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

Barral, Jérémie; Dierkes, Kai; Lindner, Benjamin; Jülicher, Frank; Martin, Pascal

doi:10.1073/pnas.0913657107

Cited by 42 publications

(43 citation statements)

References 38 publications

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“…We obtain a quality factor Q=38±16.7 of flagellar oscillations. Values estimated in other cytoskeletal oscillators are Q=2.2±1.0 (N ≈2500) for spontaneous hair bundle oscillations [36], and Q=1.4±1.1 (N =10−100) for an in-vitro acto-myosin system [16]. We find that the strength of flagellar phase fluctuations is several ordersof-magnitudes above the level corresponding to thermal noise, highlighting the active origin of flagellar fluctuations.…”

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confidence: 70%

Active Phase and Amplitude Fluctuations of Flagellar Beating

et al. 2014

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The eukaryotic flagellum beats periodically, driven by the oscillatory dynamics of molecular motors, to propel cells and pump fluids. Small, but perceivable fluctuations in the beat of individual flagella have physiological implications for synchronization in collections of flagella as well as for hydrodynamic interactions between flagellated swimmers. Here, we characterize phase and amplitude fluctuations of flagellar bending waves using shape mode analysis and limit-cycle reconstruction.We report a quality factor of flagellar oscillations, Q = 38.0 ± 16.7 (mean±s.e.). Our analysis shows that flagellar fluctuations are dominantly of active origin. Using a minimal model of collective motor oscillations, we demonstrate how the stochastic dynamics of individual motors can give rise to active small-number fluctuations in motor-cytoskeleton systems. Here, we report direct measurements of phase and amplitude fluctuations of the flagellar beat and discuss the microscopic origin of active flagellar fluctuations using a minimal model. We further illustrate the impact of flagellar fluctuations on swimming and synchronization. Our analysis contributes to a recent interest in driven, outof-equilibrium systems and their fluctuation fingerprint [15][16][17][18] by characterizing noisy limit-cycle dynamics in an ubiquitous motility system, the flagellum.Flagellar shape analysis. We characterize flagellar beat patterns as superposition of principal shape modes. This dimensionality reduction is key to our fluctuation analysis. We analyze planar beat patterns of bull sperm swimming close to a boundary surface [19], filmed at 250 frames-per-second (corresponding to about 8 frames per beat cycle). The flagellar centerline r(s, t), tracked as function of arclength position s and time t, can be expressed with respect to a material frame of the sperm head in terms of a tangent angle ψ(s, t)Here, r h (t) denotes the sperm head center, and e 1 and e 2 are ortho-normal vectors with e 1 pointing along the long head axis, see Fig. 1A. A space-timeplot of ψ(s, t) reveals the periodicity of the flagellar beat, see Fig. 1B. This high-dimensional data set can be projected on a low dimensional 'shape space' using shape mode analysis based on principal component analysis [20]. The time-averaged tangent angle ψ 0 (s)= n i=1 ψ(s, t i )/n characterizes the mean shape of the beating flagellum (n=1024 frames in each movie). We further define a two-point correlation matrix arXiv:1401.7036v2 [q-bio.CB]

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Active Phase and Amplitude Fluctuations of Flagellar Beating

et al. 2014

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“…It is noteworthy, however, that mechanical coupling between hair bundles, such as occurs through accessory structures such as tectorial and otolithic membranes (Strimbu et al 2009), increases the phase coherence of spontaneous hairbundle oscillations, extends the range of the compressive nonlinearity to smaller stimuli, sharpens the frequency selectivity, and enhances the amplification that a noisy oscillator can provide (Barral et al 2010;Dierkes et al 2008).…”

Section: Power-law Scaling Of Auditory Responsesmentioning

confidence: 99%

“…However, the waveform of the traveling wave-and especially the shape of its peak-is determined primarily by the characteristics of the local active process. Each oscillator is expected to recruit up to several tens of neighboring outer hair cells that are mechanically coupled by the tectorial membrane (Barral et al 2010). The position at which the traveling wave peaks is set by the intrinsic frequency of the critical oscillators that actively resonate at the frequency of the wave.…”

Section: Critical Oscillators and The Cochlear Traveling Wavementioning

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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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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“…Bi-directional coupling has been shown to have the potential to reduce the detrimental effects of noise [10,14,15], as evidenced, for example, by an increase of the regularity of the oscillatory behavior.…”

Section: Introductionmentioning

confidence: 99%

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

Cited by 42 publications

References 38 publications

Active Phase and Amplitude Fluctuations of Flagellar Beating

Active Phase and Amplitude Fluctuations of Flagellar Beating

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

A mean-field approach to elastically coupled hair bundles

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