Two adaptation processes in auditory hair cells together can provide an active amplifier

The hair cells of the vertebrate inner ear convert mechanical stimuli to electrical signals. Two adaptation mechanisms are known to modify the ionic current flowing through the transduction channels of the hair bundles: a rapid process involves calcium ions binding to the channels; and a slower adaptation is associated with the movement of myosin motors. We present a mathematical model of the hair cell which demonstrates that the combination of these two mechanisms can produce `self-tuned critical oscillations', i.e. maintain the hair bundle at the threshold of an oscillatory instability. The characteristic frequency depends on the geometry of the bundle and on the calcium dynamics, but is independent of channel kinetics. Poised on the verge of vibrating, the hair bundle acts as an active amplifier. However, if the hair cell is sufficiently perturbed, other dynamical regimes can occur. These include slow relaxation oscillations which resemble the hair bundle motion observed in some experimental preparations.Comment: 13 pages, 6 figures,REVTeX 4, To appear in Biophysical Journa

Forces between clustered stereocilia minimize friction in the ear on a subnanometre scale

The detection of sound begins when energy derived from acoustic stimuli deflects the hair bundles atop hair cells. As hair bundles move, the viscous friction between stereocilia and the surrounding liquid poses a fundamental challenge to the ear's high sensitivity and sharp frequency selectivity. Part of the solution to this problem lies in the active process that uses energy for frequency-selective sound amplification. Here we demonstrate that a complementary part involves the fluid-structure interaction between the liquid within the hair bundle and the stereocilia. Using force measurement on a dynamically scaled model, finite-element analysis, analytical estimation of hydrodynamic forces, stochastic simulation and high-resolution interferometric measurement of hair bundles, we characterize the origin and magnitude of the forces between individual stereocilia during small hair-bundle deflections. We find that the close apposition of stereocilia effectively immobilizes the liquid between them, which reduces the drag and suppresses the relative squeezing but not the sliding mode of stereociliary motion. The obliquely oriented tip links couple the mechanotransduction channels to this least dissipative coherent mode, whereas the elastic horizontal top connectors stabilize the structure, further reducing the drag. As measured from the distortion products associated with channel gating at physiological stimulation amplitudes of tens of nanometres, the balance of forces in a hair bundle permits a relative mode of motion between adjacent stereocilia that encompasses only a fraction of a nanometre. A combination of high-resolution experiments and detailed numerical modelling of fluid-structure interactions reveals the physical principles behind the basic structural features of hair bundles and shows quantitatively how these organelles are adapted to the needs of sensitive mechanotransduction.Comment: 21 pages, including 3 figures. For supplementary information, please see the online version of the article at http://www.nature.com/natur

Simulation of the Response of the Inner Hair Cell Stereocilia Bundle to an Acoustical Stimulus

Mammalian hearing relies on a cochlear hydrodynamic sensor embodied in the inner hair cell stereocilia bundle. It is presumed that acoustical stimuli induce a fluid shear-driven motion between the tectorial membrane and the reticular lamina to deflect the bundle. It is hypothesized that ion channels are opened by molecular gates that sense tension in tip-links, which connect adjacent stepped rows of stereocilia. Yet almost nothing is known about how the fluid and bundle interact. Here we show using our microfluidics model how each row of stereocilia and their associated tip links and gates move in response to an acoustical input that induces an orbital motion of the reticular lamina. The model confirms the crucial role of the positioning of the tectorial membrane in hearing, and explains how this membrane amplifies and synchronizes the timing of peak tension in the tip links. Both stereocilia rotation and length change are needed for synchronization of peak tip link tension. Stereocilia length change occurs in response to accelerations perpendicular to the oscillatory fluid shear flow. Simulations indicate that nanovortices form between rows to facilitate diffusion of ions into channels, showing how nature has devised a way to solve the diffusive mixing problem that persists in engineered microfluidic devices

The cochlea as a smart structure

The cochlea is part of the inner ear and its mechanical response provides us with many aspects of our amazingly sensitive and selective hearing. The human cochlea is a coiled tube, with two main fluid chambers running along its length, separated by a 35 mm-long flexible partition that has its own internal dynamics. A dispersive wave can propagate along the cochlea due to the interaction between the inertia of the fluid and the dynamics of the partition. This partition includes about 12 000 outer hair cells, which have different structures, on a micrometre and a nanometre scale, and act both as motional sensors and as motional actuators. The local feedback action of all these cells amplifies the motion inside the inner ear by more than 40 dB at low sound pressure levels. The feedback loops become saturated at higher sound pressure levels, however, so that the feedback gain is reduced, leading to a compression of the dynamic range in the cochlear amplifier. This helps the sensory cells, with a dynamic range of only about 30 dB, to respond to sounds with a dynamic range of more than 120 dB. The active and nonlinear nature of the dynamics within the cochlea give rise to a number of other phenomena, such as otoacoustic emissions, which can be used as a diagnostic test for hearing problems in newborn children, for example. In this paper we view the mechanical action of the cochlea as a smart structure. In particular a simplified wave model of the cochlear dynamics is reviewed that represents its essential features. This can be used to predict the motion along the cochlea when the cochlea is passive, at high levels, and also the effect of the cochlear amplifier, at low level

A modeling framework and toolset for simulation and characterization of the cochlea within the auditory system

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Biological Engineering, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 50-53).Purpose: This research develops a modeling approach and an implementation toolset to simulate reticular lamina displacement in response to excitation at the ear canal and to characterize the cochlear system in the frequency domain. Scope The study develops existing physical models covering the outer, middle, and inner ears. The range of models are passive linear, active linear, and active nonlinear. These models are formulated as differential algebraic equations, and solved for impulse and tone excitations to determine responses. The solutions are mapped into tuning characteristics as a function of position within the cochlear partition. Objectives The central objective of simulation is to determine the characteristic frequency (CF)-space map, equivalent rectangular bandwidth (ERB), and sharpness of tuning (QERB) of the cochlea. The focus of this research is on getting accurate characteristics, with high time and space resolution. The study compares the simulation results to empirical measurements and to predictions of a model that utilizes filter theory and coherent reflection theory. Method We develop lumped and distributed physical models based on mechanical, acoustic, and electrical phenomena. The models are structured in the form of differential-algebraic equations (DAE), discretized in the space domain. This is in contrast to existing methods that solve a set of algebraic equations discretized in both space and time. The DAEs are solved using numerical differentiation formulas (NDFs) to compute the displacement of the reticular lamina and intermediate variables such as displacement of stapes in response to impulse and tone excitations at the ear canal. The inputs and outputs of the cochlear partition are utilized in determining its resonances and tuning characteristics. Transfer functions of the cochlear system with impulse excitation are calculated for passive and active linear models to determine resonance and tuning of the cochlear partition. Output characteristics are utilized for linear systems with tone excitation and for nonlinear models with stimuli of various amplitudes. Stability of the system is determined using generalized eigenvalues and the individual subsystems are stabilized based on their poles and zeros. Results The passive system has CF map ranging from 20 kHz at the base to 10 Hz at the apex of the cochlear partition, and has the strongest resonant frequency corresponding to that of the middle ear. The ERB is on the order of the CF, and the QERB is on the order of 1. The group delay decreases with CF which is in contradiction with findings from Stimulus Frequency Otoacoustic Emissions (SFOAE) experiments. The tuning characteristics of the middle ear correspond well to experimental observations. The stability of the system varies greatly with the choice of parameters, and number of space sections used for both the passive and active implementations. Implication Estimates of cochlear partition tuning based on solution of differential algebraic equations have better time and space resolution compared to existing methods that solve discretized set of equations. Domination of the resonance frequency of the reticular lamina by that of the middle ear rather than the resonant frequency of the cochlea at that position for the passive model is in contradiction with Bekesys measurements on human cadavers. Conclusion The methodology used in the thesis demonstrate the benefits of developing models and formulating the problem as differential-algebraic equations and solving it using the NDFs. Such an approach facilitates computation of responses and transfer functions simultaneously, studying stability of the system, and has good accuracy (controlled directly by error tolerance) and resolution.by Samiya Ashraf Alkhairy.M.Eng

Could cell membranes produce acoustic streaming? Making the case for synechococcus self-propulsion

Sir James Lighthill proposed in 1992 that acoustic streaming occurs in the inner ear, as part of the cochlear amplifier mechanism. Here we hypothesize that some of the most ancient organisms use acoustic streaming not only for self-propulsion but also to enhance their nutrient uptake. We focus on a motile strain of Synechococcus, a yanobacteria whose mechanism for self-propulsion is not known. Molecular motors could work like piezoelectric transducers acting on the crystalline structure surrounding the outer cell membrane. Our calculations show that a traveling surface acoustic wave (SAW)could account for the observed velocities. These SAW waves will also produce a non-negligible Stokes layer surrounding the cell: motion within this region being essentially chaotic. Therefore, an AS mechanism would be biologically advantageous, enhancing localized diffusion processes and consequently, chemical reactions. We believe that acoustic streaming, produced by nanometer scale membrane vibrations could be widespread in cell biology. Other possible instances are yeast cells and erythrocytes. Flows generated by acoustic streaming may also be produced by silica coated diatoms along their raphe. We note that microelectromechanical (MEMS) acoustic streaming devices were first introduced in the 1990's. Nature may have preceded this invention by 2.7 Gyr