti, “Hydrophobic hydration processes: thermal and chemical denaturation of proteins,” Biophysical Chemistry, vol. 156, no. 1, pp. 51–67, 2011. View at Publisher · View at Google Scholar · View at Scopus
  17. R. Gupta and F. Ahmad, “Protein stability: functional dependence of denaturational gibbs energy on urea concentration,” Biochemistry, vol. 38, no. 8, pp. 2471–2479, 1999. View at Publisher · View at Google Scholar · View at Scopus
  18. S. T. Whitten, J. O. Wooll, R. Razeghifard, E. B. García-Moreno, and V. J. Hilser, “The origin of pH-dependent changes in m-values for the denaturant-induced unfolding of proteins,” Journal of Molecular Biology, vol. 309, no. 5, pp. 1165–1175, 2001. View at Publisher · View at Google Scholar · View at Scopus
  19. M. Hamzeh-Mivehroud, A. A. Alizade, M. Ahmadifar, and S. Dastmalchi, “In silico evaluation of crosslinking effects on denaturant meq values and ΔCp upon protein unfolding,” Avicenna Journal of Medical Biotechnology, vol. 4, no. 1, pp. 23–34, 2012. View at Google Scholar · View at Scopus
  20. M. Auton, L. M. Holthauzen, and D. W. Bolen, “Anatomy of energetic changes accompanying urea-induced protein denaturation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 104, no. 39, pp. 15317–15322, 2007. View at Publisher · View at Google Scholar
  21. B. J. Bennion and V. Daggett, “The molecular basis for the chemical denaturation of proteins by urea,” Proceedings of the National Academy of Sciences of the United States of America, vol. 100, no. 9, pp. 5142–5147, 2003. View at Publisher · View at Google Scholar
  22. D. R. Canchi, D. Paschek, and A. E. Garcia, “Equilibrium study of protein denaturation by urea,” Journal of the American Chemical Society, vol. 132, no. 7, pp. 2338–2344, 2010. View at Publisher · View at Google Scholar · View at Scopus
  23. V. Tozzini, “Coarse-grained models for proteins,” Current Opinion in Structural Biology, vol. 15, no. 2, pp. 144–150, 2005. View at Publisher · View at Google Scholar
  24. S. O. Nielsen, C. F. Lopez, G. Srinivas, and M. L. Klein, “Coarse grain models and the computer simulation of soft materials,” Journal of Physics, vol. 16, no. 15, article R481, 2004. View at Publisher · View at Google Scholar
  25. C. Clementi, “Coarse-grained models of protein folding: toy models or predictive tools?” Current Opinion in Structural Biology, vol. 18, no. 1, pp. 10–15, 2008. View at Publisher · View at Google Scholar
  26. I. Bahar and A. J. Rader, “Coarse-grained normal mode analysis in structural biology,” Current Opinion in Structural Biology, vol. 15, no. 5, pp. 586–592, 2005. View at Publisher · View at Google Scholar
  27. V. Tozzini, “Minimalist models for proteins: a comparative analysis,” Quarterly Reviews of Biophysics, vol. 43, no. 3, pp. 333–371, 2010. View at Publisher · View at Google Scholar
  28. R. Zwanzig, “Simple model of protein folding kinetics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 92, no. 21, pp. 9801–9804, 1995. View at Google Scholar
  29. S. Lifson and A. Roig, “On the theory of helix-coil transition in polypeptides,” Journal of Chemical Physics, vol. 34, pp. 1963–1974, 1961. View at Publisher · View at Google Scholar
  30. K. A. Dill and S. Bromberg, “Molecular driving forces: statistical thermodynamics,” in Biology, Physics, Chemistry and Nanosciece, Garland Science, Boca Raton, Fla, USA, 2nd edition, 2010. View at Google Scholar
  31. M. M. Tirion, “Large amplitude elastic motions in proteins from a single-parameter, atomic analysis,” Physical Review Letters, vol. 77, no. 9, pp. 1905–1908, 1996. View at Publisher · View at Google Scholar
  32. A. R. Atilgan, S. R. Durell, R. L. Jernigan, M. C. Demirel, O. Keskin, and I. Bahar, “Anisotropy of fluctuation dynamics of proteins with an elastic network model,” Biophysical Journal, vol. 80, no. 1, pp. 505–515, 2001. View at Google Scholar · View at Scopus
  33. N. Leioatts, T. D. Romo, and A. Grossfield, “Elastic network models are robust to variations in formalism,” Journal of Chemical Theory and Computation, vol. 8, no. 7, pp. 2424–2434, 2012. View at Publisher · View at Google Scholar
  34. L. Olivares-Quiroz and L. S. Garcia-Colin, “Protein's native state stability in a chemically induced denaturation mechanism,” Journal of Theoretical Biology, vol. 246, no. 2, pp. 214–224, 2007. View at Publisher · View at Google Scholar · View at Scopus
  35. P. I. Zhuravlev, C. K. Materese, and G. A. Papoian, “Deconstructing the native state: energy landscapes, function, and dynamics of globular proteins,” Journal of Physical Chemistry B, vol. 113, no. 26, pp. 8800–8812, 2009. View at Publisher · View at Google Scholar · View at Scopus
  36. L. Olivares-Quiroz, “El modelo extendido de Zwanzig y la desnaturalización de proteínas,” in La Fisica Biológica en México 2, L. G.-C. Scherer and L. Dagdug, Eds., pp. 141–171, El Colegio Nacional, Mexico City, Mexico, 1st edition, 2008. View at Google Scholar
  37. L. Olivares-Quiroz, “Thermodynamics of ideal proteinogenic homopolymer chains as a function of the energy spectrum E, helical propensity ω and enthalpic energy barrier,” Journal of Physics, vol. 25, no. 15, article 155103, 2013. View at Publisher · View at Google Scholar
  38. J. Zhang, W. Li, J. Wang et al., “Protein folding simulations: from coarse-grained model to all-atom model,” IUBMB Life, vol. 61, no. 6, pp. 627–643, 2009. View at Publisher · View at Google Scholar · View at Scopus
  39. S. Teso, C. D. Risio, A. Passerini, and R. B. Battiti, “An on/off lattice approach to protein structure prediction from contact maps,” in Pattern Recognition in Bioinformatics, T. M. H. Dijkstra, E. Tsivtsivadze, E. Marchiori, and T. Heskes, Eds., vol. 6282 of Lecture Notes in Computer Science, pp. 368–379, Springer, Berlin, Germany, 2010. View at Publisher · View at Google Scholar
  40. I. Dotu, M. Cebrián, P. Van Hentenryck, and P. Clote, “On lattice protein structure prediction revisited,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 6, pp. 1620–1632, 2011. View at Publisher · View at Google Scholar · View at Scopus
  41. D. J. Wales, Energy Landscapes: With Applications to Clusters, Biomolecules and Glasses, Cambridge Molecular Science, Cambridge University Press, New York, NY, USA, 1st edition, 2003.
  42. Z. Yang, P. Xiu, B. Shi, L. Hua, and R. Zhou, “Coherente macroscopic picture for urea-induced denaturation of proteins,” Journal of Physical Chemistry B, vol. 116, no. 30, pp. 8856–8862, 2012. View at Google Scholar
  43. E. Butkov, Mathematical Physics, Addison-Wesley, Boston, Mass, USA, 1st edition, 1968.
  44. “Here the term rate means the derivative of α with respect to ζ”.
  45. A. Chakrabartty, T. Kortemme, and R. L. Baldwin, “Helix propensities of the amino acids measured in alanine-based peptides without helix-stabilizing side-chain interactions,” Protein Science, vol. 3, no. 5, pp. 843–852, 1994. View at Google Scholar · View at Scopus
  46. G. Jaeger, “The ehrenfest classification of phase transitions: introduction and evolution,” Archive for History of Exact Sciences, vol. 53, no. 1, pp. 51–81, 1998. View at Publisher · View at Google Scholar
  47. D. P. Sheehan and D. H. E. Gross, “Extensivity and the thermodynamic limit: why size really does matter,” Physica A, vol. 370, no. 2, pp. 461–482, 2006. View at Publisher · View at Google Scholar · View at Scopus
  48. V. Daggett, P. A. Kollman, and I. D. Kuntz, “A molecular dynamics simulation of polyalanine: an analysis of equilibrium motions and helix-coil transitions,” Biopolymers, vol. 31, no. 9, pp. 1115–1134, 1991. View at Google Scholar · View at Scopus
  49. W. Greiner, L. Neise, H. Stöcker, and D. Rischke, Thermodynamics and Statistical Mechanics, Classical Theoretical Physics, Springer, New York, NY, USA, 1st edition, 1995.
  50. D. A. McQuarrie, Statistical Mechanics, University Science Books, Mill Valley, Calif, USA, 1st edition, 2000.
  51. J. K. Martens, I. Compagnon, E. Nicol, T. B. McMahon, C. Clavaguera, and G. Ohanessian, “Globule to helix transition in sodiated polyalanines,” Journal of Physical Chemistry Lettes, vol. 3, no. 22, pp. 3320–3324, 2012. View at Publisher · View at Google Scholar