Coupling between the Stereocilia of Rat Sensory Inner-Hair-Cell Hair Bundles Is Weak, Shaping Their Sensitivity to Stimulation.

The hair bundle is the universal mechanosensory organelle of auditory, vestibular, and lateral-line systems. A bundle comprises mechanically coupled stereocilia, whose displacements in response to stimulation activate a receptor current. The similarity of stereociliary displacements within a bundle regulates fundamental properties of the receptor current like its speed, magnitude, and sensitivity. However, the dynamics of individual stereocilia from the mammalian cochlea in response to a known bundle stimulus has not been quantified. We developed a novel high-speed system, which dynamically stimulates and tracks individual inner-hair-cell stereocilia from male and female rats. Stimulating two to three of the tallest stereocilia within a bundle (nonuniform stimulation) caused dissimilar stereociliary displacements. Stereocilia farther from the stimulator moved less, but with little delay, implying that there is little slack in the system. Along the axis of mechanical sensitivity, stereocilium displacements peaked and reversed direction in response to a step stimulus. A viscoelastic model explained the observed displacement dynamics, which implies that coupling between the tallest stereocilia is effectively viscoelastic. Coupling elements between the tallest inner-hair-cell stereocilia were two to three times stronger than elements anchoring stereocilia to the surface of the cell but were 100-10,000 times weaker than those of a well-studied noncochlear hair bundle. Coupling was too weak to ensure that stereocilia move similarly in response to nonuniform stimulation at auditory frequencies. Our results imply that more uniform stimulation across the tallest stereocilia of an inner-hair-cell bundle in vivo is required to ensure stereociliary displacement similarity, increasing the speed, sensitivity, and magnitude of the receptor current.SIGNIFICANCE STATEMENT Generation of the receptor current of the hair cell is the first step in electrically encoding auditory information in the hearing organs of all vertebrates. The receptor current is shaped by mechanical coupling between stereocilia in the hair bundle of each hair cell. Here, we provide foundational information on the mechanical coupling between stereocilia of cochlear inner-hair cells. In contrast to other types of hair cell, coupling between inner-hair-cell stereocilia is weak, causing slower, smaller, and less sensitive receptor currents in response to stimulation of few, rather than many, stereocilia. Our results imply that inner-hair cells need many stereocilia to be stimulated in vivo to ensure fast, large, and sensitive receptor currents.

Dimensions of a Living Cochlear Hair Bundle.

The hair bundle is the mechanosensory organelle of hair cells that detects mechanical stimuli caused by sounds, head motions, and fluid flows. Each hair bundle is an assembly of cellular-protrusions called stereocilia, which differ in height to form a staircase. Stereocilia have different heights, widths, and separations in different species, sensory organs, positions within an organ, hair-cell types, and even within a single hair bundle. The dimensions of the stereociliary assembly dictate how the hair bundle responds to stimuli. These hair-bundle properties have been measured previously only to a limited degree. In particular, mammalian data are either incomplete, lack control for age or position within an organ, or have artifacts owing to fixation or dehydration. Here, we provide a complete set of measurements for postnatal day (P) 11 C57BL/6J mouse apical inner hair cells (IHCs) obtained from living tissue, tissue mildly-fixed for fluorescent imaging, or tissue strongly fixed and dehydrated for scanning electronic microscopy (SEM). We found that hair bundles mildly-fixed for fluorescence had the same dimensions as living hair bundles, whereas SEM-prepared hair bundles shrank uniformly in stereociliary heights, widths, and separations. By determining the shrinkage factors, we imputed live dimensions from SEM that were too small to observe optically. Accordingly, we created the first complete blueprint of a living IHC hair bundle. We show that SEM-prepared measurements strongly affect calculations of a bundle's mechanical properties - overestimating stereociliary deflection stiffness and underestimating the fluid coupling between stereocilia. The methods of measurement, the data, and the consequences we describe illustrate the high levels of accuracy and precision required to understand hair-bundle mechanotransduction.

Bilateral Spontaneous Otoacoustic Emissions Show Coupling between Active Oscillators in the Two Ears.

Spontaneous otoacoustic emissions (SOAEs) are weak sounds that emanate from the ears of tetrapods in the absence of acoustic stimulation. These emissions are an epiphenomenon of the inner ear's active process, which enhances the auditory system's sensitivity to weak sounds, but their mechanism of production remains a matter of debate. We recorded SOAEs simultaneously from the two ears of the tokay gecko and found that binaural emissions could be strongly correlated: some emissions occurred at the same frequency in both ears and were highly synchronized. Suppression of the emissions in one ear often changed the amplitude or shifted the frequency of emissions in the other. Decreasing the frequency of emissions from one ear by lowering its temperature usually reduced the frequency of the contralateral emissions. To understand the relationship between binaural SOAEs, we developed a mathematical model of the eardrums as noisy nonlinear oscillators coupled by the air within an animal's mouth. By according with the model, the results indicate that some SOAEs are generated bilaterally through acoustic coupling across the oral cavity. The model predicts that sound localization through the acoustic coupling between ears is influenced by the active processes of both ears.

A Bundle of Mechanisms: Inner-Ear Hair-Cell Mechanotransduction.

In the inner ear, the deflection of hair bundles, the sensory organelles of hair cells, activates mechanically-gated channels (MGCs). Hair bundles monitor orientation of the head, its angular and linear acceleration, and detect sound. Force applied to MGCs is shaped by intrinsic hair-bundle properties, by the mechanical load on the bundle, and by the filter imparted by the environment of the hair bundle. Channel gating and adaptation, the ability of the bundle to reset its operating point, contribute to hair-bundle mechanics. Recent data from mammalian hair cells challenge longstanding hypotheses regarding adaptation mechanisms and hair-bundle coherence. Variations between hair bundles from different organs in hair-bundle mechanics, mechanical load, channel gating, and adaptation may allow a hair bundle to selectively respond to specific sensory stimuli.

Homeostatic enhancement of sensory transduction.

Our sense of hearing boasts exquisite sensitivity, precise frequency discrimination, and a broad dynamic range. Experiments and modeling imply, however, that the auditory system achieves this performance for only a narrow range of parameter values. Small changes in these values could compromise hair cells' ability to detect stimuli. We propose that, rather than exerting tight control over parameters, the auditory system uses a homeostatic mechanism that increases the robustness of its operation to variation in parameter values. To slowly adjust the response to sinusoidal stimulation, the homeostatic mechanism feeds back a rectified version of the hair bundle's displacement to its adaptation process. When homeostasis is enforced, the range of parameter values for which the sensitivity, tuning sharpness, and dynamic range exceed specified thresholds can increase by more than an order of magnitude. Signatures in the hair cell's behavior provide a means to determine through experiment whether such a mechanism operates in the auditory system. Robustness of function through homeostasis may be ensured in any system through mechanisms similar to those that we describe here.

Identification of Bifurcations from Observations of Noisy Biological Oscillators.

Hair bundles are biological oscillators that actively transduce mechanical stimuli into electrical signals in the auditory, vestibular, and lateral-line systems of vertebrates. A bundle's function can be explained in part by its operation near a particular type of bifurcation, a qualitative change in behavior. By operating near different varieties of bifurcation, the bundle responds best to disparate classes of stimuli. We show how to determine the identity of and proximity to distinct bifurcations despite the presence of substantial environmental noise. Using an improved mechanical-load clamp to coerce a hair bundle to traverse different bifurcations, we find that a bundle operates within at least two functional regimes. When coupled to a high-stiffness load, a bundle functions near a supercritical Hopf bifurcation, in which case it responds best to sinusoidal stimuli such as those detected by an auditory organ. When the load stiffness is low, a bundle instead resides close to a subcritical Hopf bifurcation and achieves a graded frequency response-a continuous change in the rate, but not the amplitude, of spiking in response to changes in the offset force-a behavior that is useful in a vestibular organ. The mechanical load in vivo might therefore control a hair bundle's responsiveness for effective operation in a particular receptor organ. Our results provide direct experimental evidence for the existence of distinct bifurcations associated with a noisy biological oscillator, and demonstrate a general strategy for bifurcation analysis based on observations of any noisy system.

Control of a hair bundle's mechanosensory function by its mechanical load.

Hair cells, the sensory receptors of the internal ear, subserve different functions in various receptor organs: they detect oscillatory stimuli in the auditory system, but transduce constant and step stimuli in the vestibular and lateral-line systems. We show that a hair cell's function can be controlled experimentally by adjusting its mechanical load. By making bundles from a single organ operate as any of four distinct types of signal detector, we demonstrate that altering only a few key parameters can fundamentally change a sensory cell's role. The motions of a single hair bundle can resemble those of a bundle from the amphibian vestibular system, the reptilian auditory system, or the mammalian auditory system, demonstrating an essential similarity of bundles across species and receptor organs.

Effects of cochlear loading on the motility of active outer hair cells.

Outer hair cells (OHCs) power the amplification of sound-induced vibrations in the mammalian inner ear through an active process that involves hair-bundle motility and somatic motility. It is unclear, though, how either mechanism can be effective at high frequencies, especially when OHCs are mechanically loaded by other structures in the cochlea. We address this issue by developing a model of an active OHC on the basis of observations from isolated cells, then we use the model to predict the response of an active OHC in the intact cochlea. We find that active hair-bundle motility amplifies the receptor potential that drives somatic motility. Inertial loading of a hair bundle by the tectorial membrane reduces the bundle's reactive load, allowing the OHC's active motility to influence the motion of the cochlear partition. The system exhibits enhanced sensitivity and tuning only when it operates near a dynamical instability, a Hopf bifurcation. This analysis clarifies the roles of cochlear structures and shows how the two mechanisms of motility function synergistically to create the cochlear amplifier. The results suggest that somatic motility evolved to enhance a preexisting amplifier based on active hair-bundle motility, thus allowing mammals to hear high-frequency sounds.

Comparison of nonlinear mammalian cochlear-partition models.

Various simple mathematical models of the dynamics of the organ of Corti in the mammalian cochlea are analyzed and their dynamics compared. The specific models considered are phenomenological Hopf and cusp normal forms, a recently proposed description combining active hair-bundle motility and somatic motility, a reduction thereof, and finally a model highlighting the importance of the coupling between the nonlinear transduction current and somatic motility. It is found that for certain models precise tuning to any bifurcation is not necessary and that a compressively nonlinear response over a range similar to experimental observations and that the normal form of the Hopf bifurcation is not the only description that reproduces compression and tuning similar to experiment.

Frequency-selective exocytosis by ribbon synapses of hair cells in the bullfrog's amphibian papilla.

The activity of auditory afferent fibers depends strongly on the frequency of stimulation. Although the bullfrog's amphibian papilla lacks the flexible basilar membrane that effects tuning in mammals, its afferents display comparable frequency selectivity. Seeking additional mechanisms of tuning in this organ, we monitored the synaptic output of hair cells by measuring changes in their membrane capacitance during sinusoidal electrical stimulation at various frequencies. Using perforated-patch recordings, we found that individual hair cells displayed frequency selectivity in synaptic exocytosis within the frequency range sensed by the amphibian papilla. Moreover, each cell's tuning varied in accordance with its tonotopic position. Using confocal imaging, we observed a tonotopic gradient in the concentration of proteinaceous Ca(2+) buffers. A model for synaptic release suggests that this gradient maintains the sharpness of tuning. We conclude that hair cells of the amphibian papilla use synaptic tuning as an additional mechanism for sharpening their frequency selectivity.

The diverse effects of mechanical loading on active hair bundles.

Hair cells in the auditory, vestibular, and lateral-line systems of vertebrates receive inputs through a remarkable variety of accessory structures that impose complex mechanical loads on the mechanoreceptive hair bundles. Although the physiological and morphological properties of the hair bundles in each organ are specialized for detecting the relevant inputs, we propose that the mechanical load on the bundles also adjusts their responsiveness to external signals. We use a parsimonious description of active hair-bundle motility to show how the mechanical environment can regulate a bundle's innate behavior and response to input. We find that an unloaded hair bundle can behave very differently from one subjected to a mechanical load. Depending on how it is loaded, a hair bundle can function as a switch, active oscillator, quiescent resonator, or low-pass filter. Moreover, a bundle displays a sharply tuned, nonlinear, and sensitive response for some loading conditions and an untuned or weakly tuned, linear, and insensitive response under other circumstances. Our simple characterization of active hair-bundle motility explains qualitatively most of the observed features of bundle motion from different organs and organisms. The predictions stemming from this description provide insight into the operation of hair bundles in a variety of contexts.

A unified model of transcription elongation: what have we learned from single-molecule experiments?

The transcription of the genetic information encoded in DNA into RNA is performed by RNA polymerase (RNAP), a complex molecular motor, highly conserved across species. Despite remarkable progress in single-molecule techniques revealing important mechanistic details of transcription elongation (TE) with up to base-pair resolution, some of the results and interpretations of these studies are difficult to reconcile, and have not yet led to a minimal unified picture of transcription. We propose a simple model that accounts quantitatively for many of the experimental observations. This model belongs to the class of isothermal ratchet models of TE involving the thermally driven stochastic backward and forward motion (backtracking and forward tracking) of RNAP along DNA between single-nucleotide incorporation events. We uncover two essential features for the success of the model. The first is an intermediate state separating the productive elongation pathway from nonelongating backtracked states. The rates of entering and exiting this intermediate state modulate pausing by RNAP. The second crucial ingredient of the model is the cotranscriptional folding of the RNA transcript, sterically inhibiting the extent of backtracking. This model resolves several apparent differences between single-molecule studies and provides a framework for future work on TE.

The interplay between active hair bundle motility and electromotility in the cochlea.

The cochlear amplifier is a nonlinear active process providing the mammalian ear with its extraordinary sensitivity, large dynamic range and sharp frequency tuning. While there is much evidence that amplification results from active force generation by mechanosensory hair cells, there is debate about the cellular processes behind nonlinear amplification. Outer hair cell electromotility has been suggested to underlie the cochlear amplifier. However, it has been shown in frog and turtle that spontaneous movements of hair bundles endow them with a nonlinear response with increased sensitivity that could be the basis of amplification. The present work shows that the properties of the cochlear amplifier could be understood as resulting from the combination of both hair bundle motility and electromotility in an integrated system that couples these processes through the geometric arrangement of hair cells embedded in the cochlear partition. In this scenario, the cochlear partition can become a dynamic oscillator which in the vicinity of a Hopf bifurcation exhibits all the key properties of the cochlear amplifier. The oscillatory behavior and the nonlinearity are provided by active hair bundles. Electromotility is largely linear but produces an additional feedback that allows hair bundle movements to couple to basilar membrane vibrations.

Thermodynamic and kinetic modeling of transcriptional pausing.

We present a statistical mechanics approach for the prediction of backtracked pauses in bacterial transcription elongation derived from structural models of the transcription elongation complex (EC). Our algorithm is based on the thermodynamic stability of the EC along the DNA template calculated from the sequence-dependent free energy of DNA-DNA, DNA-RNA, and RNA-RNA base pairing associated with (i) the translocational and size fluctuations of the transcription bubble; (ii) changes in the associated DNA-RNA hybrid; and (iii) changes in the cotranscriptional RNA secondary structure upstream of the RNA exit channel. The calculations involve no adjustable parameters except for a cutoff used to discriminate paused from nonpaused complexes. When applied to 100 experimental pauses in transcription elongation by Escherichia coli RNA polymerase on 10 DNA templates, the approach produces statistically significant results. We also present a kinetic model for the rate of recovery of backtracked paused complexes. A crucial ingredient of our model is the incorporation of kinetic barriers to backtracking resulting from steric clashes of EC with the cotranscriptionally generated RNA secondary structure, an aspect not included explicitly in previous attempts at modeling the transcription elongation process.