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.