The mechanical properties of cross-linked microtubule bundles were measured from outer pillar cells isolated from the mammalian inner ear. Measurements were made using a three-point bending test and were incorporated into a mathematical model designed to distinguish between the stiffness contributions from microtubules and their cross-linking proteins. Outer pillar cells were composed of 1000-3000 parallel bundled microtubules in a square array that was interdigitated and cross-linked with actin filaments. The average midpoint bending stiffness of intact cells was 7 x 10(-4) N/m. After removal of both the actin filaments and cross-links with detergent in the presence of DNase I, the square array was disrupted and the stiffness decreased by a factor of 4, to 1.7 x 10(-4) N/m. The bending modulus for individual microtubules was calculated to be 7 x 10(-23) Nm2, and the Young's modulus for these 15 protofilament microtubules was 2 x 10(9) Pa. The shear modulus between microtubules in intact cells was calculated to be 10(3) Pa. It was concluded that cross-linking proteins provided shear resistance between microtubules, which resulted in a fourfold increase in stiffness. The model can be used to estimate the mechanical properties of cross-linked microtubule bundles in cells from which direct measurements are not available.
Mammalian auditory outer hair cells generate high-frequency mechanical forces that enhance sound-induced displacements of the basilar membrane within the inner ear. It has been proposed that the resulting cell deformation is directed along the longitudinal axis of the cell by the cortical cytoskeleton. We have tested this proposal by making direct mechanical measurements on outer hair cells. The resultant stiffness modulus along the axis of whole dissociated cells was 3 x 10(-3) N/m, consistent with previously published values. The resultant axial and circumferential stiffness moduli for the cortical lattice were 5 x 10(-4) N/m and 3 x 10(-3) N/m, respectively. Thus the cortical lattice is a highly orthotropic structure. Its axial stiffness is small compared with that of the intact cell, but its circumferential stiffness is within the same order of magnitude. These measurements support the theory that the cortical cytoskeleton directs electrically driven length changes along the longitudinal axis of the cell. The Young's modulus of the circumferential filamentous components of the lattice were calculated to be 1 x 10(7) N/m2. The axial cross-links, believed to be a form of spectrin, were calculated to have a Young's modulus of 3 x 10(6) N/m2. Based on the measured values for the lattice and intact cell cortex, an estimate for the resultant stiffness modulus of the plasma membrane was estimated to be on the order of 10(-3) N/m. Thus, the plasma membrane appears to be relatively stiff and may be the dominant contributor to the axial stiffness of the intact cell.
The mammalian outer hair cell has been shown to possess significant coupling between mechanical and electrical properties. This electromotile property may play a key role in cochlear tuning. In order to characterize quantitatively the electrical and mechanical behavior, the cell wall is modeled as a thin linear elastic piezoelectric material. Experimental findings from several investigators are used to determine the mechanical and electrical generalized stiffness coefficients described by the model. The model analysis indicates that orthotropic mechanical properties in the plane of the cell wall are required to match experimental behavior. The calculated orthotropic coefficients predict that the outer hair cell deforms due to cilia deflection with a force gain of 0.5 for perfectly constrained end conditions and a displacement gain of 3.6 for free end conditions. These values reflect the potential role of the OHC as a feedback mechanism to the basilar membrane. Results are for small deformation and quasi-static conditions with viscosity and inertial effects neglected. It is further assumed that cell permeability is negligible at the time scale of the fast deformation considered here.
The deformation response of a guinea pig outer hair cell is modeled for mechanical and electrical stimulation up to 25 kHz. The analysis uses a Fourier series technique for a finite length cell surrounded internally and externally by a much larger continuum of viscous fluid. The analytical solution predicts that outer hair cell length changes occur due to applied mechanical or electrical stimulation without significant resonance, characteristic of a highly damped system. The deformation is found to have little attenuation up to a corner frequency of about 2 kHz for long cells and 10 kHz for short cells, in agreement with published experimental results. For electrical loading of 1 mV across the lateral cell wall, deformation for short cells is calculated to be greater than 1 nm for frequencies up to 20 kHz. These results support the proposition that in vivo the outer hair cell modifies the character of basilar membrane deformation on a cycle-by-cycle basis. An estimate of the capability of the cell to supply energy to the basilar membrane is given based on published values of outer hair cell material properties.
The mechanical properties of the mammalian organ of Corti determine its sensitivity to sound frequency and intensity, and the structure of supporting cells changes progressively with frequency along the cochlea. From the apex (low frequency) to the base (high frequency) of the guinea pig cochlea inner pillar cells decrease in length incrementally from 75–55 µm whilst the number of axial microtubules increases from 1,300–2,100. The respective values for outer pillar cells are 120–65 µm and 1,500–3,000. This correlates with a progressive decrease in the length of the outer hair cells from >100 µm to 20 µm. Deiters'cell bodies vary from 60–50 µm long with relatively little change in microtubule number. Their phalangeal processes reflect the lengths of outer hair cells but their microtubule numbers do not change systematically. Correlations between cell length, microtubule number and cochlear location are poor below 1 kHz. Cell stiffness was estimated from direct mechanical measurements made previously from isolated inner and outer pillar cells. We estimate that between 200 Hz and 20 kHz axial stiffness, bending stiffness and buckling limits increase, respectively,∼3, 6 and 4 fold for outer pillar cells, ∼2, 3 and 2.5 fold for inner pillar cells and ∼7, 20 and 24 fold for the phalangeal processes of Deiters'cells. There was little change in the Deiters'cell bodies for any parameter. Compensating for effective cell length the pillar cells are likely to be considerably stiffer than Deiters'cells with buckling limits 10–40 times greater. These data show a clear relationship between cell mechanics and frequency. However, measurements from single cells alone are insufficient and they must be combined with more accurate details of how the multicellular architecture influences the mechanical properties of the whole organ.
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