3. Calculate Q/R. This quantity is a raw evaluation of the interface “roughness”: the more Q/R is close to 1, the less is the
length of the loops formed in each subunit with respect to the
dimeric contact surface. In particular when Q ¼ 1 all the
residues are located at the interface.
4. Calculate Q n defined as: Q n ¼
Q
R
Q
N . This parameter takes
simultaneously into account the presence of loops (Q/R) and
the percentage of a.a. that are “at” or “close to” the dimeric
interface (see Note 2).
5. Calculate the Squared Loops Length, Sll, defined as the sum of
squared distances (in number of a.a. in the sequence) between
two consecutive residues involved in quaternary interactions,
weighted by the total number of amino acids. In the example of
Fig. 1: Sll ¼
ad
2 þ
de
2 þ
ep
2 þ
pq
2
N
2
where
ad
2 ¼ 9;
de
2 ¼ 1, etc:
2.3 Assigning
Dimeric Structures
to the Different
Classes
The different typologies of dimers may be ordered on the basis of
four of the main parameters introduced in Subheading 2.2. The
assignment of 50 PDB files (see Note 3) to the six classes of dimers
has been performed according to the following procedure.
1. Identify those proteins that do not contain significant loops at
the interface: as shown in Table 1, these dimers are characterized by the smallest Sll and the largest Q/R values (see Note 4).
The structural meaning of such values is shown in the examples
of Fig. 2.
2. Within the same group identified in step 1, two possibilities
may exist: (1) all (or a large part of) the a.a. are located at the
subunits interface; (2) only a segment of the polypeptide chain
is involved in quaternary interactions. These two situations may
be easily discriminated examining the IAR value. When
IAR > 0.8, the shape of the dimer looks like a flat ellipsoid
(class 1α) and a typical example is that represented by the
structure of 1rop (Fig. 2, left). On the contrary, a small IAR
(< 0.6) indicates a more prolate structure, in which a considerable fraction of a.a. are far away from the interface. Interestingly, this subgroup of proteins (class 1β) is characterized by a
larger size with respect to class 1α.
3. Identify subclasses 2α and 2β: in these cases, typically Sll ! 0.1
and Q/R ! 0.5 (Table 3 and Fig. 3), diagnostic of loops of
intermediate length (30–50 a.a.). As a consequence, class
2 includes dimers with a larger size, especially for low IAR
values (class 2β).
4. In the case Sll > 0.25 and Q/R
0.3 the dimer must be
assigned to class 3, which is characterized by very large loops
(Fig. 4). Due to this feature, both subgroups 3α and 3β display
a small contact interface with respect to the overall shape and
size of the macromolecule.
Topology of Dimeric Proteins Interfaces
83
length of the loops formed in each subunit with respect to the
dimeric contact surface. In particular when Q ¼ 1 all the
residues are located at the interface.
4. Calculate Q n defined as: Q n ¼
Q
R
Q
N . This parameter takes
simultaneously into account the presence of loops (Q/R) and
the percentage of a.a. that are “at” or “close to” the dimeric
interface (see Note 2).
5. Calculate the Squared Loops Length, Sll, defined as the sum of
squared distances (in number of a.a. in the sequence) between
two consecutive residues involved in quaternary interactions,
weighted by the total number of amino acids. In the example of
Fig. 1: Sll ¼
ad
2 þ
de
2 þ
ep
2 þ
pq
2
N
2
where
ad
2 ¼ 9;
de
2 ¼ 1, etc:
2.3 Assigning
Dimeric Structures
to the Different
Classes
The different typologies of dimers may be ordered on the basis of
four of the main parameters introduced in Subheading 2.2. The
assignment of 50 PDB files (see Note 3) to the six classes of dimers
has been performed according to the following procedure.
1. Identify those proteins that do not contain significant loops at
the interface: as shown in Table 1, these dimers are characterized by the smallest Sll and the largest Q/R values (see Note 4).
The structural meaning of such values is shown in the examples
of Fig. 2.
2. Within the same group identified in step 1, two possibilities
may exist: (1) all (or a large part of) the a.a. are located at the
subunits interface; (2) only a segment of the polypeptide chain
is involved in quaternary interactions. These two situations may
be easily discriminated examining the IAR value. When
IAR > 0.8, the shape of the dimer looks like a flat ellipsoid
(class 1α) and a typical example is that represented by the
structure of 1rop (Fig. 2, left). On the contrary, a small IAR
(< 0.6) indicates a more prolate structure, in which a considerable fraction of a.a. are far away from the interface. Interestingly, this subgroup of proteins (class 1β) is characterized by a
larger size with respect to class 1α.
3. Identify subclasses 2α and 2β: in these cases, typically Sll ! 0.1
and Q/R ! 0.5 (Table 3 and Fig. 3), diagnostic of loops of
intermediate length (30–50 a.a.). As a consequence, class
2 includes dimers with a larger size, especially for low IAR
values (class 2β).
4. In the case Sll > 0.25 and Q/R
0.3 the dimer must be
assigned to class 3, which is characterized by very large loops
(Fig. 4). Due to this feature, both subgroups 3α and 3β display
a small contact interface with respect to the overall shape and
size of the macromolecule.
Topology of Dimeric Proteins Interfaces
83