Kai Dierkes

The remarkable cochlear amplifier

This composite article is intended to give the experts in the field of cochlear mechanics an opportunity to voice their personal opinion on the one mechanism they believe dominates cochlear amplification in mammals. A collection of these ideas are presented here for the auditory community and others interested in the cochlear amplifier. Each expert has given their own personal view on the topic and at the end of their commentary they have suggested several experiments that would be required for the decisive mechanism underlying the cochlear amplifier. These experiments are presently lacking but if successfully performed would have an enormous impact on our understanding of the cochlear amplifier.

Monitoring Actin Cortex Thickness in Live Cells

Animal cell shape is controlled primarily by the actomyosin cortex, a thin cytoskeletal network that lies directly beneath the plasma membrane. The cortex regulates cell morphology by controlling cellular mechanical properties, which are determined by network structure and geometry. In particular, cortex thickness is expected to influence cell mechanics. However, cortex thickness is near the resolution limit of the light microscope, making studies relating cortex thickness and cell shape challenging. To overcome this, we developed an assay to measure cortex thickness in live cells, combining confocal imaging and subresolution image analysis. We labeled the actin cortex and plasma membrane with chromatically different fluorophores and measured the distance between the resulting intensity peaks. Using a theoretical description of cortex geometry and microscopic imaging, we extracted an average cortex thickness of ∼190 nm in mitotic HeLa cells and tested the validity of our assay using cell images generated in silico. We found that thickness increased after experimental treatments preventing F-actin disassembly. Finally, we monitored physiological changes in cortex thickness in real-time during actin cortex regrowth in cellular blebs. Our investigation paves the way to understanding how molecular processes modulate cortex structure, which in turn drives cell morphogenesis.

Enhancement of sensitivity gain and frequency tuning by coupling of active hair bundles

The vertebrate inner ear possesses an active process that provides nonlinear amplification of mechanical stimuli. A candidate for this process is active hair bundle mechanics observed, for instance, for hair cells of the bullfrogs sacculus. Hair bundles in various inner ear organs are coupled by overlying membranes. Using a stochastic description of active hair bundle dynamics, we study the consequences of an elastic coupling on the properties of amplification. We report that collective effects in arrays of hair bundles can enhance the amplification gain and the sharpness of frequency tuning as compared with the performance of an isolated hair bundle. We also discuss the transient response elicited by the sudden onset of a periodic stimulus and its relation to temporal integration curves. Simulations of systems with a gradient of intrinsic frequencies show an enhanced amplification gain while preserving a frequency gradient, provided the coupling strength is similar to the hair bundle stiffness. We relate our findings to the situation in the bullfrogs sacculus and the mammalian cochlea.

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

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.

Spontaneous voltage oscillations and response dynamics of a Hodgkin-Huxley type model of sensory hair cells

We employ a Hodgkin-Huxley-type model of basolateral ionic currents in bullfrog saccular hair cells for studying the genesis of spontaneous voltage oscillations and their role in shaping the response of the hair cell to external mechanical stimuli. Consistent with recent experimental reports, we find that the spontaneous dynamics of the model can be categorized using conductance parameters of calcium-activated potassium, inward rectifier potassium, and mechano-electrical transduction (MET) ionic currents. The model is demonstrated for exhibiting a broad spectrum of autonomous rhythmic activity, including periodic and quasi-periodic oscillations with two independent frequencies as well as various regular and chaotic bursting patterns. Complex patterns of spontaneous oscillations in the model emerge at small values of the conductance of Ca2+-activated potassium currents. These patterns are significantly affected by thermal fluctuations of the MET current. We show that self-sustained regular voltage oscillations lead to enhanced and sharply tuned sensitivity of the hair cell to weak mechanical periodic stimuli. While regimes of chaotic oscillations are argued to result in poor tuning to sinusoidal driving, chaotically oscillating cells do provide a high sensitivity to low-frequency variations of external stimuli.

Actin cortex architecture regulates cell surface tension

Animal cell shape is largely determined by the cortex, a thin actin network underlying the plasma membrane in which myosin-driven stresses generate contractile tension. Tension gradients result in local contractions and drive cell deformations. Previous cortical tension regulation studies have focused on myosin motors. Here, we show that cortical actin network architecture is equally important. First, we observe that actin cortex thickness and tension are inversely correlated during cell-cycle progression. We then show that the actin filament length regulators CFL1, CAPZB and DIAPH1 regulate mitotic cortex thickness and find that both increasing and decreasing thickness decreases tension in mitosis. This suggests that the mitotic cortex is poised close to a tension maximum. Finally, using a computational model, we identify a physical mechanism by which maximum tension is achieved at intermediate actin filament lengths. Our results indicate that actin network architecture, alongside myosin activity, is key to cell surface tension regulation.

Spontaneous movements and linear response of a noisy oscillator

A deterministic system that operates in the vicinity of a Hopf bifurcation can be described by a single equation of a complex variable, called the normal form. Proximity to the bifurcation ensures that on the stable side of the bifurcation (i.e. on the side where a stable fixed point exists), the linear-response function of the system is peaked at the frequency that is characteristic of the oscillatory instability. Fluctuations, which are present in many systems, conceal the Hopf bifurcation and lead to noisy oscillations. Spontaneous hair bundle oscillations by sensory hair cells from the vertebrate ear provide an instructive example of such noisy oscillations. By starting from a simplified description of hair bundle motility based on two degrees of freedom, we discuss the interplay of nonlinearity and noise in the supercritical Hopf normal form. Specifically, we show here that the linear-response function obeys the same functional form as for the noiseless system on the stable side of the bifurcation but with effective, renormalized parameters. Moreover, we demonstrate in specific cases how to relate analytically the parameters of the normal form with added noise to effective parameters. The latter parameters can be measured experimentally in the power spectrum of spontaneous activity and linear-response function to external stimuli. In other cases, numerical solutions were used to determine the effects of noise and nonlinearities on these effective parameters. Finally, we relate our results to experimentally observed spontaneous hair bundle oscillations and responses to periodic stimuli.

Probing tissue-scale deformation by in vivo force application reveals a fast tissue softening during early embryogenesis

During development, cell-generated forces induce tissue-scale deformations to shape the organism. Here, we present a method that allows to quantitatively relate such tissue-scale deformations to spatially localized forces and measure mechanical properties of epithelia in vivo. Our approach is based on the application of controlled forces on microparticles embedded in individual cells of an embryo. Combining measurements of the bead displacement with the analysis of induced deformation fields in a continuum mechanics framework, we can quantify tissue material properties and follow their change over time. In particular, we uncover a rapid change in tissue response occurring during Drosophila cellularization, resulting from a softening of the blastoderm and an increase of external friction. Pharmacological treatments reveal that in addition to actomyosin, the microtubule cytoskeleton is a major contributor to epithelial mechanics at that stage. Overall, our method allows for measuring essential mechanical parameters governing tissue-scale deformations and flows occurring during morphogenesis.

Voltage oscillations and response dynamics in a model of sensory hair cells

Sensory hair cells in auditory and vestibular organs rely on active mechanisms to achieve high sensitivity and frequency selectivity with respect to weak stimuli. Self-sustained oscillations in hair cells occur on two very different levels. First, the mechano-sensory hair bundle itself can undergo spontaneous mechanical oscillations. Second, self-sustained electric voltage oscillations across the membrane of the hair cell have been documented in the inner ear of lower vertebrates. The functional significance of these self-sustained voltage oscillations is currently unknown. We used a Hodgkin-Huxley type model of the baso-lateral ionic currents of bullfrog sacculus to study genesis of spontaneous voltage oscillation patterns and how the spontaneous oscillations shape the response of the hair cell to external mechanical stimuli. To examine the influence of inevitable fluctuations on the dynamical regimes, we included a stochastic transduction current originating in the Brownian motion of the hair bundle and channel noise arising due to the finite number of mechano-electrical transduction channels [1]. We determined the bifurcation structure of the model in terms of two important ionic conductances, associated with the inwardly rectifier (K1) and Ca2+-activated (BK) potassium currents. We found that for large values of BK conductance the system is either at equilibrium or exhibit tonic oscillations. For small values of BK and large values of K1 conductances the dynamics of the model shows diverse patterns of activity including quasi-periodic oscillations, large-amplitude periodic spikes, and bursts of spikes. In particular we found a peculiar transition to bursting through quasiperiodic oscillations with two independent frequencies corresponding to a 2D torus in the phase space of the system. Within small patches of parameter space at the transition from spiking to bursting and at the spike adding transition, voltage dynamics are chaotic. Furthermore, we showed that thermal fluctuations of mechano-electrical transduction current can lead to chaos in a wide area of parameter space. We found a high sensitivity and frequency selectivity for the regime of regular spontaneous oscillations in response to sinusoidal stimuli with frequencies f > 5 Hz. Hence, an oscillatory voltage compartment might constitute a biophysical implementation of a high-gain amplifier. Cells poised in the chaotic regime of low BK and high K1 conductances showed poor tuning, but provided a high sensitivity to low-frequency variations of external stimuli. In summary, this study shows that the electrical oscillator found in saccular hair cells contributes significantly to nonlinear amplification of external mechanical stimuli. This further supports the idea of nonlinear oscillators playing a crucial role in the operation of the inner ear.

Time‐Domain Representation of Active Nonlinear Cochlear Waves

The mammalian cochlea has been recognized to act as an active and nonlinear amplifier. Previously, a generic description in terms of critical oscillators has been explored in the Fourier domain. Here, we discuss a generalized variant of this model formulated in the time domain. As a first step, we verify that the models response to periodic stimulation is similar to the original Fourier‐domain model. The description in the time domain offers the possibility to study the effects of static and dynamic noise sources on the spectral statistics of spontaneous and evoked otoacoustic emissions.