Microstructure-Based Modeling of Primary Cilia Mechanics

A primary cilium, made of nine microtubule doublets enclosed in a cilium membrane, is a mechanosensing organelle that bends under an external mechanical load and sends an intracellular signal through transmembrane proteins activated by cilium bending. The nine microtubule doublets are the main load-bearing structural component, while the transmembrane proteins on the cilium membrane are the main sensing component. No distinction was made between these two components in all existing models, where the stress calculated from the structural component (nine microtubule doublets) was used to explain the sensing location, which may be totally misleading. For the first time, we developed a microstructure-based primary cilium model by considering these two components separately. First, we refined the analytical solution of bending an orthotropic cylindrical shell for individual microtubule, and obtained excellent agreement between finite element simulations and the theoretical predictions of a microtubule bending as a validation of the structural component in the model. Second, by integrating the cilium membrane with nine microtubule doublets, we found that the microtubule doublets may twist significantly as the whole cilium bends. Third, besides being cilium-length-dependent, we found the mechanical properties of the cilium are also highly deformation-dependent. More important, we found that the cilium membrane near the base is not under pure in-plane tension or compression as previously thought, but has significant local bending stress. This challenges the traditional model of cilium mechanosensing, indicating that transmembrane proteins may be activated more by membrane curvature than membrane stretching. Finally, we incorporated imaging data of primary cilia into our microstructure-based cilium model, and found that comparing to the ideal model with uniform microtubule length, the imaging-informed model shows the nine microtubule doublets interact more evenly with the cilium membrane, and their contact locations can cause even higher bending curvature in the cilium membrane than near the base.

Factors regulating the mechanical response of a primary cilium to fluid flow remain unclear. Modeling the microtubule doublet as a composite of two orthotropic shells and the ciliary axoneme as an elastic shell enclosing nine such microtubule doublets, we found that the length distribution of microtubule doublets (inferred from cryogenic electron tomography images) is the primary determining factor in the bending stiffness of primary cilia, rather than just the ciliary length. This implies ciliary-associated transmembrane proteins may be activated by membrane curvature changes rather than just membrane stretching. These insights challenge the traditional view of ciliary mechanosensation and expands our understanding of the different ways in which cells perceive and respond to mechanical stimuli.