Q1.
Are all three of
these bonds able to undergo free rotation? What factors are
responsible for any observed restriction in rotation?
The three-dimensional spatial arrangement of the peptide backbone
is determined by the relative orientation of the groups connected
by these three repeating bonds in the peptide backbone. The
relative orientation of groups attached via a series of bonds can
be described by dihedral (or torsion) angles. Therefore, the
conformation of the peptide backbone (of a polypeptide) can be
described by (a series of) three dihedral (or torsion) angles that
describe the rotation about each of the three repeating bonds in
the peptide backbone.
Q2.
What is a
dihedral (or torsion) angle? How many bonds are needed to define a
dihedral angle?
For the three repeating bonds in a peptide backbone the dihedral
angles are defined as:
ϕ
- to describe
rotation about the N-C(α)
bond and involves the C(O)-N-C(α)-C(O)
bonds
ψ-
to describe rotation about the C(α)-C(O)
bond and involves the N-C(α)-C(O)-N
bonds
ω
- to describe
rotation about the C(O)-N bond and involves the
C(α)-C(O)-N-C(α)
bonds
The diagram below may help you visualize the ϕ
dihedral
angle.
The
ϕ
dihedral angle
involves the C(O)-N-C(α)-C(O)
bonds (as shown in the illustration on the left in the figure
above). If the plane formed by the first C(O), the
C(α),
and the N atoms are co-planer to the plane formed by the
C(α),
N and the second C(O) atoms, and the first and forth atoms (in this
case the two C(O) atoms) are opposite each other when viewed from
the C(α)
towards the N (as shown in the middle illustration in the figure
above) then the dihedral angle is said to be 180. In contrast, when
the two C(O) atoms are in an eclipsed conformation the angle is
said to be 0. Rotation about the N-C(α)
bond can give various ϕ
angles, and an
angle of 45 shown in the illustration on the right in the figure
above. A dihedral angle that is greater than 180 (measured in the
clockwise direction) is expressed as an angle measured in the
counterclockwise direction. For example a dihedral angle of 270 is
expressed as -90 (where the - sign indicates measurement in the
counterclockwise direction).
Lets visualize the ϕ
and
ψ
dihedral angles
using a model polypeptide.
(1). into the JMol window (left).
Using the mouse you can interact with the molecule. Familiarize
your self with the polypeptide chain.
Q3.
How many
residues does this peptide have? What are the N and C terminal
residues?
(2). Concentrate on the third amino acid, move the molecule around,
and try to visualize the ϕ
and
ψ
angles for this
residue.
(3). It may help to
Visualizing
the
ϕ dihedral
angle.
(4). Concentrate only on the
NOTE: Atom label CA designates the C(α) atom, and label C
designates the carbonyl carbon atom.
(5). Now rotate the molecule so that you are looking down the bond
undergoing rotation. For ϕ
torsion angles
the bond undergoing rotation is the N-C(α)
bond. Rotate the molecule so that you are looking at the N with the
C(α) directly behind, and the C(O) group closest to the
N-terminus towards the top of the screen.
(6). It may help to
(6). Now estimate the angle that separates the first and fourth
C(O) groups (the first group is the one closest to the N-terminus).
This is the ϕ
torsion
angle.
Q4.
What is your
estimate for the ϕ
torsion angle
for the third residue in this peptide?
Visualizing
the
ψ dihedral
angle.
(7). Now lets concentrate on the
(8). Rotate the molecule so that you are looking down the bond
undergoing rotation. For ψ
torsion angles
the bond undergoing rotation is the C(α)-C(O)
bond. This time rotate the molecule so that you are looking at the
C(α) with the C(O) directly behind, and the N closest to the
N-terminus towards the top of the screen.
(9). Estimate the angle that separates the first and fourth N
groups (the first group is the one closest to the N-terminus). This
is the ψ
torsion
angle.
Q5. What
is your estimate for the ψ
torsion angle
for the third residue in this peptide?
Check Your
Answers:
Q4.
The
ϕ
torsion angle
for the third residue in this peptide -
Q5.
The
ψ
torsion angle
for the third residue in this peptide -
Exercises:
In the following two exercises you will measure the phi and psi
angles of residues in an alpha-helix and a beta-sheet. JMol can
measure these angles for you. To measure torsion angles click
inside the JMol window while holding down the control key.
Select measurement
from the popup
menu. Then select Click
for torsion (dihedral) measurement. The measurement mode is
now activated.
Click on the four atoms that make up the dihedral angle you want to
measure, and the angle will be displayed on the screen (when
selecting atoms move the cursor on top of the atom you want to
select and wait for the atom label to appear. Then click).
Once the measurement is made then select Delete
measurements under the
measurement menu. Repeat these steps for
each of the torsion angle measurements.
Exercise
1. Load a
model of an alpha helix by clicking on the 'Load Helix' link below.
Only the backbone atoms (N, C(α) labeled as CA, and C(O)
labeled as C) of the helix are shown. Using descriptions of the
ψ and Φ angles provided above, determine the ψ and
Φ angles for residues 1,2,5,10, 13 and 16 in the alpha helix.
Exercise
2. Load a
model of a β-sheet by clicking on the 'Load Sheet' link below.
Only the backbone atoms of the helix are shown. Using descriptions
of the ψ and Φ angles provided above, determine the ψ
and Φ angles for residues 1,2,5,10,14, and 18 of the sheet.
Q1.
What are the phi
and psi angles for the residues in the helix and residues in the
sheet? Within a given secondary structure element (i.e for the
helix or the sheet), are the phi and psi angles similar for each of
the residues?
Q2.
Where both the
phi and psi angles measurable for the terminal residues of the
helix (residues 1 and 16) and the sheet (residues 1 and 18)?
Q3.
Given the trend
you may have observed in response to Q1 describe why phi and psi
angles important in protein structure?