Helical assemblies are common in biology. Usually these have surface lattices with families of continuous helices, giving X-ray diffraction and electron micrographs that can be described by classical helical diffraction theory. The theory is inadequate for helical structures interrupted by discontinuities, called seams in the case of microtubules. A theoretical understanding of diffraction from this type of helical structure is required to allow 3D reconstructions and to determine the surface lattice organization. We consider microtubules, all of which, except the canonical 13-protofilament structures, have long-pitch helical protofilaments made from the alpha beta tubulin heterodimer packed head-to-tail. We develop a diffraction theory based on the protofilaments that is valid for all types of microtubules both with and without seams, The theory gives standard indexations for monomer- and helical dimer-lattices. A new feature predicted by the theory for microtubules with seams is that all integer Bessel function orders are present along odd branch lines giving distinctive cross-like intensity streaks. The theory will apply to X-ray fiber diffraction and solution scattering from in vitro assembled microtubules, as well as for analyzing electron cryomicrographs of microtubules decorated with motor proteins. It may apply to other dislocated helical lattices. (C) 1997 Academic Press.