Amphibian sacculus and the forced Kuramoto model with intrinsic noise and frequency dispersion

Ji, Seung; Bozovic, Dolores; Bruinsma, Robijn

doi:10.1103/physreve.97.042411

Cited by 12 publications

(10 citation statements)

References 37 publications

(49 reference statements)

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“…This regime shows a greatly enhanced signal/noise ratio in response to a driving force, making it an attractive alternative mechanism that the auditory system may utilize to achieve sensitivity in the presence of noise. Furthermore, coupling of unstable oscillators with a small difference in their characteristic frequencies reduces the effective noise level, resulting in more coherent autonomous oscillations as well as the enhanced quality factor in their response to a sinusoidal driving force ( 18 , 24 , 25 , 26 ). This has been experimentally demonstrated in a system of a small number of spontaneously oscillating hair bundles in a chemical environment that approximates the physiological conditions ( 27 , 28 ).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Mechanically Coupled Hair-Cell Bundles of the Inner Ear

Roongthumskul

Faber

Bozovic

2021

Biophysical Journal

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The high sensitivity and effective frequency discrimination of sound detection performed by the auditory system rely on the dynamics of a system of hair cells. In the inner ear, these acoustic receptors are primarily attached to an overlying structure that provides mechanical coupling between the hair bundles. Although the dynamics of individual hair bundles has been extensively investigated, the influence of mechanical coupling on the motility of the system of bundles remains underdetermined. We developed a technique of mechanically coupling two active hair bundles, enabling us to probe the dynamics of the coupled system experimentally. We demonstrated that the coupling could enhance the coherence of hair bundles’ spontaneous oscillation, as well as their phase-locked response to sinusoidal stimuli, at the calcium concentration in the surrounding fluid near the physiological level. The empirical data were consistent with numerical results from a model of two coupled nonisochronous oscillators, each displaying a supercritical Hopf bifurcation. The model revealed that a weak coupling can poise the system of unstable oscillators closer to the bifurcation by a shift in the critical point. In addition, the dynamics of strongly coupled oscillators far from criticality suggested that individual hair bundles may be regarded as nonisochronous oscillators. An optimal degree of nonisochronicity was required for the observed tuning behavior in the coherence of autonomous motion of the coupled system.

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Section: Introductionmentioning

confidence: 99%

Dynamics of Mechanically Coupled Hair-Cell Bundles of the Inner Ear

Roongthumskul

Faber

Bozovic

2021

Biophysical Journal

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“…Most fishes can only detect sounds below 0.74 kHz ( Popper and Fay, 1997 ). In some species of frogs, F max values are nearly five times higher than that of fish ( Ji et al, 2018 ). F max tends to increase phylogenetically from fish to amphibians and mammals.…”

Section: Introductionmentioning

confidence: 99%

Functional Parameters of Prestin Are Not Correlated With the Best Hearing Frequency

Wang

et al. 2021

Front. Cell Dev. Biol.

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Among the vertebrate lineages with different hearing frequency ranges, humans lie between the low-frequency hearing (1 kHz) of fish and amphibians and the high-frequency hearing (100 kHz) of bats and dolphins. Little is known about the mechanism underlying such a striking difference in the limits of hearing frequency. Prestin, responsible for cochlear amplification and frequency selectivity in mammals, seems to be the only candidate to date. Mammalian prestin is densely expressed in the lateral plasma membrane of the outer hair cells (OHCs) and functions as a voltage-dependent motor protein. To explore the molecular basis for the contribution of prestin in hearing frequency detection, we collected audiogram data from humans, dogs, gerbils, bats, and dolphins because their average hearing frequency rises in steps. We generated stable cell lines transfected with human, dog, gerbil, bat, and dolphin prestins (hPres, dPres, gPres, bPres, and nPres, respectively). The non-linear capacitance (NLC) of different prestins was measured using a whole-cell patch clamp. We found that the Qmax/Clin of bPres and nPres was significantly higher than that of humans. The V1/2 of hPres was more hyperpolarized than that of nPres. The z values of hPres and bPres were higher than that of nPres. We further analyzed the relationship between the high-frequency hearing limit (Fmax) and the functional parameters (V1/2, z, and Qmax/Clin) of NLC among five prestins. Interestingly, no significant correlation was found between the functional parameters and Fmax. Additionally, a comparative study showed that the amino acid sequences and tertiary structures of five prestins were quite similar. There might be a common fundamental mechanism driving the function of prestins. These findings call for a reconsideration of the leading role of prestin in hearing frequency perception. Other intriguing kinetics underlying the hearing frequency response of auditory organs might exist.

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“…As the most common state in the absence of external excitation, there may be many types of steady state, and their responses to external excitation may exhibit diversityBenser et al (1996). The nonlinear dynamics of spontaneous oscillations and different steady states are helpful to understand the important roles of oscillations and steady states of hair bundles in the auditory function, which is a very important research topic , Ji et al (2018), Sheth et al (2018).…”

Section: Introductionmentioning

confidence: 99%

“…In other studies Bozovic (2019, the spontaneous oscillations near saddle-node bifurcation of an invariant circle (SNIC) have also been suggested. The frequency selection of spontaneous oscillations and the ability to amplify weak signals are closely related to the SNIC bifurcation Bozovic (2019), Ji et al (2018). Although the dynamical mechanism for the spontaneous oscillations has been reported from the perspective of mainly Hopf as well as SNIC bifurcation Salvi et al (2015), Maoile ´idigh and D, Nicola EM, Hudspeth AJ, (2012), the relationship between the spontaneous oscillations and other codimension-1 bifurcations and especially the codimension-2 bifurcations modulated by the parameter D and S, i.e.…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics of hair bundle of auditory nervous system (I): spontaneous oscillations and two cases of steady states

Cao

2021

Cogn Neurodyn

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The hair bundles of inner hair cells in the auditory nervous exhibit spontaneous oscillations, which is the prerequisite for an important auditory function to enhance the sensitivity of inner ear to weak sounds, otoacoustic emission. In the present paper, the dynamics of spontaneous oscillations and relationships to steady state are acquired in a two-dimensional model with fast variable X (displacement of hair bundles) and slow variable X a . The spontaneous oscillations are derived from negative stiffness modulated by two biological factors (S and D) and are identified to appear in multiple two-dimensional parameter planes. In (S, D) plane, comprehensive bifurcations including 4 types of codimension-2 bifurcation and 5 types of codimension-1 bifurcation related to the spontaneous oscillations are acquired. The spontaneous oscillations are surrounded by supercritical and subcritical Hopf bifurcation curves, and outside of the curves are two cases of steady state. Case-1 and Case-2 steady states exhibit Z-shaped (coexistence of X) and N-shaped (coexistence of X a ) X-nullclines, respectively. In (S, D) plane, left and right to the spontaneous oscillations are two subcases of Case-1, which exhibit the stable equilibrium point locating on the upper and lower branches of X-nullcline, respectively, resembling that of the neuron. Lower to the spontaneous oscillations are 3 subcases of Case-2 from left to right, which manifest stable equilibrium point locating on left, middle, and right branches of X-nullcline, respectively, differing from that of the neuron. The phase plane for steady state is divided into four parts by nullclines, which manifest different vector fields. The phase trajectory of transient behavior beginning from a phase point in the four regions to the stable equilibrium point exhibits different dynamics determined by the vector fields, which is the basis to identify dynamical mechanism of complex forced oscillations induced by external signal. The results present comprehensive viewpoint and deep understanding for dynamics of the spontaneous oscillations and steady states of hair bundles, which can be used to well explain the experimental observations and to modulate functions of spontaneous oscillations.

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Amphibian sacculus and the forced Kuramoto model with intrinsic noise and frequency dispersion

Cited by 12 publications

References 37 publications

Dynamics of Mechanically Coupled Hair-Cell Bundles of the Inner Ear

Dynamics of Mechanically Coupled Hair-Cell Bundles of the Inner Ear

Functional Parameters of Prestin Are Not Correlated With the Best Hearing Frequency

Complex dynamics of hair bundle of auditory nervous system (I): spontaneous oscillations and two cases of steady states

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