Semicircular canals circumvent Brownian Motion overload of mechanoreceptor hair cells

<p>Vertebrate semicircular canals (SCC) first appeared in the vertebrates (i.e. ancestral fish) over 600 million years ago. In SCC the principal mechanoreceptors are hair cells, which as </p><p>compared to cochlear hair cells are distinctly longer (70 vs. 7 μm), 10 times more compliant to bending (44 vs. 500 nN/m), and have a 100-fold higher tip displacement threshold (&lt; 10 μm vs. &lt;400 nm).We have developed biomechanical models of vertebrate hair cells where the </p><p>bundle is approximated as a stiff, cylindrical elastic rod subject to friction and thermal agitation. Our models suggest that the above differences aid SCC hair cells in circumventing the masking effects of Brownian motion noise of about 70 nm, and thereby permit transduction of </p><p>very low frequency (&lt;10 Hz) signals.We observe that very low frequency mechanoreception </p><p>requires increased stimulus amplitude, and argue that this is adaptive to circumvent Brownian motion overload at the hair bundles. We suggest that the selective advantage of detecting such low frequency stimuli may have favoured the evolution of large guiding structures such as semicircular canals and otoliths to overcome Brownian Motion noise at the level of the mechanoreceptors of the SCC.</p

Coherent Optomechanical State Transfer between Disparate Mechanical Resonators

Hybrid quantum systems have been developed with various mechanical, optical and microwave harmonic oscillators. The coupling produces a rich library of interactions including two mode squeezing, swapping interactions, back-action evasion and thermal control. In a multimode mechanical system, coupling resonators of different scales (both in frequency and mass) leverages the advantages of each resonance. For example: a high frequency, easily manipulated resonator could be entangled with a low frequency massive object for tests of gravitational decoherence. Here we demonstrate coherent optomechanical state swapping between two spatially and frequency separated resonators with a mass ratio of 4. We find that, by using two laser beams far detuned from an optical cavity resonance, efficient state transfer is possible through a process very similar to STIRAP (Stimulated Raman Adiabatic Passage) in atomic physics. Although the demonstration is classical, the same technique can be used to generate entanglement between oscillators in the quantum regime

Experimental exploration of the optomechanical attractor diagram and its dynamics

We demonstrate experimental exploration of the attractor diagram of an optomechanical system where the optical forces compensate for the mechanical losses. In this case stable self-induced oscillations occur but only for specific mirror amplitudes and laser detunings. We demonstrate that we can amplify the mechanical mode to an amplitude 500 times larger than the thermal amplitude at 300K. The lack of unstable or chaotic motion allows us to manipulate our system into a non-trivial steady state and explore the dynamics of self-induced oscillations in great detail.Comment: 6 pages, 4 figure

Vibration isolation with high thermal conductance for a cryogen-free dilution refrigerator

We present the design and implementation of a mechanical low-pass filter vibration isolation used to reduce the vibrational noise in a cryogen-free dilution refrigerator operated at 10 mK, intended for scanning probe techniques. We discuss the design guidelines necessary to meet the competing requirements of having a low mechanical stiffness in combination with a high thermal conductance. We demonstrate the effectiveness of our approach by measuring the vibrational noise levels of an ultrasoft mechanical resonator positioned above a SQUID. Starting from a cryostat base temperature of 8 mK, the vibration isolation can be cooled to 10.5 mK, with a cooling power of 113 $\mu$W at 100 mK. We use the low vibrations and low temperature to demonstrate an effective cantilever temperature of less than 20 mK. This results in a force sensitivity of less than 500 zN/$\sqrt{\mathrm{Hz}}$, and an integrated frequency noise as low as 0.4 mHz in a 1 Hz measurement bandwidth

Symbols and values of used quantities.

<p>Symbols and values of used quantities.</p

Construction of hair cell amplitude spectra.

<p>Construction of hair cell amplitude spectra.</p

Schematic overview of location and dimensions of the mechano-electrical transducer system in a generalised vertebrate semicircular canal system.

<p>(<b>a</b>) <i>In situ</i> position and general shape of the vertebrate labyrinth with the semicircular canals (modified after [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.ref013" target="_blank">13</a>]). (<b>b</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. (<b>c</b>) 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.</p

Tip displacement of the hair bundle model due to Brownian motion.

<p>Calculated root-mean-square displacement of modelled hair bundle tips as a function of frequency and bundle radius. As input parameters we used (<b>a</b>) the low-frequency Group I hair bundle and (<b>b</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 [(<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.e013" target="_blank">Eq 11</a>)]. Hair bundle maximum tip displacement equals 68 nm for Group I in (<b>a</b>) and 0.6 nm for Group II in (<b>b</b>). The roll-off frequency depends on hydrodynamic friction, hair bundle morphology and endolymph viscosity [(<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.e012" target="_blank">Eq 10</a>)].</p

Stimulus displacement and frequency response of hair-cell mechanoreceptors.

<p>We compiled and transformed data from a range of vertebrate hair cells into displacement vs. frequency response curves (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#sec002" target="_blank">Methods</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.t001" target="_blank">Table 1</a>). 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 (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.g001" target="_blank">Fig 1</a>). The bars along the abscissa indicate the frequency-ranges for the auditory system of (h) human (w) whales and (b) bats [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.ref039" target="_blank">39</a>]; 1, ampulla of <i>Opsanus</i> [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.ref031" target="_blank">31</a>]; 2, <i>Homo</i> [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.ref002" target="_blank">2</a>]; 3,4, statocyst of <i>Octopus</i> and <i>Sepia</i> [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.ref029" target="_blank">29</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.ref030" target="_blank">30</a>]; 5–7, cochlea of <i>Cavia</i> [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.ref032" target="_blank">32</a>]; 8, lateral line of <i>Acerina</i> [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.ref033" target="_blank">33</a>]; 9, <i>Xenomystus</i> [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.ref033" target="_blank">33</a>]; 10, free neuromast of <i>Xenopus</i> [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159427#pone.0159427.ref034" target="_blank">34</a>]. 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.</p