United atom representation

Figure 7-14. All-atom and united-atom representation of the amino acid isoleucine. In this example, 13 atoms, which are able to form explicit non-bonding interactions, are reduced to only four pseudo-atoms,...

The OPLS force field is described in twtt papers, one discussing parameters for proteins W. L. Jorgensen and J. Tirado-Rives,/. Amer. (. hem. Soc., 110, 1557 (iy8K) and on e discii ssin g param eters for n iicleotide bases [J. Pranata, S. Wiersch ke, and W. L. Jorgen sen. , /.. Amer. Chem. Soc.. 117, 281(1 ( 1991)1. The force field uses the united atom concept ftir many, but not all. hydrttgens attached to carbons to allow faster calculation s on macromolecular systems. The amino and nucleic acid residue templates in HyperChein automatically switch to a united atom representation where appropriate when th e OPLS option is selected. 

The chemically realistic simulations we are discussing have been performed using a united atom representation of PB, which leads to the question How does one actually measure a CH vector reorientation for such a model The answer to this question is to use the trick we discussed in the analysis of the pressure dependence of the melt structure factor of PB. Hydrogen atoms are placed on the backbone carbons at their mechanical equilibrium positions for each structure that has been sampled along the MD trajectory. The CH vector dynamics we are showing in Figure 16 is solely from the backbone reorientations of the chain. 

Dynamics). The field of molecular simulations grew up independently from that of NMR structural studies and developed its own level of molecular detail. Many such force fields use the united atom representation of a molecule, in which all heavy atoms are present but only polar hydrogens are treated explicitly.12-14 An NMR restraint, however, may well refer to an aliphatic proton not explicitly treated. To handle this situation, van Gunsteren et al., applied what was called the virtual atom.ls With this method, one can take the force that one would want to impose on the proton and redistribute it on to the atoms present. For example, one may have a potential V defined in terms of the coordinates of a proton H. The force as a function of that proton s coordinates would be written as follows ... 

MD simulations with complete representation of lipids and solvent are most effective in determining the short-range structure and short-time dynamics. These simulations commonly use the united atom representation for the lipid hydrocarbon chains. Typically these simulations use several thousands of atoms and are limited to several hundred picoseconds. However, with faster computers becoming available, multinanosecond simulations should become routine in the near future. 

Within the context of the above, let us try to formulate some necessary requirements for the design of a moderate resolution reduced model (based on united-atom representation and knowledge-based potentials) of real proteins and its force field ... 

To model large closed circular DNA molecules, we use three point masses to represent each basepair (6). We chose this representation because three points define a plane, so we can monitor the variations in the angles between successive basepair planes, i.e., variations in roll, tilt, and twist. The three point masses do not correspond exactly to sets of atoms in the real molecule, so they are not properly called united atoms. Consequently, we call the point masses "pseudoatoms". (A united atom representation might use one pseudoatom for each phosphate group, one for each deoxyribose, and one for each base, but this would require six united atoms per basepair, and it would be difficult to monitor the roll, tilt, and twist angles that are of interest in our studies.)... 

The structural, thermal and mechanical characterization of the interlamellar domain and of the 201 crystal-melt interface of semicrystalline PE was performed, and compared with experimental data where available. Monte Carlo simulations complete with three-fold torsional potential were used with a united atom representation of polyethylene. We have employed two different strategies to assess the properties of the interface. 

The intramolecular parameters kf,ro, kg, and 0q from the AMBER force field [21, 22] were used. The oxygen atoms of alcohols and ethers were described by the OPLS parameters [17,18]. The Lennard-Jones parameters for halogens and the atoms of the aliphatic groups were optimized to reproduce the experimentally measured solubilities of methane and its halogenated derivatives in water and hexane, separately [23]. The resulting parameters do not follow the standard combination rules because we were unable to find a set of parameters consistent with the rules which would yield sufficiently accurate solubilities of the solutes in both phases. A similar difficulty was encountered in other studies of interfacial systems, in which the united atom representation was used to describe nonpolar molecules [24, 25]. 

The Na-AOT reverse micelle is a widely investigated reverse micelle system made up of the sodium salt of a two-tailed anionic surfactant, sodium di(2-ethylhexyl) sulfosuccinate. The interior of the aqueous reverse micelle is modeled as a rigid cavity, with a united atom representation for the sulfonate head group (Faeder and Ladanyi 2000 Pal et al. 2005). The head groups protrude from the cavity boundary and are tethered only in the radial direction by means of a harmonic potential. Interactions between reverse micelles are neglected in the model hence periodic boundary conditions and Ewald summations for the electrostatics are not required. Water is treated using the extended simple point charge, or SPC/E, model and the potential parameters for all the species are listed in Table 6.1. 

Boundaries between atomistic and coarse-grained simulation approaches are floating. Atomistic simulations of ionomer systems typically employ all-atom representations of water molecules, anionic head groups, and protons. For the remaining components, the use of a coarse-grained or united-atom representation for the CF , groups in both the fluorocarbon backbone and the sidechains could markedly improve the computational efficiency of atomistic simulations. United-atom force fields permit simulations of substantially larger systems compared to all-atom force fields. For instance, Urata et al. (2005) have employed a united-atom representation of CF , ... 

Fig. 13 Lipid-packing defects in atomistic and CG simulations. Left Molecular models of lipids using a united-atom representation (top) or a CG representation (bottom). Polar atoms/beads, grey hydrophobic atoms/beads, yellow/orange. Middle Top view of lipid bilayers using a surface representation in AA ad CG simulations. Right Top view of the lipid bilayers in the middle panel plus detected lipid-packing defects (blue, see Vanni etal. for additional details on the methodology to identify them) for the two bilayers. Moving from a united-atom (approximately 50 atoms per lipid) to a CG representation (approximately 15 beads per lipid) does not prevent a correct quantification of this microscopic membrane property.

As computational power advanced and became more accessible, so did the detail incorporated into the protein models. By 1977, work had moved toward united atom representations of proteins and the use of molecular mechanics to characterize the native state dynamics of BPTI in vacuo with no water included except for four crystalline waters.The empirical energy function used in this first protein MD simulation forms the basis of today s protein force fields. 

In the rigid model of Shim et al., the united atom representation for the CH2 and CH3 groups is used. Hence, the cation is represented by a rigid body and its geometry (bond lengths, angles) was taken from experimental x-ray diffraction data obtained from crystals of [C2-mim][Br] (Elaiwi et al., 1995). The electrostatic description of the cation consists of fixed partial charges centred on the atoms (Hanke et al., 2001). The interaction potential in the system is represented by a sum of pairwise additive interatomic LJ and Coulombic potentials ... 

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