Fig 1.
Schematic overview of location and dimensions of the mechano-electrical transducer system in a generalised vertebrate semicircular canal system.
(a) In situ position and general shape of the vertebrate labyrinth with the semicircular canals (modified after [13]). (b) Schematic overview of a single sensory ampulla. The semicircular canal is filled with endolymph fluid (light blue) that is displaced during head rotation (white arrow). The cupula (dark grey) is connected to the roof of the ampulla and embedded in a mass of mucopolysaccharide gel (orange). The sensory epithelium (light grey) contains hair cells with apical hair bundles consisting of stereovilli and one central kinocilium. The fluid flow of ampullar endolymph at the sensory epithelium is limited to the subcupular space between the sensory epithelium and cupula. (c) Schematic overview and dimensions of the cupula and apical hair bundles. The kinocilia tips penetrate tubuli in the cupula and can move freely radially and slide longitudinally, allowing Brownian Movement of the hair bundles. Dimensions are indicated in μm.
Fig 2.
Schematic representation of hair bundle models.
a, low-frequency Group I hair bundle and b, the high-frequency Group II hair bundle. Groups of water molecules (blue spheres) bombard a Group I hair bundle, which results in Brownian motion (BM) of the hair bundle tip. The cumulative bombardments result in a net force (R). Both hair bundles exhibit displacement (x) around a mean and are elastically coupled to the base with elasticity constant k.
Table 1.
Symbols and values of used quantities.
Table 2.
Construction of hair cell amplitude spectra.
Fig 3.
Tip displacement of the hair bundle model due to Brownian motion.
Calculated root-mean-square displacement of modelled hair bundle tips as a function of frequency and bundle radius. As input parameters we used (a) the low-frequency Group I hair bundle and (b) the high-frequency Group II hair bundle (see text). Please note that the frequency axis is inverted for clear display of the roll-off frequencies. The low-frequency plateau is only dependent on the elasticity constant [(Eq 11)]. Hair bundle maximum tip displacement equals 68 nm for Group I in (a) and 0.6 nm for Group II in (b). The roll-off frequency depends on hydrodynamic friction, hair bundle morphology and endolymph viscosity [(Eq 10)].
Fig 4.
Stimulus displacement and frequency response of hair-cell mechanoreceptors.
We compiled and transformed data from a range of vertebrate hair cells into displacement vs. frequency response curves (see Methods and Table 1). Neural output saturation occurs above each curve. This Fig demonstrates the complementary character of Group I hair cells (ampullary-, cephalopod statocyst- and otolith) compared to Group II sensors (lateral line, free neuromasts and cochlea) in frequency and sensitivity as indicated by the red (Group I) and blue (Group II) areas. The graded shaded areas and dashed horizontal lines indicate the Brownian motion low-frequency plateau from our numerical experiments (Fig 1). The bars along the abscissa indicate the frequency-ranges for the auditory system of (h) human (w) whales and (b) bats [39]; 1, ampulla of Opsanus [31]; 2, Homo [2]; 3,4, statocyst of Octopus and Sepia [29,30]; 5–7, cochlea of Cavia [32]; 8, lateral line of Acerina [33]; 9, Xenomystus [33]; 10, free neuromast of Xenopus [34]. This figure clearly demonstrates that the SNR for both Group I and II hair cells is in the order of magnitude of about 100. With a Brownian Motion displacement amplitude of 100 nm, the SNR for Group II hair cells would be about 1.