Analysis and modeling of the primary cilium bending response to fluid shear

Since a nonmotile, primary(9 + 0) cilium projects from most mammalian kidney epithelial cells into the tubule lumen, where it is exposed to fluid motion, the present study examined primary cilium response to fluid shear stress. The reversible, large-angle bending of the primary cilium upon exposure to fluid shear forces (10(-11)-10(-10) N . m(2) = 10(-8)-10(-7) dyn/cm) was characterized in vitro using videomicroscopic side views of PtK1 cells, and the cilium was then mathematically modeled as a cantilevered beam. The flexural rigidity of the primary cilium was calculated to be 3.1 +/- 0.8 x 10(-23) N . m(2) with a corrected quadruple integration approach and 1.4-1.6 x 10(-23) N . m(2) with the ''heavy elastica'' theory. Comparison of theoretical profiles to the experimental bending responses of cilia established the validity of the ''heavy elastica'' model; this model, in turn, was used to predict primary cilium bending behavior under representative conditions in the rat nephron. The results of the study are consistent with the hypothesis that primary cilia serve a mechanosensory function in kidney epithelial cells.