HELANAL-Plus: a web server for analysis of helix geometry in protein structures

α-Helices are the most abundant secondary structural motif in proteins (Kendrew et al., 1958, Pauling, Corey, & Branson, 1951) and an ideal linear helix can be completely described by a single value of the parameters, rise per residue, and number of residues per turn or unit twist. Occurrence of NH O hydrogen bonds between the amino acids (i+ 4→ i) in the main chain makes the α-helices quite uniform in terms of unit twist and rise per residue and these parameters lie in a well-defined range. However, most helices in proteins are somewhat irregular and often the helix axis does not follow a perfectly straight path. The reasons for these deviations are solvent induced distortions (Blundell, Barlow, Borkakoti, & Thornton, 1983), peptide bond distortions (Barlow & Thornton, 1988; Love et al., 1972), or presence of proline residues (Chakrabarti, Bernard, & Rees, 1986; MacArthur & Thornton, 1996). Blundell et al. (1983) did the first survey on the curvature of helices and noted the irregularities. Based on their studies they concluded that the majority of the helices are curved. In 1988, a systematic analysis of globular proteins was carried out and it was shown that the majority of α-helices are smoothly curved (Barlow & Thornton, 1988). Distortions caused by proline (Chakrabarti et al., 1986; Chakrabarti & Chakrabarti, 1998; MacArthur & Thornton, 1996; Sankararamakrishnan & Vishveshwara, 1990, 1992), serine, and threonine (Ballesteros, Deupi, Olivella, Haaksma, & Pardo, 2000; Deupi et al., 2004) residues have also been studied. An interesting study of kinks caused by proline residues in α-helices of transmembrane proteins (Yohannan, Faham, Yang, Whitelegge, & Bowie, 2004) reveals that the kinks are preserved even after the mutation of the prolines to other amino acids. This suggested an evolutionary conservation of proline derived kinks. These distortions in the helices do not allow the helix axis to follow a straight path. Several algorithms have been proposed for determining the helix axis. Some of the strategies followed include fitting to a cylindrical surface to the backbone atoms (Ðqvist, 1986), identification of best fit line through a selection of atoms (Christopher, Swanson, & Baldwin, 1996), superposition of an ideal helical motif (Barlow & Thornton, 1988), and construction from a vector which is defined using the terminal C atoms (Kahn, 1989) or best fit line and circle to a set of local helix origins (Kumar & Bansal, 1998; Bansal, Kumar, & Velavan, 2000). The methods described above only lead to the best linear helix axis or at best a circle in 2D plane. In the present work, we have followed the algorithm published by Shakarji (1998) to get the best fit linear and curved helix axis. Importance of helix axis trajectory especially in studying helix–helix packing has been highlighted earlier (Chothia, Levitt, & Richardson, 1981), while the importance of the geometry of the helix is highlighted by the fact that several servers and standalone programs are available apart from our in-house program HELANAL (Bansal et al., 2000; Kumar & Bansal, 1998) e.g. Prokink (Visiers, Braunheim, & Weinstein, 2000), Trajelix (Mezei & Filizola, 2006), Helfit (Enkhbayar, Damdinsuren, Osaki, & Matsushima, 2008), and MC-HELAN (Langelaan, Wieczorek, Blouin, & Rainey, 2010). HELANAL (Bansal et al., 2000) developed in our laboratory uses local helix axes for each set of four con-