Energetics of charge–charge interactions in proteins

Electrostatic interactions between pairs of atoms in proteins are calculated with a model based on the linearized Poisson‐Boltzmann equation. The equation is solved accurately by a method that takes into account the detailed shape of the protein. This paper presents applications to several systems. Experimental data for the interaction of ionized residues with an active site histidine in subtilisin BPN' allow the model to be tested, using various assumptions for the electrical properties of the protein and solvent. The electrostatic stabilization of the active site thiolate or rhodanese is analyzed, with attention to the influence of α‐helices. Finally, relationships between electrostatic potential and charge‐charge distance are reported for large and small globular proteins. The above results are compared with those of simpler electrostatic models, including Coulomb's law with both a distance‐dependent dielectric constant (ϵ = R) and a fixed dielectric constant (ϵ = 2), and Tanford‐Kirkwood theory. The primary conclusions are as follows: (1) The Poisson‐Boltzmann model agrees with the subtilisin data over a range of ionic strengths; (2) two α‐helices generate a large potential in the active site of rhodanese; (3) ϵ = R overestimates weak electrostatic interactions but yields relatively good results for strong ones; (4) Tanford‐Kirkwood theory is a useful approximation to detailed solutions of the linearized Poisson‐Boltzmann equation in globular proteins; and (5) the modified Tanford‐Kirkwood theory overscreens the measured electrostatic interactions in subtilisin.

[1]  J. Warwicker,et al.  Calculation of the electric potential in the active site cleft due to alpha-helix dipoles. , 1982, Journal of molecular biology.

[2]  Wim G. J. Hol,et al.  The role of the α-helix dipole in protein function and structure , 1985 .

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

[4]  M. Perutz.  Electrostatic effects in proteins. , 1978, Science.

[5]  J. B. Matthew.  Electrostatic effects in proteins. , 1985, Annual review of biophysics and biophysical chemistry.

[6]  M. Whitlow,et al.  An empirical examination of potential energy minimization using the well-determined structure of the protein crambin , 1986 .

[7]  Barry Honig,et al.  An external point-charge model for bacteriorhodopsin to account for its purple color , 1980 .

[8]  W. Hol,et al.  The structure of bovine liver rhodanese. II. The active site in the sulfur-substituted and the sulfur-free enzyme. , 1979, Journal of molecular biology.

[9]  M. L. Connolly.  Solvent-accessible surfaces of proteins and nucleic acids. , 1983, Science.

[10]  A. Fersht,et al.  Electrostatic effects on modification of charged groups in the active site cleft of subtilisin by protein engineering. , 1987, Journal of molecular biology.

[11]  M. Neumann.  The dielectric constant of water. Computer simulations with the MCY potential , 1985 .

[12]  O. Steinhauser.  On the Orientational Structure and Dielectric Properties of Water. A Comparison of ST2 and MCY Potential , 1983 .

[13]  M. Karplus,et al.  CHARMM: A program for macromolecular energy, minimization, and dynamics calculations , 1983 .

[14]  T Imoto,et al.  Electrostatic free energy of lysozyme. , 1983, Biophysical journal.

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

[16]  W. H. Orttung.  Proton binding and dipole moment of hemoglobin. Refined calculations. , 1970, Biochemistry.

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

[18]  Electrostatic interactions between ions and DNA estimated with an electrolyte tank , 1986 .

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

[20]  W. Hol,et al.  Structure of bovine liver rhodanese. I. Structure determination at 2.5 A resolution and a comparison of the conformation and sequence of its two domains. , 1978, Journal of molecular biology.

[21]  Kurt Wüthrich,et al.  Secondary structure of the α-amylase polypeptide inhibitor Tendamistat from Streptomyces tendae determined in solution by 1H nuclear magnetic resonance , 1985 .

[22]  M. Born.  Volumen und Hydratationswärme der Ionen , 1920 .

[23]  C Levinthal,et al.  Interactive computer graphics and representation of complex biological structures. , 1972, Annual review of biophysics and bioengineering.

[24]  Barry Honig,et al.  Focusing of electric fields in the active site of Cu‐Zn superoxide dismutase: Effects of ionic strength and amino‐acid modification , 1986, Proteins.

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

[26]  Brownian dynamics simulation of diffusion to irregular bodies , 1987 .

[27]  W G Hol,et al.  Structure of bovine liver rhodanese. I. Structure determination at 2.5 A resolution and a comparison of the conformation and sequence of its two domains. , 1978, Journal of Molecular Biology.

[28]  J. Kraut,et al.  Atomic coordinates for subtilisin BPN' (or Novo). , 1971, Biochemical and biophysical research communications.

[29]  M. Sternberg,et al.  Electrostatic interactions in globular proteins: calculation of the pH dependence of the redox potential of cytochrome c551. , 1985, Journal of molecular biology.

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

[31]  Barry Honig,et al.  ON THE MECHANISM OF WAVELENGTH REGULATION IN VISUAL PIGMENTS , 1985, Photochemistry and photobiology.

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

[33]  W G Hol,et al.  On the role of the active site helix in papain, an ab initio molecular orbital study. , 1979, Biophysical chemistry.

[34]  F M Richards,et al.  Areas, volumes, packing and protein structure. , 1977, Annual review of biophysics and bioengineering.

[35]  M J Sternberg,et al.  Electrostatic interactions in globular proteins. Different dielectric models applied to the packing of alpha-helices. , 1984, Journal of molecular biology.

[36]  B. Honig,et al.  On the calculation of electrostatic interactions in proteins. , 1985, Journal of molecular biology.

[37]  M Karplus,et al.  Picosecond dynamics of tyrosine side chains in proteins. , 1979, Biochemistry.

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

[39]  R. Zauhar,et al.  A new method for computing the macromolecular electric potential. , 1985, Journal of molecular biology.

[40]  J. Kirkwood,et al.  Theory of Solutions of Molecules Containing Widely Separated Charges with Special Application to Zwitterions , 1934 .

[41]  J. Warwicker,et al.  Continuum dielectric modelling of the protein-solvent system, and calculation of the long-range electrostatic field of the enzyme phosphoglycerate mutase. , 1986, Journal of theoretical biology.

[42]  H. Berendsen,et al.  The α-helix dipole and the properties of proteins , 1978, Nature.

[43]  B. Honig,et al.  Electrostatic interactions in membranes and proteins. , 1986, Annual review of biophysics and biophysical chemistry.

[44]  B Honig,et al.  Computer simulations of the diffusion of a substrate to an active site of an enzyme. , 1987, Science.

[45]  Alan R. Fersht,et al.  Tailoring the pH dependence of enzyme catalysis using protein engineering , 1985, Nature.

[46]  U. Singh,et al.  A NEW FORCE FIELD FOR MOLECULAR MECHANICAL SIMULATION OF NUCLEIC ACIDS AND PROTEINS , 1984 .

[47]  Barry Honig,et al.  Reevaluation of the Born model of ion hydration , 1985 .

[48]  F. Gurd,et al.  Electrostatic effects in myoglobin. Hydrogen ion equilibria in sperm whale ferrimyoglobin. , 1974, Biochemistry.

[49]  A. Warshel,et al.  Calculations of electrostatic interactions in biological systems and in solutions , 1984, Quarterly Reviews of Biophysics.

[50]  F. Richards,et al.  Electrostatic field of the large fragment of Escherichia coli DNA polymerase I. , 1985, Journal of molecular biology.

[51]  F. Quiocho,et al.  Sulphate sequestered in the sulphate-binding protein of Salmonella typhimurium is bound solely by hydrogen bonds , 1985, Nature.

[52]  B. Lee,et al.  The interpretation of protein structures: estimation of static accessibility. , 1971, Journal of molecular biology.