Local frustration determines molecular and macroscopic helix structures.

Decorative domains force amyloid fibers to adopt spiral ribbon morphologies, as opposed to the more common twisted ribbon. We model the effect of decorating domains as a perturbation to the relative orientation of β strands in a bilayered extended β-sheet. The model consists of minimal energy assemblies of rigid building blocks containing two anisotropic interacting ellipsoids. The relative orientation of the ellipsoids dictates the morphology of the resulting assembly. Amyloid structures derived from experiment are consistent with our model, and we use magnets to demonstrate that the frustration principle is scale and system independent. In contrast to other models of amyloid, our model isolates the effect of frustration from the fundamental interactions between building blocks to reveal the frustration rather than dependence of morphology on the physical interactions. Consequently, amyloid is viewed as a discrete molecular version of the more general macroscopic frustrated bilayer that is exemplified by Bauhinia seedpods. The model supports the idea that the interactions arising from an arbitrary peptide sequence can support an amyloid structure if a bilayer can form first, which suggests that supplementary protein sequences, such as chaperones or decorative domains, could play a significant role in stabilizing such bilayers and therefore in selecting morphology during nucleation. Our model provides a foundation for exploring the effects of frustration on higher-order superstructural polymorphic assemblies that may exhibit complex functional behavior. Two outstanding examples are the systematic kinking of decorated fibers and the nested frustration of the Bauhinia seedpod.