The Dihedral command gets or sets the dihedral angles between all atom quartets in the four selections.

A dihedral angle is defined by four atoms. It is the angle between the plane spanned by atoms 1+2+3 and the plane spanned by atoms 2+3+4.

If the Bound flag is set, only dihedral angles formed by chemically bound atoms will be considered. This includes improper dihedrals.

If a new dihedral is specified with the Set parameter , the fourth selected atom (and all other atoms that are covalently connected to the third selected atom) will be moved to arrive at the new dihedral. This requires that the dihedral to set is not part of a closed loop. Atoms that are not covalently bound (e.g. metals) will not be moved along, which can be fixed afterwards by additionally re-setting the distance between one coordinating atom and the metal ion.

Improper dihedrals (i.e. planarity) can also be changed with this command.

Dihedrals can be changed interactively from the atom context menu in two ways:

• If four atoms are marked with white, blue, green and red fireflies, click Geometry > Dihedral to adjust the dihedral formed by these four atoms.
• If at least two atoms are marked with white and red fireflies, click Geometry > Bond dihedrals to adjust up to four bond dihedrals that link the two marked atoms. E.g. if you mark the 'N' and 'NZ' atoms in a lysine, this option allows to adjust all four Chi-dihedrals at the same time. Note that this feature is only available in YASARA Model and above.

To measure dihedrals between arbitrary points that do not coincide with atoms (like the center of a phenyl ring) build dummy atoms at these points first or use the GroupDihedral command.

An example for rotating side-chains (note that proline cannot rotate its side-chain):

Clear
LoadPDB 1crn
Style Ribbon,Stick
Console off
while 1
  for i=-180 to 178 step 2
    Dihedral N Res !Pro,CA Res !Pro,CB Res !Pro,CG Res !Pro,bound=Yes,Set=(i)
    Wait 1

The sign of a dihedral angle is not influenced by the current coordinate system. While this is not entirely consistent, it makes sure that an alpha helix always has Phi/Psi angles around -50/-50, no matter if you are using a left- or right-handed coordinate system.

When building secondary structure elements , the following dihedral angles may be helpful:

The Dihedral command can be used to scan the energy barrier of rotation around a certain bond. The following example macro loads trypsin and rotates the active site histidine in 18 steps of 20 degrees, performing an energy minimization of the local environment after each step. The results are saved as a table and visualized on screen:

Clear
# Load clean high resolution structure of trypsin
LoadPDB 1fn8
Style Ribbon,BallStick
DelRes Hetgroup
Clean
# Set the residue and the chi dihedral to sample
residue='His 57'
chi='CA,CB,CG,ND1'
steps=18
# Set the force field parameters
ForceField Amber99
Cutoff 7.86
Longrange Coulomb
ZoomAtom CA Res (residue)
# Sample dihedral angle
for i=-180 to 180 step 360/steps
  ShowMessage 'Analyzing residue (residue) with dihedral angle (i)...'
  # Create a working copy in object 2 and remove the original protein
  DuplicateObj 1
  RemoveObj 1
  # Create the simulation cell
  Cell Auto,Extension=10
  Boundary periodic
  # Fix residue
  FixRes (residue)
  # Fix everything not close by to converge faster
  FixAtom all with distance>6 from Res (residue)
  # Set the requested dihedral
  Dihedral (chi) Res (residue),bound=Yes,set=(i)
  # Energy minimize the environment of the residue
  Experiment Minimization
  Experiment On
  Wait ExpEnd
  # Calculate energy
  potnrg=Energy
  slvnrg=SolvEnergy
  # Tabulate result, delete the working object and get backup back
  Tabulate (i),(potnrg+slvnrg)
  DelObj 2
  AddObj 1
# Save the results
SaveTab 1,dihedral.tab,Format=Text,Columns=2,NumFormat=7.2f,Degrees Energy
# Create a new table 'Graph' containing just the second column of table 1 for visualization
MakeTab Graph,1
Tabulate Tab 1,Column=2
ShowTab Graph,Width=1,Range=20

Dihedral 105,109,114,120

Calculate the dihedral/torsion angle formed by the four atoms 105, 109, 114 and 120.

Dihedral 1,5,7,CA

Calculate the dihedral angles formed by atoms 1, 5, 7 and all CA atoms.

Dihedral C,N,CA,C,bound=Yes

List all Phi angles in the protein.

Dihedral N,CA,C,N,bound=Yes

List all Psi angles in the protein.

dih = Dihedral 200,300,400,500

Assign dihedral angle between atoms 200, 300, 400 and 500 to variable 'dih'.

Dihedral 105,109,114,120,set=155

Set the dihedral angle formed by the four atoms 105, 109, 114 and 120 to 155 degrees.

# EXAMPLE Dihedral
# Requires YASARA Model
Clear
Style BallStick
BuildRes Ala
AddRes Ala,1
ColorAtom CB,Yellow
PosObj 1,-2,0,3
radius=2
# X/Y/Z POSITIONS OF THE TWO ARROW CIRCLE CENTERS
pos1='-1.8,0,3'
pos2='0.7,0.1,3'
# TILT ANGLES FOR THE TWO ARROW CIRCLES AROUND THE Z-axis
tilt=32,27
# CREATE THE CIRCLES
for i=1 to 2
  # EVERY CIRCLE CONSISTS OF EIGHT ARROWS
  for j=0 to 315 step 45
    ShowArrow Point,0,(sin j*radius),(-cos j*radius),Point,0,(sin (j+45)*radius),(-cos (j+45)*radius),
              Radius=0.1,Color=Green
  JoinObj (i+2)-(Objects),(i+1)
  PosObj (i+1),(pos(i))
  RotateObj (i+1),Z=(tilt(i))
LabelAtom CB,ATOMNAME,Height=0.5,Black
LabelRes 1,Psi,Height=1,Black,X=1,Y=-3
LabelRes 2,Phi,Height=1,Black,X=-1,Y=3
Rotate Y=-15