Minimal model of a nodal cilium - Hydrodynamic flow patterns and synchronization of two interacting cilia

Abstract

The human body is nearly left-right symmetric on the outside, but this is not the case on the inside. During the development of the body, a leftward fluid movement in the node (a cavity that will turn into the embryo) is essential for the left-right symmetry-breaking process. However, the exact role of nodal flow and the hair-like appendages (cilia) that produce this is still debated. In this thesis we study a minimal model of a nodal cilium with only one degree of freedom. In this model, originally proposed by Vilfan and J¨ulicher, Phys. Rev. Lett. 96, 058102 (2006), a cilium is replaced by a spherical bead moving on a fixed elliptic orbit. The model cilia interact hydrodynamically which allows for the study of synchronization. In this thesis we compare the minimal model to an advanced model developed concurrently in another Bachelor project by Perugachi Israels. Surprisingly, we find that the minimal model semi-quantitatively captures the features and generates fluid dynamics comparable to the advanced model. Consequently, the minimal model can be used to qualitatively study processes like the flowinduced movement of small signaling molecules. Duplicating the minimal model allows us to study synchronization between neighboring cilia. Doing so, we notice that the model cannot take into account the change in the trajectory of a cilium due to the presence of a second cilium. This problem can be solved by adding another degree of freedom to the minimal model, which is left for future study.