Force AMBER

Fig. 1. The time evolution (top) and average cumulative difference (bottom) associated with the central dihedral angle of butane r (defined by the four carbon atoms), for trajectories differing initially in 10 , 10 , and 10 Angstoms of the Cartesian coordinates from a reference trajectory. The leap-frog/Verlet scheme at the timestep At = 1 fs is used in all cases, with an all-atom model comprised of bond-stretch, bond-angle, dihedral-angle, van der Waals, and electrostatic components, a.s specified by the AMBER force field within the INSIGHT/Discover program.

In this case, only two parameters (k and Iq) per atom pair are needed, and the computation of a quadratic function is less expensive. Therefore, this type of expression is used especially by biomolecular force fields (AMBER, CHARMM, GROMOS) dealing with large molecules like proteins, lipids, or DNA. 

It is noteworthy that it is not obligatory to use a torsional potential within a PEF. Depending on the parameterization, it is also possible to represent the torsional barrier by non-bonding interactions between the atoms separated by three bonds. In fact, torsional potentials and non-bonding 1,4-interactions are in a close relationship. This is one reason why force fields like AMBER downscale the 1,4-non-bonded Coulomb and van der Waals interactions. 

N is the number of point charges within the molecule and Sq is the dielectric permittivity of the vacuum. This form is used especially in force fields like AMBER and CHARMM for proteins. As already mentioned, Coulombic 1,4-non-bonded interactions interfere with 1,4-torsional potentials and are therefore scaled (e.g., by 1 1.2 in AMBER). Please be aware that Coulombic interactions, unlike the bonded contributions to the PEF presented above, are not limited to a single molecule. If the system under consideration contains more than one molecule (like a peptide in a box of water), non-bonded interactions have to be calculated between the molecules, too. This principle also holds for the non-bonded van der Waals interactions, which are discussed in Section 7.2.3.6. 

Molecular dynamics simulation package with various force field implementations, special support for AMBER. Parallel version and Xll trajectory viewer available. http //ganter.chemie.uni-dortmund.de/MOSCITO/... 

United Atom force fieldsare used often for biological polymers. In th esc m oleciiles, a reduced ii nm ber of explicit h ydrogen s can have a notable effect on the speed of the calculation. Both the BlOn and OPLS force fields are United Atom force fields. AMBER con tain s both aU nited and an All Atom force field. 

Caution If you arc new Lo com pn taLion al chemisLry. do not use Unilcd ALoms for AMBER calciilalions. This TlypcrCh cm oplion is available for researchers who warn lo alter aiom types aiul parameters for this force field. 

TlypcrC hcm oilers four molecular mechanics force fields MM+, AMBER, BIO+, and OPES (sec References on page 106). To run a molecular mechanics calciilaLion. yon miisi lirsi choose a force Eeld. The following sections discuss considerations in choosing a force field. 

The force field ec uations for M.Vf+, AMBER, BlOg and OPES are similar in the types of terms they contain bond, angle, dihedral, van der Waals. and electrostatic. There are som e differences m the form s of the etinations that can al fect your ch oice of force field. 

Wofe." rh c BIO + force field is an im plern en lation oflheCH. ARMM (Chcmistry at H.ARvard MacromoIceular Mechanics ) force field developed in the group of Martin Karplusat Harvard University, l.ike. AMBER and OP1.S, it is primarily designed to explore rnacro-moleciilcs. 

Lsc th e force fields th at have dern on strated accuracy for particu lar molecules or simulations. For example, CiPLS reproduces physical properties in liquid simulations extremely well. MM+ reproduces the structure and thermodynamic properties of small, nonpolar molecules better than AMBER, BIO+, and OPLS. 

Hach molecular mechanics method has its own functional form MM+. AMBER, OPL.S, and BIO+. The functional form describes the an alytic form of each of th e term s in th e poteri tial. For exam pie, MM+h as both a quadratic and a cubic stretch term in th e poten tial whereas AMBER, OPES, and BIO+ have only c nadratic stretch term s, I h e functional form is referred to here as the force field. For exam pie, th e fun ction al form of a qu adratic stretch with force constant K, and equilibrium distance i q is ... 

Finally, each force field may have multiple parameter sets (the val-uesolT oand K. for example). Th e AMBER force field and AMBER set ol types may be used with, for example, the AMBER/2 or AMDER/3 set of param eters. 

The chemical environment foran atom m a molecule is probably niiit iie to th at molecule. Chem istry tries to find unify in g concepts an d the atom type Is on e of those unifying con cepts. For example, the AMBER force field defines five atom types for oxygens ... 

In principle, atom types eoiild be assoeiated wilh a partieiilar parameter set rather than the functional form or force field. In HyperChern, however, atoms types are rigorously lied to a force field . M.M-t, AMBER, OPTS, and BIO+. Each of the force fields has a... 

Xote that two dilTcren t environni cn is. although they migh t be dis-liiignisbcd by tests (such as for ether and ester) can share an atom type (such as OS), A rel inem en i of th e AMBER force field would use separate types for these two along with differen t parani eters for th e differen L types. 

This section descrihes IlyperChem s four force fields, MM-h AMBER, OPES, and BlO-h providing auxiliary information for all force field calculations. 

The AMBER (Assisted Model Building and Energy Refin emeni) is based on a force field developed for protein and nucleic acid computations by members of the Peter Kollman research group at the... 

OPTS (Optim i/.ed Potentials for Liquid Simulations) is based on a force field developed by the research group of Bill Jorgensen now at Yale University and previously at Purdue University. Like AMBER, the OPLS force field is designed for calculations on proteins an d nucleic acids. It in troduces non bonded in leraclion parameters that have been carefully developed from extensive Monte Carlo liquid sim u lation s of small molecules. These n on-bonded interactions have been added to the bonding interactions of AMBER to produce a new force field that is expected to be better than AMBER at describing simulations w here the solvent isexplic-... 

Many of the torsional terms in the AMBER force field contain just one term from the cosine series expansion, but for some bonds it was found necessary to include more than one term. For example, to correctly model the tendency of O-C—C-O bonds to adopt a gauche conformation, a torsional potential with two terms was used for the O—C—C—O contribution ... 

Fig. 4.S Variation in torsional energy (AMBER force field) with O-C-C-0 torsion angle (to) for OCH -CHjO fragment. The minimum energy conformations arise for to = 60° and 300°.

Fhe van der Waals and electrostatic interactions between atoms separated by three bonds (i.c. the 1,4 atoms) are often treated differently from other non-bonded interactions. The interaction between such atoms contributes to the rotational barrier about the central bond, in conjunction with the torsional potential. These 1,4 non-bonded interactions are often scaled down by an empirical factor for example, a factor of 2.0 is suggested for both the electrostatic and van der Waals terms in the 1984 AMBER force field (a scale factor of 1/1.2 is used for the electrostatic terms in the 1995 AMBER force field). There are several reasons why one would wish to scale the 1,4 interactions. The error associated wilh the use of an repulsion term (which is too steep compared with the more correct exponential term) would be most significant for 1,4 atoms. In addition, when two 1,4... 

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