Twisted and rope-like assemblies of filamentous molecules are common andvital structural elements in cells and tissue of living organisms. We study theintrinsic frustration occurring in these materials between the two-dimensionalorganization of filaments in cross section and out-of-plane interfilament twistin bundles. Using non-linear continuum elasticity theory of columnar materials,we study the favorable coupling of twist-induced stresses to the presence ofedge dislocations in the lattice packing of bundles, which leads to arestructuring of the ground-state order of these materials at intermediatetwist. The stability of dislocations increases as both the degree of twist andlateral bundle size grow. We show that in ground states of large bundles,multiple dislocations pile up into linear arrays, radial grain boundaries,whose number and length grows with bundle twist, giving rise to a rich class of"polycrystalline" packings.
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