Ciliary behaviour and mechano-transduction in the embryonic node: Computational testing of hypotheses

Left-right symmetry breaking in the mammalian embryo is believed to occur in a transient embryonic structure, the node: rotational motion of cilia within this structure creates a leftward flow of liquid that is the first asymmetric event observed. A hypothesis, often referred to as the "two-cilia" hypothesis, proposes that the node contains two kinds of primary cilia: motile cilia, driven by motor proteins, that rotate clockwise generating the leftward flow and passive cilia that act as mechano-sensors, reacting mechanically to the emerging flow. The exact mechanism that underlies the initial breaking of symmetry remains unclear, in spite of several studies that have attempted to elucidate the processes involved. In this paper, we present two computational models to (i) simulate the unidirectional flow induced by the active ciliary motion as well as their propulsion on the passive cilia and to (ii) investigate the protein activity that produces the active ciliary rotation-like movement. The models presented incorporate methodologies from computational fluid dynamics, deformable mesh computational techniques and fluid-structure interaction analysis. By solving the three-dimensional unsteady transport equations, with suitable boundary conditions, we confirm that the whirling motion of active cilia is capable of inducing the unidirectional flow and that the passive cilia are pushed by this flow towards the left with a visible deformation of 41.7% of the ciliary length on the tip, supporting the plausibility of the two-cilia hypothesis. Further, by applying finite element analysis and grid deformation techniques, we investigate the ciliary motion triggered by the activation of protein motors and propose a possible dynein activation pattern that is able to produce the clockwise rotation of embryonic cilia.