Semicircular Canals Circumvent Brownian Motion Overload of Mechanoreceptor Hair Cells

RESEARCH ARTICLE Semicircular Canals Circumvent Brownian Motion Overload of Mechanoreceptor Hair Cells Mees Muller1¤*, Kier Heeck2, Coen P. H. Elemans3 1 Experimental Zoology Group, Wageningen University, 6709 PG Wageningen, The Netherlands, 2 Leiden University, Dept. of Physics, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands, 3 Sound Communication Group, University of Southern Denmark, 5230 Odense M, Denmark ¤ Current address: Physical Biology Institute, Ulica Bor 56, 4750 Momchilovtsi, Bulgaria * Abstract a11111 OPEN ACCESS Citation: Muller M, Heeck K, Elemans CPH (2016) Semicircular Canals Circumvent Brownian Motion Overload of Mechanoreceptor Hair Cells. PLoS ONE 11(7): e0159427. doi:10.1371/journal.pone.0159427 Editor: Jacob Engelmann, Universität Bielefeld, GERMANY Received: February 15, 2016 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 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 (< 10 μm vs. <400 nm). We have developed biomechanical models of vertebrate hair cells where the 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 very low frequency (<10 Hz) signals. We observe that very low frequency mechanoreception 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. Accepted: July 1, 2016 Published: July 22, 2016 Copyright: © 2016 Muller et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper. Funding: The authors have no support or funding to report. Competing Interests: The authors have declared that no competing interests exist. Introduction The vertebrate semicircular canal (SCC) system helps coordinate body movement, including stabilization of an animal’s visual gaze during locomotion [1]. Specifically, this sensory system measures head rotation and consists of mutually connected toroidal loops filled with endolymph fluid. This fluid is displaced in response even to very low-frequency (0.01–10 Hz) angular movement [2–4], leading to highly viscous flow (Reynolds number 0.5 [2]). The SCC endolymph displacement deflects apical hair bundles of hair cells (Fig 1) causing sensory transduction through the gating of mechanosensitive ion channels [5,6]. A large morphological diversity of hair cell bundle morphology, e.g. kinocilia and stereocilia dimensions and PLOS ONE | DOI:10.1371/journal.pone.0159427 July 22, 2016 1 / 15 Semicircular Canals Circumvent Brownian Motion Overload 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. doi:10.1371/journal.pone.0159427.g001 arrangements is present throughout the metazoa ([7] and references therein). Hair bundles are subject to Brownian Motion or thermal noise [8–10], that results from the thermal agitation of water molecules, as first observed by Brown [11] and explained by Einstein [12] for freely diffusing particles. For cochlear and saccular hair cells, thermal (Brownian) noise amplitude PLOS ONE | DOI:10.1371/journal.pone.0159427 July 22, 2016 2 / 15 Semicircular Canals Circumvent Brownian Motion Overload varies inversely with frequency [8,9], which impedes the detection of low frequencies due to a decreasing signal-to-noise ratio. However, it is not well known how Brownian Motion noise affects the detection of hair bundle movements in SCC. In the cochlea, the effects of Brownian motion on a hair bundle displacement [14–16] are in the order of 1 nm. Free ampullary hairs of the glass eel (Anguilla sp.) demonstrate a 68 nm root-mean-square (rms) displacement due to Brownian Motion [17], a value that is almost two orders of magnitude higher than those observed in cochlear hair bundles and therefore surprisingly large [14,17]. Micromechanical models [10] and measurements [17] show that hair bundle displacement due to thermal noise increases at the low frequency end of a cochlear hair cell’s frequency sensitivity range. Because head movements provide verylow frequency input, i.e. for humans the time constants are 5 ms and 20 s, with a natural frequency of 0.5 Hz (an elaborate survey of these quantities can be found in [2]), the influence of thermal noise due to Brownian motion at the hair bundles of the SCC can be expected to be even stronger. The detection of very-low frequency head movement may thus be impeded due to a decreasing signal-to-noise ratio. What constitutes the actual micro-mechanical stimulus to SCC hair bundles is debatable. The apex of each hair cell contains hair bundles of which the single slim kinocilium is about 70 μm long [18]. In eel, about 10 μm of the kinocilia tips (1/6 of the kinocilium height) is embedded in 2–3 μm wide, mucopolysaccharide-filled channels in the gelatinous cupula [19] (Fig 1), which is anchored onto the roof of the ampulla. The cupula is generally thought to provide the mechanical stimulus to the hair cells based on experiments where cupula removal led to reduced activity in the afferent nerve [18,20]. However, experiments by Suzuki and colleagues [20] (...truncated)