(A) Cross-section of an axoneme, as seen from the basal end looking towards the distal tip. The numbering of the doublets follows the convenstion for Chlamydomonas (Hoops and Witman, 1983). The green dyneins bend the axoneme such that the center of curvature is to the right. (B) The projection of the cross section onto two filaments to form the two-dimensional model. The green and blue motors bend the filament pair in opposite directions. (C) Two-dimensional model of the axoneme, as seen in the bending plane, . The two filaments are constrained to have spacing . The point at arc-length has position vector (relative to the origin), tangent vector , normal vector , and tangent angle with respect to the horizontal axis of the lab-frame . Dyneins on the upper filament (green) have microtubule-binding domains (MTBs, denoted by filled circles) that walk along the lower filament towards the base and produce a (tensile) force density on the lower filament. This force slides the lower filament towards the distal end. The dyneins on the opposite filament (blue) create sliding (and bending) forces in the opposite direction. The local sliding displacement is given by , and the sliding at the base is . The sign convention is defined in Figure 10 and Appendix 4. The springs between the filaments oppose filament separation by the normal force, . The spring and dashpot at the base consitute the basal compliance, with stiffness and friction coefficient . (D) Schematic of dynein regulation mechanisms. In curvature control the dynein MTB detaches due to an increase in curvature. In sliding control detachment is enhanced by a tangential loading force, and in normal force control the normal force, which tends to separate the filaments, enhances detachment. Signs indicate doublet polarity.