# DIHEDRAL ANGLES

dihedral angles, phi, psi, omega, chi1, chi2, chi3, chi4, chi5, rotamers, dihedral angle, definitions, garlic, Damir Zucic.

MAIN CHAIN DIHEDRAL ANGLES
The main chain dihedral angles are defined as follows:
(1) The phi angle is the angle of right-handed rotation around N-CA bond, the value being zero if CA-C bond is cis to C-N bond. Range: from -180 to 180 degrees.
(2) The psi angle is the angle of right-handed rotation around CA-C bond, the value being zero if C-N bond is cis to N-CA bond. Range: from -180 to 180 degrees.
(3) The omega angle is the angle of right-handed rotation about C-N bond, the value being zero if CA-C bond of the preceding residue is cis to N-CA bond. Most residues in a typical protein are involved in the formation of two peptide bonds. The peptide bond formed by the residues I and I + 1 is assigned to the residue I + 1. The same applies to the omega angle. For that reason no omega angle is assigned to the first residue.
Since version 1.2, garlic uses the following procedure to calculate the main chain dihedral angles:
(1) In the first attempt, the coordinates of the main chain atoms are used to calculate the dihedral angles phi and psi. The phi angle will be missing for the first residue in each chain. The psi angle will be missing for the last residue in each chain.
(2) In the second attempt, the missing phi angles will be calculated using the coordinates of H (hydrogen) atoms, if available. The missing psi angles will be calculated using the coordinates of O (oxygen) atoms.
SIDE CHAIN DIHEDRAL ANGLES
For each side chain dihedral angle, the coordinates of four atoms are required. The table below contains the list of atoms and the range of values, for each side chain angle and for each residue. In garlic, the angle chi1 is not calculated for ALA and GLY. The angle chi2 is not calculated for ALA, CYS, GLY, SER, THR and VAL. The angle chi3 is calculated for ARG, GLN, GLU, LYS and MET, the angle chi4 is calculated for ARG and LYS and the angle CHI5 is calculated only for ARG.

CHI1
SIDE CHAIN | AXIS | ATOMS USED TO DEFINE ANGLE | ZERO VALUE | FORMAL RANGE
ARG | CA-CB | N-CA-CB-CG | CG cis to N | from -180 to +180 deg
ASN | CA-CB | N-CA-CB-CG | CG cis to N | from -180 to +180 deg
ASP | CA-CB | N-CA-CB-CG | CG cis to N | from -180 to +180 deg
CYS | CA-CB | N-CA-CB-SG | SG cis to N | from -180 to +180 deg
GLN | CA-CB | N-CA-CB-CG | CG cis to N | from -180 to +180 deg
GLU | CA-CB | N-CA-CB-CG | CG cis to N | from -180 to +180 deg
HIS | CA-CB | N-CA-CB-CG | CG cis to N | from -180 to +180 deg
ILE | CA-CB | N-CA-CB-CG1 | CG1 cis to N | from -180 to +180 deg
LEU | CA-CB | N-CA-CB-CG | CG cis to N | from -180 to +180 deg
LYS | CA-CB | N-CA-CB-CG | CG cis to N | from -180 to +180 deg
MET | CA-CB | N-CA-CB-CG | CG cis to N | from -180 to +180 deg
PHE | CA-CB | N-CA-CB-CG | CG cis to N | from -180 to +180 deg
PRO | CA-CB | N-CA-CB-CG | CG cis to N | CA-CB is part of ring
SER | CA-CB | N-CA-CB-OG | OG cis to N | from -180 to +180 deg
THR | CA-CB | N-CA-CB-OG1 | OG1 cis to N | from -180 to +180 deg
TRP | CA-CB | N-CA-CB-CG | CG cis to N | from -180 to +180 deg
TYR | CA-CB | N-CA-CB-CG | CG cis to N | from -180 to +180 deg
VAL | CA-CB | N-CA-CB-CG1 | CG1 cis to N | from -180 to +180 deg
CHI2
ARG | CB-CG | CA-CB-CG-CD | CD cis to CA | from -180 to +180 deg
ASN | CB-CG | CA-CB-CG-OD1 | OD1 cis to CA | from -180 to +180 deg
ASP | CB-CG | CA-CB-CG-OD1 | OD1 cis to CA | from -180 to +180 deg
GLN | CB-CG | CA-CB-CG-CD | CD cis to CA | from -180 to +180 deg
GLU | CB-CG | CA-CB-CG-CD | CD cis to CA | from -180 to +180 deg
HIS | CB-CG | CA-CB-CG-ND1 | ND1 cis to CA | from -180 to +180 deg
ILE | CB-CG1 | CA-CB-CG1-CD | CD cis to CA | from -180 to +180 deg
LEU | CB-CG | CA-CB-CG-CD1 | CD1 cis to CA | from -180 to +180 deg
LYS | CB-CG | CA-CB-CG-CD | CD cis to CA | from -180 to +180 deg
MET | CB-CG | CA-CB-CG-SD | SD cis to CA | from -180 to +180 deg
PHE | CB-CG | CA-CB-CG-CD1 | CD1 cis to CA | from -180 to +180 deg
PRO | CB-CG | CA-CB-CG-CD | CD cis to CA | CB-CG is part of ring
TRP | CB-CG | CA-CB-CG-CD1 | CD1 cis to CA | from -180 to +180 deg
TYR | CB-CG | CA-CB-CG-CD1 | CD1 cis to CA | from -180 to +180 deg
CHI3
ARG | CG-CD | CB-CG-CD-NE | NE cis to CB | from -180 to +180 deg
GLN | CG-CD | CB-CG-CD-OE1 | OE1 cis to CB | from -180 to +180 deg
GLU | CG-CD | CB-CG-CD-OE1 | OE1 cis to CB | from -180 to +180 deg
LYS | CG-CD | CB-CG-CD-CE | CE cis to CB | from -180 to +180 deg
MET | CG-SD | CB-CG-SD-CE | CE cis to CB | from -180 to +180 deg
CHI4
ARG | CD-NE | CG-CD-NE-CZ | CZ cis to CG | from -180 to +180 deg
LYS | CD-CE | CG-CD-CE-NZ | NZ cis to CG | from -180 to +180 deg
CHI5
ARG | NE-CZ | CD-NE-CZ-Nh1 | Nh1 cis to CD | from -180 to +180 deg