Non-Ewald methods: Theory and applications to molecular systems

Biophysical Reviews

Volumn 4, Issue 3, 2012, Pages 161-170

  Fukuda, Ikuo ^a   Nakamura, Haruki ^b  

^a INST OF PHYS AND CHEMICAL RESEARCH   (Japan)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

Electrostatic interaction; Molecular dynamics; Pre averaging method; Reaction field method; Wolf method; Zero dipole summation method

Indexed keywords

EID: 84868354049     PISSN: 18672450     EISSN: 18672469     Source Type: Journal    
DOI: 10.1007/s12551-012-0089-4     Document Type: Review

References (103)

1. Allen MP, Tildesley DJ (1987) Computer simulations of liquids. Oxford University Press, New York.
2. Alper HE, Levy RM (1989) Computer simulations of the dielectric properties of water: studies of the simple point charge and transferrable intermolecular potential models. J Chem Phys 91: 1242-1251.
3. Andrea TA, Swope WC, Andersen HC (1983) The role of long ranged forces in determining the structure and properties of liquid water. J Chem Phys 79: 4576-4584.
4. Angoshtari A, Yavari A (2011) Convergence analysis of the Wolf method for coulombic interactions. Phys Lett A 375: 1281-1285.
5. Arima T, Idemitsu K, Inagaki Y, Tsujita Y, Kinoshita M, Yakub E (2009) Evaluation of melting point of UO2 by molecular dynamics simulation. J Nucl Mater 389: 149-154.
6. Avendaño C, Gil-Villegas A (2006) Monte Carlo simulations of primitive models for ionic systems using the Wolf method. Mol Phys 104: 1475-1486.
7. Barker JA, Watts RO (1973) Monte Carlo studies of the dielectric properties of water-like models. Mol Phys 26: 789-792.
8. Baumketner A (2009) Removing systematic errors in interionic potentials of mean force computed in molecular simulations using reaction-field-based electrostatics. J Chem Phys 130: 104106.
9. Beck DA, Armen RS, Daggett V (2005) Cutoff size need not strongly influence molecular dynamics results for solvated polypeptides. Biochemistry 44: 609-616.
10. Belhadj M, Alper HE, Levy RM (1991) Molecular dynamics simulations of water with Ewald summation for the long range electrostatic interactions. Chem Phys Lett 179: 13-20.
11. Brooks CL, Pettitt BM, Karplus M (1985) Structural and energetic effects of truncating long ranged interactions in ionic and polar fluids. J Chem Phys 83: 5897-5908.
12. Buştuǧ T, Patra SM, Kuyucak S (2006) Finite system and periodicity effects in free energy simulations of membrane proteins. Chem Phys Lett 425: 320-323.
13. Carré A, Berthier L, Horbach J, Ispas S, Kob W (2007) Amorphous silica modeled with truncated and screened Coulomb interactions: a molecular dynamics simulation study. J Chem Phys 127: 114512.
14. Chen YG, Weeks JD (2006) Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions. Proc Natl Acad Sci USA 103: 7560-7565.
15. Chen DL, Stern AC, Space B, Johnson JK (2010) Atomic charges derived from electrostatic potentials for molecular and periodic systems. J Phys Chem A 114: 10225-10233.
16. Chevrot G, Calligari P, Hinsen K, Kneller GR (2011) Least constraint approach to the extraction of internal motions from molecular dynamics trajectories of flexible macromolecules. J Chem Phys 135: 084110.
17. Chipot C, Millot C, Maigret B, Kollman PA (1994) Molecular dynamics free energy simulations: influence of the truncation of long-range nonbonded electrostatic interactions on free energy calculations of polar molecules. J Chem Phys 101: 7953-7962.
18. Clarke JHR, Smith W, Woodcock LV (1986) Short range effective potentials for ionic fluids. J Chem Phys 84: 2290-2294.
19. de Leeuw SW, Perram JW, Smith ER (1980) Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants. Proc R Soc Lond A 373: 27-56.
20. de Souza ON, Ornstein R (1997) Effect of periodic box size on aqueous molecular dynamics simulation of a DNA dodecamer with particle-mesh Ewald method. Biophys J 72: 2395-2397.
21. Demontis P, Spanu S, Suffritti GB (2001) Application of the Wolf method for the evaluation of Coulombic interactions to complex condensed matter systems: aluminosilicates and water. J Chem Phys 114: 7980-7988.
22. Desai TG (2007) Molecular dynamics study of screening at ionic surfaces. J Chem Phys 127: 154707.
23. Ercolessi F, Adams JB (1994) Interatomic potentials from first-principles calculations: the force-matching method. Europhys Lett 26: 583-588.
24. Essex JW (1998) The application of the reaction-field method to the calculation of dielectric constants. Mol Sim 20: 159-178.
25. Ewald PP (1921) Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann Phys (Leipzig) 64: 253-287.
26. Fennell CJ, Gezelter JD (2006) Is the Ewald summation still necessary? Pairwise alternatives to the accepted standard for long-range electrostatics. J Chem Phys 124: 234104.
27. Fröhlich H (1958) Theory of dielectrics. Clarendon, Oxford.
28. Fukuda I, Yonezawa Y, Nakamura H (2008) Consistent molecular dynamics scheme applying the Wolf summation for calculating electrostatic interaction of particles. J Phys Soc Jpn 77: 114301.
29. Fukuda I, Yonezawa Y, Nakamura H (2011) Molecular dynamics scheme for precise estimation of electrostatic interaction via zero-dipole summation principle. J Chem Phys 134: 164107.
30. Fukunishi Y, Mikami Y, Nakamura H (2003) The filling potential method: a method for estimating the free energy surface for protein-ligand docking. J Phys Chem B 107: 13201-13210.
31. Gargallo R, Hünenberger PH, Avilés FX, Oliva B (2003) Molecular dynamics simulation of highly charged proteins: comparison of the particle-particle particle-mesh and reaction field methods for the calculation of electrostatic interactions. Protein Sci 12: 2161-2172.
32. Gdoutos EE, Agrawal R, Espinosa HD (2010) Comparison of the Ewald and Wolf methods for modeling electrostatic interactions in nanowires. Int J Numer Meth Eng 84: 1541-1551.
33. Gereben O, Pusztai L (2011) On the accurate calculation of the dielectric constant from molecular dynamics simulations: the case of SPC/E and SWM4-DP water. Chem Phys Lett 507: 80-83.
34. Goto M, Takezoe H, Ishikawa K (2007) Carrier transport simulation of anomalous temperature dependence in nematic liquid crystals. Phys Rev E 76: 040701(R).
35. Guerrero-García GI, Mozuelos PG, Olvera de la Cruz M (2011) Potential of mean force between identical charged nanoparticles immersed in a size-asymmetric monovalent electrolyte. J Chem Phys 135: 164705-164714.
36. Hansson T, Oostenbrink C, van Gunsteren WF (2002) Molecular dynamics simulations. Curr Opin Struct Biol 12: 190-196.
37. Hassan SA (2007) Liquid-structure forces and electrostatic modulation of biomolecular interactions in solution. J Phys Chem B 111: 227-241.
38. Heinz TN, Hünenberger PH (2005) Combining the lattice-sum and reaction-field approaches for evaluating long-range electrostatic interactions in molecular simulations. J Chem Phys 123: 034107.
39. Heinz TN, van Gunsteren WF, Hünenberger PH (2001) Comparison of four methods to compute the dielectric permittivity of liquids from molecular dynamics simulations. J Chem Phys 115: 1125-1136.
40. Höchtl P, Boresch S, Bitomsky W, Steinhauser O (1998) Rationalization of the dielectric properties of common three-site water models in terms of their force field parameters. J Chem Phys 109: 4927-4937.
41. Hummer G, Pratt LR, García AE, Berne BJ, Rick SW (1997) Electrostatic potentials and free energies of solvation of polar and charged molecules. Phys Chem B 101: 3017-3020.
42. Hünenberger PH, McCammon JA (1999) Effect of artificial periodicity in simulations of biomolecules under Ewald boundary conditions: a continuum electrostatics study. Biophys Chem 78: 69-88.
43. Hünenberger PH, van Gunsteren WF (1998) Alternative schemes for the inclusion of a reaction-field correction into molecular dynamics simulations: influence on the simulated energetic, structural, and dielectric properties of liquid water. J Chem Phys 108: 6117-6134.
44. Jha PK, Sknepnek R, Guerrero-García GI, Olvera de la Cruz M (2010) A graphics processing unit implementation of coulomb interaction in molecular dynamics. J Chem Theory Comput 6: 3058-3065.
45. Kannam SK, Todd BD, Hansen JS, Daivis PJ (2012) Slip length of water on graphene: limitations of non-equilibrium molecular dynamics simulations. J Chem Phys 136: 024705.
46. Kastenholz M, Hünenberger PH (2004) Influence of artificial periodicity and ionic strength in molecular dynamics simulations of charged biomolecules employing lattice-sum methods. J Phys Chem B 108: 774-788.
47. Kikugawa G, Apostolov R, Kamiya N, Taiji M, Himeno R, Nakamura H, Yonezawa Y (2009) Application of MDGRAPE-3, a special purpose board for molecular dynamics simulations, to periodic biomolecular systems. J Comput Chem 30: 110-118.
48. Koehl P (2006) Electrostatics calculations: latest methodological advances. Curr Opin Struct Biol 16: 142-151.
49. Kuang S, Gezelter JD (2010) A gentler approach to RNEMD: nonisotropic velocity scaling for computing thermal conductivity and shear viscosity. J Chem Phys 133: 164101.
50. Leach AR (2001) Molecular modelling: principles and applications, 2nd ed. Prentice Hall, Englewood Cliffs.
51. Li J, Zhou Z, Sadus RJ (2007) Role of nonadditive forces on the structure and properties of liquid water. J Chem Phys 127: 154509.
52. Lin Y, Baumketner A, Deng S, Xu Z, Jacobs D, Cai W (2009) An image-based reaction field method for electrostatic interactions in molecular dynamics simulations of aqueous solutions. J Chem Phys 131: 154103.
53. Lin Y, Baumketner A, Song W, Deng S, Jacobs D, Cai W (2011) Ionic solvation studied by image-charge reaction field method. J Chem Phys 134: 044105.
54. Lins RD, Röthlisberger U (2006) Influence of long-range electrostatic treatments on the folding of the N-Terminal H4 histone tail peptide. J Chem Theory Comput 2: 246-250.
55. Mahadevan TS, Garofalini SH (2007) Dissociative water potential for molecular dynamics simulations. J Phys Chem B 111: 8919-8927.
56. Mark P, Nilsson L (2002) Structure and dynamics of liquid water with different long-range interaction truncation and temperature control methods in molecular dynamics simulations. J Comput Chem 23: 1211-1219.
57. Mathias G, Egwolf G, Nonella M, Tavan P (2003) A fast multipole method combined with a reaction field for long-range electrostatics in molecular dynamics simulations: the effects of truncation on the properties of water. J Chem Phys 118: 10847-10860.
58. Méndez PXV, Villegas AG (2012) Computer simulation of sedimentation of ionic systems using the Wolf method. J Chem Phys 136: 154507.
59. Míguez JM, González-Salgado D, Legido JL, Piñeiro MM (2010) Calculation of interfacial properties using molecular simulation with the reaction field method: results for different water models. J Chem Phys 132: 184102.
60. Monticelli L, Simões C, Belvisi L, Colombo G (2006) Assessing the influence of electrostatic schemes on molecular dynamics simulations of secondary structure forming peptides. J Phys Cond Matt 18: S329-S345.
61. Nagata Y, Mukamel S (2010) Vibrational sum-frequency generation spectroscopy at the water/lipid interface: molecular dynamics simulation study. J Am Chem Soc 132: 6434-6442.
62. Nakamura H (1996) Roles of electrostatic interaction in proteins. Quart Rev Biophys 29: 1-90.
63. Neumann M (1983) Dipole moment fluctuation formulas in computer simulations of polar systems. Mol Phys 50: 841-858.
64. Neumann M (1985) The dielectric constant of water. Computer simulations with the MCY potential. J Chem Phys 82: 5663-5672.
65. Neumann M (1986) Dielectric relaxation in water. Computer simulations with the TIP4P potential. J Chem Phys 85: 1567-1580.
66. Ni B, Baumketner A (2011) Effect of atom- and group-based truncations on biomolecules simulated with reaction-field electrostatics. J Mol Model 17: 2883-2893.
67. Nicolas JJ, Gubbins KE, Streett WB, Tildesley DJ (1979) Equation of state for the Lennard-Jones fluid. Mol Phys 37: 1429-1454.
68. Norberg, Nilsson (2000) On the truncation of long-range electrostatic interactions in DNA. Biophys J 79: 1537-1553.
69. Onsager L (1936) Electric moments of molecules in liquids. J Am Chem Soc 58: 1486-1493.
70. Patra M, Karttunen M, Hyvönen MT, Falck E, Vattulainen I (2004) Lipid bilayers driven to a wrong lane in molecular dynamics simulations by subtle changes in long-range electrostatic interactions. J Phys Chem B 108: 4485-4494.
71. Perram JW, Smith ER (1987) Microscopic derivation of fluctuation formulas for calculating dielectric constants by simulation. J Stat Phys 46: 179-190.
72. Reif MM, Krautler V, Kastenholz MA, Daura X, Hünenberger PH (2009) Molecular dynamics simulations of a reversibly folding β-heptapeptide in methanol: influence of the treatment of long-range electrostatic interactions. J Phys Chem B 113: 3112-3128.
73. Ribeiro MCC (2007) High frequency sound velocity in the glass former 2Ca(NO3)2·3KNO3: molecular dynamics simulations. Phys Rev B 75: 144202.
74. Robertson A, Luttmann E, Pande VS (2008) Effects of long-range electrostatic forces on simulated protein folding kinetics. J Comput Chem 29: 694-700.
75. Sagui C, Darden TA (1999) Molecular dynamics simulations of biomolecules: long-range Electrostatic Effects. Annu Rev Biophys Biomol Struct 28: 155-179.
76. Saito M (1994) Molecular dynamics simulations of proteins in solution: artifacts caused by the cutoff approximation. J Chem Phys 101: 4055-4061.
77. Schreiber H, Steinhauser O (1992a) Cutoff size does strongly influence molecular dynamics results on solvated polypeptides. Biochemistry 31: 5856-5860.
78. Schreiber H, Steinhauser O (1992b) Taming cut-off induced artifacts in molecular dynamics studies of solvated polypeptides: the reaction field method. J Mol Biol 228: 909-923.
79. Schulz R, Lindner B, Petridis L, Smith JC (2009) Scaling of multimillion-atom biological molecular dynamics simulation on a petascale supercomputer. J Chem Theor Comput 5: 2798-2808.
80. 3 ultrathin films on a paraelectric substrate. Phys Rev Lett 96: 137603.
81. Shi Q, Liu P, Voth GA (2008) Coarse-graining in interaction space: an analytical approximation for the effective short-ranged electrostatics. J Phys Chem B 112: 16230-16237.
82. Srivastava S, Santos A, Critchley K, Kim KS, Podsiadlo P, Sun K, Lee J, Xu C, Lilly GD, Glotzer SC, Kotov NA (2010) Light-controlled self-assembly of semiconductor nanoparticles into twisted ribbons. Science 327: 1355-1359.
83. Steinbach PJ, Brooks BR (1994) New spherical-cutoff methods for long-range forces in macromolecular simulation. J Comput Chem 15: 667-683.
84. Steinhauser O (1982) Reaction field simulation of water. Mol Phys 45: 335-348.
85. Tironi IG, Sperb R, Smith PE, van Gunsteren WF (1995) A generalized reaction field method for molecular dynamics simulations. J Chem Phys 102: 5451-5459.
86. Tyagi S (2005) Coulomb potentials in two and three dimensions under periodic boundary conditions. J Chem Phys 122: 014101.
87. van der Spoel D, van Maaren PJ (2006) The origin of layer structure artifacts in simulations of liquid water. J Chem Theor Comput 2: 1-11.
88. van der Spoel D, van Maaren PJ, Berendsen HJC (1998) A systematic study of water models for molecular simulation: derivation of water models optimized for use with a reaction field. J Chem Phys 108: 10220-10230.
89. van Gunsteren WF, Berendsen HJC, Rullmann JAC (1978) Inclusion of reaction fields in molecular dynamics. Application to liquid water. Faraday Discuss Chem Soc 66: 58-70.
90. Vernizzi G, Guerrero-García GI, Olvera de la Cruz M (2011) Coulomb interactions in charged fluids. Phys Rev E 84: 016707.
91. Weber W, Hünenberger PH, McCammon JA (2000) Molecular dynamics simulations of a polyalanine octapeptide under Ewald boundary conditions: influence of artificial periodicity on peptide conformation. J Phys Chem B 104: 3668-3675.
92. Wohlert J, Edholm O (2004) The range and shielding of dipole-dipole interactions in phospholipid bilayers. Biophys J 87: 2433-2445.
93. Wolf D (1992) Reconstruction of NaCl surfaces from a dipolar solution to the Madelung problem. Phys Rev Lett 68: 3315-3318.
94. -1 summation. J Chem Phys 110: 8254-8282.
95. Wu X, Brooks BR (2005) Isotropic periodic sum: a method for the calculation of long-range interactions. J Chem Phys 122: 044107.
96. Wu X, Brooks BR (2008) Using the isotropic periodic sum method to calculate long-range interactions of heterogeneous systems. J Chem Phys 129: 154115.
97. Yakub E (2006) Effective computer simulation of strongly coupled Coulomb fluids. J Phys A 39: 4643-4649.
98. Yakub E, Ronchi C (2003) An efficient method for computation of long-ranged Coulomb forces in computer simulation of ionic fluids. J Chem Phys 119: 11556-11560.
99. Yakub E, Ronchi C (2005) A new method for computation of long ranged coulomb forces in computer simulation of disordered systems. J Low Temp Phys 139: 633-643.
100. Yakub E, Ronchi C, Staicu D (2007) Molecular dynamics simulation of premelting and melting phase transitions in stoichiometric uranium dioxide. J Chem Phys 127: 094508.
101. Yonetani Y (2006) Liquid water simulation: a critical examination of cutoff length. J Chem Phys 124: 204501.
102. Yonezawa Y, Fukuda I, Kamiya N, Shimoyama H, Nakamura H (2011) Free energy landscapes of alanine dipeptide in explicit water reproduced by the force-switching Wolf method. J Chem Theor Comput 7: 1484-1493.
103. Zahn D, Schilling B, Kast SM (2002) Enhancement of the Wolf damped coulomb potential: static, dynamic, and dielectric properties of liquid water from molecular simulation. J Phys Chem B 106: 10725-10732.