Title: Fitting of Line, Circle and Helix to 3D Points, and Its Application to Protein Structures

Abstract:  Helical structures such as α-helix, 3(10)-helix, p-helix and polyproline II helix (PPII) are present in proteins. Tandem repeats such as leucine rich repeats (LRRs) with 20-30 residues adopt a super helical arrangement. To understand structural features and principles of these structures, the fitting of line, circle and helix to 3D points are extensively utilized. α-Helix is approximated by a rod or a straight line. Methods determining the helix axis have been proposed by Åqvist (1986), Kahn (1989), Christopher (1996), and so on. In proteins long α-helices and their axes can be bent, twisted, or even kinked. Several methods including circle fitting have been developed; they are HBEND (Barlow & Thornton, 1988), HELANAL (Bansal et al., 2000), TWISTER (Stelkov et al., 2002), PS (Smith, 2012), and HAXIS (Guo, 2013).  For helix fitting we (2008) developed a total least squares method, HELFIT. The HELFIT method calculates not only helix axis, helix radius, helix pitch, and handedness but also a parameter representing helix regularity, p =[rmsd/(N − 1)]^1/2, where rmsd is the root mean square deviation from the best-fit helix to data points and N is the data point number (of which the minimum required is only four). Similarly, Nievergelt (1997), Ahn (2004), Kumar and Bansal (2012), and Hauser et al. (2017) also developed the helix fitting methods. However, the analysis requires at least larger than six points. We successfully applied HELFIT for 3(10)-helices, α-helices, PPIIs, and LRR structures (2006, 2010, 2014, and in preparation).

Biography: Professor Emeritus Norio Matsushima, Sapporo Medical University completed his doctorate in polymer physics at the Hokkaido University in 1976. In 1986-1988 joined the University of Virginia, USA, as the visiting associate professor. He has studied in the fields of protein science, biophysics, and bioinformatics. His recent research is the sequence analysis, structure, and evolution of leucine-rich repeats in proteins. He has published over 90 papers in peer reviewed journals. Now he is the editorial board member of “Protein and Peptide Letters and “Annals of Virology and Research”.