Helical Fourier Transforms as Multiscale Chirality Measure

While chirality, the mirror asymmetry of molecules, is a well-known determinant of the structure and properties of macromolecular complexes, the degree of a molecule's asymmetry is notoriously difficult to quantify. Ideally, such a chirality measure should report the degree of asymmetry and handedness of a given structure as a function of only its geometry. However, recent studies demonstrate that currently available measures that quantify asymmetry and handedness in simple systems fail to give a consistent measure of these properties in systems with many degrees of freedom, such as those relevant to biology or nanomaterials. Here, we consider the case of helical chirality, which, although not the most general form of chirality found in nature, is an important source of chirality in biological systems (e.g. nucleic acid helices, alpha helices). We propose a measure of helical chirality based on a three-dimensional helical Fourier transform and demonstrate its utility using several biologically relevant model systems. Furthermore, we demonstrate that this method allows for the identification of dominant pitches in complex helical assemblies and that the dominant pitches of interacting helical molecules are related. Finally, we describe how this framework may be generalized to provide a robust measure of multiscale chirality, applicable to a wide variety of chemical and biological systems.