Abstract
Assemblies with helical symmetry can be conveniently formulated in many distinct ways. Here, a new convention is presented which unifies the two most commonly used helical systems for generating helical assemblies from asymmetric units determined by X-ray fibre diffraction and EM imaging. A helical assembly is viewed as being composed of identical repetitive units in a one- or two-dimensional lattice, named 1-D and 2-D helical systems, respectively. The unification suggests that a new helical description with only four parameters [n(1), n(2), twist, rise], which is called the augmented 1-D helical system, can generate the complete set of helical arrangements, including coverage of helical discontinuities (seams). A unified four-parameter characterization implies similar parameters for similar assemblies, can eliminate errors in reproducing structures of helical assemblies and facilitates the generation of polymorphic ensembles from helical atomic models or EM density maps. Further, guidelines are provided for such a unique description that reflects the structural signature of an assembly, as well as rules for manipulating the helical symmetry presentation.
Highlights
IntroductionMany biomolecules are either organized in functional tubular forms or aggregated in disease-related filaments
Under physiological conditions, many biomolecules are either organized in functional tubular forms or aggregated in disease-related filaments
Similar to X-ray crystal structures where only the coordinates of the asymmetric units are included in the Protein Data Bank (PDB) file, most of the helical structures deposited in the PDB contain only asymmetric units
Summary
Many biomolecules are either organized in functional tubular forms or aggregated in disease-related filaments. Depending on the specificity and rigidity of the interacting molecules, some, such as the amyloidogenic peptide A 1–40 (Sachse et al, 2008; Schmidt et al, 2009), can exhibit a broad spectrum of polymorphic assemblies, whereas others only show limited variability, as in the case of microtubules (Sui & Downing, 2010). This underscores the importance of revealing the structural characteristics of helical assemblies directly from a simple helical symmetry description
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