Models of the dynamics of otolithic membrane and hair cell bundle mechanics *

Abstract

Dynamic behavior of an otolithic membrane (OM) was studied analytically using simplified homogeneous viscoelastic (Kelvin-Voight body) model of the OM. The OM was represented by a thin plate attached to a macular plane. Viscoelastic properties of the OM determine the specific times ( ${\mathit{T}}_1$ and ${\mathit{T}}_2$ ) and frequency-dependent behavior of the local displacements of the membrane caused by the inertial time-dependent forces. Two kinds of an otolith stimulation were analyzed: step-function and harmonic accelerations of the membrane. Results of the modeling were compared with the known experimental data to estimate the Young’s modulus E and viscosity μ of a gel layer: E is of order of 10 N/m ${}^2$ , μ is of order of 1 poise in the range of frequency 0.2–2 Hz. It has allowed us to estimate the values of ${\mathit{T}}_1$ ( ${10}^{-5}$ – ${10}^{-6}$ sec) and ${\mathit{T}}_2$ ( $\sim 3·{10}^{-2}$ sec). A relationship of the motion equation of the OM with well-known overdamped pendulum model of the otolith was discussed. The model of stereocilia tip-links deformation in the case, when the HCBs passively follow gel deformation, was proposed and analyzed. It was shown that for slender and long HCBs with the lengths comparable to a thickness of effective gel layer, a relative deformation of the tip-links of stereocilia caused by OM acceleration depends on time and the distance from the macular plane. The results of the modeling suggest that this type of the HCB may be responsible for analysis of fine temporal (frequency) structure of the OM acceleration.