  We develop the theory of the coupling between in-plane order and out-of-plane
geometry in twisted, two-dimensionally ordered filament bundles based on the
non-linear continuum elasticity theory of columnar materials. We show that
twisted textures of filament backbones necessarily introduce stresses into the
cross-sectional packing of bundles and that these stresses are formally
equivalent to the geometrically-induced stresses generated in thin elastic
sheets that are forced to adopt spherical curvature. As in the case of
crystalline order on curved membranes, geometrically-induced stresses couple
elastically to the presence of topological defects in the in-plane order. We
derive the effective theory of multiple disclination defects in the cross
section of bundle with a fixed twist and show that above a critical degree of
twist, one or more 5-fold disclinations is favored in the elastic energy ground
state. We study the structure and energetics of multi-disclination packings
based on models of equilibrium and non-equilibrium cross-sectional order.
