Anomalous Brownian motion discloses viscoelasticity in the ear's mechanoelectrical-transduction apparatus

Transport of probe particles in a polymer network: effects of probe size, network rigidity and probe-polymer interaction

Fundamental understanding of the effect of microscopic parameters on the dynamics of probe particles in different complex environments has wide implications. Examples include diffusion of proteins in biological hydrogels, porous media, polymer matrix, etc. Here, we use extensive molecular dynamics simulations to investigate the dynamics of the probe particle in a polymer network on a diamond lattice, which provides substantial crowding to mimic the cellular environment. Our simulations show that the dynamics of the probe increasingly becomes restricted, non-Gaussian and subdiffusive on increasing the network rigidity, binding affinity and probe size. In addition, the velocity autocorrelation functions show negative dips owing to the viscoelasticity and caging due to the surrounding network. These observations go with the general experimental findings. Importantly, for a probe particle of size comparable to the mesh size, unrestricted motion engulfing large length scales has been observed. This happens with a more flexible polymer network, which is easily pushed by the bigger probe. On increasing the rigidity of the network, the bigger probe can not efficiently push the network and as a result the long tail disappears. Our study gives a general qualitative picture of the transport of probes in a gel-like medium, as encountered in different contexts.

Models of vestibular semicircular canal afferent neuron firing activity

Semicircular canal afferent neurons transmit information about head rotation to the brain. Mathematical models of how they do this have coevolved with concepts of how brains perceive the world. A 19th-century "camera" metaphor, in which sensory neurons project an image of the world captured by sense organs into the brain, gave way to a 20th-century view of sensory nerves as communication channels providing inputs to dynamical control systems. Now, in the 21st century, brains are being modeled as Bayesian observers who infer what is happening in the world given noisy, incomplete, and distorted sense data. The semicircular canals of the vestibular apparatus provide an experimentally accessible, low-dimensional system for developing and testing dynamical Bayesian generative models of sense data. In this review, we summarize advances in mathematical modeling of information transmission by semicircular canal afferent sensory neurons since the first such model was proposed nearly a century ago. Models of information transmission by vestibular afferent neurons may provide a foundation for developing realistic models of how brains perceive the world by inferring the causes of sense data.

The Development of Cooperative Channels Explains the Maturation of Hair Cell's Mechanotransduction

Hearing relies on the conversion of mechanical stimuli into electrical signals. In vertebrates, this process of mechanoelectrical transduction (MET) is performed by specialized receptors of the inner ear, the hair cells. Each hair cell is crowned by a hair bundle, a cluster of microvilli that pivot in response to sound vibrations, causing the opening and closing of mechanosensitive ion channels. Mechanical forces are projected onto the channels by molecular springs called tip links. Each tip link is thought to connect to a small number of MET channels that gate cooperatively and operate as a single transduction unit. Pushing the hair bundle in the excitatory direction opens the channels, after which they rapidly reclose in a process called fast adaptation. It has been experimentally observed that the hair cell’s biophysical properties mature gradually during postnatal development: the maximal transduction current increases, sensitivity sharpens, transduction occurs at smaller hair-bundle displacements, and adaptation becomes faster. Similar observations have been reported during tip-link regeneration after acoustic damage. Moreover, when measured at intermediate developmental stages, the kinetics of fast adaptation varies in a given cell, depending on the magnitude of the imposed displacement. The mechanisms underlying these seemingly disparate observations have so far remained elusive. Here, we show that these phenomena can all be explained by the progressive addition of MET channels of constant properties, which populate the hair bundle first as isolated entities and then progressively as clusters of more sensitive, cooperative MET channels. As the proposed mechanism relies on the difference in biophysical properties between isolated and clustered channels, this work highlights the importance of cooperative interactions between mechanosensitive ion channels for hearing.

A New Twist on Tip Links

Auditory transduction is fast and sensitive owing to the direct detection of mechanical stimuli by hair cells, the sensory receptors of the internal ear. A study by Dionne et al. (2018) in this issue of Neuron suggests how signals propagate through tip links, the cadherin-based strands that gate mechanically sensitive channels.

Cochlear outer hair cell horizontal top connectors mediate mature stereocilia bundle mechanics

Outer hair cell (OHC) stereocilia bundle deflection opens mechanoelectrical transduction channels at the tips of the stereocilia from the middle and short rows, while bundle cohesion is maintained owing to the presence of horizontal top connectors. Here, we used a quantitative noncontact atomic force microscopy method to investigate stereocilia bundle stiffness and damping, when stimulated at acoustic frequencies and nanometer distances from the bundle. Stereocilia bundle mechanics were determined in stereocilin-deficient mice lacking top connectors and with detached tectorial membrane (Strc -/-/Tecta -/- double knockout) and heterozygous littermate controls (Strc +/-/Tecta -/-). A substantial decrease in bundle stiffness and damping by ~60 and ~74% on postnatal days P13 to P15 was observed when top connectors were absent. Additionally, we followed bundle mechanics during OHC top connectors development between P9 and P15 and quantified the observed increase in OHC bundle stiffness and damping in Strc +/-/Tecta -/- mice while no significant change was detected in Strc -/-/Tecta -/- animals.

Comparative Aspects of Hearing in Vertebrates and Insects with Antennal Ears

The evolution of hearing in terrestrial animals has resulted in remarkable adaptations enabling exquisitely sensitive sound detection by the ear and sophisticated sound analysis by the brain. In this review, we examine several such characteristics, using examples from insects and vertebrates. We focus on two strong and interdependent forces that have been shaping the auditory systems across taxa: the physical environment of auditory transducers on the small, subcellular scale, and the sensory-ecological environment within which hearing happens, on a larger, evolutionary scale. We briefly discuss acoustical feature selectivity and invariance in the central auditory system, highlighting a major difference between insects and vertebrates as well as a major similarity. Through such comparisons within a sensory ecological framework, we aim to emphasize general principles underlying acute sensitivity to airborne sounds.

Chemomechanical regulation of myosin Ic cross-bridges: Deducing the elastic properties of an ensemble from single-molecule mechanisms

Myosin Ic is thought to be the principal constituent of the motor that adjusts mechanical responsiveness during adaptation to prolonged stimuli by hair cells, the sensory receptors of the inner ear. In this context myosin molecules operate neither as filaments, as occurs in muscles, nor as single or few molecules, as characterizes intracellular transport. Instead, myosin Ic molecules occur in a complex cluster in which they may exhibit cooperative properties. To better understand the motor’s remarkable function, we introduce a theoretical description of myosin Ic’s chemomechanical cycle based on experimental data from recent single-molecule studies. The cycle consists of distinct chemical states that the myosin molecule stochastically occupies. We explicitly calculate the probabilities of the occupancy of these states and show their dependence on the external force, the availability of actin, and the nucleotide concentrations as required by thermodynamic constraints. This analysis highlights that the strong binding of myosin Ic to actin is dominated by the ADP state for small external forces and by the ATP state for large forces. Our approach shows how specific parameter values of the chemomechanical cycle for myosin Ic result in behaviors distinct from those of other members of the myosin family. Integrating this single-molecule cycle into a simplified ensemble description, we predict that the average number of bound myosin heads is regulated by the external force and nucleotide concentrations. The elastic properties of such an ensemble are determined by the average number of myosin cross-bridges. Changing the binding probabilities and myosin’s stiffness under a constant force results in a mechanical relaxation which is large enough to account for fast adaptation in hair cells.

Myosin molecules are biological nanomachines that transduce chemical energy into mechanical work and thus produce directed motion in living cells. These molecules proceed through cyclic reactions in which they change their conformational states upon the binding and release of nucleotides while attaching to and detaching from filaments. The myosin family consists of many distinct members with diverse functions such as muscle contraction, cargo transport, cell migration, and sensory adaptation. How these functions emerge from the biophysical properties of the individual molecules is an open question. We present an approach that integrates recent findings from single-molecule experiments into a thermodynamically consistent description of myosin Ic and demonstrate how the specific parameter values of the cycle result in a distinct function. The free variables of our description are the chemical input and external force, both of which are experimentally accessible and define the cellular environment in which these proteins function. We use this description to predict the elastic properties of an ensemble of molecules and discuss the implications for myosin Ic’s function in the inner ear as a tension regulator mediating adaptation, a hallmark of biological sensory systems. In this situation myosin molecules cooperate in an intermediate regime, neither as a large ensemble as in muscle nor as a single or a few molecules as in intracellular transport.

An elastic element in the protocadherin-15 tip link of the inner ear

Tip link filaments convey force and gate inner-ear hair-cell transduction channels to mediate perception of sound and head movements. Cadherin-23 and protocadherin-15 form tip links through a calcium-dependent interaction of their extracellular domains made of multiple extracellular cadherin (EC) repeats. These repeats are structurally similar, but not identical in sequence, often featuring linkers with conserved calcium-binding sites that confer mechanical strength to them. Here we present the X-ray crystal structures of human protocadherin-15 EC8-EC10 and mouse EC9-EC10, which show an EC8-9 canonical-like calcium-binding linker, and an EC9-10 calcium-free linker that alters the linear arrangement of EC repeats. Molecular dynamics simulations and small-angle X-ray scattering experiments support this non-linear conformation. Simulations also suggest that unbending of EC9-10 confers some elasticity to otherwise rigid tip links. The new structure provides a first view of protocadherin-15's non-canonical EC linkers and suggests how they may function in inner-ear mechanotransduction, with implications for other cadherins.

Semicircular Canals Circumvent Brownian Motion Overload of Mechanoreceptor Hair Cells

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.

Hopping Diffusion of Nanoparticles in Polymer Matrices

We propose a hopping mechanism for diffusion of large nonsticky nanoparticles subjected to topological constraints in both unentangled and entangled polymer solids (networks and gels) and entangled polymer liquids (melts and solutions). Probe particles with size larger than the mesh size ax of unentangled polymer networks or tube diameter ae of entangled polymer liquids are trapped by the network or entanglement cells. At long time scales, however, these particles can diffuse by overcoming free energy barrier between neighboring confinement cells. The terminal particle diffusion coefficient dominated by this hopping diffusion is appreciable for particles with size moderately larger than the network mesh size ax or tube diameter ae . Much larger particles in polymer solids will be permanently trapped by local network cells, whereas they can still move in polymer liquids by waiting for entanglement cells to rearrange on the relaxation time scales of these liquids. Hopping diffusion in entangled polymer liquids and networks has a weaker dependence on particle size than that in unentangled networks as entanglements can slide along chains under polymer deformation. The proposed novel hopping model enables understanding the motion of large nanoparticles in polymeric nanocomposites and the transport of nano drug carriers in complex biological gels such as mucus.

Non-universal tracer diffusion in crowded media of non-inert obstacles

For tracer motion in an array of attractive obstacles we observe transient, non-ergodic anomalous diffusion depending on the obstacle density.

Mechano-transduction: from molecules to tissues

Biological mechano-transduction and force-dependent changes scale from protein conformation (â„« to nm) to cell organization and multi-cell function (mm to cm) to affect cell organization, fate, and homeostasis.

External forces play complex roles in cell organization, fate, and homeostasis. Changes in these forces, or how cells respond to them, can result in abnormal embryonic development and diseases in adults. How cells sense and respond to these mechanical stimuli requires an understanding of the biophysical principles that underlie changes in protein conformation and result in alterations in the organization and function of cells and tissues. Here, we discuss mechano-transduction as it applies to protein conformation, cellular organization, and multi-cell (tissue) function.

Integrating the active process of hair cells with cochlear function

Uniquely among human senses, hearing is not simply a passive response to stimulation. Our auditory system is instead enhanced by an active process in cochlear hair cells that amplifies acoustic signals several hundred-fold, sharpens frequency selectivity and broadens the ear's dynamic range. Active motility of the mechanoreceptive hair bundles underlies the active process in amphibians and some reptiles; in mammals, this mechanism operates in conjunction with prestin-based somatic motility. Both individual hair bundles and the cochlea as a whole operate near a dynamical instability, the Hopf bifurcation, which accounts for the cardinal features of the active process.

The physics of hearing: fluid mechanics and the active process of the inner ear

Most sounds of interest consist of complex, time-dependent admixtures of tones of diverse frequencies and variable amplitudes. To detect and process these signals, the ear employs a highly nonlinear, adaptive, real-time spectral analyzer: the cochlea. Sound excites vibration of the eardrum and the three miniscule bones of the middle ear, the last of which acts as a piston to initiate oscillatory pressure changes within the liquid-filled chambers of the cochlea. The basilar membrane, an elastic band spiraling along the cochlea between two of these chambers, responds to these pressures by conducting a largely independent traveling wave for each frequency component of the input. Because the basilar membrane is graded in mass and stiffness along its length, however, each traveling wave grows in magnitude and decreases in wavelength until it peaks at a specific, frequency-dependent position: low frequencies propagate to the cochlear apex, whereas high frequencies culminate at the base. The oscillations of the basilar membrane deflect hair bundles, the mechanically sensitive organelles of the ear's sensory receptors, the hair cells. As mechanically sensitive ion channels open and close, each hair cell responds with an electrical signal that is chemically transmitted to an afferent nerve fiber and thence into the brain. In addition to transducing mechanical inputs, hair cells amplify them by two means. Channel gating endows a hair bundle with negative stiffness, an instability that interacts with the motor protein myosin-1c to produce a mechanical amplifier and oscillator. Acting through the piezoelectric membrane protein prestin, electrical responses also cause outer hair cells to elongate and shorten, thus pumping energy into the basilar membrane's movements. The two forms of motility constitute an active process that amplifies mechanical inputs, sharpens frequency discrimination, and confers a compressive nonlinearity on responsiveness. These features arise because the active process operates near a Hopf bifurcation, the generic properties of which explain several key features of hearing. Moreover, when the gain of the active process rises sufficiently in ultraquiet circumstances, the system traverses the bifurcation and even a normal ear actually emits sound. The remarkable properties of hearing thus stem from the propagation of traveling waves on a nonlinear and excitable medium.

Transduction channels' gating can control friction on vibrating hair-cell bundles in the ear

Hearing starts when sound-evoked mechanical vibrations of the hair-cell bundle activate mechanosensitive ion channels, giving birth to an electrical signal. As for any mechanical system, friction impedes movements of the hair bundle and thus constrains the sensitivity and frequency selectivity of auditory transduction. Friction is generally thought to result mainly from viscous drag by the surrounding fluid. We demonstrate here that the opening and closing of the transduction channels produce internal frictional forces that can dominate viscous drag on the micrometer-sized hair bundle. We characterized friction by analyzing hysteresis in the force-displacement relation of single hair-cell bundles in response to periodic triangular stimuli. For bundle velocities high enough to outrun adaptation, we found that frictional forces were maximal within the narrow region of deflections that elicited significant channel gating, plummeted upon application of a channel blocker, and displayed a sublinear growth for increasing bundle velocity. At low velocity, the slope of the relation between the frictional force and velocity was nearly fivefold larger than the hydrodynamic friction coefficient that was measured when the transduction machinery was decoupled from bundle motion by severing tip links. A theoretical analysis reveals that channel friction arises from coupling the dynamics of the conformational change associated with channel gating to tip-link tension. Varying channel properties affects friction, with faster channels producing smaller friction. We propose that this intrinsic source of friction may contribute to the process that sets the hair cell's characteristic frequency of responsiveness.

Subdiffusion in hair bundle dynamics: the role of protein conformational fluctuations

The detection of sound signals in vertebrates involves a complex network of different mechano-sensory elements in the inner ear. An especially important element in this network is the hair bundle, an antenna-like array of stereocilia containing gated ion channels that operate under the control of one or more adaptation motors. Deflections of the hair bundle by sound vibrations or thermal fluctuations transiently open the ion channels, allowing the flow of ions through them, and producing an electrical signal in the process, eventually causing the sensation of hearing. Recent high frequency (0.1-10 kHz) measurements by Kozlov et al. [Proc. Natl. Acad. Sci. U.S.A. 109, 2896 (2012)] of the power spectrum and the mean square displacement of the thermal fluctuations of the hair bundle suggest that in this regime the dynamics of the hair bundle are subdiffusive. This finding has been explained in terms of the simple Brownian motion of a filament connecting neighboring stereocilia (the tip link), which is modeled as a viscoelastic spring. In the present paper, the diffusive anomalies of the hair bundle are ascribed to tip link fluctuations that evolve by fractional Brownian motion, which originates in fractional Gaussian noise and is characterized by a power law memory. The predictions of this model for the power spectrum of the hair bundle and its mean square displacement are consistent with the experimental data and the known properties of the tip link.

Fluctuation-response theorem for the active noisy oscillator of the hair-cell bundle

The hair bundle of sensory cells in the vertebrate ear provides an example of a noisy oscillator close to a Hopf bifurcation. The analysis of the data from both spontaneous and forced oscillations shows a strong violation of the fluctuation-dissipation theorem, revealing the presence of an underlying active process that keeps the system out of equilibrium. Nevertheless, we show that a generalized fluctuation-dissipation theorem, valid for nonequilibrium steady states, is fulfilled within the limits of our experimental accuracy and computational approximations, when the adequate conjugate degrees of freedom are chosen.