Description of hydration free energy density as a function of molecular physical properties.

A method to calculate the solvation free energy density (SFED) at any point in the cavity surface or solvent volume surrounding a solute is proposed. In the special case in which the solvent is water, the SFED is referred to as the hydration free energy density (HFED). The HFED is described as a function of some physical properties of the molecules. These properties are represented by simple basis functions. The hydration free energy of a solute was obtained by integrating the HFED over the solvent volume surrounding the solute, using a grid model. Of 34 basis functions that were introduced to describe the HFED, only six contribute significantly to the HFED. These functions are representations of the surface area and volume of the solute, of the polarization and dispersion of the solute, and of two types of electrostatic interactions between the solute and its environment. The HFED is described as a linear combination of these basis functions, evaluated by summing the interaction energy between each atom of the solute with a grid point in the solvent, where each grid point is a representation of a finite volume of the solvent. The linear combination coefficients were determined by minimizing the error between the calculated and experimental hydration free energies of 81 neutral organic molecules that have a variety of functional groups. The calculated hydration free energies agree well with the experimental results. The hydration free energy of any other solute molecule can then be calculated by summing the product of the linear combination coefficients and the basis functions for the solute.

[1]  H A Scheraga,et al.  Minimization of polypeptide energy. I. Preliminary structures of bovine pancreatic ribonuclease S-peptide. , 1967, Proceedings of the National Academy of Sciences of the United States of America.

[2]  D. Rinaldi,et al.  Fast geometry optimizationin self‐cosistent reaction field computations on solvated molecules , 1992 .

[3]  Kenneth B. Wiberg,et al.  Solvent effects. 1. The mediation of electrostatic effects by solvents , 1991 .

[4]  Harold A. Scheraga,et al.  Free energies of hydration of solute molecules. IV: Revised treatment of the hydration shell model , 1988 .

[5]  Anna Tempczyk,et al.  Electrostatic contributions to solvation energies: comparison of free energy perturbation and continuum calculations , 1991 .

[6]  C. Cramer,et al.  An SCF Solvation Model for the Hydrophobic Effect and Absolute Free Energies of Aqueous Solvation , 1992, Science.

[7]  Kenneth B. Wiberg,et al.  Solvent effects. 3. Tautomeric equilibria of formamide and 2-pyridone in the gas phase and solution: an ab initio SCRF study , 1992 .

[8]  A. Rashin.  Continuum electrostatics and hydration phenomena , 1988 .

[9]  Arieh Warshel,et al.  Microscopic models for quantum mechanical calculations of chemical processes in solutions: LD/AMPAC and SCAAS/AMPAC calculations of solvation energies , 1992 .

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

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

[12]  A. Shrake,et al.  Environment and exposure to solvent of protein atoms. Lysozyme and insulin. , 1973, Journal of molecular biology.

[13]  K. D. Gibson,et al.  Surface area of the intersection of three spheres with unequal radii A simplified analytical formula , 1988 .

[14]  O. Tapia,et al.  An inhomogeneous self‐consistent reaction field theory of protein core effects. Towards a quantum scheme for describing enzyme reactions , 1981 .

[15]  Ralph G. Pearson,et al.  Ionization potentials and electron affinities in aqueous solution , 1986 .

[16]  M. Huron,et al.  Calculation of the interaction energy of one molecule with its whole surrounding. II. Method of calculating electrostatic energy , 1974 .

[17]  H A Scheraga,et al.  Ab initio self‐consistent field and potential‐dependent partial equalization of orbital electronegativity calculations of hydration properties of N‐acetyl‐N′‐methyl‐alanineamide , 1990, Biopolymers.

[18]  Michael H. Abraham,et al.  Hydrogen bonding. Part 34. The factors that influence the solubility of gases and vapours in water at 298 K, and a new method for its determination , 1994 .

[19]  Akbar Nayeem,et al.  MSEED: A program for the rapid analytical determination of accessible surface areas and their derivatives , 1992 .

[20]  M. Huron,et al.  Calculation of the interaction energy of one molecule with its whole surrounding. III. Application to pure polar compounds , 1974 .

[21]  P. Kollman,et al.  Protein structure prediction with a combined solvation free energy-molecular mechanics force field , 1993 .

[22]  Manuel F. Ruiz-López,et al.  Ab initio SCF calculations on electrostatically solvated molecules using a deformable three axes ellipsoidal cavity , 1983 .

[23]  Kenneth M. Merz,et al.  Rapid approximation to molecular surface area via the use of Boolean logic and look‐up tables , 1993, J. Comput. Chem..

[24]  Jacopo Tomasi,et al.  Electrostatic interaction of a solute with a continuum. Improved description of the cavity and of the surface cavity bound charge distribution. , 1987 .

[25]  Harold A. Scheraga,et al.  An empirical method to calculate average molecular polarizabilities from the dependence of effective atomic polarizabilities on net atomic charge , 1993 .

[26]  M. B. Pinto,et al.  Optimized δ expansion for relativistic nuclear models , 1997, nucl-th/9709049.

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

[28]  Harold A. Scheraga,et al.  A combined iterative and boundary-element approach for solution of the nonlinear Poisson-Boltzmann equation , 1992 .

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

[30]  Bhyravabhotla Jayaram,et al.  Free energy calculations of ion hydration: an analysis of the Born model in terms of microscopic simulations , 1989 .

[31]  Alexander A. Rashin,et al.  A simple method for the calculation of hydration enthalpies of polar molecules with arbitrary shapes , 1987 .

[32]  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.

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

[34]  Jean-Louis Rivail,et al.  LIQUID-STATE QUANTUM CHEMISTRY : AN IMPROVED CAVITY MODEL , 1994 .

[35]  H. Scheraga,et al.  Model for the conformational analysis of hydrated peptides. Effect of hydration on the conformational stability of the terminally blocked residues of the 20 naturally occurring amino acids , 1979 .

[36]  Harold A. Scheraga,et al.  Free energies of hydration of solute molecules. 3. Application of the hydration shell model to charged organic molecules , 1987 .

[37]  B. J. Yoon,et al.  A boundary element method for molecular electrostatics with electrolyte effects , 1990 .

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

[39]  Determination of Nonbonded Potential Parameters for Peptides , 1995 .

[40]  Haruki Nakamura,et al.  Numerical Calculations of Reaction Fields of Protein-Solvent Systems , 1988 .

[41]  Michael L. Connolly,et al.  Computation of molecular volume , 1985 .

[42]  Intramolecular electron correlation in the self-consistent reaction field model of solvation. A MP2/6-31G** ab initio study of the NH3HCl complex , 1992 .

[43]  J. Tomasi,et al.  A new formulation of the PCM solvation method: PCM-QINTn , 1997 .

[44]  Harold A. Scheraga,et al.  Determination of net atomic charges using a modified partial equalization of orbital electronegativity method. 1. Application to neutral molecules as models for polypeptides , 1990 .

[45]  Jacopo Tomasi,et al.  Analytical derivatives for molecular solutes. II. Hartree–Fock energy first and second derivatives with respect to nuclear coordinates , 1994 .

[46]  N. K. Rogers,et al.  The modelling of electrostatic interactions in the function of globular proteins. , 1986, Progress in biophysics and molecular biology.

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

[48]  M. L. Connolly.  Analytical molecular surface calculation , 1983 .

[49]  J. A. McCammon,et al.  Solving the finite difference linearized Poisson‐Boltzmann equation: A comparison of relaxation and conjugate gradient methods , 1989 .

[50]  K. D. Gibson,et al.  Exact calculation of the volume and surface area of fused hard-sphere molecules with unequal atomic radii , 1987 .

[51]  Harold A. Scheraga,et al.  Structure of Water and Hydrophobic Bonding in Proteins. II. Model for the Thermodynamic Properties of Aqueous Solutions of Hydrocarbons , 1962 .

[52]  Jacopo Tomasi,et al.  Molecular Interactions in Solution: An Overview of Methods Based on Continuous Distributions of the Solvent , 1994 .

[53]  A. J. Hopfinger,et al.  Polymer-Solvent Interactions for Homopolypeptides in Aqueous Solution , 1971 .

[54]  R. Zauhar,et al.  The rigorous computation of the molecular electric potential , 1988 .

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

[56]  D. Eisenberg,et al.  Atomic solvation parameters applied to molecular dynamics of proteins in solution , 1992, Protein science : a publication of the Protein Society.

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

[58]  Harold A. Scheraga,et al.  Free energies of hydration of solute molecules. 1. Improvement of the hydration shell model by exact computations of overlapping volumes , 1987 .

[59]  R. Bell,et al.  The electrostatic energy of dipole molecules in different media , 1931 .

[60]  R. Levy,et al.  Viewing the born model for ion hydration through a microscope , 1988 .

[61]  Orlando Tapia,et al.  Self-consistent reaction field theory of solvent effects , 1975 .

[62]  K. Wiberg,et al.  Solvent Effects. 5. Influence of Cavity Shape, Truncation of Electrostatics, and Electron Correlation on ab Initio Reaction Field Calculations , 1996 .

[63]  P. Claverie,et al.  Calculation of the interaction energy of one molecule with its whole surrounding. I. Method and application to pure nonpolar compounds , 1972 .

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

[65]  J. Andrew McCammon,et al.  Electrostatic energy calculations by a Finite‐difference method: Rapid calculation of charge–solvent interaction energies , 1992 .

[66]  Jacopo Tomasi,et al.  Approximate evaluations of the electrostatic free energy and internal energy changes in solution processes , 1982 .

[67]  B Maigret,et al.  New determinations and simplified representations of macromolecular surfaces. , 1990, Journal of molecular graphics.

[68]  C. Cramer,et al.  PM3‐SM3: A general parameterization for including aqueous solvation effects in the PM3 molecular orbital model , 1992 .

[69]  Michael J. E. Sternberg,et al.  Regular representation of irregular charge distributions , 1984 .

[70]  John C. Slater,et al.  The Van Der Waals Forces in Gases , 1931 .

[71]  C. Cramer,et al.  General parameterized SCF model for free energies of solvation in aqueous solution , 1991 .

[72]  J. Tomasi,et al.  Electrostatic interaction of a solute with a continuum. A direct utilizaion of AB initio molecular potentials for the prevision of solvent effects , 1981 .

[73]  T. Richmond,et al.  Solvent accessible surface area and excluded volume in proteins. Analytical equations for overlapping spheres and implications for the hydrophobic effect. , 1984, Journal of molecular biology.

[74]  H. Scheraga,et al.  Empirical solvation models can be used to differentiate native from near‐native conformations of bovine pancreatic trypsin inhibitor , 1991, Proteins.

[75]  H. Scheraga,et al.  Effect of protein-solvent interactions on protein conformation. , 1981, Annual review of biophysics and bioengineering.

[76]  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.

[77]  H. Scheraga,et al.  Interaction of a biomolecule with mobile ions in aqueous solution: comparison of three fast approximate methods with the direct solution of the nonlinear Poisson-Boltzmann equation , 1993 .

[78]  H. Scheraga,et al.  A fast adaptive multigrid boundary element method for macromolecular electrostatic computations in a solvent , 1997 .

[79]  Vincenzo Mollica,et al.  Group contributions to the thermodynamic properties of non-ionic organic solutes in dilute aqueous solution , 1981 .

[80]  K. Sharp,et al.  Macroscopic models of aqueous solutions : biological and chemical applications , 1993 .

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

[82]  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.

[83]  Donald G. Truhlar,et al.  AM1-SM2 and PM3-SM3 parameterized SCF solvation models for free energies in aqueous solution , 1992, J. Comput. Aided Mol. Des..

[84]  Donald G. Truhlar,et al.  MODEL FOR AQUEOUS SOLVATION BASED ON CLASS IV ATOMIC CHARGES AND FIRST SOLVATION SHELL EFFECTS , 1996 .

[85]  Malcolm E. Davis,et al.  Electrostatics in biomolecular structure and dynamics , 1990 .

[86]  J. Mccammon,et al.  Continuum model calculations of solvation free energies: accurate evaluation of electrostatic contributions , 1992 .

[87]  Amatzya Y. Meyer,et al.  Molecular mechanics and molecular shape. Part 1. van der Waals descriptors of simple molecules , 1985 .

[88]  K. Wiberg,et al.  Hartree–Fock second derivatives and electric field properties in a solvent reaction field: Theory and application , 1991 .

[89]  B. Honig,et al.  Calculation of the total electrostatic energy of a macromolecular system: Solvation energies, binding energies, and conformational analysis , 1988, Proteins.

[90]  H. Scheraga,et al.  Accessible surface areas as a measure of the thermodynamic parameters of hydration of peptides. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[91]  A. Y. Meyer.  Molecular mechanics and molecular shape. III. Surface area and cross‐sectional areas of organic molecules , 1986, Journal of computational chemistry.

[92]  Jacopo Tomasi,et al.  Analytical derivatives for molecular solutes. I. Hartree–Fock energy first derivatives with respect to external parameters in the polarizable continuum model , 1994 .

[93]  P. Claverie,et al.  Improvements of the continuum model. 1. Application to the calculation of the vaporization thermodynamic quantities of nonassociated liquids , 1988 .

[94]  Harold A. Scheraga,et al.  A Simple Functional Representation of Angular-Dependent Hydrogen-Bonded Systems. 1. Amide, Carboxylic Acid, and Amide-Carboxylic Acid Pairs , 1995 .

[95]  M. Frisch,et al.  Solvent effects. 2. Medium effect on the structure, energy, charge density, and vibrational frequencies of sulfamic acid , 1992 .

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

[97]  Kenji Morihashi,et al.  MNDO-effective charge model study of solvent effect on the potential energy surface of the SN2 reaction , 1989 .

[98]  Frederic M. Richards,et al.  Packing of α-helices: Geometrical constraints and contact areas☆ , 1978 .

[99]  Alexander A. Rashin,et al.  Hydration phenomena, classical electrostatics, and the boundary element method , 1990 .

[100]  Iñaki Tuñón,et al.  Continuum-uniform approach calculations of the solubility of hydrocarbons in water , 1993 .

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

[102]  H. Scheraga,et al.  Theoretical Modeling of Electrostatic Effects of Titratable Side-Chain Groups on Protein Conformation in a Polar Ionic Solution. 1. Potential of Mean Force between Charged Lysine Residues and Titration of Poly(L-lysine) in 95% Methanol Solution , 1994 .

[103]  H. Scheraga,et al.  Theoretical Modeling of Electrostatic Effects of Titratable Side Chain Groups on Protein Conformation in a Polar Ionic Solution. 2. pH-Induced Helix-Coil Transition of Poly(L-lysine) in Water and Methanol Ionic Solutions , 1995 .

[104]  Benedetta Mennucci,et al.  Self-Consistent-Field Calculation of Pauli Repulsion and Dispersion Contributions to the Solvation Free Energy in the Polarizable Continuum Model , 1997 .

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