The alternative scenario of twist-free torsion of the axoneme, where the rotation of the bending plane (green) is caused by bending into different directions relative to the bridge (dashed dark-red line). In this scenario, the rotation of the cross-section (with attached GNP) by an angle Δ ω GNP is different from the rotation angle of the bending plane {Δ ω }_{3{rm{D}}} . The planar axoneme (transparent grey) in c and d depicts a reference shape (with no torsion) of the axoneme and the reference position of the GNP. The insets in c and d show axonemal cross-sections at the indicated light-blue planes. The red and yellow spheres show the GNP in its reference position (planar shape) and its final position (non-planar shape), respectively. Note that the magnitude of deformations is exaggerated for display purposes. For an animated version of Fig. 1c,d , see Supplementary Movie 1 .
