Research PaperA simple model of the inner-hair-cell ribbon synapse accounts for mammalian auditory-nerve-fiber spontaneous spike times
Introduction
Acoustic information from the auditory periphery is relayed to the brain via primary auditory afferents and encoded in the timing of the spikes generated by them. In the mammalian cochlea, the peripheral axon of each primary auditory afferent (type-I auditory-nerve fiber; ANF) usually contacts only one sensory receptor cell (inner hair cell; IHC) at one private ribbon synapse, which converts the graded IHC membrane potential to a train of ANF spikes via the release of glutamate (Matthews and Fuchs, 2010). Release events also occur spontaneously in the absence of acoustic stimulation, and nearly all cause a spike unless the ANF is refractory (Siegel, 1992, Rutherford et al., 2012, Zhang-Hooks et al., 2016). Spike timing in ANF spontaneous activity therefore provides an indirect view of ribbon synapse function in vivo.
Spontaneous activity has been modeled by point processes in which stochastic trains of excitatory events are modified by postsynaptic refractoriness to yield spike trains (e.g., Kiang et al., 1965, Gaumond et al., 1983, Bibikov and Ivanitskii, 1985, Teich and Khanna, 1985, Young and Barta, 1986, Teich et al., 1990a, Teich et al., 1990b, Lowen and Teich, 1992, Carney, 1993, Li and Young, 1993, Miller and Wang, 1993, Prijs et al., 1993, Delgutte, 1996, Johnson, 1996, Zhang et al., 2001, Jackson and Carney, 2005, Heil et al., 2007, Peterson et al., 2014; for review, see Heil and Peterson, 2015, Heil and Peterson, 2017). Event trains were often assumed to be Poisson renewal point processes, with all history effects in the subsequent spike trains being attributed to postsynaptic refractoriness. Several observations contradict such an assumption. First, mean refractory periods are short (∼1 ms; Brown, 1994, Cartee et al., 2000, Miller et al., 2001, Shepherd et al., 2004, Morsnowski et al., 2006, Joshi et al., 2017), whereas interspike interval (ISI) distributions deviate over tens of milliseconds from the exponential distribution expected for a Poisson process. Second, similar deviations were also reported for distributions of intervals between excitatory postsynaptic currents (EPSCs), which occur prior to postsynaptic refractoriness (Wu et al., 2016). Third, predominantly negative serial correlations exist between low-order (e.g., adjacent) ISIs (Prijs et al., 1993, Peterson et al., 2014), and positive correlations exist between higher-order ISIs (Lowen and Teich, 1992, Teich and Lowen, 1994). These history effects in the distribution and ordering of ISIs manifest in the Fano factor, which measures spike-count variability (Teich and Khanna, 1985, Lowen and Teich, 1992, Peterson et al., 2014). The spike trains are less variable than a Poisson process over short time scales, due to refractoriness and negative serial ISI correlations, but more variable than a Poisson process over long time scales, due to rate fluctuations that generate positive long-range correlations and cause the Fano factor to grow in a power-law-like fashion with increasing counting time (Teich, 1989, Teich et al., 1990a, Teich et al., 1990b, Lowen and Teich, 1992, Teich and Lowen, 1994, Delgutte, 1996, Kelly et al., 1996, Chacron et al., 2001, Jackson and Carney, 2005, Moezzi et al., 2014, Moezzi et al., 2016). Such fluctuations likely originate presynaptically (Wu et al., 2016).
Here, we describe an alternative to the point process model used by Peterson et al. (2014) to account for the major history effects in cat-ANF spontaneous spike trains. Each train of excitatory release events is generated via the depletion and replenishment of a small number of presynaptic release sites and is then modified by ANF refractoriness to yield a spike train. Unlike in the previous model, each release site is depleted and replenished independently and stochastically, which enables the model to better account for spontaneous (and even steady-state sound-driven) activity having a high spike rate and allows for interevent interval (IEI) distributions to be derived analytically. The structure of the model is nearly identical (see 2.3) to that proposed by Frank et al. (2010), but our estimates of the model parameters differ markedly from theirs. We demonstrate that the model, with our parameter estimates, accounts for the major properties of a population of cat-ANF spontaneous spike trains much better than popular comprehensive models of the auditory periphery (Meddis, 1986, Zilany et al., 2014). We show that the model also accounts for the IEI distributions of individual EPSC trains and the ISI distributions of individual spike trains from several mammalian species, and that the effects of long-range correlations on spike-count variability can be reproduced using fractional Gaussian noise. We also explore more complex model variants having an additional rate-limiting step in the vesicle cycle, but find no reason to prefer them to the simpler version. Finally, we explore a more complex variant having both short and long relative refractory components and find that it cannot account for all aspects of the data.
Section snippets
Data
Most of the data for this study were used in two previous studies of the first-order ISI distributions from spontaneous spike trains of cat ANFs (Heil et al., 2007, Peterson et al., 2014), with the details of data acquisition given in the former. Briefly, in five barbiturate-anesthetized adult cats (three females, two males), spikes of 171 individual ANFs were recorded extracellularly, with microelectrodes, from the left auditory nerve near its exit from the internal auditory meatus. Continuous
Results
The results are organized into several sections. We first demonstrate that the previous synapse model of Peterson et al. (2014), in which the replenishment of empty release sites occurs deterministically, does not yield realistic IEI and ISI distributions when the mean rate is too high. We then demonstrate that the current synapse model, in which the replenishment of empty release sites occurs stochastically, yields realistic IEI and ISI distributions even at high rates and can account for the
Discussion
We have shown that a synapse model (Fig. 2) with a small number of independently and stochastically depleted and replenished release sites, combined with short postsynaptic absolute and relative refractory periods, can account for all history effects observed in mammalian ANF spontaneous spike trains over short time scales (Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 11).
Acknowledgements
This work was supported by the Deutsche Forschungsgemeinschaft (Priority Program 1608 “Ultrafast and temporally precise information processing: Normal and dysfunctional hearing”, He1721/11-1 and He1721/11-2 to PH). Data collection in the lab of Dexter R.F. Irvine at Monash University, Melbourne, Australia, was supported by other grants (He1721/5-1 and He1721/5-2). We are grateful to Dexter R.F. Irvine and Mel Brown for helping with data collection, to Robert E. Wickesberg for providing
References (113)
- et al.
Evaluation of a model of the cochlear neural membrane. I. Physiological measurement of membrane characteristics in response to intrameatal electrical stimulation
Hear Res.
(2000) - et al.
Uniquantal release through a dynamic fusion pore is a candidate mechanism of hair cell exocytosis
Neuron
(2014) - et al.
Bassoon and the synaptic ribbon organize Ca2+ channels and vesicles to add release sites and promote refilling
Neuron
(2010) - et al.
A stochastic model of the repetitive activity of neurons
Biophys. J.
(1966) - et al.
The diameters of Guinea pig auditory nerve fibres: distribution and correlation with spontaneous rate
Hear Res.
(1993) Conditional probability analyses of the spike activity of single neurons
Biophys. J.
(1967)- et al.
Towards a unifying basis of auditory thresholds: distributions of the first-spike latencies of auditory-nerve fibers
Hear Res.
(2008) - et al.
Sound coding in the auditory nerve of gerbils
Hear Res.
(2016) - et al.
Testing the null hypothesis of stationarity against the alternative of a unit root
J. Econ.
(1992) - et al.
Depolarization redistributes synaptic membrane and creates a gradient of vesicles on the synaptic body at a ribbon synapse
Neuron
(2002)
Morphological differences among radial afferent fibers in the cat cochlea- an electron-microscopic study of serial sections
Hear Res.
Postnatal maturation of auditory-nerve heterogeneity, as seen in spatial gradients of synapse morphology in the inner hair cell area
Hear Res.
Measurement of variability dynamics in cortical spike trains (2008)
J. Neurosci. Methods
Multiple roles of calcium ions in the regulation of neurotransmitter release
Neuron
Otoferlin: a multi-C2 domain protein essential for hearing
Trends Neurosci.
Neuronal spike trains and stochastic point processes. I. The single spike train
Biophys. J.
Congenital deafness and sinoatrial node dysfunction in mice lacking class D L-type Ca2+ channels
Cell
Recovery characteristics of auditory nerve fibres in the normal and noise-damaged Guinea pig cochlea
Hear Res.
The ubiquitous nature of multivesicular release
Trends Neurosci.
Calcium-dependent synaptic vesicle trafficking underlies indefatigable release at the hair cell afferent fiber synapse
Neuron
Spontaneous synaptic potentials from afferent terminals in the Guinea pig cochlea
Hear Res.
Rate fluctuations and fractional power-law noise recorded from cells in the auditory pathway of the cat
Hear Res.
Spike count reliability and the Poisson hypothesis
J. Neurosci.
Modeling the resonant release of synaptic transmitter by hair cells as an example of biological oscillators with cooperative steps
Proc. Natl. Acad. Sci. U. S. A.
Refractoriness and neural precision
J. Neurosci.
Modelling spontaneous pulsation and short-term adaptation in the fibres of the auditory nerve
Biophysics
The antidromic compound action potential of the auditory nerve
J. Neurophysiol.
A Phenomenological Model of the Synapse between the Inner Hair Cell and Auditory Nerve: Implications of Limited Neurotransmitter Release Sites
Onset coding is degraded in auditory nerve fibers from mutant mice lacking synaptic ribbons
J. Neurosci.
A model for the responses of low-frequency auditory-nerve fibers in cat
J. Acoust. Soc. Am.
Role of intracellular calcium stores in hair-cell ribbon synapse
Front. Cell Neurosci.
Negative interspike interval correlations increase the neuronal capacity for encoding time-dependent stimuli
J. Neurosci.
Suprathreshold stochastic firing dynamics with memory in P-type electroreceptors
Phys. Rev. Lett.
Point processes
The Statistical Analysis of Series of Events
On the superposition of renewal processes
Biometrika
Physiological models for basic auditory percepts
Ionization yield of radiation. II. The fluctuations of the number of ions
Phys. Rev.
Serial correlation in neural spike trains: experimental evidence, stochastic modeling, and single neuron variability
Phys. Rev. E
Mechanisms contributing to synaptic Ca2+ signals and their heterogeneity in hair cells
Proc. Natl. Acad. Sci. U. S. A.
Responses of cochlear nerve fibers to brief acoustic stimuli: role of discharge history effects
J. Acoust. Soc. Am.
Stimulus and recovery dependence of cat cochlear nerve fiber spike discharge probability
J. Neurophysiol.
Transmitter release at the hair cell ribbon synapse
Nat. Neurosci.
Redundancy reduction and sustained firing with stochastic depressing synapses
J. Neurosci.
Time course and calcium dependence of transmitter release at a single ribbon synapse
Proc. Natl. Acad. Sci. U. S. A.
Two modes of release shape the postsynaptic response at the inner hair cell ribbon synapse
J. Neurosci.
Sharp Ca2+ nanodomains beneath the ribbon promote highly synchronous multivesicular release at hair cell synapses
J. Neurosci.
Spontaneous activity of auditory-nerve fibers: insights into stochastic processes at ribbon synapses
J. Neurosci.
Summing across different active zones can explain the quasi-linear Ca2+−dependencies of exocytosis by receptor cells
Front. Synaptic Neurosci.
An improved model for the rate – level functions of auditory-nerve fibers
J. Neurosci.
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2021, Hearing ResearchCitation Excerpt :It is unclear whether the lowpass filtering performed by entry and accumulation of calcium (Kidd and Weiss, 1990; Borst and Abarbanel, 2007) would suffice. Another potential cause for the saturation of the mean spike rate is the noninstantaneous replenishment of empty synaptic release sites (e.g., Peterson and Heil, 2018). Such a process imposes an upper limit on the mean rate, but not on the instantaneous rate, and therefore does not lead to peak clipping.
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2018, Hearing ResearchCitation Excerpt :Peterson and Heil (In Press) argued that the standard deviation of the fGn in the Zilany et al. (2009, 2014) models was too large to accurately predict their Fano factor data when coupled with their synapse model. We did indeed find in this study that we needed to reduce the standard deviation of the fGn in our new model, but not to the same degree as Peterson and Heil (In Press), because they passed the fGn directly into their synaptic release model, whereas in our model the fGn passes first through the slow PLA (see Fig. 2), which effectively low-pass filters the fGn and reduces its magnitude at the input to our synaptic release model. In conclusion, we have found that incorporating a limited number of synaptic release sites with adaptive redocking dynamics produces improved predictions of both spontaneous and sound-driven ANF spiking statistics.
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