A sliding microtubule model incorporating axonemal twist and compatible with three-dimensional ciliary bending

1. Equations are developed to calculate the relative displacements of the doublet microtubules at the tip of a cilium when the microtubules twist about the axis of the organelle. 2. Displacements measured from electron micrographs show asymmetry (or skew) which can be matched quantitatively by the theoretical model with the appropriate selection of twist angle and orientation of the axoneme with respect to the plane of beat. 3. For Elliptio cilia the experimental results are consistent with a planar effective stroke and a recovery stroke involving a three-dimensional bend. The plane of the effective stroke is not normal to a surface containing the central pair of microtubules but contains microtubule 2 to produce the observed skew. 4. This model for the beat also explains the range of orientations of axoneme observed in sections through the metachronal wave.