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

Vestibular Drop Attacks and Meniere's Disease as Results of Otolithic Membrane Damage-A Numerical Model

Meniere's disease (MD) is a condition of the inner ear with symptoms affecting both vestibular and hearing functions. Some patients with MD experience vestibular drop attacks (VDAs), which are violent falls caused by spurious vestibular signals from the utricle and/or saccule. Recent surgical work has shown that patients who experience VDAs also show disrupted utricular otolithic membranes. The objective of this study is to determine if otolithic membrane damage alone is sufficient to induce spurious vestibular signals, thus potentially eliciting VDAs and the vestibular dysfunction seen in patients with MD. We use a previously developed numerical model to describe the nonlinear dynamics of an array of active, elastically coupled hair cells. We then reduce the coupling strength of a selected region of the membrane to model the effects of tissue damage. As we reduce the coupling strength, we observe large and abrupt spikes in hair bundle position. As bundle displacements from the equilibrium position have been shown to lead to depolarization of the hair-cell soma and hence trigger neural activity, this spontaneous activity could elicit false detection of a vestibular signal. The results of this numerical model suggest that otolithic membrane damage alone may be sufficient to induce VDAs and the vestibular dysfunction seen in patients with MD. Future experimental work is needed to confirm these results in vitro.

Complex dynamics of hair bundle of auditory nervous system (II): forced oscillations related to two cases of steady state

The forced oscillations of hair bundle of inner hair cells of auditory nervous system evoked by external force from steady state are related to the fast adaption of hair cells, which are very important for auditory amplification. In the present paper, comprehensive and deep understandings to nonlinear dynamics of forced oscillations are acquired in four aspects. Firstly, the complex dynamics underlying the twitch (fast recoil of displacement X which is fast variable) induced from Case-1 and Case-2 steady states by external pulse force are obtained. With help of vector fields and nullclines, the phase trajectory of forced oscillations is identified to be an evolution process between two equilibrium points corresponding to zero force and pulse force, respectively, and then the twitch is obtained as the behavior running along the nonlinear part of X-nullcline. Especially, twitch observed in experiment are classified into 6 types, which are induced by negative change of force, negative and positive changes of force, and positive change of force, respectively, and further build relationships to three subcases of Case-2 steady state with N-shaped X-nullcline (equilibrium point locates on the left, middle, and right branches of X-nullcline, respectively). Secondly, the experimental observation of fatigue of twitch induced by continual two pulse forces, i.e. the reduced amplitude of the latter twitch when interval between two forces is short, is also explained as a nonlinear behavior beginning from an initial value different from that of the former one. Thirdly, the experimental observation of transition between sustained oscillations and steady state induced by pulse force can be simulated for Case-1 steady state with Z-shaped X-nullcline instead of Case-2, due to that there exists bifurcations with respect to external force for Case-1 while no bifurcations for Case-2. Last, the threshold phenomenon induced by simple pulse stimulation exists for Case-1 steady state rather than Case-2, due to that the upper and lower branches of Z-shaped X-nullcline close to the middle branch exhibit coexisting behaviors of variable X while N-shaped X-nullcline does not. The nonlinear dynamics of forced oscillations are helpful for explanations to the complex experimental observations, which presents potential measures to modulate the functions of twitch such as the fast adaption.

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

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.

Chimera states and frequency clustering in systems of coupled inner-ear hair cells

Coupled hair cells of the auditory and vestibular systems perform the crucial task of converting the energy of sound waves and ground-borne vibrations into ionic currents. We mechanically couple groups of living, active hair cells with artificial membranes, thus mimicking in vitro the coupled dynamical system. We identify chimera states and frequency clustering in the dynamics of these coupled nonlinear, autonomous oscillators. We find that these dynamical states can be reproduced by our numerical model with heterogeneity of the parameters. Furthermore, we find that this model is most sensitive to external signals when poised at the onset of synchronization, where chimera and cluster states are likely to form. We, therefore, propose that the partial synchronization in our experimental system is a manifestation of a system poised at the verge of synchronization with optimal sensitivity.

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

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 Q_max/C_lin of bPres and nPres was significantly higher than that of humans. The V_1/2 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 (F_max) and the functional parameters (V_1/2, z, and Q_max/C_lin) of NLC among five prestins. Interestingly, no significant correlation was found between the functional parameters and F_max. 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.

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

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.

An In Vitro Study on Prestin Analog Gene in the Bullfrog Hearing Organs

The prestin-based active process in the mammalian outer hair cells (OHCs) is believed to play a crucial role in auditory signal amplification in the cochlea. Prestin belongs to an anion transporter family (SLC26A). It is densely expressed in the OHC lateral plasma membrane and functions as a voltage-dependent motor protein. Analog genes can be found in the genome of nonmammalian species, but their functions in hearing are poorly understood. In the present study, we used the gerbil prestin sequence as a template and identified an analog gene in the bullfrog genome. We expressed the gene in a stable cell line (HEK293T) and performed patch-clamp recording. We found that these cells exhibited prominent nonlinear capacitance (NLC), a widely accepted assay for prestin functioning as a motor protein. Upon close examination, the key parameters of this NLC are comparable to that conferred by the gerbil prestin, and nontransfected cells failed to display NLC. Lastly, we performed patch-clamp recording in HCs of all three hearing organs in bullfrog. HCs in both the sacculus and the amphibian papilla exhibited a capacitance profile that is similar to NLC while HCs in the basilar papilla showed no sign of NLC. Whether or not this NLC-like capacitance change is involved in auditory signal amplification certainly requires further examination; our results represent the first and necessary step in revealing possible roles of prestin in the active hearing processes found in many nonmammalian species.

Optimal global synchronization of partially forced Kuramoto oscillators

We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and introduce an effective two-dimensional description for the problem. From the dimensionally reduced model, we obtain analytical predictions for some critical parameters necessary for the onset of a globally synchronized state in the system. Moreover, the low dimensional model also allows us to introduce an optimization scheme for the problem. Our main conclusion, which has been corroborated by exhaustive numerical simulations, is that for a given large random network of Kuramoto oscillators, with random natural frequencies ω_i, such that a fraction of them is subject to an external periodic force with frequency Ω, the best global synchronization properties correspond to the case where the fraction of the forced oscillators is chosen to be those ones such that |ω_i-Ω| is maximal. Our results might shed some light on the structure and evolution of natural systems for which the presence or the absence of global synchronization is a desired property. Some properties of the optimal forced networks and their relation to recent results in the literature are also discussed.