Structure and mechanics of supporting cells in the guinea pig organ of Corti.

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

Dynamic Analysis of Shells

Shell structures are indispensable in virtually every industry. However, in the design, analysis, fabrication, and maintenance of such structures, there are many pitfalls leading to various forms of disaster. The experience gained by engineers over some 200 years of disasters and brushes with disaster is expressed in the extensive archival literature, national codes, and procedural documentation found in larger companies. However, the advantage of the richness in the behavior of shells is that the way is always open for innovation. In this survey, we present a broad overview of the dynamic response of shell structures. The intention is to provide an understanding of the basic themes behind the detailed codes and stimulate, not restrict, positive innovation. Such understanding is also crucial for the correct computation of shell structures by any computer code. The physics dictates that the thin shell structure offers a challenge for analysis and computation. Shell response can be generally categorized by states of extension, inextensional bending, edge bending, and edge transverse shear. Simple estimates for the magnitudes of stress, deformation, and resonance in the extensional and inextensional states are provided by ring response. Several shell examples demonstrate the different states and combinations. For excitation frequency above the extensional resonance, such as in impact and acoustic excitation, a fine mesh is needed over the entire shell surface. For this range, modal and implicit methods are of limited value. The example of a sphere impacting a rigid surface shows that plastic unloading occurs continuously. Thus, there are no short cuts; the complete material behavior must be included

Electron micrograph of a section cut in the same plane as the basilar membrane.

<p>The section passes at a slightly oblique angle to cut supporting cells transversely across their axes at different levels along the organ of Corti between the basilar membrane and the reticular lamina. The insets are representative of the regions to which they refer.IPC(a) – inner pillar cell at level equivalent to that labeled a in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049338#pone-0049338-g001" target="_blank">figure 1</a> OPC(b) – outer pillar cell at level equivalent to that labeled b in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049338#pone-0049338-g001" target="_blank">figure 1</a> DC(c) – Deiters' cell at level equivalent to that labeled c in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049338#pone-0049338-g001" target="_blank">figure 1</a> DC(d) – Deiters' cell phalangeal process at level equivalent to that labeled d in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049338#pone-0049338-g001" target="_blank">figure 1</a> Note that inner pillar cell shafts are oval in cross-section and lie adjacent to the inner hair cells, that outer pillar cell shafts are rounded in cross-section with no mechanical support from adjacent cells, that the basal portion of Deiters' cells contain relatively small bundles of microtubules with a much higher proportion of cytoplasm than that seen in PCs, and that the phalangeal processes of Deiters' cells are thin and rounded in cross-section with no mechanical support from adjacent cells. A - Dense actin networks at the bases and apices of the pillar cells IHC – inner hair cells OHC – outer hair cells (distorted during preparation) Scale bar = 10 µ (insets = 500 nm).</p

Axial, bending, and buckling stiffness of supporting cells at selected frequency regions of the cochlea.

<p>Axial, bending, and buckling stiffness of supporting cells at selected frequency regions of the cochlea.</p

Number of microtubules plotted against Greenwood frequency along the cochlear duct.

<p>Inner (a) and outer (b) pillar cells contained more microtubules in the basal, higher frequency regions. There was no obvious relationship with frequency for numbers of microtubules in the Deiters' cell bodies (c) or phalangeal processes (d). Vertical and horizontal lines indicate measurement uncertainty as determined by two standard deviations about the mean from repeated measurement.</p

Diagrammatic cross-section of the organ of Corti to illustrate main cytoskeletal components.

<p>Structures containing actin filaments and microtubules are lightly and darkly shaded, respectively. Numbers of microtubules were counted from transverse sections at 4 different levels: a) the axial region of inner pillar cells (IPC) b) the axial region of outer pillar cells (OPC) c) the basal part of each row of Deiters' cells (DC1–3) d) the phalangeal processes of each row of Deiters' cells. The bases and apices of both pillar cells and Deiters' cells included dense actin meshes into which the microtubules were embedded. The axial regions of all cells were composed of parallel arrays of both microtubules and actin filaments. IHC – inner hair cell, OHC - outer hair cells, RL – reticular lamina, BM – basilar membrane, TM – tectorial membrane, a-d – levels of section illustrated in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049338#pone-0049338-g002" target="_blank">figure 2</a>.</p

The data from <b>Table 1</b> plotted to show relative stiffness values between cells.

<p>The data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049338#pone-0049338-t001" target="_blank"><b>Table 1</b></a> plotted to show relative stiffness values between cells.</p

Cell length measurements plotted against Greenwood frequency along the cochlear duct.

<p>The mean length of inner pillar cells (a) decreased towards the basal high frequency end of the cochlea and a similar but more pronounced decrease was measured for outer pillar cells (b). The arch of Corti was consequently smaller at the high frequency end of the cochlea. The mean length of the outer hair cells decreased more dramatically (c) whilst there was only a relatively small decrease in the mean length of the Deiters' cell bodies (d). Dashed boxes indicate verification of measurements obtained from dissociated cells from individual cochlear turns. Lines are linear regression fits to raw data. Error bars are two standard deviations about the mean. All correlation coefficients are highly significant. Mean values were derived from three animals.</p

Structure and buckling of outer pillar cells.

<p>Outer pillar cells are normally straight (a) and span the space between the reticular lamina (RL) and the basilar membrane (BM). In many histological sections of the organ of Corti the central shaft is deformed (b) as if the structure has been subjected to a compressional force (arrow). Under these conditions the shapes of the actin-rich apical and basal cones remain unchanged (b). This implies that the cones are relatively stiff compared with the shaft and that the effective length of the cell is considerably shorter than the full length in terms of our microtubule model.</p