Refractoriness enhances temporal coding by auditory nerve fibers

The Determining Role of Covariances in Large Networks of Stochastic Neurons

Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active and refractory neurons in the network's populations. We do so by describing the evolution of the states of individual neurons with a continuous-time Markov chain, from which we formally derive a low-dimensional dynamical system. This is done by solving a moment closure problem in a way that is compatible with the nonlinearity and boundedness of the activation function. Our dynamical system captures the behavior of the high-dimensional stochastic model even in cases where the mean-field approximation fails to do so. Taking into account the second-order moments modifies the solutions that would be obtained with the mean-field approximation and can lead to the appearance or disappearance of fixed points and limit cycles. We moreover perform numerical experiments where the mean-field approximation leads to periodically oscillating solutions, while the solutions of the second-order model can be interpreted as an average taken over many realizations of the stochastic model. Altogether, our results highlight the importance of including higher moments when studying stochastic networks and deepen our understanding of correlated neuronal activity.

Beyond Wilson-Cowan dynamics: oscillations and chaos without inhibition

Fifty years ago, Wilson and Cowan developed a mathematical model to describe the activity of neural populations. In this seminal work, they divided the cells in three groups: active, sensitive and refractory, and obtained a dynamical system to describe the evolution of the average firing rates of the populations. In the present work, we investigate the impact of the often neglected refractory state and show that taking it into account can introduce new dynamics. Starting from a continuous-time Markov chain, we perform a rigorous derivation of a mean-field model that includes the refractory fractions of populations as dynamical variables. Then, we perform bifurcation analysis to explain the occurrence of periodic solutions in cases where the classical Wilson-Cowan does not predict oscillations. We also show that our mean-field model is able to predict chaotic behavior in the dynamics of networks with as little as two populations.

Comparison of response properties of the electrically stimulated auditory nerve reported in human listeners and in animal models

Cochlear implants (CIs) provide acoustic information to implanted patients by electrically stimulating nearby auditory nerve fibers (ANFs) which then transmit the information to higher-level neural structures for further processing and interpretation. Computational models that simulate ANF responses to CI stimuli enable the exploration of the mechanisms underlying CI performance beyond the capacity of in vivo experimentation alone. However, all ANF models developed to date utilize to some extent anatomical/morphometric data, biophysical properties and/or physiological data measured in non-human animal models. This review compares response properties of the electrically stimulated auditory nerve (AN) in human listeners and different mammalian models. Properties of AN responses to single pulse stimulation, paired-pulse stimulation, and pulse-train stimulation are presented. While some AN response properties are similar between human listeners and animal models (e.g., increased AN sensitivity to single pulse stimuli with long interphase gaps), there are some significant differences. For example, the AN of most animal models is typically more sensitive to cathodic stimulation while the AN of human listeners is generally more sensitive to anodic stimulation. Additionally, there are substantial differences in the speed of recovery from neural adaptation between animal models and human listeners. Therefore, results from animal models cannot be simply translated to human listeners. Recognizing the differences in responses of the AN to electrical stimulation between humans and other mammals is an important step for creating ANF models that are more applicable to various human CI patient populations.

Theoretical Relationship Between Two Measures of Spike Synchrony: Correlation Index and Vector Strength

Information processing in the nervous system critically relies on temporally precise spiking activity. In the auditory system, various degrees of phase-locking can be observed from the auditory nerve to cortical neurons. The classical metric for quantifying phase-locking is the vector strength (VS), which captures the periodicity in neuronal spiking. More recently, another metric, called the correlation index (CI), was proposed to quantify the temporally reproducible response characteristics of a neuron. The CI is defined as the peak value of a normalized shuffled autocorrelogram (SAC). Both VS and CI have been used to investigate how temporal information is processed and propagated along the auditory pathways. While previous analyses of physiological data in cats suggested covariation of these two metrics, general characterization of their connection has never been performed. In the present study, we derive a rigorous relationship between VS and CI. To model phase-locking, we assume Poissonian spike trains with a temporally changing intensity function following a von Mises distribution. We demonstrate that VS and CI are mutually related via the so-called concentration parameter that determines the degree of phase-locking. We confirm that these theoretical results are largely consistent with physiological data recorded in the auditory brainstem of various animals. In addition, we generate artificial phase-locked spike sequences, for which recording and analysis parameters can be systematically manipulated. Our analysis results suggest that mismatches between empirical data and the theoretical prediction can often be explained with deviations from the von Mises distribution, including skewed or multimodal period histograms. Furthermore, temporal relations of spike trains across trials can contribute to higher CI values than predicted mathematically based on the VS. We find that, for most applications, a SAC bin width of 50 ms seems to be a favorable choice, leading to an estimated error below 2.5% for physiologically plausible conditions. Overall, our results provide general relations between the two measures of phase-locking and will aid future analyses of different physiological datasets that are characterized with these metrics.

A comprehensive computational model of animal biosonar signal processing

Computational models of animal biosonar seek to identify critical aspects of echo processing responsible for the superior, real-time performance of echolocating bats and dolphins in target tracking and clutter rejection. The Spectrogram Correlation and Transformation (SCAT) model replicates aspects of biosonar imaging in both species by processing wideband biosonar sounds and echoes with auditory mechanisms identified from experiments with bats. The model acquires broadband biosonar broadcasts and echoes, represents them as time-frequency spectrograms using parallel bandpass filters, translates the filtered signals into ten parallel amplitude threshold levels, and then operates on the resulting time-of-occurrence values at each frequency to estimate overall echo range delay. It uses the structure of the echo spectrum by depicting it as a series of local frequency nulls arranged regularly along the frequency axis of the spectrograms after dechirping them relative to the broadcast. Computations take place entirely on the timing of threshold-crossing events for each echo relative to threshold-events for the broadcast. Threshold-crossing times take into account amplitude-latency trading, a physiological feature absent from conventional digital signal processing. Amplitude-latency trading transposes the profile of amplitudes across frequencies into a profile of time-registrations across frequencies. Target shape is extracted from the spacing of the object's individual acoustic reflecting points, or glints, using the mutual interference pattern of peaks and nulls in the echo spectrum. These are merged with the overall range-delay estimate to produce a delay-based reconstruction of the object's distance as well as its glints. Clutter echoes indiscriminately activate multiple parts in the null-detecting system, which then produces the equivalent glint-delay spacings in images, thus blurring the overall echo-delay estimates by adding spurious glint delays to the image. Blurring acts as an anticorrelation process that rejects clutter intrusion into perceptions.

Phase Locking of Auditory Nerve Fibers: The Role of Lowpass Filtering by Hair Cells

Phase locking of auditory-nerve-fiber (ANF) responses to the temporal fine structure of acoustic stimuli, a hallmark of the auditory system's temporal precision, is important for many aspects of hearing. Previous work has shown that phase-locked period histograms are often well described by exponential transfer functions relating instantaneous stimulus pressure to instantaneous spike rate, with no observed clipping of the histograms. The operating points and slopes of these functions change with stimulus level. The mechanism underlying this apparent gain control is unclear but is distinct from mechanical compression, is independent of refractoriness and spike-rate adaptation, and is apparently instantaneous. Here we show that these findings can be accounted for by a model consisting of a static Boltzmann transducer function yielding a clipped output, followed by a lowpass filter and a static exponential transfer function. Using responses to tones of ANFs from cats of both sexes, we show that, for a given ANF, the period histograms obtained at all stimulus levels for a given stimulus frequency can be described using one set of level-independent model parameters. The model also accounts for changes in the maximum and minimum instantaneous spike rates with changes in stimulus level. Notably, the estimated cutoff frequency is lower for low- than for high-spontaneous-rate ANFs, implying a synapse-specific contribution to lowpass filtering. These findings advance our understanding of ANF phase locking by highlighting the role of peripheral filtering mechanisms in shaping responses of individual ANFs.SIGNIFICANCE STATEMENT Phase locking of auditory-nerve-fiber responses to the temporal fine structure of acoustic stimuli is important for many aspects of hearing. Period histograms typically retain an approximately sinusoidal shape across stimulus levels, with the peripheral auditory system operating as though its overall transfer function is an exponential function whose slope decreases with increasing stimulus level. This apparent gain control can be accounted for by a static saturating transducer function followed by a lowpass filter. In addition to attenuating the AC component, the filter approximately recovers the sinusoidal waveform of the stimulus. The estimated cutoff frequency varies with spontaneous rate, revealing a synaptic contribution to lowpass filtering. These findings highlight the significant impact of peripheral filtering mechanisms on phase locking.

Effect of neural adaptation and degeneration on pulse-train ECAPs: A model study

Electrically evoked compound action potentials (eCAPs) are measurements of the auditory nerve's response to electrical stimulation. ECAP amplitudes during pulse trains can exhibit temporal alternations. The magnitude of this alternation tends to diminish over time during the stimulus. How this pattern relates to the temporal behavior of nerve fibers is not known. We hypothesized that the stochasticity, refractoriness, adaptation of the threshold and spike-times influence pulse-train eCAP responses. Thirty thousand auditory nerve fibers were modeled in a three-dimensional cochlear model incorporating pulse-shape effects, pulse-history effects, and stochasticity in the individual neural responses. ECAPs in response to pulse trains of different rates and amplitudes were modeled for fibers with different stochastic properties (by variation of the relative spread) and different temporal properties (by variation of the refractory periods, adaptation and latency). The model predicts alternation of peak amplitudes similar to available human data. In addition, the peak alternation was affected by changing the refractoriness, adaptation, and relative spread of auditory nerve fibers. As these parameters are related to factors such as the duration of deafness and neural survival, this study suggests that the eCAP pattern in response to pulse trains could be used to assess the underlying temporal and stochastic behavior of the auditory nerve. As these properties affect the nerve's response to pulse trains, they are of uttermost importance to sound perception with cochlear implants.

Phase Locking of Auditory-Nerve Fibers Reveals Stereotyped Distortions and an Exponential Transfer Function with a Level-Dependent Slope

Phase locking of auditory-nerve-fiber (ANF) responses to the fine structure of acoustic stimuli is a hallmark of the auditory system's temporal precision and is important for many aspects of hearing. Period histograms from phase-locked ANF responses to low-frequency tones exhibit spike-rate and temporal asymmetries, but otherwise retain an approximately sinusoidal shape as stimulus level increases, even beyond the level at which the mean spike rate saturates. This is intriguing because apical cochlear mechanical vibrations show little compression, and mechanoelectrical transduction in the receptor cells is thought to obey a static sigmoidal nonlinearity, which might be expected to produce peak clipping at moderate and high stimulus levels. Here we analyze phase-locked responses of ANFs from cats of both sexes. We show that the lack of peak clipping is due neither to ANF refractoriness nor to spike-rate adaptation on time scales longer than the stimulus period. We demonstrate that the relationship between instantaneous pressure and instantaneous rate is well described by an exponential function whose slope decreases with increasing stimulus level. Relatively stereotyped harmonic distortions in the input to the exponential can account for the temporal asymmetry of the period histograms, including peak splitting. We show that the model accounts for published membrane-potential waveforms when assuming a power-of-three, but not a power-of-one, relationship to exocytosis. Finally, we demonstrate the relationship between the exponential transfer functions and the sigmoidal pseudotransducer functions obtained in the literature by plotting the maxima and minima of the voltage responses against the maxima and minima of the stimuli.SIGNIFICANCE STATEMENT Phase locking of auditory-nerve-fiber responses to the temporal fine structure of acoustic stimuli is important for many aspects of hearing, but the mechanisms underlying phase locking are not fully understood. Intriguingly, period histograms retain an approximately sinusoidal shape across sound levels, even when the mean rate has saturated. We find that neither refractoriness nor spike-rate adaptation is responsible for this behavior. Instead, the peripheral auditory system operates as though it contains an exponential transfer function whose slope changes with stimulus level. The underlying mechanism is distinct from the comparatively weak cochlear mechanical compression in the cochlear apex, and likely resides in the receptor cells.

Intrinsic physiological properties underlie auditory response diversity in the avian cochlear nucleus

Sensory systems exploit parallel processing of stimulus features to enable rapid, simultaneous extraction of information. Mechanisms that facilitate this differential extraction of stimulus features can be intrinsic or synaptic in origin. A subdivision of the avian cochlear nucleus, nucleus angularis (NA), extracts sound intensity information from the auditory nerve and contains neurons that exhibit diverse responses to sound and current injection. NA neurons project to multiple regions ascending the auditory brain stem including the superior olivary nucleus, lateral lemniscus, and avian inferior colliculus, with functional implications for inhibitory gain control and sound localization. Here we investigated whether the diversity of auditory response patterns in NA can be accounted for by variation in intrinsic physiological features. Modeled sound-evoked auditory nerve input was applied to NA neurons with dynamic clamp during in vitro whole cell recording at room temperature. Temporal responses to auditory nerve input depended on variation in intrinsic properties, and the low-threshold K⁺ current was implicated as a major contributor to temporal response diversity and neuronal input-output functions. An auditory nerve model of acoustic amplitude modulation produced synchrony coding of modulation frequency that depended on the intrinsic physiology of the individual neuron. In Primary-Like neurons, varying low-threshold K⁺ conductance with dynamic clamp altered temporal modulation tuning bidirectionally. Taken together, these data suggest that intrinsic physiological properties play a key role in shaping auditory response diversity to both simple and more naturalistic auditory stimuli in the avian cochlear nucleus. NEW & NOTEWORTHY This article addresses the question of how the nervous system extracts different information in sounds. Neurons in the cochlear nucleus show diverse responses to acoustic stimuli that may allow for parallel processing of acoustic features. The present studies suggest that diversity in intrinsic physiological features of individual neurons, including levels of a low voltage-activated K⁺ current, play a major role in regulating the diversity of auditory responses.

Modeling elucidates how refractory period can provide profound nonlinear gain control to graded potential neurons

Refractory period (RP) plays a central role in neural signaling. Because it limits an excitable membrane's recovery time from a previous excitation, it can restrict information transmission. Classically, RP means the recovery time from an action potential (spike), and its impact to encoding has been mostly studied in spiking neurons. However, many sensory neurons do not communicate with spikes but convey information by graded potential changes. In these systems, RP can arise as an intrinsic property of their quantal micro/nanodomain sampling events, as recently revealed for quantum bumps (single photon responses) in microvillar photoreceptors. Whilst RP is directly unobservable and hard to measure, masked by the graded macroscopic response that integrates numerous quantal events, modeling can uncover its role in encoding. Here, we investigate computationally how RP can affect encoding of graded neural responses. Simulations in a simple stochastic process model for a fly photoreceptor elucidate how RP can profoundly contribute to nonlinear gain control to achieve a large dynamic range.

Small conductance Ca2+-activated K+ channels induce the firing pause periods during the activation of Drosophila nociceptive neurons

In Drosophila larvae, Class IV sensory neurons respond to noxious thermal stimuli and provoke heat avoidance behavior. Previously, we showed that the activated neurons displayed characteristic fluctuations of firing rates, which consisted of repetitive high-frequency spike trains and subsequent pause periods, and we proposed that the firing rate fluctuations enhanced the heat avoidance (Terada et al., 2016). Here, we further substantiate this idea by showing that the pause periods and the frequency of fluctuations are regulated by small conductance Ca²⁺-activated K⁺ (SK) channels, and the SK knockdown larvae display faster heat avoidance than control larvae. The regulatory mechanism of the fluctuations in the Class IV neurons resembles that in mammalian Purkinje cells, which display complex spikes. Furthermore, our results suggest that such fluctuation coding in Class IV neurons is required to convert noxious thermal inputs into effective stereotyped behavior as well as general rate coding.

Tonotopic Optimization for Temporal Processing in the Cochlear Nucleus

In the auditory system, sounds are processed in parallel frequency-tuned circuits, beginning in the cochlea. Auditory nerve fibers reflect this tonotopy and encode temporal properties of acoustic stimuli by "locking" discharges to a particular stimulus phase. However, physiological constraints on phase-locking depend on stimulus frequency. Interestingly, low characteristic frequency (LCF) neurons in the cochlear nucleus improve phase-locking precision relative to their auditory nerve inputs. This is proposed to arise through synaptic integration, but the postsynaptic membrane's selectivity for varying levels of synaptic convergence is poorly understood. The chick cochlear nucleus, nucleus magnocellularis (NM), exhibits tonotopic distribution of both input and membrane properties. LCF neurons receive many small inputs and have low input thresholds, whereas high characteristic frequency (HCF) neurons receive few, large synapses and require larger currents to spike. NM therefore presents an opportunity to study how small membrane variations interact with a systematic topographic gradient of synaptic inputs. We investigated membrane input selectivity and observed that HCF neurons preferentially select faster input than their LCF counterparts, and that this preference is tolerant of changes to membrane voltage. We then used computational models to probe which properties are crucial to phase-locking. The model predicted that the optimal arrangement of synaptic and membrane properties for phase-locking is specific to stimulus frequency and that the tonotopic distribution of input number and membrane excitability in NM closely tracks a stimulus-defined optimum. These findings were then confirmed physiologically with dynamic-clamp simulations of inputs to NM neurons.

SIGNIFICANCE STATEMENT

One way that neurons represent temporal information is by phase-locking, which is discharging in response to a particular phase of the stimulus waveform. In the auditory system, central neurons are optimized to retain or improve phase-locking precision compared with input from the auditory nerve. However, the difficulty of this computation varies systematically with stimulus frequency. We examined properties that contribute to temporal processing both physiologically and in a computational model. Neurons processing low-frequency input benefit from integration of many weak inputs, whereas those processing higher frequencies progressively lose precision by integration of multiple inputs. Here, we reveal general features of input-output optimization that apply to all neurons that process time varying input.

The Electrically Evoked Compound Action Potential: From Laboratory to Clinic

The electrically evoked compound action potential (eCAP) represents the synchronous firing of a population of electrically stimulated auditory nerve fibers. It can be directly recorded on a surgically exposed nerve trunk in animals or from an intra-cochlear electrode of a cochlear implant. In the past two decades, the eCAP has been widely recorded in both animals and clinical patient populations using different testing paradigms. This paper provides an overview of recording methodologies and response characteristics of the eCAP, as well as its potential applications in research and clinical situations. Relevant studies are reviewed and implications for clinicians are discussed.

Temporal Considerations for Stimulating Spiral Ganglion Neurons with Cochlear Implants

A wealth of knowledge about different types of neural responses to electrical stimulation has been developed over the past 100 years. However, the exact forms of neural response properties can vary across different types of neurons. In this review, we survey four stimulus-response phenomena that in recent years are thought to be relevant for cochlear implant stimulation of spiral ganglion neurons (SGNs): refractoriness, facilitation, accommodation, and spike rate adaptation. Of these four, refractoriness is the most widely known, and many perceptual and physiological studies interpret their data in terms of refractoriness without incorporating facilitation, accommodation, or spike rate adaptation. In reality, several or all of these behaviors are likely involved in shaping neural responses, particularly at higher stimulation rates. A better understanding of the individual and combined effects of these phenomena could assist in developing improved cochlear implant stimulation strategies. We review the published physiological data for electrical stimulation of SGNs that explores these four different phenomena, as well as some of the recent studies that might reveal the biophysical bases of these stimulus-response phenomena.

Basic response properties of auditory nerve fibers: a review

All acoustic information from the periphery is encoded in the timing and rates of spikes in the population of spiral ganglion neurons projecting to the central auditory system. Considerable progress has been made in characterizing the physiological properties of type-I and type-II primary auditory afferents and understanding the basic properties of type-I afferents in response to sounds. Here, we review some of these properties, with emphasis placed on issues such as the stochastic nature of spike timing during spontaneous and driven activity, frequency tuning curves, spike-rate-versus-level functions, dynamic-range and spike-rate adaptation, and phase locking to stimulus fine structure and temporal envelope. We also review effects of acoustic trauma on some of these response properties.

Phase-locking precision is enhanced by multiquantal release at an auditory hair cell ribbon synapse

Sound-evoked spikes in the auditory nerve can phase-lock with submillisecond precision for prolonged periods of time. However, the synaptic mechanisms that enable this accurate spike firing remain poorly understood. Using paired recordings from adult frog hair cells and their afferent fibers, we show here that during sine-wave stimuli, synaptic failures occur even during strong stimuli. However, exclusion of these failures leads to mean excitatory postsynaptic current (EPSC) amplitudes that are independent of Ca(2+) current. Given the intrinsic jitter in spike triggering, evoked synaptic potentials and spikes had surprisingly similar degrees of synchronization to a sine-wave stimulus. This similarity was explained by an unexpected finding: large-amplitude evoked EPSCs have a significantly larger synchronization index than smaller evoked EPSCs. Large EPSCs therefore enhance the precision of spike timing. The hair cells' unique capacity for continuous, large-amplitude, and highly synchronous multiquantal release thus underlies its ability to trigger phase-locked spikes in afferent fibers.

Independent population coding of speech with sub-millisecond precision

To understand the strategies used by the brain to analyze complex environments, we must first characterize how the features of sensory stimuli are encoded in the spiking of neuronal populations. Characterizing a population code requires identifying the temporal precision of spiking and the extent to which spiking is correlated, both between cells and over time. In this study, we characterize the population code for speech in the gerbil inferior colliculus (IC), the hub of the auditory system where inputs from parallel brainstem pathways are integrated for transmission to the cortex. We find that IC spike trains can carry information about speech with sub-millisecond precision, and, consequently, that the temporal correlations imposed by refractoriness can play a significant role in shaping spike patterns. We also find that, in contrast to most other brain areas, the noise correlations between IC cells are extremely weak, indicating that spiking in the population is conditionally independent. These results demonstrate that the problem of understanding the population coding of speech can be reduced to the problem of understanding the stimulus-driven spiking of individual cells, suggesting that a comprehensive model of the subcortical processing of speech may be attainable in the near future.