Determination of solvation free energy using molecular dynamics with solute Cartesian mapping: An application to the solvation of 18‐crown‐6

The determination of relative stabilities of conformations of a molecule in solution has received much interest due to its relevance to chemical and biological properties in solution. Free energy perturbation (FEP) methodologies using molecular dynamics simulations have been used for the evaluation of free energy differences between two similar molecular systems. We present here a FEP method for the evaluation of the solvation free energy difference between two conformations. The simulations are carried out by fixing the Cartesian coordinates of a solute molecule. The molecule is switched from one conformer to another through a linear couping of the Cartesian coordinates of the two conformers. The solvation free energy is calculated from the interactions between the solvent and the solute using the standard FEP approach. This method is expected to be particularly useful for molecules with complicated conformational changes involving a large number of dihedral angle rotations. A crown ether, 18‐crown‐6, a ...

[1]  J. Uiterwijk,et al.  A molecular mechanics study of 18-crown-6 and its complexes with neutral organic molecules , 1987 .

[2]  I. Harada,et al.  Structures of 18-crown-6, 15-crown-5 and their metal complexes in methanol solution as studied by Raman spectroscopy , 1986 .

[3]  M. Karplus,et al.  Method for estimating the configurational entropy of macromolecules , 1981 .

[4]  Ron Elber,et al.  Calculation of the potential of mean force using molecular dynamics with linear constraints: An application to a conformational transition in a solvated dipeptide , 1990 .

[5]  Mihaly Mezei,et al.  Monte Carlo determination of the free energy and internal energy of hydration for the Ala dipeptide at 25.degree.C , 1985 .

[6]  W. L. Jorgensen,et al.  Comparison of simple potential functions for simulating liquid water , 1983 .

[7]  J. Dunitz,et al.  1,4,7,10,13,16‐Hexaoxacyclooctadecane: crystal structure at 100 K , 1980 .

[8]  William L. Jorgensen,et al.  Monte Carlo simulation of n‐butane in water. Conformational evidence for the hydrophobic effect , 1982 .

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

[10]  M Karplus,et al.  Dynamical theory of activated processes in globular proteins. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[11]  William L. Jorgensen,et al.  Cis-trans energy difference for the peptide bond in the gas phase and in aqueous solution , 1988 .

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

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

[14]  D. Beveridge,et al.  Free energy via molecular simulation: applications to chemical and biomolecular systems. , 1989, Annual review of biophysics and biophysical chemistry.

[15]  R. Zwanzig.  High‐Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases , 1954 .

[16]  Irwin D. Kuntz,et al.  A new technique to calculate low-energy conformations of cyclic molecules utilizing the ellipsoid algorithm and molecular dynamics: application to 18-crown-6 , 1988 .

[17]  G. Ciccotti,et al.  Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes , 1977 .

[18]  Peter A. Kollman,et al.  Conformational sampling and ensemble generation by molecular dynamics simulations: 18‐Crown‐6 as a test case , 1992 .

[19]  Charles L. Brooks,et al.  Molecular dynamics with internal coordinate constraints , 1988 .

[20]  P. Auffinger,et al.  Hydration of the 222 cryptand and 222 cryptates studied by molecular dynamics simulations , 1991 .

[21]  P. Kollman,et al.  An all atom force field for simulations of proteins and nucleic acids , 1986, Journal of computational chemistry.

[22]  T. P. Straatsma,et al.  Treatment of rotational isomers in free energy calculations. II. Molecular dynamics simulation study of 18‐crown‐6 in aqueous solution as an example of systems with large numbers of rotational isomeric states , 1989 .

[23]  J. Andrew McCammon,et al.  Free energy difference calculations by thermodynamic integration: Difficulties in obtaining a precise value , 1991 .

[24]  G. Torrie,et al.  Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling , 1977 .

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

[26]  Peter A. Kollman,et al.  The overlooked bond‐stretching contribution in free energy perturbation calculations , 1991 .

[27]  Peter A. Kollman,et al.  A molecular-mechanics study of 18-crown-6 and its alkali complexes: an analysis of structural flexibility, ligand specificity, and the macrocyclic effect , 1982 .