The frequency of ion‐pair substructures in proteins is quantitatively related to electrostatic potential: A statistical model for nonbonded interactions

A statistical analysis of ion pairs in protein crystal structures shows that their abundance with respect to uncharged controls is accurately predicted by a Botlzmann‐like function of electrostatic potential. It appears that the mechanisms of protein folding and/or evolution combine to produce a “thermal” distribution of local nonbonded interactions, as has been suggested by statistical–mechanical theories. Using this relationship, we develop a maximum likelihood methodology for estimation of apparent energetic parameters from the data base of known structures, and we derive electrostatic potential functions that lead to optimal agreement of observed and predicted ion‐pair frequencies. These are similar to potentials of mean force derived from electrostatic theory, but departure from Coulombic behavior is less than has been suggested.

[1]  T. L. Hill,et al.  An Introduction to Statistical Thermodynamics , 1960 .

[2]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[3]  F. Pohl.  Empirical protein energy maps. , 1971, Nature: New biology.

[4]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[5]  S. Gill,et al.  An equation of state describing hydrophobic interactions. , 1976, Proceedings of the National Academy of Sciences of the United States of America.

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

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

[8]  A. Khokhlov,et al.  Some problems of the statistical physics of polymer chains with volume interaction , 1978 .

[9]  J. Janin,et al.  Surface and inside volumes in globular proteins , 1979, Nature.

[10]  A. Kolaskar,et al.  Empirical torsional potential functions from protein structure data. Phi- and psi-potentials for non-glycyl amino acid residues. , 2009, International journal of peptide and protein research.

[11]  Haruki Nakamura,et al.  Nature of the charge distribution in proteins , 1981, Nature.

[12]  G. M. Smith,et al.  Electronic distributions within protein phenylalanine aromatic rings are reflected by the three-dimensional oxygen atom environments. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[13]  J. Thornton,et al.  Ion-pairs in proteins. , 1983, Journal of molecular biology.

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

[15]  M. Karplus,et al.  An analysis of incorrectly folded protein models. Implications for structure predictions. , 1984, Journal of molecular biology.

[16]  A. Warshel,et al.  Macroscopic models for studies of electrostatic interactions in proteins: limitations and applicability. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[17]  E. Baker,et al.  Hydrogen bonding in globular proteins. , 1984, Progress in biophysics and molecular biology.

[18]  G. Rose,et al.  Hydrophobicity of amino acid residues in globular proteins. , 1985, Science.

[19]  R. Jernigan,et al.  Estimation of effective interresidue contact energies from protein crystal structures: quasi-chemical approximation , 1985 .

[20]  R. H. Ritchie,et al.  Dielectric effects in biopolymers: The theory of ionic saturation revisited , 1985 .

[21]  K. Dill.  Theory for the folding and stability of globular proteins. , 1985, Biochemistry.

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

[23]  D J Barlow,et al.  The distribution of charged groups in proteins , 1986, Biopolymers.

[24]  A. D. McLachlan,et al.  Solvation energy in protein folding and binding , 1986, Nature.

[25]  R. L. Baldwin,et al.  Temperature dependence of the hydrophobic interaction in protein folding. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[26]  A. Lesk,et al.  Determinants of a protein fold. Unique features of the globin amino acid sequences. , 1987, Journal of molecular biology.

[27]  J. Ponder,et al.  Tertiary templates for proteins. Use of packing criteria in the enumeration of allowed sequences for different structural classes. , 1987, Journal of molecular biology.

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

[29]  C. Mannella,et al.  Distribution of accessible surfaces of amino acids in globular proteins , 1987, Proteins.

[30]  P. V. von Hippel,et al.  Selection of DNA binding sites by regulatory proteins. Statistical-mechanical theory and application to operators and promoters. , 1987, Journal of molecular biology.

[31]  M. Sundaralingam,et al.  Ion pairs in alpha helices , 1987, Proteins.

[32]  M. Karplus,et al.  Electrostatic effects of charge perturbations introduced by metal oxidation in proteins. A theoretical analysis. , 1988, Journal of molecular biology.

[33]  R W Pickersgill,et al.  A rapid method of calculating charge-charge interaction energies in proteins. , 1988, Protein engineering.

[34]  G. Petsko,et al.  Weakly polar interactions in proteins. , 1988, Advances in protein chemistry.

[35]  N Go,et al.  The effect of amino acid substitution on protein‐folding and ‐unfolding transition studied by computer simulation , 1988, Biopolymers.

[36]  J. Dunitz,et al.  Can statistical analysis of structural parameters from different crystal environments lead to quantitative energy relationships , 1988 .

[37]  R. Bruccoleri,et al.  Criteria that discriminate between native proteins and incorrectly folded models , 1988, Proteins.

[38]  J. Skolnick,et al.  Monte Carlo simulations of the folding of beta-barrel globular proteins. , 1988, Proceedings of the National Academy of Sciences of the United States of America.

[39]  P. Privalov,et al.  Stability of protein structure and hydrophobic interaction. , 1988, Advances in protein chemistry.

[40]  C Chothia,et al.  Surface, subunit interfaces and interior of oligomeric proteins. , 1988, Journal of molecular biology.

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

[42]  S H Bryant,et al.  PKB: A program system and data base for analysis of protein structure , 1989, Proteins.

[43]  A Godzik,et al.  Conservation of residue interactions in a family of Ca-binding proteins. , 1989, Protein engineering.

[44]  K. Kuwajima,et al.  The molten globule state as a clue for understanding the folding and cooperativity of globular‐protein structure , 1989, Proteins.

[45]  E I Shakhnovich,et al.  Theory of cooperative transitions in protein molecules. I. Why denaturation of globular protein is a first‐order phase transition , 1989, Biopolymers.

[46]  S. Harvey.  Treatment of electrostatic effects in macromolecular modeling , 1989, Proteins.

[47]  W. Lim,et al.  Alternative packing arrangements in the hydrophobic core of λrepresser , 1989, Nature.

[48]  K. Dill,et al.  Theory for protein mutability and biogenesis. , 1990, Proceedings of the National Academy of Sciences of the United States of America.