Modeling the deformation of primary cilium

Abstract

In this thesis we developed a new mechanics model of the primary cilium and analyzed its bending behavior. The primary cilium that extends from the cell surface can detect the mechanical signals of the surrounding environment. Moreover, through its deflection and bending angle, the primary cilium can communicate with the cell regarding the extracellular. Scientists have shown that dysfunction of primary cilia can lead to many diseases as cilia are believed to play an important role in transmitting signals in cells.

A good model of primary cilium can aid in the understanding of the mechanism of its bending movement. Furthermore, a good model is important for determining how the primary cilium contributes to convert mechanical signals into biochemical ones. Previous models have ignored the basal body and transition fiber that are located at the base of the primary cilium.

However, it is clear that the elastic basal body and transition fibers should have a significant effect on the deformation of the whole structure. Aiming to address this issue, we established a model with a rotational spring representing the confinement induced by the basal body and transition fibers. Specially, we developed two governing equations for two different conditions, namely uniformly distributed load and spatially varying load. In addition, this model is valid for situations where the deflection is large.

To obtain the results the shooting and Newton-Raphson methods are used to solve the governing equations numerically. Then, we compared the numerical results with experimental data to test the validity of the model.

Comparison between our model predictions and experimental data showed that the governing equation for spatially varying load described the bending behavior of the primary cilium very well under various realistic conditions, including cases where the flow field is not uniform both spatially and temporally fluid flow with variable velocity.