Morphology Selection through Geometric Frustration in Twisted Filament Bundles and Fibers

Abstract

Rope-like assemblies of twisted protein filaments constitute a common materials archetype appearing in a range of biological contexts from extracellular filament bundles to amyloid fibrils. Owing to the numerous distinctions in molecular structure and interactions underlying these diverse assemblies, a common framework to predict and classify the basic mechanisms of structure formation in twisted filament assemblies is still lacking. In this study, we exploit a recent and surprising connection between the assembly of self-twisting filaments and assembly on spherically-curved 2D surfaces to develop a universal theory of morphology selection in twisted fibers and bundles. This theory shows that the size and cross-sectional shape of self-assembled fibers is determined by competition between the elastic costs of inter-filament frustration, bending deformation of constituent filaments and surface energy of fibers. We find that for sufficiently large twist, isotropic (cylindrical) bundles are generically unstable to developing anisotropic cross-sections (helical tapes). Critically, the anisotropy of fiber cross-sections is found to give a direct measure of the anisotropy of inter-filament vs. intra-filament elasticity. We corroborate the universal predictions of our theory with numerical simulations of self-twisting fibers and compare the morphology diagram structural observations of anisotropy of micron-scale amyloid fibers assembled from hydrolyzed protein fragments.