Helix endpoints redefined based on RMSD and angle between their axial vectors. 8a: Vectors representing a short opened up helix by two different methods. The red arrow shows the axis obtained by using the largest spread of the Cα atoms (vector corresponding to the largest eigenvalue). The green arrow shows the rotational axis obtained when the helix that is shifted by one residue, is aligned to the original helix. The first method is unsuitable for representing this helix and does not work for π and short helices. Our algorithm uses the rotational-fit method (described below, 8b) for all helices. RMSD of residues are calculated over this vector. Angles between vectors, calculated from residues of consecutive helices, are used to determine whether to break them so as to appropriately define the helices as linear elements. 8b: Helix RMSD data calculated using the rotational fit vector. Average RMSD of unbroken helices from our algorithm varies widely. The helices were broken multiple times and the angle of break was analyzed (data not shown). The mode of the angle of break (22°) for long (>15 residue) helices was used to determine the break point of consecutive helices. Helices that break at >22° were chosen for the dataset for calculation of RMSD and angle of break (fig. c). Average RMSD of broken helices is shown in this figure. A line was fitted using "gnuplot"  to approximate the RMSD of broken helices. A Z-score of 2.5 is used to limit breaking helices that deviate less than 2.5 times sigma around the approximated RMSD value for broken helices at a particular helix length. 8c: Angle of helix break calculated from dataset of helices used in fig. b. Data were collected from helices broken once, twice and thrice. The normalized data are shown. Helices that show an angle greater than c1 (20°) between broken parts are split. 8d: Helix split by our algorithm. All possibilities of broken pieces are assessed with respect to the RMSD of the pieces and angle of break. Helices i, i+5 and i+4, i+15 are finally chosen as correctly broken. Helices i, i+8 and i+15; and i, i+11 and i+10, i+15 are also possibilities that are analyzed but not chosen as the optimum break. Residues i+4, i+5 are shared by the two helix pieces (Cα shown as spheres).
Majumdar et al. BMC Bioinformatics 2005 6:202 doi:10.1186/1471-2105-6-202