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.