Characterization of Biomolecular Helices and Their Complementarity Using Geometric Analysis

A general method is presented to characterize the helical properties of potentially irregular helices, such as those found in protein secondary and tertiary structures and nucleic acids. The method was validated using artificial helices with varying numbers of points, points per helical turn, pitch, and radius. The sensitivity of the method was validated by applying increasing amounts of random perturbation to the coordinates of these helices; 399-360 helices in total were evaluated. In addition, the helical parameters of protein secondary structure elements and nucleic acid helices were analyzed. Generally, at least seven points were required to recapitulate the parameters of a helix using our method. The method can also be used to calculate the helical parameters of nucleic acid-binding proteins, like TALE, enabling direct analysis of their helix complementarity to sequence-dependent DNA distortions.