Charged systems, simulations

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]. 

Another difference between the force fields is the calculation of electrostatic interactions. AMBER, BIO+, and OPLS use point charges to model electrostatic interactions. MM+ calculates electrostatic interactions using bond dipoles. The bond dipole method may not adequately simulate very polar or charged systems. 

In order to probe cation occupation in the active site in the absence of Mg2+ ions, we examined Na+ distributions in the reactant and activated precursor (deprotonated 20H nucleophile) states. It has been noted in the recent literature that the modeling of ions in highly charged systems such as HHR affords tremendous challenges with regard to simulation time scales [129], This section presents the results of series of five 300 ns simulations of the full length HHR, in both the reactant and activated precursor states, in order to ascertain the cation occupation requirement of the active site to maintain catalytic integrity. 

Bernacki, K., Hetenyi, B., Berne, B.J. Multiple "time step" Monte Carlo simulations application to charged systems with Ewald summation. J. Chem. Phys. 2004, 121, 44-50. 

Robinson et al. [69] studied the influence of cholesterol on molecular ordering of phospholipids by MD simulation. They used a more detailed description of the phospholipids including the head groups and charges. The simulated system contained two cholesterol molecules and 18 DMPC molecules in each leaflet of the bilayer (10 mol% cholesterol) and was simulated after equilibrium for 400 ps employing NVT conditions. They observed an increase in the fraction of trans conformations of the lipid alkyl chains with a decrease in kinks. Also, the dynamic and conformation of the flexible cholesterol side chains was characterized and it was found that they had a smaller tilt angle than the lipid chains with respect to the bilayer normal. 

Simulations of charged systems are very important. Common examples are plasmas, ionic solutions, dipole system and electronic systems. Because all pairs are included in the sum of eq. (2), the computer time only depends on the number of atoms and the number of time steps. For this reason my results should be applicable to all similar systems. I will discuss here only results for molecular dynamics simulations. The situation for Monte Carlo is completely parallel, although the actual coding is different since atoms are moved singly rather than all together. 

A. Arnold et al. Simulating Charged Systems with ESPResSo, Lect. Notes Phys. 703, 193-221... 

Simulating Charged Systems with ESPResSo 203 The near formula, i.e. the replacement for z 0, reads... 

Simulating Charged Systems with ESPResSo 217 Collapsed... 

J. Kolafa and J. W. Perram (1992) Cutoff errors in the ewald summation formulae for point charge systems. Molecular Simulation 9(5), pp. 351-68... 

FIG. 7 Counterion distribution functions P(r) (solid lines) for seven systems with the same dimensions as the ones in Figure 6, but with a Bjerrum length tB/Manning parameter = 0.959 < 1, counterion condensation is not expected to occur. This is borne out by the observation that the functions are convex up already at r = r0. In these weakly charged systems the predictions of PB theory (dotted lines) are excellent and can hardly be distinguished from the simulation results. 

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