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Ionic Charging Free Energies Using Ewald Summation

  • Tom Darden
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 108)

Abstract

Recently, a number of groups have discovered that the use of Ewald summation leads to greatly improved stability in molecular dynamics simulations of nucleic acids, proteins and membrane bilayers. This presentation will discuss the effect of boundary conditions and treatment of long-range electrostatics on molecular dynamics simulations, as well as on the important problem of calculating free energy differences. Due to its simplicity, we focus on the problem of calculating ionic charging free energies. We review recent results that suggest Ewald summation gives appropriate values for this free energy, at least for the simple case of ion charging.

Keywords

Free Energy Molecular Dynamic Simulation Periodic Boundary Condition Radial Distribution Function Point Charge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    P. E. Smith and B. M. Pettitt, Modeling solvent in biomolecular systems, J. Phys. Chem., 98:9700–9711, 1994.CrossRefGoogle Scholar
  2. [2]
    J. E. Ladbury, Just add water: The effect of water on the specificity of protein-ligand binding sites and its potential application to drug design, Chemistry and Biology, 3:973–982, 1996.CrossRefGoogle Scholar
  3. [3]
    P. Kollman, Free energy calculations: Applications to chemical and biochemical phenomena, Chem. Rev., 93:2395–2417, 1993.CrossRefGoogle Scholar
  4. [4]
    P. Kollman, Advances and continuing challenges in achieving realistic and predictive simulations of the properties of organic and biological molecules, Acc. Chem. Res., 29:461–469, 1996.CrossRefGoogle Scholar
  5. [5]
    M. Parrinello, From silicon to rna: The coming of age of ab initio molecular dynamics, Solid State Commun., 102:107–120, 1997.CrossRefGoogle Scholar
  6. [6]
    M. E. Tuckerman, P. J. Ungar, T. Von Rosenvinge, and M. L. Klein, Ab initio molecular dynamics simulations, J. Phys. Chem., 100:12878–12887, 1996.CrossRefGoogle Scholar
  7. [7]
    B. J. Berne and J. E. Straub, Novel methods of sampling phase space in the simulation of biological systems, Curr. Opin. Str. Bio., 7:181–189, 1997.CrossRefGoogle Scholar
  8. [8]
    L. Greengard and V. Rokhlin, A fast algorithm for particle simultations, J. Comp. Phys., 73:325–348, 1987.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    Lu Wang and Jan Hermans, Reaction field molecular dynamics simulation with Friedman’s image charge method, J. Phys. Chem., 99:12001–12007, 1995.CrossRefGoogle Scholar
  10. [10]
    Arieh Warshel and Michae Levitt, Theroretical studies of enzymatic reaction: Dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme, J. Mol. Biol., 103:227–249, 1976.CrossRefGoogle Scholar
  11. [11]
    Thomas Simonson, Accurate calculation of the dielectric constant of water from simulations of a microscopic droplet in vacuum, Chem. Phys. Lett., 250:450–454, 1996.CrossRefGoogle Scholar
  12. [12]
    Jonathan W. Essex and William L. Jorgensen, An empirical boundary potential for water droplet simulations, J Comp. Chem., 16:951–972, 1995.CrossRefGoogle Scholar
  13. [13]
    J. Aqvist, Ion-water interaction potentials derived from free energy perturbation simulations, J. Phys. Chem., 94:8021–8024, 1990.CrossRefGoogle Scholar
  14. [14]
    N. Metropolis A. Rosenbluth, M. Rosenbluth, andE. Teller, Equation of state calculations by fast computing machine, J. Chem. Phys., 21:1087–1092, 1953.CrossRefGoogle Scholar
  15. [15]
    S. W.Deleeuw, J. W. Perram, and E. R. Smith, Simulation of electrostatic systems in periodic boundary conditions I: Lattice sums and dielectric constants, Proc. R. Soc. Lond., A373:27–56, 1980.MathSciNetGoogle Scholar
  16. [16]
    S. Boresch and O. Steinhauser, Presumed versus real artifacts of the ewald summation technique: The importance of dielectric boundary conditions, Ber. Bunseges. Phys. Chem., 101:1019–1029, 1997.Google Scholar
  17. [17]
    J. P. Valleau and S. G. Whittington, A guide to Monte Carlo for statistical mechanics: 1. Highways, In B. J. Berne, editor, Statistical Mechanics, Part A: Equilibrium Techniques, volume 5, New York, NY, 1977, Plenum.Google Scholar
  18. [18]
    G. Hummer, D. M. Soumpasis, and M. Neumann, Computer simulation of aqueous Na-Cl electrolyte, J. Phys. Condens. Matt., 23A: A141–A144, 1994.CrossRefGoogle Scholar
  19. [19]
    S. W. Deleeuw, J. W. Perram, and E. R. Smith, Computer simulation of the static dielectric constant of systems with permanent dipole moments, Ann. Rev. Phys. Chem., 37:245–270, 1986.CrossRefGoogle Scholar
  20. [20]
    A. Toukmaji and J. A. Board, Ewald sum techniques in perspective: A survey, Comp. Phys. Comm., 95:78–92, 1996.Google Scholar
  21. [21]
    Pascal Auffinger and David L. Beveridge, A simple test for evaluating the truncation effects in simulations of systems involving charged groups, Chem. Phys. Lett., 234:413–415, 1995.CrossRefGoogle Scholar
  22. [22]
    David H. Kitson, FrancAvbelj, John Moult, Dzung T.Nguyen, John E. Mertz, D. Hatzi, and Arnold T. Hagler, On achieving better than 1 Angstrom accuracy in a simulation of a large protein: Streptomyces griseus protease A, Proc. Nat. Acad. Sci., 90:8920–8924, 1993.CrossRefGoogle Scholar
  23. [23]
    S. Louise-May, P. Auffinger, and E. Westhof, Calculations of nucleic acid conformations, Curr. Opin. Str. Biol., 6:289–298, 1996.CrossRefGoogle Scholar
  24. [24]
    A. D. Mackerrell, Influence of magnesium ions on duplex dna structural, dynamic, and solvation properties, J. Phys. Chem. B, 101:646–650, 1997.CrossRefGoogle Scholar
  25. [25]
    P. J. Steinbach and B. R. Brooks, New spherical cutoff methods for long-range forces in macromolecular simulation, J. Comp. Chem., 15:667–683, 1994.CrossRefGoogle Scholar
  26. [26]
    Lalith Perera, Ulrich Essmann, and Max L. Berkowitz, Effect of the treat ment of long-range forces on the dynamics of ions in aqueous solutions, J. Chem. Phys., 102:450–456, 1995.CrossRefGoogle Scholar
  27. [27]
    S. E. Feller, R. W. Pastor, A. Rojnuckarin, S. Bogusz, and B. R. Brooks, Effect of electrostatic force truncation on interfacial and transport properties of water, J. Phys. Chem., 100:17011–17020, 1996.CrossRefGoogle Scholar
  28. [28]
    P. E. Smith AND B. M. Pettitt, Ewald artifacts in liquid state molecular dynamics simulations, J. Chem. Phys., 105:4289–4293, 1996.CrossRefGoogle Scholar
  29. [29]
    P. E. Smith AND B. M. Pettitt, On the presence of rotational ewald artifacts in the equilibrium and dynamical properties of a zwitterionic tetrapeptide in aqueous solution, J. Phys. Chem. B, 101:3886–3890, 1997.CrossRefGoogle Scholar
  30. [30]
    T. E. Cheatham III AND P. A. Kollman, Observation of the a-dna to b-dna transition during unrestrained molecular dynamics in aqueous solution, J.Mol. Bio., 1996:434–444, 259.CrossRefGoogle Scholar
  31. [31]
    Ulrich Essmann, Lalith Perera, Max L. Berkowitz, Tom Darden, Hsing Lee, and Lee G. Pedersen, A smooth particle mesh Ewald method, J. Chem. Phys., 103:8577–8593, 1995.CrossRefGoogle Scholar
  32. [32]
    F. Figuerido, G. S. DelBuono, and R. M. Levy, On finite-size effects in computer simulations using the Ewald potential, J. Chem. Phys., 103:6133, 1995.CrossRefGoogle Scholar
  33. [33]
    B. A. Luty and W. F. Van Gunsteren, Calculating electrostatic interactions using the particle-particle particle-mesh method with nonperiodic long-range interactions, J. Phys. Chem., 100:2581–2587, 1996.CrossRefGoogle Scholar
  34. [34]
    G. Hummer, L. R. Pratt, and A. E. Garcia, On the free energy of ionic hydration, J. Phys. Chem., 100:1206–1215, 1996.CrossRefGoogle Scholar
  35. [35]
    G. Hummer, L. R. Pratt, A. E. Garcia, B. J. Berne, and S. W. Rick, Electrostatic potentials and free energies of solvation of polar and charged molecules, J. Phys. Chem. B, 101:3017–3020, 1997.CrossRefGoogle Scholar
  36. [36]
    G. Hummer, L. R. Pratt, and A. E. Garcia, Ion sizes and finite-size corrections for ionic-solvation free energies, J. Chem. Phys., 107:9275–9277, 1997.CrossRefGoogle Scholar
  37. [37]
    J. Aqvist and T. Hansson, On the validity of electrostatic linear response in polar solvents, J. Phys. Chem., 100:9512–9521, 1996.CrossRefGoogle Scholar
  38. [38]
    S. W. Rick and B. J. Berne, The aqueous solvation of water: A comparison of continuum methods with molecular dynamics, J. Am. Chem. Soc., 116:3949–3954, 1994.CrossRefGoogle Scholar
  39. [39]
    H. Ashbaugh and R. Wood, Effects of long-range electrostatic potential truncation on the free energy of ionic hydration, J. Chem. Phys., 106:8135–8139, 1997.CrossRefGoogle Scholar
  40. [40]
    D. Adams and G. Dubey, Taming the Ewald sum in the computer simulation of charged systems, J. Comp. Phys., 72:156–176, 1987.MathSciNetMATHCrossRefGoogle Scholar
  41. [41]
    T. P. Straatsma and H. J. C. Berendsen, Free energy of ionic hydration: Analysis of a thermodynamic integration technique to evaluate free energy differences by molecular dynamics simulations, J. Chem. Phys., 89:5876–5886, 1988.CrossRefGoogle Scholar
  42. [42]
    R. H. Wood, Continuum electrostatics in a computational universe with finite cutoff radii and periodic boundary conditions: Correction to computed free energies of ionic solvation, J. Chem. Phys., 103:6177–6187, 1995.CrossRefGoogle Scholar
  43. [43]
    S. Bogusz, T. Cheatham III, and B. Brooks, Removal of pressure and free energy artifacts in charged periodic systems via net charge corrections to the ewald potential, J. Chem. Phys., 1998, 103:6177–6187 in press.Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Tom Darden
    • 1
  1. 1.National Institute of Environmental Health Science ResearchUSA

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