Ion channel regulation of the dynamical instability of the resting membrane potential in saccular hair cells of the green frog (Rana esculenta)

Mathematical Modeling and Analyses of Interspike-Intervals of Spontaneous Activity in Afferent Neurons of the Zebrafish Lateral Line

Without stimuli, hair cells spontaneously release neurotransmitter leading to spontaneous generation of action potentials (spikes) in innervating afferent neurons. We analyzed spontaneous spike patterns recorded from the lateral line of zebrafish and found that distributions of interspike intervals (ISIs) either have an exponential shape or an "L" shape that is characterized by a sharp decay but wide tail. ISI data were fitted to renewal-process models that accounted for the neuron refractory periods and hair-cell synaptic release. Modeling the timing of synaptic release using a mixture of two exponential distributions yielded the best fit for our ISI data. Additionally, lateral line ISIs displayed positive serial correlation and appeared to exhibit switching between faster and slower modes of spike generation. This pattern contrasts with previous findings from the auditory system where ISIs tended to have negative serial correlation due to synaptic depletion. We propose that afferent neuron innervation with multiple and heterogenous hair-cells synapses, each influenced by changes in calcium domains, can serve as a mechanism for the random switching behavior. Overall, our analyses provide evidence of how physiological similarities and differences between synapses and innervation patterns in the auditory, vestibular, and lateral line systems can lead to variations in spontaneous activity.

Enlargement of Ribbons in Zebrafish Hair Cells Increases Calcium Currents But Disrupts Afferent Spontaneous Activity and Timing of Stimulus Onset

In sensory hair cells of auditory and vestibular organs, the ribbon synapse is required for the precise encoding of a wide range of complex stimuli. Hair cells have a unique presynaptic structure, the synaptic ribbon, which organizes both synaptic vesicles and calcium channels at the active zone. Previous work has shown that hair-cell ribbon size is correlated with differences in postsynaptic activity. However, additional variability in postsynapse size presents a challenge to determining the specific role of ribbon size in sensory encoding. To selectively assess the impact of ribbon size on synapse function, we examined hair cells in transgenic zebrafish that have enlarged ribbons, without postsynaptic alterations. Morphologically, we found that enlarged ribbons had more associated vesicles and reduced presynaptic calcium-channel clustering. Functionally, hair cells with enlarged ribbons had larger global and ribbon-localized calcium currents. Afferent neuron recordings revealed that hair cells with enlarged ribbons resulted in reduced spontaneous spike rates. Additionally, despite larger presynaptic calcium signals, we observed fewer evoked spikes with longer latencies from stimulus onset. Together, our work indicates that hair-cell ribbon size influences the spontaneous spiking and the precise encoding of stimulus onset in afferent neurons.

SIGNIFICANCE STATEMENT Numerous studies support that hair-cell ribbon size corresponds with functional sensitivity differences in afferent neurons and, in the case of inner hair cells of the cochlea, vulnerability to damage from noise trauma. Yet it is unclear whether ribbon size directly influences sensory encoding. Our study reveals that ribbon enlargement results in increased ribbon-localized calcium signals, yet reduces afferent spontaneous activity and disrupts the timing of stimulus onset, a distinct aspect of auditory and vestibular encoding. These observations suggest that varying ribbon size alone can influence sensory encoding, and give further insight into how hair cells transduce signals that cover a wide dynamic range of stimuli.

The interplay between genetic and bioelectrical signaling permits a spatial regionalisation of membrane potentials in model multicellular ensembles

The single cell-centred approach emphasises ion channels as specific proteins that determine individual properties, disregarding their contribution to multicellular outcomes. We simulate the interplay between genetic and bioelectrical signals in non-excitable cells from the local single-cell level to the long range multicellular ensemble. The single-cell genetic regulation is based on mean-field kinetic equations involving the mRNA and protein concentrations. The transcription rate factor is assumed to depend on the absolute value of the cell potential, which is dictated by the voltage-gated cell ion channels and the intercellular gap junctions. The interplay between genetic and electrical signals may allow translating single-cell states into multicellular states which provide spatio-temporal information. The model results have clear implications for biological processes: (i) bioelectric signals can override slightly different genetic pre-patterns; (ii) ensembles of cells initially at the same potential can undergo an electrical regionalisation because of persistent genetic differences between adjacent spatial regions; and (iii) shifts in the normal cell electrical balance could trigger significant changes in the genetic regulation.

Bioelectrical Signals and Ion Channels in the Modeling of Multicellular Patterns and Cancer Biophysics

Bioelectrical signals and ion channels are central to spatial patterns in cell ensembles, a problem of fundamental interest in positional information and cancer processes. We propose a model for electrically connected cells based on simple biological concepts: i) the membrane potential of a single cell characterizes its electrical state; ii) the long-range electrical coupling of the multicellular ensemble is realized by a network of gap junction channels between neighboring cells; and iii) the spatial distribution of an external biochemical agent can modify the conductances of the ion channels in a cell membrane and the multicellular electrical state. We focus on electrical effects in small multicellular ensembles, ignoring slow diffusional processes. The spatio-temporal patterns obtained for the local map of cell electric potentials illustrate the normalization of regions with abnormal cell electrical states. The effects of intercellular coupling and blocking of specific channels on the electrical patterns are described. These patterns can regulate the electrically-induced redistribution of charged nanoparticles over small regions of a model tissue. The inclusion of bioelectrical signals provides new insights for the modeling of cancer biophysics because collective multicellular states show electrical coupling mechanisms that are not readily deduced from biochemical descriptions at the individual cell level.

Electrical coupling in ensembles of nonexcitable cells: modeling the spatial map of single cell potentials

We analyze the coupling of model nonexcitable (non-neural) cells assuming that the cell membrane potential is the basic individual property. We obtain this potential on the basis of the inward and outward rectifying voltage-gated channels characteristic of cell membranes. We concentrate on the electrical coupling of a cell ensemble rather than on the biochemical and mechanical characteristics of the individual cells, obtain the map of single cell potentials using simple assumptions, and suggest procedures to collectively modify this spatial map. The response of the cell ensemble to an external perturbation and the consequences of cell isolation, heterogeneity, and ensemble size are also analyzed. The results suggest that simple coupling mechanisms can be significant for the biophysical chemistry of model biomolecular ensembles. In particular, the spatiotemporal map of single cell potentials should be relevant for the uptake and distribution of charged nanoparticles over model cell ensembles and the collective properties of droplet networks incorporating protein ion channels inserted in lipid bilayers.

Effect of bidirectional mechanoelectrical coupling on spontaneous oscillations and sensitivity in a model of hair cells

Sensory hair cells of amphibians exhibit spontaneous activity in their hair bundles and membrane potentials, reflecting two distinct active amplification mechanisms employed in these peripheral mechanosensors. We use a two-compartment model of the bullfrog's saccular hair cell to study how the interaction between its mechanical and electrical compartments affects the emergence of distinct dynamical regimes, and the role of this interaction in shaping the response of the hair cell to weak mechanical stimuli. The model employs a Hodgkin-Huxley-type system for the basolateral electrical compartment and a nonlinear hair bundle oscillator for the mechanical compartment, which are coupled bidirectionally. In the model, forward coupling is provided by the mechanoelectrical transduction current, flowing from the hair bundle to the cell soma. Backward coupling is due to reverse electromechanical transduction, whereby variations of the membrane potential affect adaptation processes in the hair bundle. We isolate oscillation regions in the parameter space of the model and show that bidirectional coupling affects significantly the dynamics of the cell. In particular, self-sustained oscillations of the hair bundles and membrane potential can result from bidirectional coupling, and the coherence of spontaneous oscillations can be maximized by tuning the coupling strength. Consistent with previous experimental work, the model demonstrates that dynamical regimes of the hair bundle change in response to variations in the conductances of basolateral ion channels. We show that sensitivity of the hair cell to weak mechanical stimuli can be maximized by varying coupling strength, and that stochasticity of the hair bundle compartment is a limiting factor of the sensitivity.

Membrane potential bistability in nonexcitable cells as described by inward and outward voltage-gated ion channels

The membrane potential of nonexcitable cells, defined as the electrical potential difference between the cell cytoplasm and the extracellular environment when the current is zero, is controlled by the individual electrical conductance of different ion channels. In particular, inward- and outward-rectifying voltage-gated channels are crucial for cell hyperpolarization/depolarization processes, being amenable to direct physical study. High (in absolute value) negative membrane potentials are characteristic of terminally differentiated cells, while low membrane potentials are found in relatively depolarized, more plastic cells (e.g., stem, embryonic, and cancer cells). We study theoretically the hyperpolarized and depolarized values of the membrane potential, as well as the possibility to obtain a bistability behavior, using simplified models for the ion channels that regulate this potential. The bistability regions, which are defined in the multidimensional state space determining the cell state, can be relevant for the understanding of the different model cell states and the transitions between them, which are triggered by changes in the external environment.

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 to study 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 ionic currents. The model is demonstrated to exhibit a broad spectrum of autonomous rhythmic activity, including periodic and quasiperiodic 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 Ca(2+) activated potassium currents. These patterns are significantly affected by thermal fluctuations of the mechano-electrical transduction 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.

Mechanism of spontaneous activity in afferent neurons of the zebrafish lateral-line organ

Many auditory, vestibular, and lateral-line afferent neurons display spontaneous action potentials. This spontaneous spiking is thought to result from hair-cell glutamate release in the absence of stimuli. Spontaneous release at hair-cell resting potentials presumably results from Ca(V)1.3 L-type calcium channel activity. Here, using intact zebrafish larvae, we recorded robust spontaneous spiking from lateral-line afferent neurons in the absence of external stimuli. Consistent with the above assumptions, spiking was absent in mutants that lacked either Vesicular glutamate transporter 3 (Vglut3) or Ca(V)1.3. We then tested the hypothesis that spontaneous spiking resulted from sustained Ca(V)1.3 activity due to depolarizing currents that are active at rest. Mechanotransduction currents (I(MET)) provide a depolarizing influence to the resting potential. However, following block of I(MET), spontaneous spiking persisted and was characterized by longer interspike intervals and increased periods of inactivity. These results suggest that an additional depolarizing influence maintains the resting potential within the activation range of Ca(V)1.3. To test whether the hyperpolarization-activated cation current, I(h) participates in setting the resting potential, we applied I(h) antagonists. Both ZD7288 and DK-AH 269 reduced spontaneous activity. Finally, concomitant block of I(MET) and I(h) essentially abolished spontaneous activity, ostensibly by hyperpolarization outside of the activation range for Ca(V)1.3. Together, our data support a mechanism for spontaneous spiking that results from Ca(2+)-dependent neurotransmitter release at hair-cell resting potentials that are maintained within the activation range of Ca(V)1.3 channels through active I(MET) and I(h).

Spontaneous dynamics and response properties of a Hodgkin-Huxley-type neuron model driven by harmonic synaptic noise

We study statistical properties, response dynamics, and information transmission in a Hodgkin-Huxley-type neuron system, modeling peripheral electroreceptors in paddlefish. In addition to sodium and potassium currents, the neuron model includes fast calcium and slow afterhyperpolarization (AHP) potassium currents. The synaptic transmission from sensory epithelium is modeled by a Poission process with a rate modulated by narrow-band noise, mimicking stochastic epithelial oscillations observed experimentally. We study how the interplay of parameters of AHP current and synaptic noise affects the statistics of spontaneous dynamics and response properties of the system. In particular, we confirm predictions made earlier with perfect integrate and fire and phase neuron models that epithelial oscillations enhance stimulus-response coherence and thus information transmission in electroreceptor system. In addition, we consider a strong stimulus regime and show that coherent epithelial oscillations may reduce variability of electroreceptor responses to time-varying stimuli.

Spontaneous oscillations, signal amplification, and synchronization in a model of active hair bundle mechanics

We study spontaneous dynamics and signal transduction in a model of active hair bundle mechanics of sensory hair cells. The hair bundle motion is subjected to internal noise resulted from thermal fluctuations and stochastic dynamics of mechanoelectrical transduction ion channels. Similar to other studies we found that in the presence of noise the coherence of stochastic oscillations is maximal at a point on the bifurcation diagram away from the Andronov-Hopf bifurcation and is close to the point of maximum sensitivity of the system to weak periodic mechanical perturbations. Despite decoherent effect of noise the stochastic hair bundle oscillations can be synchronized by external periodic force of few pN amplitude in a finite range of control parameters. We then study effects of receptor potential oscillations on mechanics of the hair bundle and show that the hair bundle oscillations can be synchronized by oscillating receptor voltage. Moreover, using a linear model for the receptor potential we show that bidirectional coupling of the hair bundle and the receptor potential results in significant enhancement of the coherence of spontaneous oscillations and of the sensitivity to the external mechanical perturbations.

Spikes and membrane potential oscillations in hair cells generate periodic afferent activity in the frog sacculus

To look for membrane potential oscillations that may contribute to sensory coding or amplification in the ear, we made whole-cell and perforated-patch recordings from hair cells and postsynaptic afferent neurites in the explanted frog sacculus, with mechanoelectrical transduction (MET) blocked. Small depolarizing holding currents, which may serve to replace the in vivo resting MET current, evoked all-or-none calcium spikes (39-75 mV amplitude) in 37% of hair cells tested, and continuous membrane potential oscillations (14-28 mV; 15-130 Hz) in an additional 14% of cells. Spiking hair cells were on average taller and thinner than nonspiking hair cells, and had smaller outward currents through delayed rectifier channels (I(KV)) and noninactivating calcium-activated potassium channels (I(BK,steady)), and larger inward rectifier currents (I(K1)). Some spiking hair cells fired only a brief train at the onset of a current step, but others could sustain repetitive firing (3-70 Hz). Partial blockade of I(BK) changed the amplitude and frequency of oscillations and spikes, and converted some nonspiking cells into spiking cells. Oscillatory hair cells preferentially amplified sinusoidal stimuli at frequencies near their natural oscillation frequency. Postsynaptic recordings revealed regularly timed bursts of EPSPs in some afferent neurites. EPSP bursts were able to trigger afferent spikes, which may be initiated at the sodium channel cluster located adjacent to the afferent axon's most peripheral myelin segment. These results show that some frog saccular hair cells can generate spontaneous rhythmic activity that may drive periodic background activity in afferent axons.

Spontaneous firing statistics and information transfer in electroreceptors of paddlefish

We study information processing in a peripheral sensory receptor system which possesses spontaneous dynamics with two distinct rhythms. Such organization was found in the electrosensory system of paddlefish and is represented by two distinct and unidirectionally coupled oscillators, resulting in biperiodic spontaneous firing patterns of sensory neurons. We use computational modeling to elucidate the functional role of spontaneous oscillations in conveying information from sensory periphery to the brain. We show that biperiodic organization resulting in nonrenewal statistics of background neuronal activity leads to significant improvement in information transfer through the system as compared to an equivalent renewal model.

Linear and nonlinear processing in hair cells

Mechanosensory hair cells in the ear are exquisitely responsive to minute sensory inputs, nearly to the point of instability. Active mechanisms bias the transduction apparatus and subsequent electrical amplification away from saturation in either the negative or positive direction, to an operating point where the response to small signals is approximately linear. An active force generator coupled directly to the transducer enhances sensitivity and frequency selectivity, and counteracts energy loss to viscous drag. Active electrical amplification further enhances gain and frequency selectivity. In both cases, nonlinear properties may maintain the system close to instability, as evidenced by small spontaneous oscillations, while providing a compressive nonlinearity that increases the cell's operating range. Transmitter release also appears to be frequency selective and biased to operate most effectively near the resting potential. This brief overview will consider the resting stability of hair cells, and their responses to small perturbations that correspond to soft sounds or small accelerations.

Steady-state adaptation of mechanotransduction modulates the resting potential of auditory hair cells, providing an assay for endolymph [Ca2+]

The auditory hair cell resting potential is critical for proper translation of acoustic signals to the CNS, because it determines their filtering properties, their ability to respond to stimuli of both polarities, and, because the hair cell drives afferent firing rates, the resting potential dictates spontaneous transmitter release. In turtle auditory hair cells, the filtering properties are established by the interactions between BK calcium-activated potassium channels and an L-type calcium channel (electrical resonance). However, both theoretical and in vitro recordings indicate that a third conductance is required to set the resting potential to a point on the I(Ca) and I(BK) activation curves in which filtering is optimized like that found in vivo. Present data elucidate a novel mechanism, likely universal among hair cells, in which mechanoelectric transduction (MET) and its calcium-dependent adaptation provide the depolarizing current to establish the hair cell resting potential. First, mechanical block of the MET current hyperpolarized the membrane potential, resulting in broadband asymmetrical resonance. Second, altering steady-state adaptation by altering the [Ca2+] bathing the hair bundle changed the MET current at rest, the magnitude of which resulted in membrane potential changes that encompassed the best resonant voltage. The Ca2+ sensitivity of adaptation allowed for the first physiological estimate of endolymphatic Ca2+ near the MET channel (56 +/- 11 microM), a value similar to bulk endolymph levels. These effects of MET current on resting potential were independently confirmed using a theoretical model of electrical resonance that included the steady-state MET conductance.