Defining the axis of a helix

Abstract A simple method for finding the axis of a helix is presented. Although described in terms of protein alpha helices, the method is generally applicable to helices whose defining units are more or less regularly spaced. Absolute mathematical regularity of the helical parameters is not required. The procedure can be applied at several levels of rigor. At its simplest it involves simple vector operations only and yields two points that define the axis along with the axis direction cosines. No regression analysis is needed. The minimum length helix required for the algorithm is four residues, which define an axis segment between residues 2 and 3. In its more rigorous form the algorithm scans along the chain one residue at a time, yielding a set of axis segments to which a linear least squares regression fits the axis. Non-linear, iterative procedures are not necessary. For each consecutive set of four residues the pitch, radius, rise per residue, rotation per residue about the axis and number of residues per turn are also obtained. Methods are also outlined for distinguishing between smoothly curved and sharply kinked helices and for extracting from these structures the radius of curvature and the location and angle of the kink.