Effects of cochlear loading on the motility of active outer hair cells Dáibhid Ó Maoiléidigha,b and A. J. Hudspetha,b,1 aHoward Hughes Medical Institute and bLaboratory of Sensory Neuroscience, The Rockefeller University, New York, NY 10065 Contributed by A. J. Hudspeth, February 21, 2013 (sent for review December 13, 2012) Outer hair cells (OHCs) power the amplification of sound-induced in experiments (11), the organ of Corti and associated structures in vibrations in the mammalian inner ear through an active process that contact with each OHC might likewise limit the response rate in an involves hair-bundle motility and somatic motility. It is unclear, intact cochlea (12). though, how either mechanism can be effective at high frequencies, Somatic motility, also known as electromotility, is the capacity of especially when OHCs are mechanically loaded by other structures in OHCs to alter the length of their cell bodies in response to a change the cochlea. We address this issue by developing a model of an active in membrane potential (13). These length changes are as great as OHC on the basis of observations from isolated cells, then we use the 5% in isolated cells, operate to frequencies exceeding 80 kHz, and model to predict the response of an active OHC in the intact cochlea. are required for sensitive hearing (14, 15). The extent of somatic We find that active hair-bundle motility amplifies the receptor po- motility in the cochlea is limited, however, by the mechanical load tential that drives somatic motility. Inertial loading of a hair bundle by imposed by surrounding structures (16). Furthermore, the receptor the tectorial membrane reduces the bundle’s reactive load, allowing potential that drives electromotility suffers severe attenuation at the OHC’s active motility to influence the motion of the cochlear high frequencies by the resistance and capacitance of the OHC’s partition. The system exhibits enhanced sensitivity and tuning only membrane, an issue known as the RC time-constant problem (14, when it operates near a dynamical instability, a Hopf bifurcation. This 17). It therefore remains unclear how somatic motility can augment analysis clarifies the roles of cochlear structures and shows how the the motion of the cochlea at high frequencies. two mechanisms of motility function synergistically to create the co- Although models have been developed to incorporate both chlear amplifier. The results suggest that somatic motility evolved to types of motility (18–21), their complexity obfuscates how an ac- enhance a preexisting amplifier based on active hair-bundle motility, tive OHC can influence the motion of structures that are much thus allowing mammals to hear high-frequency sounds. stiffer, more damped, and more massive than the cell itself. In this paper, we attempt to bridge this gap by using experimental data to adaptation | electromotility | hearing | nonlinear dynamics construct a simple model OHC with physiologically realistic properties for a high-frequency location in the cochlea. We then ur ears are amazing signal detectors that reconcile great use the model to examine the effects of coupling an active OHC to Osensitivity with an enormous dynamic range. The faintest structures with the mass, damping, and stiffness found in the sounds that we can hear vibrate our eardrums by less than 1 pm actual cochlea. and are a trillion times less intense than the loudest sounds that To distinguish the effects of hair-bundle motility from those of we can tolerate (1, 2). We can distinguish pure tones that differ somatic motility we hold the apical surface of the OHC in a fixed in frequency by less than 0.2%, yet the frequency range of our position and consider each form of motility separately before ears exceeds a thousandfold (2). These features are all the more analyzing how these processes interact with one another to am- remarkable given that the mechanoreceptive organ of Corti plify the motion of the cochlear partition. Because the apex of the operates in liquid and is therefore highly damped (3). OHC is prevented from moving in this model, the hair bundle An active process enhances the performance of the mammalian cannot apply forces on the basilar membrane. Nonetheless, we ear by augmenting sound-induced vibrations in the cochlea (2–6). find that active hair-bundle motility amplifies the transduction This process results from the action of specialized outer hair cells current and can thus influence the basilar membrane by enhanc- (OHCs) whose motility boosts the motion of the cochlea in response ing the receptor potential that drives somatic motility. to sounds, thus amplifying the signal transmitted to the brain. These cells counteract the damping that would otherwise limit the co- Results chlea’s sensitivity and frequency discrimination (3, 7). OHCs exhibit Active Hair-Bundle Motility. The hair bundle comprises dozens to two forms of mechanical activity, hair-bundle motility and somatic hundreds of actin-packed tubular processes, the stereocilia, that motility, which may both contribute to the cochlear amplifier. protrude from a hair cell’s apex (9) (Fig. 1A). Each stereocilium is Named for the mechanosensitive hair bundles protruding from connected to its tallest neighbor by a proteinaceous tip link at their apices, hair cells transduce vibrations of their bundles into an whose lower end are thought to lie two mechanoelectrical-trans- electrical response. Cochlear hair cells are housed in the cochlear duction channels (Fig. 1B) (22). Increased tension in the tip link as partition, which includes the organ of Corti sandwiched between the a result of hair-bundle deflection promotes opening of these tectorial and basilar membranes (Fig. 1A). The hair bundle of each channels and thus initiates a transduction current. + OHC is connected at its tip to the acellular tectorial membrane, and Active hair-bundle motility stems from a Ca2 -dependent ad- the soma of each OHC is linked to the basilar membrane through aptation process that alters the channel’s open probability during a rigid Deiters’ cell (8). These membranes mechanically load each bundle displacement (9). Adaptation manifests itself most clearly OHC with mass, damping, and stiffness. Hair bundles produce a variety of active movements including spontaneous oscillations (9). The significance of active hair-bundle Author contributions: D.Ó M. and A.J.H. designed research; D.Ó M. performed research; motility in mammals is uncertain, however: Hair bundles do not D.Ó M. analyzed data; and D.Ó M. and A.J.H. wrote the paper. seem to be well positioned to apply forces that amplify the The authors declare no conflict of interest. movements of the basilar membrane (5, 10). Moreover, only low- Freely available online through the PNAS open access option. frequency spontaneous oscillations have been observed in non- 1To whom correspondence should be addressed. E-mail: [email protected]. mammals. Finally, inasmuch as the mechanical properties of ex- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. perimental probes restrict the speed at which hair bundles respond 1073/pnas.1302911110/-/DCSupplemental. 5474–5479 | PNAS | April 2, 2013 | vol. 110 | no. 14 www.pnas.org/cgi/doi/10.1073/pnas.1302911110 Downloaded by guest on October 1, 2021 A B C The machinery for fast adaptation must be in close proximity to K the transduction channels so that the speed of adaptation is not tm 2+ 0.2 unduly limited by the diffusion of Ca (23). We accordingly in- mtm λ 0.3 troduce a model for fast adaptation at the base of each tip link, the tm Tip link 0.4 probable location of the transduction channels (22). The model X Current (nA) hb accords with the observation that the membrane of a stereociliary 0.6 tip is sometimes observed to bulge outward, or “tent,” at the site of 0.4 the tip link’s insertion (24), which may reflect the extension of an Channel 0.2 intracellular element in series with the tip link (Fig. 1B). We X 0.0 ohc Hair-bundle propose that each channel is anchored to the stereociliary cyto- Zohc displacement skeleton by a viscoelastic connection whose stiffness decreases Adaptation 1.0 2+ spring dynamically as the local Ca concentration grows. An influx of 0.8 2+ 0.6 Ca thus causes the channel to reclose as the adaptation spring m 0.4 extends owing to its increased compliance. This mechanism could bm 0.2 Fiber-base easily be quick enough to account for fast adaptation. λ 0.0 displacement X Kbm bm The hair-bundle displacement hb and the adaptation-spring 0 5 10 15 X Time (ms) extension a are described by two nonlinear, coupled differential DE equations (SI Appendix, section 1). The activity of the bundle 1 fl 10 1.0 re ects the force in the adaptation springs, 4, 5 4 0 K ð − αP ÞðX − X Þ; [1] 10 0.8 a 1 o a r 1 5 in which K is the springs’ maximal stiffness and X is their refer- −1 0.6 a r 10 3 ence length. If the adaptation springs lie sufficiently close to the 2 + α 2 −2 transduction channels then the local Ca concentration is pro- 10 0.4 portional to the channels’ open probability Po (23); α is then the dimensionless sensitivity of channel opening. The hair bundle’s −3 2-5 10 0.2 1 Hair-bundle displacement (nm) activity is maintained by three energy sources: the endocochlear + potential, the OHC’s resting potential, and the Ca2 gradient −4 10 0 SI Appendix 0.1 1 10 100 200 250 300 350 400 across the stereociliary membrane ( , section 2). Be- μ -1 K α Frequency (kHz) Ka ( Nm ) cause these sources of energy determine a and , altering either of these two parameter values adjusts the level of bundle activity.