(k, a) angle
A structure fragment (five residues long) is defined by the
(k, a)pair
angles as shown in Figure A.
The k angle,
ranging from 0¢X to 180¢X, of a residue i is defined as a bond angle formed by three
C_{a}
atoms of residues i2, i, and i+2.
The a
angle, ranging from 180¢X to 180¢X, of a residue i is a dihedral angle formed by the four
C_{a}
atoms of residues i1, i, i+1, and i+2.


Figure A. The definitions of the kappa
(k) and alpha
(a) angles.

(k, a) map
We aim to use structural alphabets to represent pattern profiles of the backbone
fragments by clustering the accumulated
(k, a)map
plot (Figure B), which consists of 225523 protein fragments summarized from the pair database.
A specific serial of structure fragments, called
(k, a)map,
is able to represent a protein structure. Therefore, each protein structure may
form a specific
(k, a)map
distribution. The accumulated
(k, a)map
is similar to the concept of Ramachandran plot, which represents a residue by using
angles f and y.


Figure B. The accumulated
(k, a)map
plot consists of 225523 protein fragments. The plot, 648 cells (36¡Ñ18),
is clustered into 23 groups based on the similarity of representative
segments of each cell. The number of 3D segments in each cell ranges from 0 to
22310 and the color bar on the right side shows the distribution scale.
According to the definitions of DSSP, the numbers of
ahelix and
bstrand segments
are 82482 (36.57%) and 52371 (23.33%), respectively. In the
(k, a)map
plot, most of the
ahelix segments
are located on four cells in which the
a angle ranges
from 40¢X to 60¢X and
k angle ranges
from 100¢X to 120¢X. In contrast, the
k angle of
bstand segments
roughly ranges from 0¢X to 30¢X and the
a angle ranges
from 180¢X to 140¢X and from 150¢X to 180¢X. The number of the cells, which have
zero segments, is 183.

