Biology Reference
In-Depth Information
between these different implementations, we will describe the CHARMM
force field in more detail below.
The all-atom PARAM 22 CHARMM force field
10
was parametrized
using quantum calculations of small-molecule properties as well as exper-
imental results. The bonded and nonbonded energy terms are illustrated
in Fig. 1 and the full functional form of the potential is given in Eq. (4).
1
2
1
2
Â
Â
2
2
Vr
()
=
K b b
(
-
)
+
K
(
qq
-
)
b
0
q
0
Bonds
Angles
1
2
2
Â
K
ww
+
(
-
)
w
0
Improp
ers
1
2
Â
+
K
( (
1
+
n
fd
-
)
f
Dihedrals
È
Ê
Á
ˆ
˜
-
Ê
ˆ
˜
˘
s
s
qq
r
ij
y
ij
Â
Â
.
+
4
e
Í
Í
˙
˙
+
Á
(4)
ij
r
r
e
Ë
Î
ij
ij
˚
ij
ij
ij
,
The first four terms of Eq. (4) are collectively referred to as bonded
energy terms; and the last two, the van der Waals and electrostatic terms,
are called nonbonded energy terms. The bonded energy terms describe
the energy associated with the covalent structure of the molecules. The
nonbonded terms have to be computed for all possible atom pairs in the
system, resulting in a numerically expensive
N
2
computation, where
N
is
the number of atoms. To limit the computation cost, cut-offs are fre-
quently introduced, where atom pairs distant of more than a certain value
are not considered interacting. Compared to nonbonded interactions,
the cost of bonded terms is negligible.
The van der Waals energy is described by the Lennard-Jones term,
which is the fifth term in Eq. (4); and accounts for the unspecific inter-
action between all atoms. The attractive term results from fluctuations in
the electronic cloud that induces an instantaneous dipole momentum,
which polarizes the electronic cloud of neighboring atoms or molecules
and vice versa. The net effect of the dipole-dipole interaction is attractive
