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.