The AMBER Forcefield

Contents

Introduction

The standard AMBER forcefield, which is attributable to Kollman and coworkers (Weiner et al. 1984, 1986) at the University of California, San Francisco, is parameterized and defined only for proteins and DNA. However, it has been widely used not only for proteins and DNA, but also for many other classes of molecules, such as polymers and small molecules. For the latter classes of molecules, various authors have added parameters and extended AMBER in other ways to suit their calculations. The AMBER forcefield has also been made specifically applicable to polysaccharides (Homans 1990).

Standard AMBER Forcefield

Functional Form

The coordinates and functional form of the energy terms used by AMBER are given in Eq. 3-11.

Eq. 3-11:
The first three terms in Eq. 3-11 handle the internal coordinates of bonds, angles, and dihedrals. Term 3 is also used to maintain the correct chirality and tetrahedral nature of sp3 centers in the united-atom representation. In the united-atom representation, nonpolar hydrogen atoms are not represented explicitly, but are coalesced into the description of the heavy atoms to which they are bonded. Terms 4 and 5 account for the van der Waals and electrostatic interactions. The final term, 6, is a hydrogen-bond term that augments the electrostatic description of the hydrogen bond. This term in AMBER adds only about 0.5 kcal mol-1 to the hydrogen-bond energy in AMBER, so the bulk of the hydrogen-bond energy still arises from the dipole-dipole interaction of the donor and acceptor groups.

AMBER Atom Types

The atom types in AMBER are quite specific to amino acids and DNA bases. In the original publications, the atoms types and charges are defined by means of diagrams of the amino acids and nucleotide bases. In the Biosym/MSI environment, this information has been placed in a residue library. Descriptions of the atom types, from the original papers defining the AMBER forcefield, are shown in Table 3-4.

Table 3-4. Atom Types--AMBER

The format is:

atom type
description
and you may quickly jump to the classes of atom types by clicking:

hydrogen types

H
amide or imino hydrogen
HC
explicit hydrogen attached to carbon
HO
hydrogen on hydroxyl oxygen
HS
hydrogen attached to sulfur
HW
hydrogen in water
H2
amino hydrogen in NH2
H3
hydrogen of lysine or arginine (positively charged)

all-atom carbon types

C
sp2 carbonyl carbon and aromatic carbon with hydroxyl substituent in tyrosine
CA
sp2 aromatic carbon in 6-membered ring with 1 substituent
CB
sp2 aromatic carbon at junction between 5- and 6-membered rings
CC
sp2 aromatic carbon in 5-membered ring with 1 substituent and next to a nitrogen
CK
sp2 aromatic carbon in 5-membered ring between 2 nitrogens and bonded to 1 hydrogen (in purine)
CM
sp2 same as CJ but one substituent
CN
sp2 aromatic junction carbon in between 5- and 6-membered rings
CQ
sp2 carbon in 6-membered ring of purine between 2 NC nitrogens and bonded to 1 hydrogen
CR
sp2 aromatic carbon in 5-membered ring between 2 nitrogens and bonded to 1 H (in his)
CT
sp3 carbon with 4 explicit substituents
CV
sp2 aromatic carbon in 5-membered ring bonded to 1 N and bonded to an explicit hydrogen
CW
sp2 aromatic carbon in 5-membered ring bonded to 1 N-H and bonded to an explicit hydrogen
C*
sp2 aromatic carbon in 5-membered ring with 1 substituent

united-atom carbon types

CD
sp2 aromatic carbon in 6-membered ring with 1 hydrogen
CE
sp2 aromatic carbon in 5-membered ring between 2 nitrogens with 1 hydrogen (in purines)
CF
sp2 aromatic carbon in 5-membered ring next to a nitrogen without a hydrogen
CG
sp2 aromatic carbon in 5-membered ring next to an N-H
CH
sp2 carbon with 1 hydrogen
CI
sp2 carbon in 6-membered ring of purines between 2 NC nitrogens
CJ
sp2 carbon in pyrimidine at positions 5 or 6 (more pure double bond than aromatic with 1 hydrogen)
CP
sp2 aromatic carbon in 5-membered ring between 2 nitrogens with one hydrogen (in his)
C2
sp2 carbon with 2 hydrogens
C3
sp2 carbon with 3 hydrogens

nitrogen types

N
sp2 nitrogen in amide group
NA
sp2 nitrogen in 5-membered ring with hydrogen attached
NB
sp2 nitrogen in 5-membered ring with lone pairs
NC
sp2 nitrogen in 6-membered ring with lone pairs
NT
sp2 nitrogen with 3 substituents
N2
sp2 nitrogen in base NH2 group or arginine NH2
N3
sp2 nitrogen with 4 substituents
N*
sp2 nitrogen in purine or pyrimidine with alkyl group attached

oxygen types

O
carbonyl oxygen
OH
alcohol oxygen
OS
ether or ester oxygen
OW
water oxygen
O2
carboxyl or phosphate nonbonded oxygen

sulfur types

S
sulfur in disulfide linkage or methionine
SH
sulfur in cystine

phosphorus

P
phosphorus in phosphate group

ion types

CU
copper ion (Cu+2 )
CO
calcium ion (Ca+2 )
I
iodine ion (I- )
IM
chlorine ion (Cl- )
MG
magnesium ion (Mg+2 )
QC
cesium ion (Cs+ )
QK
potassium ion (K+ )
QL
lithium ion (Li+ )
QN
sodium ion (Na+ )
QR
rubidium ion (Rb+ )

other

LP
lone pair

Homans' Carbohydrate Forcefield

Extension of AMBER to Carbohydrates

Homans' forcefield for oligosaccharides (Homans 1990) has been incorporated into the AMBER forcefield available in the Discover program. It uses the same functional form as AMBER and extends its applicability to polysaccharides and glycoproteins. Homans' approach in developing the carbohydrate forcefield was to combine the parameters for monosaccharides (Ha et al. 1988) with the results of ab initio calculations on model compounds relevant to the glycosidic linkage (Wiberg and Murcko 1989), to generate an AMBER-compatible forcefield. The bond, angle, and torsion parameters for each monosaccharide residue were, in general, taken directly from Ha et al. (1988). However, certain parameters required adjustment and others were added, to account for the glycosidic linkage between contiguous monosaccharide residues. The torsion parameters were adjusted to fit the quantum mechanical data (6-31G*) of Wiberg and Murcko (1980) for dimethyloxymethane.

In addition, the carbohydrate forcefield utilizes charges and van der Waals parameters derived for monosaccharides by Ha et al. (1988). Since the latter parameters were derived without an explicit hydrogen-bonding term, the carbohydrate forcefield also does not contain hydrogen-bonding parameters.

Homans-Specific Atom Types

To account for the anomeric effect associated with carbohydrates, the linking atoms were defined as different atom types. Table 3-5 lists these atom types, as well as the types corresponding to the ring atoms of sugars.

Table 3-5. Atom Types--Homans

The format is:

atom type
description
and you may quickly jump to the classes of atom types by clicking:

carbohydrate-hydrogen types

AH
a anomeric hydrogen
BH
b anomeric hydrogen
HT
sp2 hydrogen
HY
hydroxyl hydrogen

carbohydrate-carbon types

AC
a anomeric carbon
BC
b anomeric carbon
CS
sp2 carbon in sugar ring

carbohydrate-oxygen types

OA
a anomeric oxygen
OB
b anomeric oxygen
OE
ring oxygen
OT
hydroxyl oxygen

Special Considerations for the AMBER Forcefield: 1-4 Interactions and the Dielectric Constant

Two aspects of the AMBER forcefield require special treatment in the Discover program. First, all the 1-4 nonbond interactions are scaled by a factor of 0.5 by default; and second, in most applications a distance-dependent dielectric ( = f (r)) is used. Thus, the denominator in Term 5 of Eq. 3-11 involves the square of the distance, rather than just the distance as found in Coulomb's law. Another way of looking at this term is that the dielectric ``constant'' is (r) = r.

Scaling is done with the vdw_1_4 and coulomb_1_4 keywords of the forcefield scale command.

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