Relationship between moiré patterns, tubulin shape, and microtubule polarity

The polarity of microtubules is reflected in cryo-electron microscope images and in three-dimensional reconstructions [Chrétien et al., 1996: Structure 4:1031-1040; Sosa and Milligan, 1996: J. Mol. Biol. 260:743-755]. This paper shows how the directionality of the moiré patterns and the shape of the tubulin subunits are related. Microtubules observed by cryo-electron microscopy show an arrowhead moiré pattern that points toward the plus end of microtubules with a right-handed protofilament skew and toward the minus end of microtubules with a left-handed protofilament skew. On the other hand, three-dimensional reconstructions of microtubules observed from the plus end reveal a radial counterclockwise slew of the tubulin subunits. We show how these polar features are related and present unambiguous rules for determining the polarity on longitudinal and axial views of microtubules.