Biomechanics of hair cell kinocilia: experimental measurement of kinocilium shaft stiffness and base rotational stiffness with Euler–Bernoulli and Timoshenko beam analysis

Abstract

the OL movement is transmitted to the mechanotransducing part of the hair bundle. Previous computational studies have shown that the tall and compliant kinocilia of extrastriolar bundles increase the hair cells' operating range (range of deflections over which vestibular sensory cell can encode) to several microns compared with that of striolar bundles, which is ~0.1m (Nam et al., 2005). Knowing the mechanical properties of the kinocilium will further our understanding of how these hair cells operate.Kinocilia are composed of a microtubular core, a 9+2 axoneme, composed of nine peripheral doublet microtubules encircling two central single tubules. This configuration is common to motile cilia and eukaryotic flagella (Fig.1A) but, despite their common structure, kinocilia are thought to be non-motile, unlike flagella, as they lack the inner arms of the motor protein dynein, which are essential for motility (Kikuchi et al., 1989). A limited number of spontaneous flagella-like oscillations have been observed in ampullary kinocilia but were limited in number and suggested to result from tissue Accepted 23 November 2010 SUMMARY Vestibular hair cell bundles in the inner ear contain a single kinocilium composed of a 9+2 microtubule structure. Kinocilia play a crucial role in transmitting movement of the overlying mass, otoconial membrane or cupula to the mechanotransducing portion of the hair cell bundle. Little is known regarding the mechanical deformation properties of the kinocilium. Using a force-deflection technique, we measured two important mechanical properties of kinocilia in the utricle of a turtle, Trachemys (Pseudemys) scripta elegans. First, we measured the stiffness of kinocilia with different heights. These kinocilia were assumed to be homogenous cylindrical rods and were modeled as both isotropic Euler-Bernoulli beams and transversely isotropic Timoshenko beams. Two mechanical properties of the kinocilia were derived from the beam analysis: flexural rigidity (EI) and shear rigidity (kGA). The Timoshenko model produced a better fit to the experimental data, predicting EI10,400pNm 2 and kGA247pN. Assuming a homogenous rod, the shear modulus (G1.9kPa) was four orders of magnitude less than Young's modulus (E14.1MPa), indicating that significant shear deformation occurs within deflected kinocilia. When analyzed as an Euler-Bernoulli beam, which neglects translational shear, EI increased linearly with kinocilium height, giving underestimates of EI for shorter kinocilia. Second, we measured the rotational stiffness of the kinocilium insertion () into the hair cell's apical surface. Following BAPTA treatment to break the kinocilial links, the kinocilia remained upright, and  was measured as 177±47pNmrad -1 . The mechanical parameters we quantified are important for understanding how forces arising from head movement are transduced and encoded by hair cells.

Sustained and Transient Vestibular Systems: A Physiological Basis for Interpreting Vestibular Function

“…Remarkably, this height difference can even be seen in Hunter-Duvar’s scanning electron micrograph of the whole utricular macula of the chinchilla (39). Morphological evidence shows apparently looser tethering of the hair bundles of striolar receptors to the overlying otolithic membrane in comparison with comparable receptors in the periphery of the macula (extrastriolar receptors) (38–44). …”

“…Striola receptors are predominantly amphora-shaped type I receptors (37) and have short stiff hair bundles (44, 49), apparently loosely attached to the overlying otolithic membrane (38). This fluid motion within the fluid-filled hole in the gel-filament layer of the otolithic membrane produces a drag force on the hair bundle, causing it to deflect.…”

Mechanisms of otoconia and otolith development

“…Otolithic seeding particles normally attach to kinocilia, a specialized, immotile cilium on hair cells in zebrafish and higher vertebrates (Spoon and Grant, 2011). Additionally, zebrafish have motile cilia that are located near the early zebrafish hair cells (tether cells), require a dynein regulatory complex for their function, and contribute to the asymmetric otolith shape (Colantonio et al, 2009; Wu et al, 2011).…”

Breakup and then makeup: a predictive model of how cilia self-regulate hardness for posture control

“…If we add a damping term to the simple oscillator equation given earlier, the expression for the unforced vibration of a damped pendulum is where θ is the torsional angle, J is the moment of inertia of the pendulum, and are torsional damping and spring coefficients36, respectively. The moment of inertia37 of a rod-like pendulum of length L about its base is where ρ and d are the volumetric density and diameter of the rod, respectively.…”