A model of a local dielectric constant in proteins

A model for the calculation of the scalar, position-dependent static dielectric function of an ensemble consisting of polarizable sites and of free relaxing point dipoles at fixed positions is proposed. It is based on classical electrostatics and leads to an iteration equation or nonlinear partial differential equation for the local dielectric constant. The expressions contain the equations of Debye, Onsager, and Neumann as special cases and thus might be considered as an extension to inhomogeneous matter. The model may have applications in the case of biological macromolecules in particular proteins where the polar side chains can be identified with the model’s dipoles. The algorithm leads to a position dependent dielectric constant in the protein interior in contrast to the assumption of a homogeneous permittivity throughout the protein. By taking into account the dielectric fine structure inside the macromolecules we hope that our approach may help to improve continuum electrostatic models of these mol...

[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]  A. Wada,et al.  A theoretical study of the dielectric constant of protein. , 1988, Protein engineering.

[3]  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.

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

[5]  J. Andrew McCammon,et al.  Computation of electrostatic forces on solvated molecules using the Poisson-Boltzmann equation , 1993 .

[6]  L. Onsager.  Electric Moments of Molecules in Liquids , 1936 .

[7]  A. Warshel.  What about protein polarity? , 1987, Nature.

[8]  G Bricogne,et al.  Intramolecular dielectric screening in proteins. , 1991, Journal of molecular biology.

[9]  A. Karshikoff.  A simple algorithm for the calculation of multiple site titration curves. , 1995, Protein engineering.

[10]  Alan E. Mark,et al.  Dielectric properties of trypsin inhibitor and lysozyme calculated from molecular dynamics simulations , 1993 .

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

[12]  B. Honig,et al.  Classical electrostatics in biology and chemistry. , 1995, Science.

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

[14]  Arieh Warshel,et al.  Microscopic simulations of macroscopic dielectric constants of solvated proteins , 1991 .

[15]  Barry Honig,et al.  A local dielectric constant model for solvation free energies which accounts for solute polarizability , 1992 .

[16]  Arieh Warshel,et al.  Microscopic and semimicroscopic calculations of electrostatic energies in proteins by the POLARIS and ENZYMIX programs , 1993, J. Comput. Chem..

[17]  J. Kirkwood.  The Dielectric Polarization of Polar Liquids , 1939 .

[18]  J. Kirkwood,et al.  The Electrostatic Influence of Substituents on the Dissociation Constants of Organic Acids. II , 1938 .

[19]  D. D. Yue,et al.  Theory of Electric Polarization , 1974 .

[20]  Martin Neumann,et al.  Consistent calculation of the static and frequency-dependent dielectric constant in computer simulations , 1984 .

[21]  Martin Karplus,et al.  pH-Dependence of Protein Stability: Absolute Electrostatic Free Energy Differences between Conformations† , 1997 .

[22]  Arieh Warshel,et al.  A surface constrained all‐atom solvent model for effective simulations of polar solutions , 1989 .

[23]  M. Gilson,et al.  Prediction of pH-dependent properties of proteins. , 1994, Journal of molecular biology.

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

[25]  A. Warshel,et al.  Why ion pair reversal by protein engineering is unlikely to succeed , 1988, Nature.

[26]  C. P. Smyth.  Dielectric behavior and structure , 1956 .

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

[28]  D. Rees.  Experimental evaluation of the effective dielectric constant of proteins. , 1980, Journal of molecular biology.

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

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

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

[32]  Ronald Pethig,et al.  Dielectric and electronic properties of biological materials , 1979 .

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