HELFIT: Helix fitting by a total least squares method

The problem of fitting a helix to data arises in analysis of protein structure, in nuclear physics, and in engineering. A continuous helix is described by five parameters: helix axis, helix radius, and helix pitch. One of these helix parameters is frequently predefined in the helix fitting. Other algorithms find only the helix axis or determine separately the helix axis, the helix radius, or the helix pitch. Here we describe a total least squares method, HELFIT, for helix fitting. HELFIT enables one to calculate simultaneously all five of the helix parameters with high accuracy. The minimum number of data points required for the analysis is only four. HELFIT is very insensitive to noise even in short helices. HELFIT also calculates a parameter, p=rmsd/(N-1)(1/2), which estimates the regularity of helical structures independent of the number of data points, where rmsd is the root mean square distance from the best-fit helix to data points and N is the number of data points. It should become a basic tool of structural bioinformatics.

[1]  R. Frühwirth,et al.  Helix fitting by an extended Riemann fit , 2002 .

[2]  M. Perutz,et al.  New X-Ray Evidence on the Configuration of Polypeptide Chains: Polypeptide Chains in Poly-γ-benzyl-L-glutamate, Keratin and Hæmoglobin , 1951, Nature.

[3]  Peter C. Kahn,et al.  Defining the axis of a helix , 1989, Comput. Chem..

[4]  Peter C. Kahn.  Simple methods for computing the least squares line in three dimensions , 1989, Comput. Chem..

[5]  L. Pauling,et al.  The structure of proteins; two hydrogen-bonded helical configurations of the polypeptide chain. , 1951, Proceedings of the National Academy of Sciences of the United States of America.

[6]  R. Kretsinger,et al.  310‐helices in proteins are parahelices , 2006, Proteins.

[7]  Rosemarie Swanson,et al.  Algorithms for Finding the Axis of a Helix: Fast Rotational and Parametric Least-squares Methods , 1996, Comput. Chem..

[8]  Johan Åqvist,et al.  A simple way to calculate the axis of an -helix , 1986, Comput. Chem..

[9]  H. Sugeta,et al.  General method for calculating helical parameters of polymer chains from bond lengths, bond angles, and internal‐rotation angles , 1967 .

[10]  Craig M. Shakarji,et al.  Least-Squares Fitting Algorithms of the NIST Algorithm Testing System , 1998, Journal of research of the National Institute of Standards and Technology.

[11]  M. Bansal,et al.  HELANAL: A Program to Characterize Helix Geometry in Proteins , 2000, Journal of biomolecular structure & dynamics.

[12]  A. Mclachlan.  Gene duplications in the structural evolution of chymotrypsin. , 1979, Journal of molecular biology.

[13]  L. Pauling,et al.  Atomic coordinates and structure factors for two helical configurations of polypeptide chains. , 1951, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Masakatsu Kamiya,et al.  Structural principles of leucine‐rich repeat (LRR) proteins , 2003, Proteins.

[15]  S. Kumar,et al.  Structural and sequence characteristics of long alpha helices in globular proteins. , 1996, Biophysical journal.

[16]  Yves Nievergelt.  Fitting helices to data by total least squares , 1997, Comput. Aided Geom. Des..