Local Exponents of Nonlinear Compression in Periodically Driven Noisy Oscillators

Lindner, Benjamin; Dierkes, Kai; Jülicher, Frank

doi:10.1103/physrevlett.103.250601

Cited by 44 publications

(75 citation statements)

References 15 publications

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“…Furthermore, also the response of this hair bundle system to external driving matches quantitatively the behavior observed experimentally [23]. We have chosen a set of parameters studied previously [23,30,33] (see table 1), which we will refer to as standard parameters. Unless indicated otherwise, simulations were performed using these standard parameters.…”

Section: Model Of Coupled Hair Bundlesmentioning

confidence: 54%

A mean-field approach to elastically coupled hair bundles

2012

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Abstract.We study the dynamics of oscillatory hair bundles which are coupled elastically in their deflection variable and are subject to noise. We present a stochastic description capturing the dynamics of the hair bundles' mean field. In particular, the presented derivation elucidates the origin of the previously described noise reduction by coupling. By comparison of simulations of the approximate dynamics and the full system, we verify our results. Furthermore, we demonstrate that the specific type of coupling considered implies coupling-induced changes in the dynamics beyond mere noise reduction.

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Section: Model Of Coupled Hair Bundlesmentioning

confidence: 54%

A mean-field approach to elastically coupled hair bundles

2012

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“…The dynamic behavior of a noisy oscillator can still be described by a normal form (Eq. 2) but with an effective contribution to the linear coefficient A that remains finite at the characteristic frequency Lindner et al 2009). A noisy oscillator thus provides amplification with a gain that reaches a maximal value for low stimuli.…”

Section: Power-law Scaling Of Auditory Responsesmentioning

confidence: 99%

A Critique of the Critical Cochlea: Hopf—a Bifurcation—Is Better Than None

Hudspeth

Jülicher

Martin

2010

Journal of Neurophysiology

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126

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Hudspeth AJ, Jülicher F, Martin P. A critique of the critical cochlea: Hopf-a bifurcation-is better than none. J Neurophysiol 104: 1219-1229. First published June 10, 2010 doi:10.1152/jn.00437.2010. The sense of hearing achieves its striking sensitivity, frequency selectivity, and dynamic range through an active process mediated by the inner ear's mechanoreceptive hair cells. Although the active process renders hearing highly nonlinear and produces a wealth of complex behaviors, these various characteristics may be understood as consequences of a simple phenomenon: the Hopf bifurcation. Any critical oscillator operating near this dynamic instability manifests the properties demonstrated for hearing: amplification with a specific form of compressive nonlinearity and frequency tuning whose sharpness depends on the degree of amplification. Critical oscillation also explains spontaneous otoacoustic emissions as well as the spectrum and level dependence of the ear's distortion products. Although this has not been realized, several valuable theories of cochlear function have achieved their success by incorporating critical oscillators.The technical specifications of the human ear are remarkable. We can hear sounds that evoke mechanical vibrations of magnitudes comparable to those produced by thermal noise (de Vries 1948;Sivian and White 1933). Hearing is so sharply tuned to specific frequencies that trained musicians can distinguish tones differing in frequency by only 0.1% (Spiegel and Watson 1984). Finally, our ears can process sounds over a range of amplitudes encompassing six orders of magnitude, which corresponds to a trillionfold range in stimulus power (Knudsen 1923).These striking characteristics of our hearing emerge because the ear is not a passive sensory receptor, but possesses an active process that augments audition in three ways (reviewed in Hudspeth 2008;Manley 2000Manley , 2001. First, amplification renders hearing several hundred times as sensitive as would be expected for a passive system. The active process next exhibits tuning that sharpens our frequency discrimination. Finally, a compressive nonlinearity ensures that inputs spanning an enormous range of sound-pressure levels are systematically encoded by a modest range of mechanical vibrations and in turn of receptor potentials and nerve-fiber firing rates. The active process additionally exhibits the striking epiphenomenon of spontaneous otoacoustic emission, the production of sound by an ear in the absence of external stimulation. Although considerable attention has been devoted to these properties in mammalian and especially human hearing, the four defining features of the active process are equally characteristic of nonmammalian tetrapods (reviewed in Manley 2001).

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“…Why does coupling boost the hair-bundle amplifier? The gain of individual hair bundles is limited by intrinsic fluctuations (18)(19)(20). Coupling resulted in partial synchronization of the noisy oscillators and in an increased regularity of spontaneous oscillatory movements (Fig.…”

Section: Discussionmentioning

confidence: 99%

“…Although active hair-bundle motility provides a plausible component of the active process in vivo, amplification at the scale of a single hair bundle (10) is much less effective than the active process in an intact organ (17). Intrinsic fluctuations destroy the phase coherence of hair-bundle oscillations and limit the gain of the hair-bundle amplifier (18)(19)(20). In vivo, hair bundles are generally mechanically coupled by an overlying gelatinous matrix.…”

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confidence: 99%

Coupling a sensory hair-cell bundle to cyber clones enhances nonlinear amplification

Barral

Dierkes

Lindner

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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The vertebrate ear benefits from nonlinear mechanical amplification to operate over a vast range of sound intensities. The amplificatory process is thought to emerge from active force production by sensory hair cells. The mechano-sensory hair bundle that protrudes from the apical surface of each hair cell can oscillate spontaneously and function as a frequency-selective, nonlinear amplifier. Intrinsic fluctuations, however, jostle the response of a single hair bundle to weak stimuli and seriously limit amplification. Most hair bundles are mechanically coupled by overlying gelatinous structures. Here, we assayed the effects of mechanical coupling on the hair-bundle amplifier by combining dynamic force clamp of a hair bundle from the bullfrog’s saccule with real-time stochastic simulations of hair-bundle mechanics. This setup couples the hair bundle to two virtual hair bundles, called cyber clones, and mimics a situation in which the hair bundle is elastically linked to two neighbors with similar characteristics. We found that coupling increased the coherence of spontaneous hair-bundle oscillations. By effectively reducing noise, the synergic interplay between the hair bundle and its cyber clones also enhanced amplification of sinusoidal stimuli. All observed effects of coupling were in quantitative agreement with simulations. We argue that the auditory amplifier relies on hair-bundle cooperation to overcome intrinsic noise limitations and achieve high sensitivity and sharp frequency selectivity.

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Local Exponents of Nonlinear Compression in Periodically Driven Noisy Oscillators

Cited by 44 publications

References 15 publications

A mean-field approach to elastically coupled hair bundles

A mean-field approach to elastically coupled hair bundles

A Critique of the Critical Cochlea: Hopf—a Bifurcation—Is Better Than None

Coupling a sensory hair-cell bundle to cyber clones enhances nonlinear amplification

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