Synchronization of Spontaneous Active Motility of Hair Cell Bundles

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.

Fast adaptation of cooperative channels engenders Hopf bifurcations in auditory hair cells

Since the pioneering work of Thomas Gold, published in 1948, it has been known that we owe our sensitive sense of hearing to a process in the inner ear that can amplify incident sounds on a cycle-by-cycle basis. Called the active process, it uses energy to counteract the viscous dissipation associated with sound-evoked vibrations of the ear's mechanotransduction apparatus. Despite its importance, the mechanism of the active process and the proximate source of energy that powers it have remained elusive, especially at the high frequencies characteristic of amniote hearing. This is partly due to our insufficient understanding of the mechanotransduction process in hair cells, the sensory receptors and amplifiers of the inner ear. It has been proposed previously that cyclical binding of Ca2+ ions to individual mechanotransduction channels could power the active process. That model, however, relied on tailored reaction rates that structurally forced the direction of the cycle. Here we ground our study on our previous model of hair-cell mechanotransduction, which relied on cooperative gating of pairs of channels, and incorporate into it the cyclical binding of Ca2+ ions. With a single binding site per channel and reaction rates drawn from thermodynamic principles, the current model shows that hair cells behave as nonlinear oscillators that exhibit Hopf bifurcations, dynamical instabilities long understood to be signatures of the active process. Using realistic parameter values, we find bifurcations at frequencies in the kilohertz range with physiological Ca2+ concentrations. The current model relies on the electrochemical gradient of Ca2+ as the only energy source for the active process and on the relative motion of cooperative channels within the stereociliary membrane as the sole mechanical driver. Equipped with these two mechanisms, a hair bundle proves capable of operating at frequencies in the kilohertz range, characteristic of amniote hearing.

Intermodulation distortions from an array of active nonlinear oscillators

Coupling is critical in nonlinear dynamical systems. It affects the stabilities of individual oscillators as well as the characteristics of their response to external forces. In the auditory system, the mechanical coupling between sensory hair cells has been proposed as a mechanism that enhances the inner ear's sensitivity and frequency discrimination. While extensive studies investigate the effects of coupling on the detection of a sinusoidal signal, the role of coupling underlying the response to a complex tone remains elusive. In this study, we measured the acoustic intermodulation distortions (IMDs) produced by the inner ears of two frog species stimulated simultaneously by two pure tones. The distortion intensity level displayed multiple peaks across stimulus frequencies, in contrast to the generic response from a single nonlinear oscillator. The multiple-peaked pattern was altered upon varying the stimulus intensity or an application of a perturbation tone near the distortion frequency. Numerical results of IMDs from a chain of coupled active nonlinear oscillators driven by two sinusoidal forces reveal the effects of coupling on the variation profile of the distortion amplitude. When the multiple-peaked pattern is observed, the chain's motion at the distortion frequency displays both a progressive wave and a standing wave. The latter arises due to coupling and is responsible for the multiple-peaked pattern. Our results illustrate the significance of mechanical coupling between active hair cells in the generation of auditory distortions, as a mechanism underlying the formation of in vivo standing waves of distortion signals.

One-carbon metabolism and global DNA methylation in mothers of individuals with Down syndrome

Down syndrome (DS) is the most common chromosomal disorder, resulting from the failure of normal chromosome 21 segregation. Studies have suggested that impairments within the one-carbon metabolic pathway can be of relevance for the global genome instability observed in mothers of individuals with DS. Based on the association between global DNA hypomethylation, genome instability, and impairments within the one-carbon metabolic pathway, the present study aimed to identify possible predictors, within the one-carbon metabolism, of global DNA methylation, measured by methylation patterns of LINE-1 and Alu repetitive sequences, in mothers of individuals with DS and mothers of individuals without the syndrome. In addition, we investigated one-carbon genetic polymorphisms and metabolites as maternal predisposing factors for the occurrence of trisomy 21 in children. Eighty-three samples of mothers of children with DS with karyotypically confirmed free trisomy 21 (case group) and 84 of mothers who had at least one child without DS or any other aneuploidy were included in the study. Pyrosequencing assays were performed to access global methylation. The results showed that group affiliation (case or control), betaine-homocysteine methyltransferase (BHMT) G742A and transcobalamin 2 (TCN2) C776G polymorphisms, and folate concentration were identified as predictors of global Alu DNA methylation values. In addition, thymidylate synthase (TYMS) 28-bp repeats 2R/3R or 3R/3R genotypes are independent maternal predisposing factors for having a child with DS. This study adds evidence that supports the association of impairments in the one-carbon metabolism, global DNA methylation, and the possibility of having a child with DS.

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.

Spontaneous Otoacoustic Emissions in TectaY1870C/+ Mice Reflect Changes in Cochlear Amplification and How It Is Controlled by the Tectorial Membrane

Spontaneous otoacoustic emissions (SOAEs) recorded from the ear canal in the absence of sound reflect cochlear amplification, an outer hair cell (OHC) process required for the extraordinary sensitivity and frequency selectivity of mammalian hearing. Although wild-type mice rarely emit, those with mutations that influence the tectorial membrane (TM) show an incidence of SOAEs similar to that in humans. In this report, we characterized mice with a missense mutation in Tecta, a gene required for the formation of the striated-sheet matrix within the core of the TM. Mice heterozygous for the Y1870C mutation (Tecta^Y1870C/+) are prolific emitters, despite a moderate hearing loss. Additionally, Kimura’s membrane, into which the OHC stereocilia insert, separates from the main body of the TM, except at apical cochlear locations. Multimodal SOAEs are also observed in Tecta^Y1870C/+ mice where energy is present at frequencies that are integer multiples of a lower-frequency SOAE (the primary). Second-harmonic SOAEs, at twice the frequency of a lower-frequency primary, are the most frequently observed. These secondary SOAEs are found in spatial regions where stimulus-evoked OAEs are small or in the noise floor. Introduction of high-level suppressors just above the primary SOAE frequency reduce or eliminate both primary and second-harmonic SOAEs. In contrast, second-harmonic SOAEs are not affected by suppressors, either above or below the second-harmonic SOAE frequency, even when they are much larger in amplitude. Hence, second-harmonic SOAEs do not appear to be spatially separated from their primaries, a finding that has implications for cochlear mechanics and the consequences of changes to TM structure.

A model for studying the energetics of sustained high frequency firing

Regulating membrane potential and synaptic function contributes significantly to the energetic costs of brain signaling, but the relative costs of action potentials (APs) and synaptic transmission during high-frequency firing are unknown. The continuous high-frequency (200-600Hz) electric organ discharge (EOD) of Eigenmannia, a weakly electric fish, underlies its electrosensing and communication. EODs reflect APs fired by the muscle-derived electrocytes of the electric organ (EO). Cholinergic synapses at the excitable posterior membranes of the elongated electrocytes control AP frequency. Based on whole-fish O₂ consumption, ATP demand per EOD-linked AP increases exponentially with AP frequency. Continual EOD-AP generation implies first, that ion homeostatic processes reliably counteract any dissipation of posterior membrane E_Na and E_K and second that high frequency synaptic activation is reliably supported. Both of these processes require energy. To facilitate an exploration of the expected energy demands of each, we modify a previous excitability model and include synaptic currents able to drive APs at frequencies as high as 600 Hz. Synaptic stimuli are modeled as pulsatile cation conductance changes, with or without a small (sustained) background conductance. Over the full species range of EOD frequencies (200–600 Hz) we calculate frequency-dependent “Na⁺-entry budgets” for an electrocyte AP as a surrogate for required 3Na⁺/2K⁺-ATPase activity. We find that the cost per AP of maintaining constant-amplitude APs increases nonlinearly with frequency, whereas the cost per AP for synaptic input current is essentially constant. This predicts that Na⁺ channel density should correlate positively with EOD frequency, whereas AChR density should be the same across fish. Importantly, calculated costs (inferred from Na⁺-entry through Nav and ACh channels) for electrocyte APs as frequencies rise are much less than expected from published whole-fish EOD-linked O₂ consumption. For APs at increasingly high frequencies, we suggest that EOD-related costs external to electrocytes (including packaging of synaptic transmitter) substantially exceed the direct cost of electrocyte ion homeostasis.