Resolution:
standard / ## Figure 5.
The three parameters on which quadruplets scoring is based. In figs. a, d, g, a quadruplet
is formed from residues i, i+1, j-1 and j. The score is used to select the best quadruplets
to join and form β-sheets. Each scoring parameter has been chosen such that they least
influence each other. Residues i-1, i+2, j+1 and j-2 are required to calculate angles
for quadruplet scoring. The first parameter is C
_{α}-C_{α }distance between paired residues (fig. a). Blue lines joining i, j and i+1, j-1 show
the distance being scored. This parameter approximates the deviation of the triangle
apex i with reference to the triangle apex j in fig. b due to rotation of the plane
i-1, i, i+1 on the X axis. Fig. c shows the C_{α}-C_{α }distances for parallel and antiparallel β-strands obtained from DSSP [8] output. Data
is binned at 0.1 Å intervals and fit to a normal distribution using "gnuplot" [40].
Distribution for parallel β-strands has a mean at c1 (4.81 Å) with a sigma of 0.22.
Distance for antiparallel β-strands follows a bi-modal distribution with means (μ)
at c2 (4.46 Å) and c3(5.24 Å) and a standard deviation (σ) of 0.26. These μ and σ
values were used to calculate the probability of occurrence of C_{α}-C_{α }pairing distances while scoring quadruplets by our algorithm. A C_{α}-C_{α }maximum distance of 7.5 Å (not shown) was used to limit pairing between residues.
The second parameter is angle between lines (shown in blue) joining the vertices i,
j and the base j-1, j+1 of the imaginary triangles j-1, j, j+1 and i+1, i, i-1 (fig.
d). Only one of the four cases is shown. The other angles are between lines j, i and
i+1, i-1; j-1, i+1 and i, i+2; i+1, j-1 and j, j-2. Deviation of this angle approximates
the deviation of the triangle apex i-1 with reference to the triangle apex j+1 in
fig. b due to rotation of the plane i-1, i, i+1 on the Y axis. Fig. e shows the distribution
of angles, binned at 5° intervals, obtained from parallel and antiparallel β-strands
defined by DSSP where c1 (87°) and c2 (82.2°) are the respective means. Fig. f shows
the probability of obtaining a parameter-2 angle at different multipliers of the standard
deviation for data shown in fig. e. The probability obtained is used for scoring quadruplets.
The third parameter is a torsion angle (fig. g) between the points j, mj, mi, i. mj
is the midpoint between j+i, j-1. mi is the midpoint between i-1, i+1. Lines joining
residues and the midpoints are shown in blue. A similar torsion angle involving residues
j-1, i+1 as end points and midpoints between j, j-2 and i, i+2 is computed (not shown).
Deviation of the torsion angle approximates the deviation of vertex i in fig. b with
respect to vertex j due to rotation of the plane i-1, i, i+1 on the Z axis. Fig. h
shows the distribution of torsion angles (binned at 5° intervals) obtained from DSSP
output where c1 (-20.9) and c2 (-27.9) are the respective means for data from parallel
and antiparallel β-strands. Fig. i shows the probability of obtaining a torsion angle
at different multipliers of the standard deviation for the data in fig. h.
Majumdar |