A simple model of the inner-hair-cell ribbon synapse accounts for mammalian auditory-nerve-fiber spontaneous spike times

Estimation of firing rate from instantaneous interspike intervals

The rate coding hypothesis is the oldest and still one of the most accepted hypotheses of neural coding. Consequently, many approaches have been devised for the firing rate estimation, ranging from simple binning of the time axis to advanced statistical methods. Nonetheless the concept of firing rate, while informally understood, can be mathematically defined in several distinct ways. These definitions may yield mutually incompatible results unless implemented properly. Recently it has been shown that the notions of the instantaneous and the classical firing rates can be made compatible, at least in terms of their averages, by carefully discerning the time instant at which the neuronal activity is observed. In this paper we revisit the properties of instantaneous interspike intervals in order to derive several novel firing rate estimators, which are free of additional assumptions or parameters and their temporal resolution is 'locally self-adaptive'. The estimators are simple to implement and are numerically efficient even for very large sets of data.

Predicting early auditory evoked potentials using a computational model of auditory-nerve processing

Non-invasive electrophysiological measures, such as auditory evoked potentials (AEPs), play a crucial role in diagnosing auditory pathology. However, the relationship between AEP morphology and cochlear degeneration remains complex and not well understood. Dau [J. Acoust. Soc. Am. 113, 936-950 (2003)] proposed a computational framework for modeling AEPs that utilized a nonlinear auditory-nerve (AN) model followed by a linear unitary response function. While the model captured some important features of the measured AEPs, it also exhibited several discrepancies in response patterns compared to the actual measurements. In this study, an enhanced AEP modeling framework is presented, incorporating an improved AN model, and the conclusions from the original study were reevaluated. Simulation results with transient and sustained stimuli demonstrated accurate auditory brainstem responses (ABRs) and frequency-following responses (FFRs) as a function of stimulation level, although wave-V latencies remained too short, similar to the original study. When compared to physiological responses in animals, the revised model framework showed a more accurate balance between the contributions of auditory-nerve fibers (ANFs) at on- and off-frequency regions to the predicted FFRs. These findings emphasize the importance of cochlear processing in brainstem potentials. This framework may provide a valuable tool for assessing human AN models and simulating AEPs for various subtypes of peripheral pathologies, offering opportunities for research and clinical applications.

Cochlear aging disrupts the correlation between spontaneous rate- and sound-level coding in auditory nerve fibers

The spiking activity of auditory nerve fibers (ANFs) transmits information about the acoustic environment from the cochlea to the central auditory system. Increasing age leads to degeneration of cochlear tissues, including the sensory hair cells and stria vascularis. Here, we aim to identify the functional effects of such age-related cochlear pathologies of ANFs. Rate-level functions (RLFs) were recorded from single-unit ANFs of young adult (n = 52, 3-12 months) and quiet-aged (n = 24, >36 months) Mongolian gerbils of either sex. RLFs were used to determine sensitivity and spontaneous rates (SRs) and were classified into flat-saturating, sloping-saturating, and straight categories, as previously established. A physiologically based cochlear model, adapted for the gerbil, was used to simulate the effects of cochlear degeneration on ANF physiology. In ANFs tuned to low frequencies (<3.5 kHz), SR was lower in those of aged gerbils, while an age-related loss of low-SR fibers was evident in ANFs tuned to high frequencies. These changes in SR distribution did not affect the typical SR versus sensitivity correlation. The distribution of RLF types among low-SR fibers, however, shifted toward that of high-SR fibers, specifically showing more fast-saturating and fewer sloping-saturating RLFs. A modeled striatal degeneration, which affects the combined inner hair cell and synaptic output, reduced SR but left RLF type unchanged. An additional reduced basilar membrane gain, which decreased sensitivity, explained the changed RLF types. Overall, the data indicated age-related changes in the characteristics of single ANFs that blurred the established relationships between SR and RLF types.NEW & NOTEWORTHY Auditory nerve fibers, which connect the cochlea to the central auditory system, change their encoding of sound level in aged gerbils. In addition to a general shift to higher levels, indicative of decreased sensitivity, level coding was also differentially affected in fibers with low- and high-spontaneous rates. Loss of low-spontaneous rate fibers, combined with a general decrease of spontaneous rate, further blurs the categorization of auditory nerve fiber types in the aged gerbil.

A comparative study of eight human auditory models of monaural processing

A number of auditory models have been developed using diverging approaches, either physiological or perceptual, but they share comparable stages of signal processing, as they are inspired by the same constitutive parts of the auditory system. We compare eight monaural models that are openly accessible in the Auditory Modelling Toolbox. We discuss the considerations required to make the model outputs comparable to each other, as well as the results for the following model processing stages or their equivalents: Outer and middle ear, cochlear filter bank, inner hair cell, auditory nerve synapse, cochlear nucleus, and inferior colliculus. The discussion includes a list of recommendations for future applications of auditory models.

A simplified physiological model of rate-level functions of auditory-nerve fibers

Several approaches have been used to describe the rate-level functions of auditory-nerve fibers (ANFs). One approach uses descriptive models that can be fitted easily to data. Another derives rate-level functions from comprehensive physiological models of auditory peripheral processing. Here, we seek to identify the minimal set of components needed to provide a physiologically plausible account of rate-level functions. Our model consists of a first-order Boltzmann mechanoelectrical transducer function relating the instantaneous stimulus pressure to an instantaneous output, followed by a lowpass filter that eliminates the AC component, followed by an exponential synaptic transfer function relating the DC component to the mean spike rate. This is perhaps the simplest physiologically plausible model capable of accounting for rate-level functions under the assumption that the model parameters for a given ANF and stimulus frequency are level-independent. We find that the model typically accounts well for rate-level functions from cat ANFs for all stimulus frequencies. More complicated model variants having saturating synaptic transfer functions do not perform significantly better, implying the system operates far away from synaptic saturation. Rate saturation in the model is caused by saturation of the DC component of the filter output (e.g., the receptor potential), which in turn is due to the saturation of the transducer function. The maximum mean spike rate is approximately constant across ANFs, such that the slope parameter of the exponential synaptic transfer function decreases with increasing spontaneous rate. If the synaptic parameters for a given ANF are assumed to be constant across stimulus frequencies, then frequency- and level-dependent input nonlinearities are derived that are qualitatively similar to those reported in the literature. Contrary to assumptions in the literature, such nonlinearities are obtained even for ANFs having high spontaneous rates. Finally, spike-rate adaptation is examined and found to be accounted for by a decrease in the slope parameter of the synaptic transfer function over time following stimulus onset.

Encoding sound in the cochlea: from receptor potential to afferent discharge

Ribbon-class synapses in the ear achieve analog to digital transformation of a continuously graded membrane potential to all-or-none spikes. In mammals, several auditory nerve fibres (ANFs) carry information from each inner hair cell (IHC) to the brain in parallel. Heterogeneity of transmission among synapses contributes to the diversity of ANF sound-response properties. In addition to the place code for sound frequency and the rate code for sound level, there is also a temporal code. In series with cochlear amplification and frequency tuning, neural representation of temporal cues over a broad range of sound levels enables auditory comprehension in noisy multi-speaker settings. The IHC membrane time constant introduces a low-pass filter that attenuates fluctuations of the receptor potential above 1-2 kHz. The ANF spike generator adds a high-pass filter via its depolarization-rate threshold that rejects slow changes in the postsynaptic potential and its phasic response property that ensures one spike per depolarization. Synaptic transmission involves several stochastic subcellular processes between IHC depolarization and ANF spike generation, introducing delay and jitter that limits the speed and precision of spike timing. ANFs spike at a preferred phase of periodic sounds in a process called phase-locking that is limited to frequencies below a few kilohertz by both the IHC receptor potential and the jitter in synaptic transmission. During phase-locking to periodic sounds of increasing intensity, faster and facilitated activation of synaptic transmission and spike generation may be offset by presynaptic depletion of synaptic vesicles, resulting in relatively small changes in response phase. Here we review encoding of spike-timing at cochlear ribbon synapses.

A numerical method for computing interval distributions for an inhomogeneous Poisson point process modified by random dead times

The inhomogeneous Poisson point process is a common model for time series of discrete, stochastic events. When an event from a point process is detected, it may trigger a random dead time in the detector, during which subsequent events will fail to be detected. It can be difficult or impossible to obtain a closed-form expression for the distribution of intervals between detections, even when the rate function (often referred to as the intensity function) and the dead-time distribution are given. Here, a method is presented to numerically compute the interval distribution expected for any arbitrary inhomogeneous Poisson point process modified by dead times drawn from any arbitrary distribution. In neuroscience, such a point process is used to model trains of neuronal spikes triggered by the detection of excitatory events while the neuron is not refractory. The assumptions of the method are that the process is observed over a finite observation window and that the detector is not in a dead state at the start of the observation window. Simulations are used to verify the method for several example point processes. The method should be useful for modeling and understanding the relationships between the rate functions and interval distributions of the event and detection processes, and how these relationships depend on the dead-time distribution.

Fano Factor: A Potentially Useful Information

The Fano factor, defined as the variance-to-mean ratio of spike counts in a time window, is often used to measure the variability of neuronal spike trains. However, despite its transparent definition, careless use of the Fano factor can easily lead to distorted or even wrong results. One of the problems is the unclear dependence of the Fano factor on the spiking rate, which is often neglected or handled insufficiently. In this paper we aim to explore this problem in more detail and to study the possible solution, which is to evaluate the Fano factor in the operational time. We use equilibrium renewal and Markov renewal processes as spike train models to describe the method in detail, and we provide an illustration on experimental data.

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.

Volume gradients in inner hair cell-auditory nerve fiber pre- and postsynaptic proteins differ across mouse strains

In different animal models, auditory nerve fibers display variation in spontaneous activity and response threshold. Functional and structural differences among inner hair cell ribbon synapses are believed to contribute to this variation. The relative volumes of synaptic proteins at individual synapses might be one such difference. This idea is based on the observation of opposing volume gradients of the presynaptic ribbons and associated postsynaptic glutamate receptor patches in mice along the pillar modiolar axis of the inner hair cell, the same axis along which fibers were shown to vary in their physiological properties. However, it is unclear whether these opposing gradients are expressed consistently across animal models. In addition, such volume gradients observed for separate populations of presynaptic ribbons and postsynaptic glutamate receptor patches suggest different relative volumes of these synaptic structures at individual synapses; however, these differences have not been examined in mice. Furthermore, it is unclear whether such gradients are limited to these synaptic proteins. Therefore, we analyzed organs of Corti isolated from CBA/CaJ, C57BL/6, and FVB/NJ mice using immunofluorescence, confocal microscopy, and quantitative image analysis. We find consistent expression of presynaptic volume gradients across strains of mice and inconsistent expression of postsynaptic volume gradients. We find differences in the relative volume of synaptic proteins, but these are different between CBA/CaJ mice, and C57BL/6 and FVB/NJ mice. We find similar results in C57BL/6 and FVB/NJ mice when using other postsynaptic density proteins (Shank1, Homer, and PSD95). These results have implications for the mechanisms by which volumes of synaptic proteins contribute to variations in the physiology of individual auditory nerve fibers and their vulnerability to excitotoxicity.

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.

Statistics of inverse interspike intervals: The instantaneous firing rate revisited

The rate coding hypothesis is the oldest and still one of the most accepted and investigated scenarios in neuronal activity analyses. However, the actual neuronal firing rate, while informally understood, can be mathematically defined in several different ways. These definitions yield distinct results; even their average values may differ dramatically for the simplest neuronal models. Such an inconsistency, together with the importance of "firing rate," motivates us to revisit the classical concept of the instantaneous firing rate. We confirm that different notions of firing rate can in fact be compatible, at least in terms of their averages, by carefully discerning the time instant at which the neuronal activity is observed. Two general cases are distinguished: either the inspection time is synchronised with a reference time or with the neuronal spiking. The statistical properties of the instantaneous firing rate, including parameter estimation, are analyzed, and compatibility with the intuitively understood concept is demonstrated.