Force united atom representations

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. 

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 ... 

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 ... 

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]. 

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 , ... 

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. 

United Atom Force Fields and Reduced Representations... 

Cui et al. performed similar analyses to fhose of Dupuis and co-workers. The side chain-side chain radial disfribufion functions (RDFs) reported by Cui et al. show remarkable qualitative deviation from fhose in Zhou et al. i It is of note that the united atom approach used by Cui and co-workers ignored electrostatic interactions between CP2 groups of the polymeric backbone. This can lead to a poor description of fhe hydrated structure in the regions close to the polymeric backbones, unlike the all-atom force field used in Zhou et al. ° For the sake of limited computational resources, Cui et al. used a relatively short representation of Nation ionomer chains consisting of three monomers as compared to the ten monomers used by Vishnyakov and Neimark or Urata et al. It can be expected that structural correlations will strongly depend on this choice. 

In some force field models, even simpler representations are used than the united atom approach, with entire groups of atoms being modelled as single interaction points. For example, a benzene ring might be modelled as a single site with appropriately chosen parameters. 

The first molecular dynamics simulations of a lipid bilayer which used an explicit representation of all the molecules was performed by van der Ploeg and Berendsen in 1982 [van der Ploeg and Berendsen 1982]. Their simulation contained 32 decanoate molecules arranged in two layers of sixteen molecules each. Periodic boundary conditions were employed and a united atom force potential was used to model the interactions. The head groups were restrained using a harmonic potential of the form ... 

FIGURE 2.1. As seen in a two-dimensional representation, the net force acting on a unit (atom or molecule shown in black) in the interior of a bulk phase (a) will essentially be zero, assuming the absence of faults in a solid that would alter interactions with neighboring units. The net forces acting on a unit at the surface (f>) will be unbalanced... 

Both SD and MD simulations of alkanes melts confined by solid surfaces (solid/liquid interfaces) and MD simulations of liquid alkanes at free surfaces (liquid/vapor interfaces) have been performed. The alkane molecules were represented by realistic atomistic force fields with constrained bond lengths. In all cases except Refs 29 and 30, the bond angle flexibility was maintained and in all cases the torsional flexibility was maintained. In most simulations the methyl and methylene groups were represented by single, spherically symmetric Lennard-Jones (LJ) force centers, i.e., the united atom (UA) approximation. Results from simulations which explicitly include the pendant hydrogen atoms as individual force centers, which we refer to as the explicit atom (EA) representation, will also be discussed. 

The individual components of a force field reflect established physical principles, such as representing bond lengths and angles as harmonic oscillators, and using Lennard-Jones 12-6 and Coulomb-type functions for the van der Waals and electrostatic nonbonding interactions, respectively. FIow-ever, the force fields are not independent of the protein models used. Each force field has associated with it atomic and molecular definitions and parameters, definitions that will differ between united atom and all-atom representations, for example. Similarly, water models are parameterized for use with certain force fields and are not necessarily interchangeable. ... 

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