Fig 1.
Outer shape and inner structure of human otoconia.
(A) Intact human otoconium showing the bulbous (cylindrical) belly and the terminal rhombohedral faces representing the visible part of the 3+3 branches inside the volume. ESEM (Environmental scanning electron microscope)-image, high vacuum mode (HV), 15 kV. (B) 3D visualization of the inner architecture of an otoconium, keeping point group -3m for calcite. Less dense belly area (transparent) and 3+3 dense (compact) branches starting from the center of symmetry. Scale bar (A): 5 μm.
Fig 2.
Variations in the size of the terminal faces of human otoconia.
(A,B,C) Vital human otoconia show an asymmetric size distribution of the terminal faces indicating that there is non-centrosymmetric mass distribution parallel to the long axis of each single otoconium. ESEM, LV, low vacuum, 15 kV. Scale bar in (A,B,C) 3 μm. Scale bar in (C), also for (A,B): 3 μm.
Fig 3.
Human otoconia after treatment with EDTA (c = 0,107mol/l).
(A,B,C) Dissolution of the belly area. The more dense non-centrosymmetric branches remain as residues. The technique of partial dissolution of the calcite component gives insight into the inner structure of otoconia and clearly reveals an asymmetric mass distribution within single otoconia specimens. ESEM, LV, low vacuum, 15 kV. Scale bar in (C), also for (A,B): 3 μm.
Fig 4.
Biomimetic otoconia (Calcite Gelatin Composits, CGC) with different sizes of their rhombohedral faces.
(A,B,C) As a consequence the mass-distribution parallel to the long axis of specimen is non-centrosymmetric (see Fig 4). ESEM, LV, low vacuum, 15 kV. Scale bar in (A) and (B): 50μm. Scale bar (C): 100 μm.
Fig 5.
Biomimetic otoconia (Calcite Gelatin Composit, CGC) before and after treatment with EDTA (c = 0,107mol/l).
(A,B,C) The preferred dissolution of the belly area clearly reveals non-centrosymmetric mass distribution of the branches (top and bottom along an idealized 3-fold axis). ESEM, LV, low vacuum, 15 kV. Scale bar in (A): 500 μm, in (B): 200μm and in (C): 100 μm.
Fig 6.
3 D-model of the inner structure of a single human otoconium.
Differences in size among the rhombohedral faces clearly correlate with variations in volume among the 3+3 branches. The inner structure deviates from centrosymmetry indicating non-centrosymmetric mass distribution parallel to the long axis of the otoconium.
Fig 7.
Biomimetic otoconium within a tube of artificial endolymph under the influence of gravity.
(A-C) Directional changes in time steps of 3 sec indicating the movement of the heavier mass fraction (red point) in the direction of the gravitational vector (G), indicating the non-centrosymmetric mass distribution. CGC, size about 700 μm, recorded by means of a Nikon SMZ 1500 stereomicroscope in combination with a ProgRes SpeedXT core 5 camera during sinking (about 20 sec.) in the liquid medium (artificial endolymph). Scale bar in (A) also for (B-F) 200 μm.
Fig 8.
Simulation model of a single asymmetric otoconium represented by a rigid unit of 3 linearly arranged spheres (blue, purple).
(A,B) Two independent simulation setups were dedicated to the purpose of studying acceleration parallel (A) and normal (B) to the long axis of the otoconium fixed to the substrate layer. The otoconium is bound to a substrate layer via two polymer chains (green), each mimicked by a series of harmonic springs. The overall system is subjected to periodic boundary conditions along the y and z directions, respectively. Acceleration (blue arrows) is applied along the x-direction, resulting in a density gradient of the model liquid (grey dots). Because of its larger specific weight, the otoconium moves into the opposite direction. Note the tilting of the otoconium resulting from its asymmetric mass distribution (assumed as 20% larger for the bottom end, and 12.5% less for the other two building blocks as colored in purple and blue, respectively). Scale bar in (A) also for (B) 10 μm.
Fig 9.
Elongation of the polymer strands resulting from acceleration normal and parallel to the orientation of otoconium fixation to the substrate.
The simulation (see also Fig 7) encompasses the dynamics at equilibrium (a = 0), acceleration to a = ±1, a = ±2, a = ±4 (× 9.81 m∙s-2) and relaxation to a = 0 within subsequent runs of 100.000 time frames each and illustrates responses of the otoconium when arranged parallel and normal to the direction of acceleration. The purple line indicates elongation of the polymer strand which is attached to the denser end, whilst the blue curves refers to the polymer fixating the opposite end of the otoconium. For comparison, responses to a perfectly symmetric otoconium are illustrated by the black and brown curves, respectively.
Fig 10.
Displacement and rearrangement of symmetric and asymmetric otoconia in a simplified otolith membrane upon linear acceleration.
Left: Membranes with symmetric otoconia show homogeneous displacement patterns according to the density gradient along the direction of acceleration. Right: Otoconia of asymmetric mass distribution (heavier ends shown in darker color) experience tilting/rotation in addition to dislocation. Note that the random pattern of clockwise/counter-clockwise tilting causes defects in the initially ordered matrix. While the pristine matrix reflects a more dense packing, defect formation demands additional volume and thus leads to an expansion/stiffening of the otolith membrane along the direction of acceleration. This affects the coupling of the otoconia-matrix with vestibular hair cells and leads to an increased signal strength being transmitted. The blue arrows show the direction of acceleration, whilst the green lines indicate the displacement of otoconia with respect to the otolith membrane in absence of acceleration (center).