A mathematical approach to study the bending behavior of the primary cilium

The primary cilium, a hair-like projection from the cellular membrane, is involved in fluid flow sensing. In this study, the primary cilium is modeled as a thin beam undergoing large deflection due to fluid drag forces. For the first time, the bending response is analyzed with a model combining large angle rotations with the assumption of a linear drag force along the ciliary length. The model is applied on published pictures of bent cilia. Incorporating a linear drag force and allowing for a basal tilt is an important step towards a more realistic mechanical model of the primary cilium and towards more accurate values of its flexural rigidity. The model will be a useful tool to study the mechanical behavior of the primary cilium and will eventually lead to new insight in the poorly understood mechanisms of mechanotransduction.