Topology in Molecular Biology

7 Combinatories and Topology of theβ-Sandwich andβ-Barrel Proteins 139

structures, which are formed by six strands (n∗= 6), is equal to 360 (6!/2).

However, only eight variants with different arrangements are found among all

beta-barrel structures in SCOP database. These eight variants can be repre-

sented as follows: (1) 1-2-3-4-5-6-1 (folds ## 48, 49,64, 65); (2) 1-2-5-4-3-6-1

(folds ## 50, 54, 57); (3) 1-4-3-2-5-6-1 ((folds ## 51, 55); (4) 1-2-3-6-5-4-1

(folds ## 52, 56); (5) 1-3-2-6-5-4-1 (fold # 63); (6) 1-2-6-3-5-4-1 (folds ##

59, 60); (7) 1-5-6-2-3-4-1 (fold # 61); (8) 1-5-2-4-3-6-1 (fold # 62).

Thus from our analysis follows that structures from different folds can

have the similar arrangement of the strands (see variants ## 1, 2, 3, 4 and 6

above).

7.4.5 Two Subsheets in the Barrel Structures

The mainβ-sheet of barrel structures can be divided into two groups of strands

or two subsheets. The strands in each subsheet are approximately parallel to

each other, and make an angle of about 90◦with the strands of the other

subsheet. This orthogonal beta sheet packing makes possible the formation of

the cylindrical “barrel” structure.

7.4.6 Four Types of Connection Between the Strands

in Two Subsheets

There are four ways whereby strands of two orthogonal subsheets can come
together to form a singleβ-sheet in the barrel structures (Fig. 7.3):
(a) The edge strands a and k are located in close proximity to each other
allowing for one or two H-bonds to be formed between the two strands
(Fig. 7.3a).
(b) Two orthogonal strands are connected by means of a long, 90◦bent strand.
Let us denote the two “legs” of the long strand as k′and k′′(Fig. 7.3b).
Residues of k′part form H-bonds with residues from the strand in one
subsheet (strand m), while residues of k′′part form H-bonds with residues
of the strands in the other subsheet (strand a). We observed that k′′part
always forms H-bonds only with the edge strand (strand a), as shown in
Fig. 7.3b. This unique conformation of k strand allows for folding of the
β-sheet into barrel structure. This long bentβ-strand will be referred to
as the “linking” strand. In the 1bia structure, strand #2 is the linking
strand (Fig. 7.2).
(c) Some structures contain not one, but two neighboring H-bonded long an-
tiparallel “linking strands.” These two 90◦bent strands cross over from
one part ofβ-sheet to the other as shown in Fig. 7.2c. Residues in k′and
a′′will be found in one subsheet, while k′′and a′will be found in the
other one.
(d) Lastly, some barrel structures contain three linking strands. Typical rela-
tive orientation of the three strands in the mainβ-sheet is shown in
Fig. 7.2d.