Appendix 1—figure 1. Sketch of two MTs’ centerlines during deformation.

The sliding ${\sigma }_j(s)$ is defined as the difference between the arc lengths ${\displaystyle s}$ and ${\mathrm{\Pi }}_j(s)$. The latter is the arc length corresponding to the projection of ${\mathbf{𝐫}}^{j+1}(s)$ on the curve ${\mathbf{𝐫}}^j$. We have positive sliding when dyneins push the ${\displaystyle j}$-th MT toward the distal end of the flagellum and the $(j+1)$-th MT toward the proximal end.