Supplementary Material for: The Motion of An Inv Nodal Cilium: a Realistic Model Revealing Dynein-Driven Ciliary Motion with Microtubule Mislocalization

Background/Aims: Nodal cilia that rotate in the ventral node play an important role in establishing left-right asymmetry during embryogenesis; however, inv mutant cilia present abnormal movement and induce laterality defects. The mechanism of their motility, which is regulated by dynein activation and microtubule arrangement, has not been fully understood. This study analyzed the dynein-triggered ciliary motion in the abnormal ultrastructure of the inv mutant, aiming to quantitatively evaluate the influence of microtubule mislocalization on the movement of the cilium. Methods: We established a realistic 3-D model of an inv mutant cilium with an ultrastructure based on tomographic datasets generated by ultra-high voltage electron microscopy. The time-variant activation of the axonemal dynein force was simulated by pairs of point loads and embedded at dynein-mounted positions between adjacent microtubule doublets in this mathematical model. Utilizing the finite element method and deformable grid, the motility of the mutant cilium that is induced by various dynein activation hypotheses was investigated and compared to experimental observation. Results: The results indicate that for the inv mutant, simulations of the ciliary movement with the engagement of dyneins based on the distance-controlled pattern in the partially activation scenario are broadly consistent with the observation; the shortening of the microtubules induces smaller movement amplitudes, while the angles of the mislocalized microtubules affect the pattern of the ciliary movement, and during the ciliary movement, the microtubules swing and twist in the mutant ciliary body. Conclusion: More generally, this study implies that dynein engagement is sensitive to subtle geometric changes in the axoneme, and thus, this geometry greatly influences the integrity of a well-formed ciliary rotation.