Morphology selection via geometric frustration in chiral filament bundles

Geometric frustration selects the equilibrium morphology of cohesive bundles of chiral filaments by controlling the relative costs of filament bending and the straining of the cohesive bonds. In assemblies, the geometric frustration of a locally preferred packing motif leads to anomalous behaviours, from self-limiting growth to defects in the ground state 1 . Here, we demonstrate that geometric frustration selects the equilibrium morphology of cohesive bundles of chiral filaments, an assembly motif critical to a broad range of biological and synthetic nanomaterials. Frustration of inter-filament spacing leads to optimal shapes of self-twisting bundles that break the symmetries of packing and of the underlying inter-filament forces, paralleling a morphological instability in spherical two-dimensional crystals 2 , 3 , 4 . Equilibrium bundle morphology is controlled by a parameter that characterizes the relative costs of filament bending and the straining of cohesive bonds between filaments. This parameter delineates the boundaries between stable, isotropic cylindrical bundles and anisotropic, twisted-tape bundles. We also show how the mechanical and interaction properties of constituent amyloid fibrils may be extracted from the mesoscale dimensions of the anisotropic bundles that they form.