Correlation between Nanomechanics and Polymorphic Conformations in Amyloid Fibrils

Amyloid fibrils occur in diverse morphologies, but how polymorphism affects the resulting mechanical properties is still not fully appreciated. Using formalisms from the theory of elasticity, we propose an original way of averaging the second area moment of inertia for non-axisymmetric fibrils, which constitutes the great majority of amyloid fibrils. By following this approach, we derive theoretical expressions for the bending properties of the most common polymorphic forms of amyloid fibrils (twisted ribbons, helical ribbons, and nanotubes), and we benchmark the predictions to experimental cases. These results not only allow an accurate estimation of the amyloid fibrils' elastic moduli but also bring insight into the structure-property relationships in the nanomechanics of amyloid systems, such as in the closure of helical ribbons into nanotubes.