Particle mesh Ewald simulation

U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen. The smooth particle mesh ewald method. J. Chem. Phys., 103 8577, 1995. Brock A. Luty, Ilario G. Tironi, and Wilfried F. van Gunsteren. Lattice-sum methods for calculating electrostatic interactions in molecular simulations. J. Chem. Phys., 103 3014-3021, 1995. 

In periodic boimdary conditions, one possible way to avoid truncation of electrostatic interaction is to apply the so-called Particle Mesh Ewald (PME) method, which follows the Ewald summation method of calculating the electrostatic energy for a number of charges [27]. It was first devised by Ewald in 1921 to study the energetics of ionic crystals [28]. PME has been widely used for highly polar or charged systems. York and Darden applied the PME method already in 1994 to simulate a crystal of the bovine pancreatic trypsin inhibitor (BPTI) by molecular dynamics [29]. 

Cheatham T E III, J L Miller, T Fox, T A Darden and P A Kollman 1995. Molecular Dynamics Simulations on Solvated Biomolecular Systems The Particle Mesh Ewald Method Leads to Stable Trajectories of DNA, RNA and Proteins. Journal of the American Chemical Society 117 4193-4194. 

Darden T A, L Perera, L Li and L Pedersen 1999. New Tricks for Modelers from the Crystallography Toolkit The Particle Mesh Ewald Algorithm and Its Use in Nucleic Acid Simulations. Structure with Folding and Design 7 R55-R60. 

Darden T, Perera L, Li LP, Pedersen L (1999) New tricks for modelers from the crystallography toolkit the particle mesh Ewald algorithm and its use in nucleic acid simulations. Struct Fold Des 7(3) R55-R60... 

Cheatham T. E., Ill, Miller J. L, FoxT., Darden T. A. and Kollman P. A. Molecular dynamics simulations on solvated biomolecu-lar systems the particle mesh Ewald method leads to stable trajectories of DNA, RNA, and proteins. J. Am. Chem. Soc. (1995) 117(14) 4193-4194. 

The probably most delicate aspect of nucleic-acid modeling is the treatment of long-range interactions. The particle-mesh Ewald method, introduced by Darden et al. [109] [110] has yielded very promising results in a number of recent molecular-dynamics simulations of oligonucleotides... 

The motions of proteins are usually simulated in aqueous solvent. The water molecules can be represented either explicitly or implicitly. To include water molecules explicitly implies more time-consuming calculations, because the interactions of each protein atom with the water atoms and the water molecules with each other are computed at each integration time step. The most expensive part of the energy and force calculations is the nonbonded interactions because these scale as 77 where N is the number of atoms in the system. Therefore, it is common to neglect nonbonded interactions between atoms separated by more than a defined cut-off ( 10 A). This cut-off is questionable for electrostatic interactions because of their 1/r dependence. Therefore, in molecular dynamics simulations, a Particle Mesh Ewald method is usually used to approximate the long-range electrostatic interactions (71, 72). 

In recent years, a number of models have been introduced which permit the inclusion of long-range electrostatic interactions in molecular dynamics simulation. For simulations of proteins and enzymes in a crystalline state, the Ewald summation is considered to be the correct treatment for long range electrostatic interactions (Ewald 1921 Allen and Tildesley 1989). Variations of the Ewald method for periodic systems include the particle-mesh Ewald method (York et al. 1993). To treat non-periodic systems, such as an enzyme in solution other methods are required. Kuwajima et al. (Kuwajima and Warshel 1988) have presented a model which extends the Ewald method to non-periodic systems. Other methods for treating explicitly long-range interactions... 

P. F. Batcho, D. A. Case, and T. Schlick, Optimized particle mesh Ewald/multiple time step integration for molecular dynamics simulations. J. Chem. Phys. 115, 4003 4018 (2001). 

Qian, X.L., Schlick, T. Efficient multiple-time-step integrators with distance-based force spHtting for particle-mesh-Ewald molecular dynamics simulations, J. Chem. Phys. 2002,116,5971-83. 

Within the last decade important progress has been made in the reliability of MD simulations of solvated nucleic acids using improved force fields and, in particular, a better treatment of electrostatics by the particle-mesh Ewald method. For the first time unrestrained simulations have become possible. Starting out firom experimental geometries it is now possible to explore the conformational space in the vicinity of the starting geometry and to study conformational transitions. ... 

From a methodological point of view it has to be noted that the reliability of MD simulations on biopolymers, and in particular on nucleic acids, has been substantially improved since the particle-mesh Ewald summation for an appropriate treatment of longe-range electrostatics has become available in the second half of the nineties. A second point that is worth mentioning refers... 

As already noted, metal ions play a vital role in DNA tetraplex structures. The first MD study that did address this point was published in 1994. It was found that the simulation could reproduce a few properties of the structure but could not correctly describe the metal ion nucleic acid interaction. This is not surprising as at that time the particle-mesh Ewald roach was not yet available. Later simulations do not suffer from this deficioicy. 

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