Primary cilium: a paradigm for integrating mathematical modeling with experiments and numerical simulations in mechanobiology

Abstract

Primary cilia are non-motile, solitary (one per cell) microtubule-based organelles that emerge from the mother centriole after cells have exited the mitotic cycle. Identified as a mechanosensing organelle that responds to both mechanical and chemical stimuli, the primary cilium provides a fertile ground for integrative investigations of mathematical modeling, numerical simulations, and experiments. Recent experimental findings revealed considerable complexity to the underlying mechanosensory mechanisms that transmit extracellular stimuli to intracellular signaling many of which include primary cilia. In this invited review, we provide a brief survey of experimental findings on primary cilia and how these results lead to various mathematical models of the mechanics of the primary cilium bent under an external forcing such as a fluid flow or a trap. Mathematical modeling of the primary cilium as a fluid-structure interaction problem highlights the importance of basal anchorage and the anisotropic moduli of the microtubules. As theoretical modeling and numerical simulations progress, along with improved state-of-the-art experiments on primary cilia, we hope that details of ciliary regulated mechano-chemical signaling dynamics in cellular physiology will be understood in the near future.

Microstructure-Based Modeling of Primary Cilia Mechanics

“…In addition, the traditional paradigm of modeling ciliary axoneme assumes that the nine microtubule doublets have the same length as the axonemal centerline (26). However, Sun et al (27) reported a very different micro architecture of epithelial primary cilia, where the nine microtubule doublets, or microtubule complexes (MtCs), have different lengths along the axoneme axis and not all MtCs reach the axoneme tip.…”