The Protein Journal

, Volume 30, Issue 7, pp 490–498 | Cite as

Influence of pK a Shifts on the Calculated Dipole Moments of Proteins

  • Brett L. Mellor
  • Shiul Khadka
  • David D. Busath
  • Brian A. Mazzeo


The protein dipole moment is a low-resolution parameter that characterizes the second-order charge organization of a biomolecule. Theoretical approaches to calculate protein dipole moments rely on pK a values, which are either computed individually for each ionizable residue or obtained from model compounds. The influence of pK a shifts are evaluated first by comparing calculated and measured dipole moments of β-lactoglobulin. Second, calculations are made on a dataset of 66 proteins from the Protein Data Bank, and average differences are determined between dipole moments calculated with model pK as, pK as derived using a Poisson–Boltzmann approach, and empirically-calculated pK as. Dipole moment predictions that neglect pK a shifts are consistently larger than predictions in which they are included. The importance of pK a shifts are observed to vary with protein size, internal permittivity, and solution pH.


Protein electrostatics pKa shifts Dielectric spectroscopy Poisson–Boltzmann Permittivity 




\( \Updelta {\text{p}}K_{\text{a}}^{\text{calc}} \)

Calculated pK a shift

\( \mu_{{}} \)

Dipole moment

\( \mu_{\text{m}} \)

Dipole moment calculated using \( {\text{p}}K_{\text{a}}^{\text{m}} {\text{s}} \)

\( \mu_{\text{pb}} \)

Dipole moment calculated using \( {\text{p}}K_{\text{a}}^{\text{pb}} {\text{s}} \)


Estimation bias


Average percentage difference


Deoxyribonucleic acid


Nuclear magnetic resonance


Protein data bank


Isoelectric point

\( {\text{p}}K_{\text{a}}^{\text{calc}} \)

Calculated pK a

\( {\text{p}}K_{\text{a}}^{\text{e}} \)

Empirically-calculated pK a

\( {\text{p}}K_{\text{a}}^{\text{m}} \)

Model pK a

\( {\text{p}}K_{\text{a}}^{\text{pb}} \)

PoissonBoltzmann calculated pK a

RNase A

Ribonuclease A


Formal charge of the ion


  1. 1.
    Ahmad S, Sarai A (2004) J Mol Biol 341:65–71CrossRefGoogle Scholar
  2. 2.
    Antosiewicz J, Porschke D (1989) Biochem US 28:10072–10078CrossRefGoogle Scholar
  3. 3.
    Bashford D, Karplus M (1990) Biochem US 29:10219–10225CrossRefGoogle Scholar
  4. 4.
    Beroza P, Case DA (1996) J Phys Chem US 100:20156–20163CrossRefGoogle Scholar
  5. 5.
    Cohn EJ, Edsall JT (1943) Proteins, amino acids and peptides. Reinhold Publishing CorporationGoogle Scholar
  6. 6.
    Creighton TE (1993) Proteins: structures and molecular properties, 2nd edn. W H Freeman, New YorkGoogle Scholar
  7. 7.
    Davies MN, Toseland CP, Moss DS, Flower DR (2006) BMC Biochem 7:18CrossRefGoogle Scholar
  8. 8.
    Demchuk E, Wade RC (1996) J Phys Chem US 100:17373–17387CrossRefGoogle Scholar
  9. 9.
    Diamond R (1974) J Mol Biol 82:371–391CrossRefGoogle Scholar
  10. 10.
    Dwyer JJ, Gittis AG, Karp DA, Lattman EE, Spencer DS, Stites WE, Garcia-Moreno B (2000) Biophys J 79:1610–1620CrossRefGoogle Scholar
  11. 11.
    Felder CE, Prilusky J, Silman I, Sussman JL (2007) Nucleic Acids Res 35:W512–W521CrossRefGoogle Scholar
  12. 12.
    Fogolari F, Brigo A, Molinari H (2002) J Mol Recognit 15:377–392CrossRefGoogle Scholar
  13. 13.
    Georgescu RE, Alexov EG, Gunner MR (2002) Biophys J 83:1731–1748CrossRefGoogle Scholar
  14. 14.
    Gordon JC, Myers JB, Folta T, Shoja V, Heath LS, Onufriev A (2005) Nucleic Acids Res 33:W368–W371CrossRefGoogle Scholar
  15. 15.
    Grant JA, Pickup BT, Nicholls A (2001) J Comput Chem 22:608–640CrossRefGoogle Scholar
  16. 16.
    Hasselbalch KA (1916) Biochem US 78:112–144Google Scholar
  17. 17.
    He Y, Xu J, Pan XM (2007) Proteins 69:75–82CrossRefGoogle Scholar
  18. 18.
    Jean-Charles A, Nicholls A, Sharp K, Honig B, Tempczyk A, Hendrickson TF, Still WC (1991) J Am Chem Soc 113:1454–1455CrossRefGoogle Scholar
  19. 19.
    Kantardjiev AA, Atanasov BP (2009) Nucleic Acids Res 37:W422–W427CrossRefGoogle Scholar
  20. 20.
    Keefe SE, Grant EH (1974) Phys Med Biol 19:701–707CrossRefGoogle Scholar
  21. 21.
    Keszthelyi L (2002) Colloid Surf A 209:173–183CrossRefGoogle Scholar
  22. 22.
    Kieseritzky G, Knapp EW (2008) J Comput Chem 29:2575–2581CrossRefGoogle Scholar
  23. 23.
    Kuwata K, Hoshino M, Forge V, Era S, Batt CA, Goto Y (1999) Protein Sci 8:2541–2545CrossRefGoogle Scholar
  24. 24.
    Li H, Robertson AD, Jensen JH (2005) Proteins 61:704–721CrossRefGoogle Scholar
  25. 25.
    Liang ZX, Kurnikov IV, Nocek JM, Mauk AG, Beratan DN, Hoffman BM (2004) J Am Chem Soc 126:2785–2798CrossRefGoogle Scholar
  26. 26.
    MacKenzie H (1971) Milk proteins: chemistry and molecular biology. Academic Press, New YorkGoogle Scholar
  27. 27.
    Madura JD, Briggs JM, Wade RC, Davis ME, Luty BA, Ilin A, Antosiewicz J, Gilson MK, Bagheri B, Scott LR, Mccammon JA (1995) Comput Phys Commun 91:57–95CrossRefGoogle Scholar
  28. 28.
    Mehler EL, Guarnieri F (1999) Biophys J 75:3–22CrossRefGoogle Scholar
  29. 29.
    Mellor BL, Cortes EC, Busath DD, Mazzeo BA (2011) J Phys Chem B 115:2205–2213CrossRefGoogle Scholar
  30. 30.
    Mozo-Villarias A, Cedano J, Querol E (2003) Protein Eng 16:279–286CrossRefGoogle Scholar
  31. 31.
    Nielsen JE (2007) J Mol Graph Model 25:691–699CrossRefGoogle Scholar
  32. 32.
    Nielsen JE, Vriend G (2001) Proteins 43:403–412CrossRefGoogle Scholar
  33. 33.
    Nimrod G, Schushan M, Szilágyi A, Leslie C, Ben-Tal N (2010) Bioinformatics 26:692–693CrossRefGoogle Scholar
  34. 34.
    Nimrod G, Szilagyi A, Leslie C, Ben-Tal N (2009) J Mol Biol 387:1040–1053CrossRefGoogle Scholar
  35. 35.
    Nozaki Y, Tanford C (1967) Method Enzymol 11:715–734CrossRefGoogle Scholar
  36. 36.
    Osapay K, Theriault Y, Wright PE, Case DA (1994) J Mol Biol 244:183–197CrossRefGoogle Scholar
  37. 37.
    Perutz MF (1978) Science 201:1187–1191CrossRefGoogle Scholar
  38. 38.
    Sharp KA, Honig B (1990) Annu Rev Biophys Bio 19:301–332CrossRefGoogle Scholar
  39. 39.
    Smyth CP (1955) Dielectric behavior and structure: dielectric constant and loss, dipole moment and molecular structure. McGraw Hill, New YorkGoogle Scholar
  40. 40.
    South GP, Grant EH (1972) Proc R Soc Lond A Mat 328:371–387CrossRefGoogle Scholar
  41. 41.
    Stanton CL, Houk KN (2001) J Chem Theory Comput 4:951–966CrossRefGoogle Scholar
  42. 42.
    Takashima S (2001) Biopolymers 58:398–409CrossRefGoogle Scholar
  43. 43.
    Tartaglia GG, Cavalli A, Pellarin R, Caflisch A (2004) Protein Sci 13:1939–1941CrossRefGoogle Scholar
  44. 44.
    Thurlkill RL, Grimsley GR, Scholtz JM, Pace CN (2006) Protein Sci 15:1214–1218CrossRefGoogle Scholar
  45. 45.
    Warshel A, Aqvist J (1991) Annu Rev Biophys Bio 20:267–298CrossRefGoogle Scholar
  46. 46.
    Warshel A, Russell ST (1984) Q Rev Biophys 17:283–422CrossRefGoogle Scholar
  47. 47.
    Wlodawer A, Borkakoti N, Moss DS, Howlin B (1986) Acta Crystallogr B 42:379–387CrossRefGoogle Scholar
  48. 48.
    Yang AS, Honig B (1993) J Mol Biol 231:459–474CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Brett L. Mellor
    • 1
  • Shiul Khadka
    • 1
  • David D. Busath
    • 2
  • Brian A. Mazzeo
    • 1
  1. 1.Department of Electrical and Computer EngineeringBrigham Young UniversityProvoUSA
  2. 2.Department of Physiology and Developmental BiologyBrigham Young UniversityProvoUSA

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