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 Cα-Cα 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 Cα-Cα distances for parallel and antiparallel β-strands obtained from DSSP  output. Data is binned at 0.1 Å intervals and fit to a normal distribution using "gnuplot" . 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 Cα-Cα pairing distances while scoring quadruplets by our algorithm. A Cα-Cα 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 et al. BMC Bioinformatics 2005 6:202 doi:10.1186/1471-2105-6-202