Logo of biophysjLink to Publisher's site
Biophys J. 2002 Oct; 83(4): 1731–1748.
PMCID: PMC1302268

Combining conformational flexibility and continuum electrostatics for calculating pK(a)s in proteins.


Protein stability and function relies on residues being in their appropriate ionization states at physiological pH. In situ residue pK(a)s also provides a sensitive measure of the local protein environment. Multiconformation continuum electrostatics (MCCE) combines continuum electrostatics and molecular mechanics force fields in Monte Carlo sampling to simultaneously calculate side chain ionization and conformation. The response of protein to charges is incorporated both in the protein dielectric constant (epsilon(prot)) of four and by explicit conformational changes. The pK(a) of 166 residues in 12 proteins was determined. The root mean square error is 0.83 pH units, and >90% have errors of <1 pH units whereas only 3% have errors >2 pH units. Similar results are found with crystal and solution structures, showing that the method's explicit conformational sampling reduces sensitivity to the initial structure. The outcome also changes little with protein dielectric constant (epsilon(prot) 4-20). Multiconformation continuum electrostatics titrations show coupling of conformational flexibility and changes in ionization state. Examples are provided where ionizable side chain position (protein G), Asn orientation (lysozyme), His tautomer distribution (RNase A), and phosphate ion binding (RNase A and H) change with pH. Disallowing these motions changes the calculated pK(a).

Full Text

The Full Text of this article is available as a PDF (324K).

Supplementary Material

[Data Supplement]

Selected References

These references are in PubMed. This may not be the complete list of references from this article.
  • Akke M, Forsén S, Chazin WJ. Solution structure of (Cd2+)1-calbindin D9k reveals details of the stepwise structural changes along the Apo-->(Ca2+)II1-->(Ca2+)I,II2 binding pathway. J Mol Biol. 1995 Sep 8;252(1):102–121. [PubMed]
  • Alexov EG, Gunner MR. Calculated protein and proton motions coupled to electron transfer: electron transfer from QA- to QB in bacterial photosynthetic reaction centers. Biochemistry. 1999 Jun 29;38(26):8253–8270. [PubMed]
  • Alexov E, Miksovska J, Baciou L, Schiffer M, Hanson DK, Sebban P, Gunner MR. Modeling the effects of mutations on the free energy of the first electron transfer from QA- to QB in photosynthetic reaction centers. Biochemistry. 2000 May 23;39(20):5940–5952. [PubMed]
  • Alexov EG, Gunner MR. Incorporating protein conformational flexibility into the calculation of pH-dependent protein properties. Biophys J. 1997 May;72(5):2075–2093. [PMC free article] [PubMed]
  • Antosiewicz J, McCammon JA, Gilson MK. Prediction of pH-dependent properties of proteins. J Mol Biol. 1994 May 6;238(3):415–436. [PubMed]
  • Antosiewicz J, McCammon JA, Gilson MK. The determinants of pKas in proteins. Biochemistry. 1996 Jun 18;35(24):7819–7833. [PubMed]
  • Bartik K, Redfield C, Dobson CM. Measurement of the individual pKa values of acidic residues of hen and turkey lysozymes by two-dimensional 1H NMR. Biophys J. 1994 Apr;66(4):1180–1184. [PMC free article] [PubMed]
  • Bashford D, Karplus M. pKa's of ionizable groups in proteins: atomic detail from a continuum electrostatic model. Biochemistry. 1990 Nov 6;29(44):10219–10225. [PubMed]
  • Berndt KD, Güntert P, Orbons LP, Wüthrich K. Determination of a high-quality nuclear magnetic resonance solution structure of the bovine pancreatic trypsin inhibitor and comparison with three crystal structures. J Mol Biol. 1992 Oct 5;227(3):757–775. [PubMed]
  • Beroza P, Fredkin DR, Okamura MY, Feher G. Protonation of interacting residues in a protein by a Monte Carlo method: application to lysozyme and the photosynthetic reaction center of Rhodobacter sphaeroides. Proc Natl Acad Sci U S A. 1991 Jul 1;88(13):5804–5808. [PMC free article] [PubMed]
  • Bode W, Wei AZ, Huber R, Meyer E, Travis J, Neumann S. X-ray crystal structure of the complex of human leukocyte elastase (PMN elastase) and the third domain of the turkey ovomucoid inhibitor. EMBO J. 1986 Oct;5(10):2453–2458. [PMC free article] [PubMed]
  • Brown LR, De Marco A, Wagner G, Wüthrich K. A study of the lysyl residues in the basic pancreatic trypsin inhibitor using 1H nuclear magnetic resonance at 360 Mhz. Eur J Biochem. 1976 Feb 2;62(1):103–107. [PubMed]
  • Buckle AM, Henrick K, Fersht AR. Crystal structural analysis of mutations in the hydrophobic cores of barnase. J Mol Biol. 1993 Dec 5;234(3):847–860. [PubMed]
  • Bycroft M, Ludvigsen S, Fersht AR, Poulsen FM. Determination of the three-dimensional solution structure of barnase using nuclear magnetic resonance spectroscopy. Biochemistry. 1991 Sep 3;30(35):8697–8701. [PubMed]
  • Chen HA, Pfuhl M, McAlister MS, Driscoll PC. Determination of pK(a) values of carboxyl groups in the N-terminal domain of rat CD2: anomalous pK(a) of a glutamate on the ligand-binding surface. Biochemistry. 2000 Jun 13;39(23):6814–6824. [PubMed]
  • Cohen JS, Griffin JH, Schechter AN. Nuclear magnetic resonance titration curves of histidine ring protons. IV. The effects of phosphate and sulfate on ribonuclease. J Biol Chem. 1973 Jun 25;248(12):4305–4310. [PubMed]
  • Demchuk E, Genick UK, Woo TT, Getzoff ED, Bashford D. Protonation states and pH titration in the photocycle of photoactive yellow protein. Biochemistry. 2000 Feb 8;39(5):1100–1113. [PubMed]
  • Driscoll PC, Cyster JG, Campbell ID, Williams AF. Structure of domain 1 of rat T lymphocyte CD2 antigen. Nature. 1991 Oct 24;353(6346):762–765. [PubMed]
  • Dunbrack RL, Jr, Cohen FE. Bayesian statistical analysis of protein side-chain rotamer preferences. Protein Sci. 1997 Aug;6(8):1661–1681. [PMC free article] [PubMed]
  • Dunbrack RL, Jr, Karplus M. Conformational analysis of the backbone-dependent rotamer preferences of protein sidechains. Nat Struct Biol. 1994 May;1(5):334–340. [PubMed]
  • Dyson HJ, Jeng MF, Tennant LL, Slaby I, Lindell M, Cui DS, Kuprin S, Holmgren A. Effects of buried charged groups on cysteine thiol ionization and reactivity in Escherichia coli thioredoxin: structural and functional characterization of mutants of Asp 26 and Lys 57. Biochemistry. 1997 Mar 4;36(9):2622–2636. [PubMed]
  • Elcock AH, McCammon JA. Electrostatic contributions to the stability of halophilic proteins. J Mol Biol. 1998 Jul 24;280(4):731–748. [PubMed]
  • Ferguson-Miller Shelagh, Babcock Gerald T. Heme/Copper Terminal Oxidases. Chem Rev. 1996 Nov 7;96(7):2889–2908. [PubMed]
  • Forsyth WR, Gilson MK, Antosiewicz J, Jaren OR, Robertson AD. Theoretical and experimental analysis of ionization equilibria in ovomucoid third domain. Biochemistry. 1998 Jun 16;37(24):8643–8652. [PubMed]
  • Fujinaga M, Sielecki AR, Read RJ, Ardelt W, Laskowski M, Jr, James MN. Crystal and molecular structures of the complex of alpha-chymotrypsin with its inhibitor turkey ovomucoid third domain at 1.8 A resolution. J Mol Biol. 1987 May 20;195(2):397–418. [PubMed]
  • Gallagher T, Alexander P, Bryan P, Gilliland GL. Two crystal structures of the B1 immunoglobulin-binding domain of streptococcal protein G and comparison with NMR. Biochemistry. 1994 Apr 19;33(15):4721–4729. [PubMed]
  • García-Moreno B, Dwyer JJ, Gittis AG, Lattman EE, Spencer DS, Stites WE. Experimental measurement of the effective dielectric in the hydrophobic core of a protein. Biophys Chem. 1997 Feb 28;64(1-3):211–224. [PubMed]
  • Gibas CJ, Subramaniam S. Explicit solvent models in protein pKa calculations. Biophys J. 1996 Jul;71(1):138–147. [PMC free article] [PubMed]
  • Giletto A, Pace CN. Buried, charged, non-ion-paired aspartic acid 76 contributes favorably to the conformational stability of ribonuclease T1. Biochemistry. 1999 Oct 5;38(40):13379–13384. [PubMed]
  • Gilson MK, Honig BH. Energetics of charge-charge interactions in proteins. Proteins. 1988;3(1):32–52. [PubMed]
  • Gilson MK, Rashin A, Fine R, Honig B. On the calculation of electrostatic interactions in proteins. J Mol Biol. 1985 Aug 5;184(3):503–516. [PubMed]
  • Gronenborn AM, Filpula DR, Essig NZ, Achari A, Whitlow M, Wingfield PT, Clore GM. A novel, highly stable fold of the immunoglobulin binding domain of streptococcal protein G. Science. 1991 Aug 9;253(5020):657–661. [PubMed]
  • Gunner MR, Alexov E. A pragmatic approach to structure based calculation of coupled proton and electron transfer in proteins. Biochim Biophys Acta. 2000 May 12;1458(1):63–87. [PubMed]
  • Gunner MR, Saleh MA, Cross E, ud-Doula A, Wise M. Backbone dipoles generate positive potentials in all proteins: origins and implications of the effect. Biophys J. 2000 Mar;78(3):1126–1144. [PMC free article] [PubMed]
  • Havranek JJ, Harbury PB. Tanford-Kirkwood electrostatics for protein modeling. Proc Natl Acad Sci U S A. 1999 Sep 28;96(20):11145–11150. [PMC free article] [PubMed]
  • Hendsch ZS, Jonsson T, Sauer RT, Tidor B. Protein stabilization by removal of unsatisfied polar groups: computational approaches and experimental tests. Biochemistry. 1996 Jun 18;35(24):7621–7625. [PubMed]
  • Honig B, Nicholls A. Classical electrostatics in biology and chemistry. Science. 1995 May 26;268(5214):1144–1149. [PubMed]
  • Hooft RW, Sander C, Vriend G. Positioning hydrogen atoms by optimizing hydrogen-bond networks in protein structures. Proteins. 1996 Dec;26(4):363–376. [PubMed]
  • Hoogstraten CG, Choe S, Westler WM, Markley JL. Comparison of the accuracy of protein solution structures derived from conventional and network-edited NOESY data. Protein Sci. 1995 Nov;4(11):2289–2299. [PMC free article] [PubMed]
  • Howlin B, Moss DS, Harris GW. Segmented anisotropic refinement of bovine ribonuclease A by the application of the rigid-body TLS model. Acta Crystallogr A. 1989 Dec 1;45(Pt 12):851–861. [PubMed]
  • Hyland LJ, Tomaszek TA, Jr, Meek TD. Human immunodeficiency virus-1 protease. 2. Use of pH rate studies and solvent kinetic isotope effects to elucidate details of chemical mechanism. Biochemistry. 1991 Aug 27;30(34):8454–8463. [PubMed]
  • Ido E, Han HP, Kezdy FJ, Tang J. Kinetic studies of human immunodeficiency virus type 1 protease and its active-site hydrogen bond mutant A28S. J Biol Chem. 1991 Dec 25;266(36):24359–24366. [PubMed]
  • Inagaki F, Kawano Y, Shimada I, Takahashi K, Miyazawa T. Nuclear magnetic resonance study on the microenvironments of histidine residues of ribonuclease T1 and carboxymethylated ribonuclease T1. J Biochem. 1981 Apr;89(4):1185–1195. [PubMed]
  • Jones EY, Davis SJ, Williams AF, Harlos K, Stuart DI. Crystal structure at 2.8 A resolution of a soluble form of the cell adhesion molecule CD2. Nature. 1992 Nov 19;360(6401):232–239. [PubMed]
  • Katayanagi K, Miyagawa M, Matsushima M, Ishikawa M, Kanaya S, Nakamura H, Ikehara M, Matsuzaki T, Morikawa K. Structural details of ribonuclease H from Escherichia coli as refined to an atomic resolution. J Mol Biol. 1992 Feb 20;223(4):1029–1052. [PubMed]
  • Katayanagi K, Okumura M, Morikawa K. Crystal structure of Escherichia coli RNase HI in complex with Mg2+ at 2.8 A resolution: proof for a single Mg(2+)-binding site. Proteins. 1993 Dec;17(4):337–346. [PubMed]
  • Kesvatera T, Jönsson B, Thulin E, Linse S. Measurement and modelling of sequence-specific pKa values of lysine residues in calbindin D9k. J Mol Biol. 1996 Jun 21;259(4):828–839. [PubMed]
  • Kesvatera T, Jönsson B, Thulin E, Linse S. Ionization behavior of acidic residues in calbindin D(9k). Proteins. 1999 Oct 1;37(1):106–115. [PubMed]
  • Khare D, Alexander P, Antosiewicz J, Bryan P, Gilson M, Orban J. pKa measurements from nuclear magnetic resonance for the B1 and B2 immunoglobulin G-binding domains of protein G: comparison with calculated values for nuclear magnetic resonance and X-ray structures. Biochemistry. 1997 Mar 25;36(12):3580–3589. [PubMed]
  • Kostrewa D, Choe HW, Heinemann U, Saenger W. Crystal structure of guanosine-free ribonuclease T1, complexed with vanadate (V), suggests conformational change upon substrate binding. Biochemistry. 1989 Sep 19;28(19):7592–7600. [PubMed]
  • Kuramitsu S, Hamaguchi K. Analysis of the acid-base titration curve of hen lysozyme. J Biochem. 1980 Apr;87(4):1215–1219. [PubMed]
  • Laskowski M, Jr, Kato I, Ardelt W, Cook J, Denton A, Empie MW, Kohr WJ, Park SJ, Parks K, Schatzley BL, et al. Ovomucoid third domains from 100 avian species: isolation, sequences, and hypervariability of enzyme-inhibitor contact residues. Biochemistry. 1987 Jan 13;26(1):202–221. [PubMed]
  • Loewenthal R, Sancho J, Reinikainen T, Fersht AR. Long-range surface charge-charge interactions in proteins. Comparison of experimental results with calculations from a theoretical method. J Mol Biol. 1993 Jul 20;232(2):574–583. [PubMed]
  • Luecke H, Schobert B, Richter HT, Cartailler JP, Lanyi JK. Structural changes in bacteriorhodopsin during ion transport at 2 angstrom resolution. Science. 1999 Oct 8;286(5438):255–261. [PubMed]
  • March KL, Maskalick DG, England RD, Friend SH, Gurd FR. Analysis of electrostatic interactions and their relationship to conformation and stability of bovine pancreatic trypsin inhibitor. Biochemistry. 1982 Oct 12;21(21):5241–5251. [PubMed]
  • Martin C, Richard V, Salem M, Hartley R, Mauguen Y. Refinement and structural analysis of barnase at 1.5 A resolution. Acta Crystallogr D Biol Crystallogr. 1999 Feb;55(Pt 2):386–398. [PubMed]
  • Matthew JB, Gurd FR, Garcia-Moreno B, Flanagan MA, March KL, Shire SJ. pH-dependent processes in proteins. CRC Crit Rev Biochem. 1985;18(2):91–197. [PubMed]
  • Matthews CR, Westmoreland DG. A Fourier transform NMR study of the thermal denaturation of ribonuclease A at low pH. Ann N Y Acad Sci. 1973 Dec 31;222:240–254. [PubMed]
  • Mauguen Y, Hartley RW, Dodson EJ, Dodson GG, Bricogne G, Chothia C, Jack A. Molecular structure of a new family of ribonucleases. Nature. 1982 May 13;297(5862):162–164. [PubMed]
  • McAlister MS, Mott HR, van der Merwe PA, Campbell ID, Davis SJ, Driscoll PC. NMR analysis of interacting soluble forms of the cell-cell recognition molecules CD2 and CD48. Biochemistry. 1996 May 14;35(19):5982–5991. [PubMed]
  • McNutt M, Mullins LS, Raushel FM, Pace CN. Contribution of histidine residues to the conformational stability of ribonuclease T1 and mutant Glu-58----Ala. Biochemistry. 1990 Aug 21;29(33):7572–7576. [PubMed]
  • Meadows DH, Roberts GC, Jardetzky O. Nuclear magnetic resonance studies of the structure and binding sites of enzymes. 8. Inhibitor binding to ribonuclease. J Mol Biol. 1969 Nov 14;45(3):491–511. [PubMed]
  • Mehler EL, Guarnieri F. A self-consistent, microenvironment modulated screened coulomb potential approximation to calculate pH-dependent electrostatic effects in proteins. Biophys J. 1999 Jul;77(1):3–22. [PMC free article] [PubMed]
  • Mellor GW, Patel M, Thomas EW, Brocklehurst K. Clarification of the pH-dependent kinetic behaviour of papain by using reactivity probes and analysis of alkylation and catalysed acylation reactions in terms of multihydronic state models: implications for electrostatics calculations and interpretation of the consequences of site-specific mutations such as Asp-158-Asn and Asp-158-Glu. Biochem J. 1993 Aug 15;294(Pt 1):201–210. [PMC free article] [PubMed]
  • Murzin AG, Brenner SE, Hubbard T, Chothia C. SCOP: a structural classification of proteins database for the investigation of sequences and structures. J Mol Biol. 1995 Apr 7;247(4):536–540. [PubMed]
  • Nielsen JE, Vriend G. Optimizing the hydrogen-bond network in Poisson-Boltzmann equation-based pK(a) calculations. Proteins. 2001 Jun 1;43(4):403–412. [PubMed]
  • Oda Y, Yamazaki T, Nagayama K, Kanaya S, Kuroda Y, Nakamura H. Individual ionization constants of all the carboxyl groups in ribonuclease HI from Escherichia coli determined by NMR. Biochemistry. 1994 May 3;33(17):5275–5284. [PubMed]
  • Oda Y, Yoshida M, Kanaya S. Role of histidine 124 in the catalytic function of ribonuclease HI from Escherichia coli. J Biol Chem. 1993 Jan 5;268(1):88–92. [PubMed]
  • Oliveberg M, Arcus VL, Fersht AR. pKA values of carboxyl groups in the native and denatured states of barnase: the pKA values of the denatured state are on average 0.4 units lower than those of model compounds. Biochemistry. 1995 Jul 25;34(29):9424–9433. [PubMed]
  • Onufriev A, Case DA, Ullmann GM. A novel view of pH titration in biomolecules. Biochemistry. 2001 Mar 27;40(12):3413–3419. [PubMed]
  • Quirk DJ, Raines RT. His ... Asp catalytic dyad of ribonuclease A: histidine pKa values in the wild-type, D121N, and D121A enzymes. Biophys J. 1999 Mar;76(3):1571–1579. [PMC free article] [PubMed]
  • Read RJ, Fujinaga M, Sielecki AR, James MN. Structure of the complex of Streptomyces griseus protease B and the third domain of the turkey ovomucoid inhibitor at 1.8-A resolution. Biochemistry. 1983 Sep 13;22(19):4420–4433. [PubMed]
  • Ripoll DR, Vorobjev YN, Liwo A, Vila JA, Scheraga HA. Coupling between folding and ionization equilibria: effects of pH on the conformational preferences of polypeptides. J Mol Biol. 1996 Dec 13;264(4):770–783. [PubMed]
  • Rüterjans H, Witzel H. NMR-studies on the structure of the active site of pancreatic ribonuclease A. Eur J Biochem. 1969 May 1;9(1):118–127. [PubMed]
  • Santoro J, González C, Bruix M, Neira JL, Nieto JL, Herranz J, Rico M. High-resolution three-dimensional structure of ribonuclease A in solution by nuclear magnetic resonance spectroscopy. J Mol Biol. 1993 Feb 5;229(3):722–734. [PubMed]
  • Schaller W, Robertson AD. pH, ionic strength, and temperature dependences of ionization equilibria for the carboxyl groups in turkey ovomucoid third domain. Biochemistry. 1995 Apr 11;34(14):4714–4723. [PubMed]
  • Schutz CN, Warshel A. What are the dielectric "constants" of proteins and how to validate electrostatic models? Proteins. 2001 Sep 1;44(4):400–417. [PubMed]
  • Schwalbe H, Grimshaw SB, Spencer A, Buck M, Boyd J, Dobson CM, Redfield C, Smith LJ. A refined solution structure of hen lysozyme determined using residual dipolar coupling data. Protein Sci. 2001 Apr;10(4):677–688. [PMC free article] [PubMed]
  • Sham YY, Muegge I, Warshel A. The effect of protein relaxation on charge-charge interactions and dielectric constants of proteins. Biophys J. 1998 Apr;74(4):1744–1753. [PMC free article] [PubMed]
  • Sham YY, Muegge I, Warshel A. Simulating proton translocations in proteins: probing proton transfer pathways in the Rhodobacter sphaeroides reaction center. Proteins. 1999 Sep 1;36(4):484–500. [PubMed]
  • Sheinerman FB, Norel R, Honig B. Electrostatic aspects of protein-protein interactions. Curr Opin Struct Biol. 2000 Apr;10(2):153–159. [PubMed]
  • Simonson T. Macromolecular electrostatics: continuum models and their growing pains. Curr Opin Struct Biol. 2001 Apr;11(2):243–252. [PubMed]
  • Sindelar CV, Hendsch ZS, Tidor B. Effects of salt bridges on protein structure and design. Protein Sci. 1998 Sep;7(9):1898–1914. [PMC free article] [PubMed]
  • Skelton NJ, Kördel J, Chazin WJ. Determination of the solution structure of Apo calbindin D9k by NMR spectroscopy. J Mol Biol. 1995 Jun 2;249(2):441–462. [PubMed]
  • Smith LJ, Sutcliffe MJ, Redfield C, Dobson CM. Structure of hen lysozyme in solution. J Mol Biol. 1993 Feb 20;229(4):930–944. [PubMed]
  • Song J, Markley JL. NMR chemical shift mapping of the binding site of a protein proteinase inhibitor: changes in the (1)H, (13)C and (15)N NMR chemical shifts of turkey ovomucoid third domain upon binding to bovine chymotrypsin A(alpha). J Mol Recognit. 2001 May-Jun;14(3):166–171. [PubMed]
  • Spassov VZ, Ladenstein R, Karshikoff AD. Optimization of the electrostatic interactions between ionized groups and peptide dipoles in proteins. Protein Sci. 1997 Jun;6(6):1190–1196. [PMC free article] [PubMed]
  • Sunder-Plassmann R, Reinherz EL. A p56lck-independent pathway of CD2 signaling involves Jun kinase. J Biol Chem. 1998 Sep 11;273(37):24249–24257. [PubMed]
  • Szebenyi DM, Moffat K. The refined structure of vitamin D-dependent calcium-binding protein from bovine intestine. Molecular details, ion binding, and implications for the structure of other calcium-binding proteins. J Biol Chem. 1986 Jul 5;261(19):8761–8777. [PubMed]
  • Takahashi T, Nakamura H, Wada A. Electrostatic forces in two lysozymes: calculations and measurements of histidine pKa values. Biopolymers. 1992 Aug;32(8):897–909. [PubMed]
  • Takashima S, Schwan HP. Dielectric dispersion of crystalline powders of amino acids, peptides, and proteins. J Phys Chem. 1965 Dec;69(12):4176–4182. [PubMed]
  • Tashiro M, Montelione GT. Structures of bacterial immunoglobulin-binding domains and their complexes with immunoglobulins. Curr Opin Struct Biol. 1995 Aug;5(4):471–481. [PubMed]
  • Thanki N, Rao JK, Foundling SI, Howe WJ, Moon JB, Hui JO, Tomasselli AG, Heinrikson RL, Thaisrivongs S, Wlodawer A. Crystal structure of a complex of HIV-1 protease with a dihydroxyethylene-containing inhibitor: comparisons with molecular modeling. Protein Sci. 1992 Aug;1(8):1061–1072. [PMC free article] [PubMed]
  • van der Merwe PA, McNamee PN, Davies EA, Barclay AN, Davis SJ. Topology of the CD2-CD48 cell-adhesion molecule complex: implications for antigen recognition by T cells. Curr Biol. 1995 Jan 1;5(1):74–84. [PubMed]
  • van Vlijmen HW, Schaefer M, Karplus M. Improving the accuracy of protein pKa calculations: conformational averaging versus the average structure. Proteins. 1998 Nov 1;33(2):145–158. [PubMed]
  • Vaney MC, Maignan S, Riès-Kautt M, Ducriux A. High-resolution structure (1.33 A) of a HEW lysozyme tetragonal crystal grown in the APCF apparatus. Data and structural comparison with a crystal grown under microgravity from SpaceHab-01 mission. Acta Crystallogr D Biol Crystallogr. 1996 May 1;52(Pt 3):505–517. [PubMed]
  • Vocadlo DJ, Davies GJ, Laine R, Withers SG. Catalysis by hen egg-white lysozyme proceeds via a covalent intermediate. Nature. 2001 Aug 23;412(6849):835–838. [PubMed]
  • Walters DE, Allerhand A. Tautomeric states of the histidine residues of bovine pancreatic ribonuclease A. Application of carbon 13 nuclear magnetic resonance spectroscopy. J Biol Chem. 1980 Jul 10;255(13):6200–6204. [PubMed]
  • Warshel A, Russell ST. Calculations of electrostatic interactions in biological systems and in solutions. Q Rev Biophys. 1984 Aug;17(3):283–422. [PubMed]
  • Warwicker J. Simplified methods for pKa and acid pH-dependent stability estimation in proteins: removing dielectric and counterion boundaries. Protein Sci. 1999 Feb;8(2):418–425. [PMC free article] [PubMed]
  • Warwicker J, Watson HC. Calculation of the electric potential in the active site cleft due to alpha-helix dipoles. J Mol Biol. 1982 Jun 5;157(4):671–679. [PubMed]
  • Wilson KP, Malcolm BA, Matthews BW. Structural and thermodynamic analysis of compensating mutations within the core of chicken egg white lysozyme. J Biol Chem. 1992 May 25;267(15):10842–10849. [PubMed]
  • Wlodawer A, Svensson LA, Sjölin L, Gilliland GL. Structure of phosphate-free ribonuclease A refined at 1.26 A. Biochemistry. 1988 Apr 19;27(8):2705–2717. [PubMed]
  • Wolfenden R, Radzicka A. On the probability of finding a water molecule in a nonpolar cavity. Science. 1994 Aug 12;265(5174):936–937. [PubMed]
  • Yamazaki T, Hasebe T, Shouguchi J, Amano H, Kajiwara S, Shishido K. Structure and function in Escherichia coli of plasmids containing pyrimidine/purine-biased stretch originated from the 5'-flanking region of the basidiomycete ras gene. J Biochem. 1997 Oct;122(4):696–702. [PubMed]
  • Yang AS, Honig B. On the pH dependence of protein stability. J Mol Biol. 1993 May 20;231(2):459–474. [PubMed]
  • Yang AS, Gunner MR, Sampogna R, Sharp K, Honig B. On the calculation of pKas in proteins. Proteins. 1993 Mar;15(3):252–265. [PubMed]
  • Yang W, Hendrickson WA, Crouch RJ, Satow Y. Structure of ribonuclease H phased at 2 A resolution by MAD analysis of the selenomethionyl protein. Science. 1990 Sep 21;249(4975):1398–1405. [PubMed]
  • You TJ, Bashford D. Conformation and hydrogen ion titration of proteins: a continuum electrostatic model with conformational flexibility. Biophys J. 1995 Nov;69(5):1721–1733. [PMC free article] [PubMed]
  • Zhou HX, Vijayakumar M. Modeling of protein conformational fluctuations in pKa predictions. J Mol Biol. 1997 Apr 11;267(4):1002–1011. [PubMed]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society


Save items

Related citations in PubMed

See reviews...See all...

Cited by other articles in PMC

See all...


  • Compound
    PubChem Compound links
  • PubMed
    PubMed citations for these articles
  • Substance
    PubChem Substance links

Recent Activity

Your browsing activity is empty.

Activity recording is turned off.

Turn recording back on

See more...