On the calculation of pKas in proteins

This paper describes a general method to calculate the pKas of ionizable groups in proteins. Electrostatic calculations are carried out using the finite difference Poisson–Boltzmann (FDPB) method. A formal treatment of the calculation of pKas within the framework of the FDPB method is presented. The major change with respect to previous work is the specific incorporation of the complete charge distribution of both the neutral and charged forms of each ionizable group into the formalism. This is extremely important for the treatment of salt bridges. A hybrid statistical mechanical/Tanford–Roxby method, which is found to be significantly faster than previous treatments, is also introduced. This simplifies the problem of summing over the large number of possible ionization states for a complex polyion. Applications to BPTI and serine proteases suggest that the calculations can be quite reliable. However, the necessity of including bound waters in the treatment of the Asp‐70…His‐31 salt bridge in T4 lysozyme and experience with other proteins suggest that additional factors ultimately need to be considered in a comprehensive treatment of pKas in proteins. © 1993 Wiley‐Liss, Inc.

[1]  C. Tanford,et al.  Theory of Protein Titration Curves. I. General Equations for Impenetrable Spheres , 1957 .

[2]  C. Tanford,et al.  Interpretation of protein titration curves. Application to lysozyme. , 1972, Biochemistry.

[3]  D. M. Blow,et al.  Structure of crystalline -chymotrypsin. V. The atomic structure of tosyl- -chymotrypsin at 2 A resolution. , 1972, Journal of molecular biology.

[4]  S. Lifson,et al.  Energy functions for peptides and proteins. I. Derivation of a consistent force field including the hydrogen bond from amide crystals. , 1974, Journal of the American Chemical Society.

[5]  K. Wüthrich,et al.  A study of the lysyl residues in the basic pancreatic trypsin inhibitor using 1H nuclear magnetic resonance at 360 Mhz. , 1976, European journal of biochemistry.

[6]  G J Williams,et al.  The Protein Data Bank: a computer-based archival file for macromolecular structures. , 1977, Journal of molecular biology.

[7]  A. Fersht.  Enzyme structure and mechanism , 1977 .

[8]  K Wüthrich,et al.  High-field 13C nuclear magnetic resonance studies at 90.5 MHz of the basic pancreatic trypsin inhibitor. , 1978, Biochemistry.

[9]  K Wüthrich,et al.  The influence of a single salt bridge on static and dynamic features of the globular solution conformation of the basic pancreatic trypsin inhibitor. 1H and 13C nuclear-magnetic-resonance studies of the native and the transaminated inhibitor. , 1978, European journal of biochemistry.

[10]  K. Wüthrich,et al.  Nuclear magnetic resonance of labile protons in the basic pancreatic trypsin inhibitor. , 1979, Journal of molecular biology.

[11]  R. Huber,et al.  The Geometry of the Reactive Site and of the Peptide Groups in Trypsin, Trypsinogen and its Complexes with Inhibitors , 1983 .

[12]  A. Warshel,et al.  Calculations of electrostatic energies in proteins. The energetics of ionized groups in bovine pancreatic trypsin inhibitor. , 1985, Journal of molecular biology.

[13]  F. Gurd,et al.  pH-dependent processes in proteins. , 1985, CRC critical reviews in biochemistry.

[14]  M K Gilson,et al.  The dielectric constant of a folded protein , 1986, Biopolymers.

[15]  A. Warshel,et al.  Free energy of charges in solvated proteins: microscopic calculations using a reversible charging process. , 1986, Biochemistry.

[16]  James B. Matthew,et al.  [17] Calculation of electrostatic interactions in proteins , 1986 .

[17]  B. Honig,et al.  Calculation of electrostatic potentials in an enzyme active site , 1987, Nature.

[18]  A Wlodawer,et al.  Comparison of two highly refined structures of bovine pancreatic trypsin inhibitor. , 1987, Journal of molecular biology.

[19]  Alan R. Fersht,et al.  Prediction of electrostatic effects of engineering of protein charges , 1987, Nature.

[20]  C. Woodward,et al.  Structure of form III crystals of bovine pancreatic trypsin inhibitor. , 1987, Journal of molecular biology.

[21]  B. Matthews,et al.  Structure of bacteriophage T4 lysozyme refined at 1.7 A resolution. , 1987, Journal of molecular biology.

[22]  O. Epp,et al.  Structure of native porcine pancreatic elastase at 1.65 A resolutions. , 1988, Acta crystallographica. Section B, Structural science.

[23]  M K Gilson,et al.  Energetics of charge–charge interactions in proteins , 1988, Proteins.

[24]  K. Sharp,et al.  Calculating the electrostatic potential of molecules in solution: Method and error assessment , 1988 .

[25]  A. Warshel,et al.  How do serine proteases really work? , 1989, Biochemistry.

[26]  B Honig,et al.  Electrical potentials in trypsin isozymes. , 1989, Biochemistry.

[27]  M. Karplus,et al.  pKa's of ionizable groups in proteins: atomic detail from a continuum electrostatic model. , 1990, Biochemistry.

[28]  K. Sharp,et al.  Electrostatic interactions in macromolecules: theory and applications. , 1990, Annual review of biophysics and biophysical chemistry.

[29]  D. E. Anderson,et al.  pH-induced denaturation of proteins: a single salt bridge contributes 3-5 kcal/mol to the free energy of folding of T4 lysozyme. , 1990, Biochemistry.

[30]  B. Matthews,et al.  Comparison of the crystal structure of bacteriophage T4 lysozyme at low, medium, and high ionic strengths , 1991, Proteins.

[31]  A. Warshel,et al.  Electrostatic energy and macromolecular function. , 1991, Annual review of biophysics and biophysical chemistry.

[32]  M. Karplus,et al.  Multiple-site titration curves of proteins: an analysis of exact and approximate methods for their calculation , 1991 .

[33]  K. Sharp,et al.  Linkage of thioredoxin stability to titration of ionizable groups with perturbed pKa. , 1991, Biochemistry.

[34]  B. Honig,et al.  A rapid finite difference algorithm, utilizing successive over‐relaxation to solve the Poisson–Boltzmann equation , 1991 .

[35]  P. Beroza,et al.  Protonation of interacting residues in a protein by a Monte Carlo method: application to lysozyme and the photosynthetic reaction center of Rhodobacter sphaeroides. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[36]  An-Suei Yang,et al.  Electrostatic effects on protein stability: Current Opinion in Structural Biology 1992, 2:40…-45 , 1992 .

[37]  D. Bashford,et al.  Electrostatic calculations of the pKa values of ionizable groups in bacteriorhodopsin , 1992 .