The Protein Journal

, Volume 29, Issue 8, pp 617–630 | Cite as

Planck-Benzinger Thermal Work Function: Thermodynamic Characterization of the Carboxy-Terminus of p53 Peptide Fragments



The thermodynamic parameters for six p53 carboxy-terminus peptide fragments as determined by analytical ultracentrifugal analysis were compared over the experimental temperature range of 275–310 K to evaluate the Gibbs free energy change as a function of temperature, ΔG o (T), from 0 to 400 K using our general linear third-order fitting function, ΔG o (T) = α + βT 2 + γT 3. Data obtained at the typical experimental temperature range are not sufficient to accurately describe the variations observed in the oligomerization of these p53 fragments. It is necessary to determine a number of thermodynamic parameters, all of which can be precisely assessed using this general third-order linear fitting function. These are the heat of reaction, innate temperature-invariant enthalpy, compensatory temperatures and the thermodynamic molecular switch occurring at the thermal set point. This methodology can be used to distinguish the characteristic structure and stability of p53 carboxy-terminal fragments or other p53 mutants. It should be used for the thermodynamic characterization of any interacting biological system.


Compensatory Temperature Gibbs Free Energy Change Oligomerization Domain Partial Specific Volume Tetramerization Domain 
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.

List of symbols


Kelvin, one degree on the absolute temperature scale


Melting temperature at which ΔH o (T m ) and TΔS o (T m ) intersect and the ΔG o (T m ) value reaches zero


Harmonious temperature at which ΔH o (T h ) and TΔS o (T h ) intersect and the ΔG o (T h ) value reaches zero


Thermal set point

\( T_{{C_{p} }} \)

Temperature at which ΔC p o (T) value reaches zero


International mathematical subroutine library






Helmholtz free energy


Gibbs free energy change as a function of temperature


Heat flux term

ΔWo(T) = ΔHo(T0) − ΔGo(T)

Planck-Benzinger thermal work function


Innate temperature-invariant enthalpy


Effective free energy from the partition function


Equilibrium constant

ΔCp(T)(+) → ΔCp(T)(−)

Thermodynamic molecular switch at which the Gibbs free energy of reaction reaches a true negative minimum, changing in sign from positive to negative



I wish to thank Dr. Ettore Appella, of the Laboratory of Cell Biology, National Cancer Institute, National Institutes of Health, for providing us the samples of six p53 fragments for the sedimentation equilibrium measurements.


  1. 1.
    Appella E, Sakaguchi K, Sakamoto H, Lewis MS, Omichinski JG, Gronenborn, CGM, Anderson CW (1995) In: Atassi ME, Appella E (eds) Methods in protein structure analysis, chap 36. Plenum Press, New York, pp 397–418Google Scholar
  2. 2.
    Barr DJ, Goodnight P, Helwig JT (1985) SASD GLM 27 and GLM 131 statistical analysis. SAS Institute Inc, CaryGoogle Scholar
  3. 3.
    Bell S, Klein C, Muller L, Hansen S, Buchner J (2002) J Mol Biol 322:017–927CrossRefGoogle Scholar
  4. 4.
    Benzinger TH (1971) Nature (Lond) 229:100–103CrossRefGoogle Scholar
  5. 5.
    Bode AM, Dong Z (2004) Nat Rev Cancer 7:793–805CrossRefGoogle Scholar
  6. 6.
    Chase MW Jr, Davis CA, Downey JK, Fruri JD, McDonald JR, Syverud AN (1985) JANAF thermodynamic tables; Part I, II; 3rd edn, vol 14 American Chemical Society/American Institute of Physics/National Bureau of Standards, Washington DCGoogle Scholar
  7. 7.
    Chun PW (1988) Int J Quantum Chem 15:247–258CrossRefGoogle Scholar
  8. 8.
    Chun PW (1994) J Phys Chem 86:6851–6861CrossRefGoogle Scholar
  9. 9.
    Chun PW (1995) J Biol Chem 270:13925–13931CrossRefGoogle Scholar
  10. 10.
    Chun PW (1996) J Phys Chem 100:7283–7292CrossRefGoogle Scholar
  11. 11.
    Chun PW (1997) J Phys Chem B 101:7835–7843CrossRefGoogle Scholar
  12. 12.
    Chun PW (1998) Application of Planck-Benzinger relationships to biology: methods in enzymol, vol 295, Chap 12:227–268, Academic Press, New YorkGoogle Scholar
  13. 13.
    Chun PW (1999) Int J Quantum Chem 75:1027–1042CrossRefGoogle Scholar
  14. 14.
    Chun PW (2000) Biophys J 78:416–429CrossRefGoogle Scholar
  15. 15.
    Chun PW (2000) Cell Biochem Biophys 33:149–169CrossRefGoogle Scholar
  16. 16.
    Chun PW (2000) Int J Quantum Chem 80:1181–1198CrossRefGoogle Scholar
  17. 17.
    Chun PW (2001) J Colloid Surf 118:183–203CrossRefGoogle Scholar
  18. 18.
    Chun PW (2001) Int J Quantum Chem 85:697–712CrossRefGoogle Scholar
  19. 19.
    Chun PW (2002) Per-Olov Lowdin memorial symposium. Int J Quantum Chem 87:323–353CrossRefGoogle Scholar
  20. 20.
    Chun PW (2003) Biophys J 84:1–18CrossRefGoogle Scholar
  21. 21.
    Chun PW (2003) ScientificWorld J 3:176–193CrossRefGoogle Scholar
  22. 22.
    Chun PW (2004) Int J Quantum Chem 100:994–1002CrossRefGoogle Scholar
  23. 23.
    Chun PW (2005) Physica Scripta T118:219–222CrossRefGoogle Scholar
  24. 24.
    Chun PW (2006) Int J Quantum Chem 106:3018–3031CrossRefGoogle Scholar
  25. 25.
    Chun PW (2007) Int J Quantum Chem 107:3272–3279CrossRefGoogle Scholar
  26. 26.
    Chun PW (2008) Int J Quantum Chem 108:2746–2755CrossRefGoogle Scholar
  27. 27.
    Chun PW (2009) Int J Quantum Chem 109:3827–3839CrossRefGoogle Scholar
  28. 28.
    Chun PW (1991) Manual for computer-aided analysis of biochemical processes. University of Florida PressGoogle Scholar
  29. 29.
    Clore GM, Ernst J, Clubb R, Omichinski JG, Kennedy WM, Sakaguchi K, Appella E, Gronenborn AM (1995) Nat Struct Biol 2:321–333CrossRefGoogle Scholar
  30. 30.
    Clore GM, Omichinski JG, Sakaguchi K, Zambrano N, Sakamoto H, Appella E, Gronenborn AM (1995) Science 267:1515–1516CrossRefGoogle Scholar
  31. 31.
    Davison TS, Nie X, Ma W, Lin Y, Kay C, Benchimol S, Arrowsmith CH (2001) J Mol Biol 307:605–617CrossRefGoogle Scholar
  32. 32.
    Freidler A, Veprintsev DB, Freund SM, von Glos KI, Fersht AR (2005) Structure 13:629–636CrossRefGoogle Scholar
  33. 33.
    Giauque WF (1930) J Am Chem Soc 52:4808–4815CrossRefGoogle Scholar
  34. 34.
    Giauque WF (1930) J Am Chem Soc 52:4816–4831CrossRefGoogle Scholar
  35. 35.
    Giauque WF, Blue RW (1930) J Am Chem Soc 58:831–837CrossRefGoogle Scholar
  36. 36.
    Giauque WF, Kemp JD (1938) J Chem Phys 6:40–52CrossRefGoogle Scholar
  37. 37.
    Giauque WF, Meads PF (1941) J Am Chem Soc 63:1897–1901CrossRefGoogle Scholar
  38. 38.
    Hollestein M, Rice K, Greenblott MS, Sausis T, Fuchs R, Sorlie T, Hovig E, Smith-Soresen B, Montesano RR, Harris CC (1994) Nucl Acid Res 22:3551–3555Google Scholar
  39. 39.
    Itahana Y, Kie H, Zhang Y (2008) J Biol Chem 284:5158–5164CrossRefGoogle Scholar
  40. 40.
    Jeffrey PD, Gorina S, Pavletich NP (1995) Science 267:1498–1502CrossRefGoogle Scholar
  41. 41.
    Joerger AC, Allen MD, Fersht AR (2004) J Biol Chem 792:1291–1296Google Scholar
  42. 42.
    Joerger AC, Fersht AR (2007) Oncogene. 20:2226–2242 via Joerger AC, Fersht AR (2008) Ann Rev Biochem 77:557–582Google Scholar
  43. 43.
    Lee W, Harvey TS, Yin Y, Yau P, Litchfield D, Arrowsmith CH (1994) Nat Struct Biol 1:877–890CrossRefGoogle Scholar
  44. 44.
    Levine AJ, Hu W, Feng Z (2006) Cell Death Differ 13:1027–1036CrossRefGoogle Scholar
  45. 45.
    Levine AJ (1997) Cell 88:323–331CrossRefGoogle Scholar
  46. 46.
    Lewis GN, Randall M (1961) Thermodynamics. In: Pitzer KS, Brewer L (eds) McGraw Hill, New York, pp 164–162, appendix 665–668Google Scholar
  47. 47.
    Lewis MS (1995) Tables of p53 peptide fragments containing mean values of ln K as a function of temperature. Personal communicationGoogle Scholar
  48. 48.
    Luo J, Su F, Chen D, Shiloh A, Gu W (2000) Nature 408:377–381CrossRefGoogle Scholar
  49. 49.
    Magar EM, Chun PW (1973) Biophys Chem 1:18–27CrossRefGoogle Scholar
  50. 50.
    Mateu MG, Fersht AR (1998) EMBO J 17:2748–2758CrossRefGoogle Scholar
  51. 51.
    Mateu MG, Sanchez Del Pino MM, Fersht AR (1999) Nat Struct Biol 6:191–198CrossRefGoogle Scholar
  52. 52.
    Miller M, Libkowski JL, Mohan Rao JK, Danishesky AT, Omichinski JG, Sakaguchi K, Sakamoto H, Appella E, Gronenborn AM, Clore GM (1996) FEBS Lett 399:166–170CrossRefGoogle Scholar
  53. 53.
    Mittl PR, Chen P, Grutter MG (1998) Acta Crystallogr 54:86–89Google Scholar
  54. 54.
    Moelwyn-Hughes EA (1957) Physical chemistry. Pergamon Press, New York, pp 90–103 264–279, 560–569Google Scholar
  55. 55.
    Mujata S, He Y, Zang L, Yan S, Plotnikova O, Sanchez SR, Zeleznik-Le NJ, Ronai Z, Zhou MM (2004) Mol Cell 13:251–263CrossRefGoogle Scholar
  56. 56.
    Pavletich N, Chambers KA, Pablo CO (1993) Genes Dev 7:2556–2564CrossRefGoogle Scholar
  57. 57.
    Pietsch EC, Sykes SM, McMahen SB, Murphy ME (2008) Oncogene 27:6507–6521CrossRefGoogle Scholar
  58. 58.
    Pise-Masison CA, Radonovich M, Sakaguchi K, Appella E, Brady JN (1998) J Virol 72:6348–6355Google Scholar
  59. 59.
    Planck M (1927) Vorlesungen-uber thermodynamics, 7th edn (trans: Ogg JG) as Treatise on thermodynamics, Longmans Green and Co., London, pp 164–182, appendix 665–668Google Scholar
  60. 60.
    Rossin FD, Wagnman DD (1952) Circular of the national bureau of standards 500 related values of chemical thermodynamic properties. US Government Printing Office, Washington, DCGoogle Scholar
  61. 61.
    Rustandi RR, Baldisseri DM, Weber DJ (2000) Nat Struct Biol 7:570–574CrossRefGoogle Scholar
  62. 62.
    Sakamoto H, Lewis MS, Kodama H, Appella E, Sakaguchi A (1994) Pro Nat Acad Sci USA 91:8974–8978CrossRefGoogle Scholar
  63. 63.
    Sakaguchi K, Herrera J, Sato S, Miki T, Bustin M, Vassilev A, Anderson CW, Appella E (1998) Cell 89:1175–1184Google Scholar
  64. 64.
    Sakaguchi K, Sakamoto H, Xie D, Erickson W, Lewis MS, Anderson CW, Appella E (1997) J Protein Chem 16:553–556CrossRefGoogle Scholar
  65. 65.
    Sakagichi K, Sakamoto H, Lewis MS, Anderson CW, Erickson JW, Appella E, Xie D (1997) Biochemistry 36:10117–10124CrossRefGoogle Scholar
  66. 66.
    Sakaguchi K, Saito S, Higashimoto Y, Roy S, Anderson CW, Appella E (1997) J Biol Chem 275:9278–9283CrossRefGoogle Scholar
  67. 67.
    Shaulian E, Zauberman A, Ginsberg D, Oren M (1992) Mol Cell Biol 12:5581Google Scholar
  68. 68.
    Steegena WT, van der Eb AJ, Jochemson AG (2007) J Mol Biol 263:103–113CrossRefGoogle Scholar
  69. 69.
    Sturzbeche HW, Brain R, Addison C, Rudge R, Remm M, Grimaldi M, Keenan E, Jenkins JR (1992) Oncogene 7:1513–1523Google Scholar
  70. 70.
    Toledo F, Wahl GM (2006) Nat Rev Cancer 6:909–923CrossRefGoogle Scholar
  71. 71.
    Vogelstein B, Lane D, Levine AJ (2000) Nature 408:307–310CrossRefGoogle Scholar
  72. 72.
    Vousden KH, Lu X (2000) Nat Rev Cancer 2:594–604CrossRefGoogle Scholar
  73. 73.
    Wang P, Reed M, Wang Y, Mayr G, Stenger J, Anderson ME, Schwedes ME, Tegtmeyer P (1994) Mol Cell Biol 14:5182–5191Google Scholar
  74. 74.
    Weinberg RL, Freund SM, Veprintsev DB, Bycroft M, Fersht AR (2004) J Mol Biol 341:1145–1159CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Biochemistry and Molecular Biology, College of MedicineUniversity of FloridaGainesvilleUSA
  2. 2.Analytical Ultracentrifugation by Marc S. Lewis, formerly of the Biomedical Engineering and Instrumentation ProgramNational Center for Research ResourcesBethesdaUSA

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