Introduction to Molecular Dynamics: Theory and Applications in Biomolecular Modeling - Computational Modeling of Biological Systems - page 9

2

4

1

3

1000 400 8

800

300 6

600

200 4

400

100 2

200

0 0 0

0 0.5 1 1.5 2 0 50 100 150 −100 0 100

b (A) theta (degree) chi (degree)

1

+

-

2

4

3

1500 200 0

0.8

0.6

150 −10 0.4

1000

0.2

100 −20

0

−0.2

50 −30

3 4 5 6

500

rij (A)

0 −40

0 −50 −50

−100 0 100

2 4 6 8 10 12 14

2 4 6 8 10 12 14

psi (degree) rij (A) rij (A)

Fig. 2 Potential energy terms in a force field. Schematic representations are shown for the bond,
angle, dihedral, improper, vdW and electrostatic interactions. The corresponding energy values
for selected atom types in the CHARMM force field are plotted, including the C-O bond, the
CA-C-O angle, the CA-C-N-CA (˚) dihedral and the C-CA-N-O (peptide bond) improper. To
demonstrate the nonbonded interactions, we also plotted the vdW and electrostatic energy values
for a pair of C-O atoms. The atom names used here are consistent with the naming convention of
protein data bank, where CA represents the C˛ atom of the protein backbone

plane containing the first three atoms and the plane containing the last three atoms.
A dihedral controls the rotation about the bond between the second and the third
atom, while an improper controls the “planarity” of the four atoms. For instance,
the ˚- backbone dihedrals of proteins are primarily controlled by dihedral terms,
whereas the planarity of a peptide bond (-C( O)NH-) is controlled by an improper

term. As for the nonbonded interactions, the electrostatic term describes the familiar
Coulombic interactions between two charged atoms, while the vdW term describes
interactions arising from induced dipoles and excluded volumes of pairs of atoms.
The vdW potential is attractive at long distance, but quickly becomes repulsive at
very short distance between two atoms, the latter of which has the effect of a “hard
core” potential and prevents atoms from overlapping with each other.
Among the bonded interactions, the bond, angle and improper terms all have
the form of a harmonic potential. Their corresponding spring constants are usually
quite large, which means that small changes in the above quantities can result in
a huge difference in the corresponding energy. For instance, increasing the length

D