Mathematical models of cochlear nucleus onset neurons: I. Point neuron with many weak synaptic inputs

A Computational Model of Auditory Chirp-Velocity Sensitivity and Amplitude-Modulation Tuning in Inferior Colliculus Neurons

We demonstrate a model of chirp-velocity sensitivity in the inferior colliculus (IC) that retains the tuning to amplitude modulation (AM) that was established in earlier models. The mechanism of velocity sensitivity is sequence detection by octopus cells of the posteroventral cochlear nucleus, which have been proposed in physiological studies to respond preferentially to the order of arrival of cross-frequency inputs of different amplitudes. Model architecture is based on coincidence detection of a combination of excitatory and inhibitory inputs. Chirp-sensitivity of the IC output is largely controlled by the strength and timing of the chirp-sensitive octopus-cell inhibitory input. AM tuning is controlled by inhibition and excitation that are tuned to the same frequency. We present several example neurons that demonstrate the feasibility of the model in simulating realistic chirp-sensitivity and AM tuning for a wide range of characteristic frequencies. Additionally, we explore the systematic impact of varying parameters on model responses. The proposed model can be used to assess the contribution of IC chirp-velocity sensitivity to responses to complex sounds, such as speech.

Mammalian octopus cells are direction selective to frequency sweeps by excitatory synaptic sequence detection

Octopus cells are remarkable projection neurons of the mammalian cochlear nucleus, with extremely fast membranes and wide-frequency tuning. They are considered prime examples of coincidence detectors but are poorly characterized in vivo. We discover that octopus cells are selective to frequency sweep direction, a feature that is absent in their auditory nerve inputs. In vivo intracellular recordings reveal that direction selectivity does not derive from across-frequency coincidence detection but hinges on the amplitudes and activation sequence of auditory nerve inputs tuned to clusters of hot spot frequencies. A simple biophysical octopus cell model excited with real nerve spike trains recreates direction selectivity through interaction of intrinsic membrane conductances with the activation sequence of clustered excitatory inputs. We conclude that octopus cells are sequence detectors, sensitive to temporal patterns across cochlear frequency channels. The detection of sequences rather than coincidences is a much simpler but powerful operation to extract temporal information.

Information Processing by Onset Neurons in the Cat Auditory Brainstem

Octopus cells in the ventral cochlear nucleus (VCN) have been difficult to study because of the very features that distinguish them from other VCN neurons. We performed in vivo recordings in cats on well-isolated units, some of which were intracellularly labeled and histologically reconstructed. We found that responses to low-frequency tones with frequencies < 1 kHz reveal higher levels of neural synchrony and entrainment to the stimulus than the auditory nerve. In responses to higher frequency tones, the neural discharges occur mostly near the stimulus onset. These neurons also respond in a unique way to 100 % amplitude-modulated (AM) tones with discharges exhibiting a bandpass tuning. Responses to frequency-modulated sounds (FM) are unusual: Octopus cells react more vigorously during the ascending than the descending parts of the FM stimulus. We examined responses of neurons in the ventral nucleus of the lateral lemniscus (VNLL) whose discharges to tones and AM sounds are similar to octopus cells. Repeated stimulation with short tone pips of VCN and VNLL onset neurons evokes trains of action potentials with gradual shifts toward later times in their first spike latency. This behavior parallels short-term post-synaptic depression observed by other authors in in vitro VCN recordings of octopus cells. VCN and VNLL onset units in cats respond to frozen noise stimuli with gaps as narrow as 1 ms with a robust discharge near the stimulus onset following the gap. This finding suggests that VCN and VNLL onset cells play a role in gap detection, which is of great importance to speech perception.

Neuronal population model of globular bushy cells covering unit-to-unit variability

Computations of acoustic information along the central auditory pathways start in the cochlear nucleus. Bushy cells in the anteroventral cochlear nucleus, which innervate monaural and binaural stations in the superior olivary complex, process and transfer temporal cues relevant for sound localization. These cells are categorized into two groups: spherical and globular bushy cells (SBCs/GBCs). Spontaneous rates of GBCs innervated by multiple auditory nerve (AN) fibers are generally lower than those of SBCs that receive a small number of large AN synapses. In response to low-frequency tonal stimulation, both types of bushy cells show improved phase-locking and entrainment compared to AN fibers. When driven by high-frequency tones, GBCs show primary-like-with-notch or onset-L peristimulus time histograms and relatively irregular spiking. However, previous in vivo physiological studies of bushy cells also found considerable unit-to-unit variability in these response patterns. Here we present a population of models that can simulate the observed variation in GBCs. We used a simple coincidence detection model with an adaptive threshold and systematically varied its six parameters. Out of 567000 parameter combinations tested, 7520 primary-like-with-notch models and 4094 onset-L models were selected that satisfied a set of physiological criteria for a GBC unit. Analyses of the model parameters and output measures revealed that the parameters of the accepted model population are weakly correlated with each other to retain major GBC properties, and that the output spiking patterns of the model are affected by a combination of multiple parameters. Simulations of frequency-dependent temporal properties of the model GBCs showed a reasonable fit to empirical data, supporting the validity of our population modeling. The computational simplicity and efficiency of the model structure makes our approach suitable for future large-scale simulations of binaural information processing that may involve thousands of GBC units.

In the auditory system, specialized neuronal circuits process various types of acoustic information. A group of neurons, called globular bushy cells (GBCs), faithfully transfer timing information of acoustic signals to their downstream neurons responsible for the perception of sound location. Previous physiological studies found representative activity patterns of GBCs, but with substantial individual variations among them. In this study, we present a population of models, instead of creating one best model, to account for the observed variations of GBCs. We varied all six parameters of a simple auditory neuron model and selected the combinations of parameters that led to acceptable activity patterns of GBCs. In total, we tested more than half a million combinations and accepted ~11600 GBC models. Temporal spiking patterns of real GBCs depend on the sound frequency, and our model population was able to replicate this trend. The model used here is computationally efficient and can thus serve as a building block for future large-scale simulations of auditory information processing.

A biophysical modelling platform of the cochlear nucleus and other auditory circuits: From channels to networks

Models of the auditory brainstem have been an invaluable tool for testing hypotheses about auditory information processing and for highlighting the most important gaps in the experimental literature. Due to the complexity of the auditory brainstem, and indeed most brain circuits, the dynamic behavior of the system may be difficult to predict without a detailed, biologically realistic computational model. Despite the sensitivity of models to their exact construction and parameters, most prior models of the cochlear nucleus have incorporated only a small subset of the known biological properties. This confounds the interpretation of modelling results and also limits the potential future uses of these models, which require a large effort to develop. To address these issues, we have developed a general purpose, biophysically detailed model of the cochlear nucleus for use both in testing hypotheses about cochlear nucleus function and also as an input to models of downstream auditory nuclei. The model implements conductance-based Hodgkin-Huxley representations of cells using a Python-based interface to the NEURON simulator. Our model incorporates most of the quantitatively characterized intrinsic cell properties, synaptic properties, and connectivity available in the literature, and also aims to reproduce the known response properties of the canonical cochlear nucleus cell types. Although we currently lack the empirical data to completely constrain this model, our intent is for the model to continue to incorporate new experimental results as they become available.

Neural Coding of Interaural Time Differences with Bilateral Cochlear Implants in Unanesthetized Rabbits

Although bilateral cochlear implants (CIs) provide improvements in sound localization and speech perception in noise over unilateral CIs, bilateral CI users' sensitivity to interaural time differences (ITDs) is still poorer than normal. In particular, ITD sensitivity of most CI users degrades with increasing stimulation rate and is lacking at the high carrier pulse rates used in CI processors to deliver speech information. To gain a better understanding of the neural basis for this degradation, we characterized ITD tuning of single neurons in the inferior colliculus (IC) for pulse train stimuli in an unanesthetized rabbit model of bilateral CIs. Approximately 73% of IC neurons showed significant ITD sensitivity in their overall firing rates. On average, ITD sensitivity was best for pulse rates near 80-160 pulses per second (pps) and degraded for both lower and higher pulse rates. The degradation in ITD sensitivity at low pulse rates was caused by strong, unsynchronized background activity that masked stimulus-driven responses in many neurons. Selecting synchronized responses by temporal windowing revealed ITD sensitivity in these neurons. With temporal windowing, both the fraction of ITD-sensitive neurons and the degree of ITD sensitivity decreased monotonically with increasing pulse rate. To compare neural ITD sensitivity to human performance in ITD discrimination, neural just-noticeable differences (JNDs) in ITD were computed using signal detection theory. Using temporal windowing at lower pulse rates, and overall firing rate at higher pulse rates, neural ITD JNDs were within the range of perceptual JNDs in human CI users over a wide range of pulse rates.

SIGNIFICANCE STATEMENT

Many profoundly deaf people wearing cochlear implants (CIs) still face challenges in everyday situations, such as understanding conversations in noise. Even with CIs in both ears, they have difficulty making full use of subtle differences in the sounds reaching the two ears [interaural time difference (ITD)] to identify where the sound is coming from. This problem is especially acute at the high stimulation rates used in clinical CI processors. This study provides a better understanding of ITD processing with bilateral CIs and shows a parallel between human performance in ITD discrimination and neural responses in the auditory midbrain. The present study is the first report on binaural properties of auditory neurons with CIs in unanesthetized animals.

A review of the methods for neuronal response latency estimation

Neuronal response latency is usually vaguely defined as the delay between the stimulus onset and the beginning of the response. It contains important information for the understanding of the temporal code. For this reason, the detection of the response latency has been extensively studied in the last twenty years, yielding different estimation methods. They can be divided into two classes, one of them including methods based on detecting an intensity change in the firing rate profile after the stimulus onset and the other containing methods based on detection of spikes evoked by the stimulation using interspike intervals and spike times. The aim of this paper is to present a review of the main techniques proposed in both classes, highlighting their advantages and shortcomings.

Modeling binaural responses in the auditory brainstem to electric stimulation of the auditory nerve

Bilateral cochlear implants (CIs) provide improvements in sound localization and speech perception in noise over unilateral CIs. However, the benefits arise mainly from the perception of interaural level differences, while bilateral CI listeners' sensitivity to interaural time difference (ITD) is poorer than normal. To help understand this limitation, a set of ITD-sensitive neural models was developed to study binaural responses to electric stimulation. Our working hypothesis was that central auditory processing is normal with bilateral CIs so that the abnormality in the response to electric stimulation at the level of the auditory nerve fibers (ANFs) is the source of the limited ITD sensitivity. A descriptive model of ANF response to both acoustic and electric stimulation was implemented and used to drive a simplified biophysical model of neurons in the medial superior olive (MSO). The model's ITD sensitivity was found to depend strongly on the specific configurations of membrane and synaptic parameters for different stimulation rates. Specifically, stronger excitatory synaptic inputs and faster membrane responses were required for the model neurons to be ITD-sensitive at high stimulation rates, whereas weaker excitatory synaptic input and slower membrane responses were necessary at low stimulation rates, for both electric and acoustic stimulation. This finding raises the possibility of frequency-dependent differences in neural mechanisms of binaural processing; limitations in ITD sensitivity with bilateral CIs may be due to a mismatch between stimulation rate and cell parameters in ITD-sensitive neurons.

Refractoriness enhances temporal coding by auditory nerve fibers

A universal property of spiking neurons is refractoriness, a transient decrease in discharge probability immediately following an action potential (spike). The refractory period lasts only one to a few milliseconds, but has the potential to affect temporal coding of acoustic stimuli by auditory neurons, which are capable of submillisecond spike-time precision. Here this possibility was investigated systematically by recording spike times from chicken auditory nerve fibers in vivo while stimulating with repeated pure tones at characteristic frequency. Refractory periods were tightly distributed, with a mean of 1.58 ms. A statistical model was developed to recapitulate each fiber's responses and then used to predict the effect of removing the refractory period on a cell-by-cell basis for two largely independent facets of temporal coding: faithful entrainment of interspike intervals to the stimulus frequency and precise synchronization of spike times to the stimulus phase. The ratio of the refractory period to the stimulus period predicted the impact of refractoriness on entrainment and synchronization. For ratios less than ∼0.9, refractoriness enhanced entrainment and this enhancement was often accompanied by an increase in spike-time precision. At higher ratios, little or no change in entrainment or synchronization was observed. Given the tight distribution of refractory periods, the ability of refractoriness to improve temporal coding is restricted to neurons responding to low-frequency stimuli. Enhanced encoding of low frequencies likely affects sound localization and pitch perception in the auditory system, as well as perception in nonauditory sensory modalities, because all spiking neurons exhibit refractoriness.

An investigation of dendritic delay in octopus cells of the mammalian cochlear nucleus

Octopus cells, located in the mammalian auditory brainstem, receive their excitatory synaptic input exclusively from auditory nerve fibers (ANFs). They respond with accurately timed spikes but are broadly tuned for sound frequency. Since the representation of information in the auditory nerve is well understood, it is possible to pose a number of questions about the relationship between the intrinsic electrophysiology, dendritic morphology, synaptic connectivity, and the ultimate functional role of octopus cells in the brainstem. This study employed a multi-compartmental Hodgkin-Huxley model to determine whether dendritic delay in octopus cells improves synaptic input coincidence detection in octopus cells by compensating for the cochlear traveling wave delay. The propagation time of post-synaptic potentials from synapse to soma was investigated. We found that the total dendritic delay was approximately 0.275 ms. It was observed that low-threshold potassium channels in the dendrites reduce the amplitude dependence of the dendritic delay of post-synaptic potentials. As our hypothesis predicted, the model was most sensitive to acoustic onset events, such as the glottal pulses in speech when the synaptic inputs were arranged such that the model's dendritic delay compensated for the cochlear traveling wave delay across the ANFs. The range of sound frequency input from ANFs was also investigated. The results suggested that input to octopus cells is dominated by high frequency ANFs.

Sensitivity of cochlear nucleus neurons to spatio-temporal changes in auditory nerve activity

The spatio-temporal pattern of auditory nerve (AN) activity, representing the relative timing of spikes across the tonotopic axis, contains cues to perceptual features of sounds such as pitch, loudness, timbre, and spatial location. These spatio-temporal cues may be extracted by neurons in the cochlear nucleus (CN) that are sensitive to relative timing of inputs from AN fibers innervating different cochlear regions. One possible mechanism for this extraction is "cross-frequency" coincidence detection (CD), in which a central neuron converts the degree of coincidence across the tonotopic axis into a rate code by preferentially firing when its AN inputs discharge in synchrony. We used Huffman stimuli (Carney LH. J Neurophysiol 64: 437-456, 1990), which have a flat power spectrum but differ in their phase spectra, to systematically manipulate relative timing of spikes across tonotopically neighboring AN fibers without changing overall firing rates. We compared responses of CN units to Huffman stimuli with responses of model CD cells operating on spatio-temporal patterns of AN activity derived from measured responses of AN fibers with the principle of cochlear scaling invariance. We used the maximum likelihood method to determine the CD model cell parameters most likely to produce the measured CN unit responses, and thereby could distinguish units behaving like cross-frequency CD cells from those consistent with same-frequency CD (in which all inputs would originate from the same tonotopic location). We find that certain CN unit types, especially those associated with globular bushy cells, have responses consistent with cross-frequency CD cells. A possible functional role of a cross-frequency CD mechanism in these CN units is to increase the dynamic range of binaural neurons that process cues for sound localization.

Identification of noisy response latency

In many physical systems there is a time delay before an applied input (stimulation) has an impact on the output (response), and the quantification of this delay is of paramount interest. If the response can only be observed on top of an indistinguishable background signal, the estimation can be highly unreliable, unless the background signal is accounted for in the analysis. In fact, if the background signal is ignored, however small it is compared to the response and however large the delay is, the estimate of the time delay will go to zero for any reasonable estimator when increasing the number of observations. Here we propose a unified concept of response latency identification in event data corrupted by a background signal. It is done in the context of information transfer within a neural system, more specifically on spike trains from single neurons. The estimators are compared on simulated data and the most suitable for specific situations are recommended.

Neuronal spike-train responses in the presence of threshold noise

The variability of neuronal firing has been an intense topic of study for many years. From a modelling perspective it has often been studied in conductance based spiking models with the use of additive or multiplicative noise terms to represent channel fluctuations or the stochastic nature of neurotransmitter release. Here we propose an alternative approach using a simple leaky integrate-and-fire model with a noisy threshold. Initially, we develop a mathematical treatment of the neuronal response to periodic forcing using tools from linear response theory and use this to highlight how a noisy threshold can enhance downstream signal reconstruction. We further develop a more general framework for understanding the responses to large amplitude forcing based on a calculation of first passage times. This is ideally suited to understanding stochastic mode-locking, for which we numerically determine the Arnol'd tongue structure. An examination of data from regularly firing stellate neurons within the ventral cochlear nucleus, responding to sinusoidally amplitude modulated pure tones, shows tongue structures consistent with these predictions and highlights that stochastic, as opposed to deterministic, mode-locking is utilised at the level of the single stellate cell to faithfully encode periodic stimuli.

First-Spike Latency in the Presence of Spontaneous Activity

A new statistical method for the estimation of the response latency is proposed. When spontaneous discharge is present, the first spike after the stimulus application may be caused by either the stimulus itself, or it may appear due to the prevailing spontaneous activity. Therefore, an appropriate method to deduce the response latency from the time to the first spike after the stimulus is needed. We develop a nonparametric estimator of the response latency based on repeated stimulations. A simulation study is provided to show how the estimator behaves with an increasing number of observations and for different rates of spontaneous and evoked spikes. Our nonparametric approach requires very few assumptions. For comparison, we also consider a parametric model. The proposed probabilistic model can be used for both single and parallel neuronal spike trains. In the case of simultaneously recorded spike trains in several neurons, the estimators of joint distribution and correlations of response latencies are also introduced. Real data from inferior colliculus auditory neurons obtained from a multielectrode probe are studied to demonstrate the statistical estimators of response latencies and their correlations in space.

The role of auditory nerve innervation and dendritic filtering in shaping onset responses in the ventral cochlear nucleus

Neurons in the ventral cochlear nucleus (VCN) that respond primarily at the onset of a pure tone stimulus show diversity in terms of peri-stimulus-time-histograms (PSTHs), rate-level functions, frequency tuning, and also their responses to broad band noise. A number of different mechanisms have been proposed as contributing to the onset characteristic: e.g. coincidence, depolarisation block, and low-threshold potassium currents. We show that a simple point neuron receiving convergent inputs from high-spontaneous rate auditory nerve (AN) fibers, with no special currents and no peri-stimulatory shifts in firing threshold, is sufficient to produce much of the diversity seen experimentally. Three sub-classes of onset PSTHs: onset-ideal (OI), onset-chopper (OC) and onset-locker (OL) are reproduced by variations in innervation patterns and dendritic filtering. The factors shaping responses were explored by systematically varying key parameters. An OI response in this model requires a narrow range of AN input best frequencies (BF) which only produce supra-threshold depolarizations during the stimulus onset. For OC and OL responses, receptive fields were wider. Considerable low pass filtering of AN inputs away from BF results in an OL, whilst relatively unfiltered inputs produce an OC response. Rate-level functions in response to pure tones can be sloping, or plateau. These can be also reproduced in the model by the manipulation of the AN innervation. The model supports the coincidence detection hypothesis, and suggests that differences in excitatory innervation and dendritic filtering constant are important factors to consider when accounting for the variation in response characteristics seen in VCN onset units.

The volley theory and the spherical cell puzzle

Temporal coding in the auditory nerve is strikingly transformed in the cochlear nucleus. In contrast to fibers in the auditory nerve, some neurons in the cochlear nucleus can show "picket fence" phase-locking to low-frequency pure tones: they fire a precisely timed action potential at every cycle of the stimulus. Such synchronization enhancement and entrainment is particularly prominent in neurons with the spherical and globular morphology, described by Osen [Osen KK (1969) Cytoarchitecture of the cochlear nuclei in the cat. J Comp Neurol 136:453-483]. These neurons receive large axosomatic terminals from the auditory nerve--the end bulbs and modified end bulbs of Held--and project to binaural comparator nuclei in the superior olivary complex. The most popular model to account for picket fence phase-locking is monaural coincidence detection. This mechanism is plausible for globular neurons, which receive a large number of inputs. We draw attention to the existence of enhanced phase-locking and entrainment in spherical neurons, which receive too few end-bulb inputs from the auditory nerve to make a coincidence detection of end-bulb firings a plausible mechanism of synchronization enhancement.

First-spike latency information in single neurons increases when referenced to population onset

It is well known that many stimulus parameters, such as sound location in the auditory system or contrast in the visual system, can modulate the timing of the first spike in sensory neurons. Could first-spike latency be a candidate neural code? Most studies measuring first-spike latency information assume that the brain has an independent reference for stimulus onset from which to extract latency. This assumption creates an obvious confound that casts doubt on the feasibility of first-spike latency codes. If latency is measured relative to an internal reference of stimulus onset calculated from the responses of the neural population, the information conveyed by the latency of single neurons might decrease because of correlated changes in latency across the population. Here we assess the effects of a realistic model of stimulus onset detection on the first-spike latency information conveyed by single neurons in the auditory system. Contrary to expectation, we find that on average, the information contained in single neurons does not decrease; in fact, the majority of neurons show a slight increase in the information conveyed by latency referenced to a population onset. Our results show that first-spike latency codes are a feasible mechanism for information transfer even when biologically plausible estimates of stimulus onset are taken into account.

Structural and functional classes of multipolar cells in the ventral cochlear nucleus

Multipolar cells in the ventral cochlear nucleus (VCN) are a structurally and functionally diverse group of projection neurons. Understanding their role in the ascending pathway involves partitioning multipolar cells into distinct populations and determining where in the brain each sends its coded messages. In this study, we used retrograde labeling techniques in rats to identify multipolar neurons that project their axons to the ipsilateral dorsal cochlear nucleus (DCN), the contralateral CN, or both structures. Three rats received injections of biotinylated dextran amine in the ipsilateral DCN and diamidino yellow in the contralateral CN. Several radiate multipolar neurons (defined by their axonal projections to the ipsilateral DCN and their dendrites that traverse VCN isofrequency sheets) were double-labeled but over 70% were not. This result suggests two distinct populations: (1) radiate-commissural (RC) multipolar cells that project to the ipsilateral DCN and the contralateral CN, and (2) radiate multipolar cells that project exclusively (in this context) to the ipsilateral DCN. In a different group of animals, we retrogradely labeled multipolar neurons that project their axons to the contralateral CN and measured the size of their cell bodies. The mean size of this population (266 +/- 156 microm2) was significantly smaller than those of RC-multipolar cells (418 +/- 140 microm2). We conclude that the CN commissural pathway is composed of at least two components: (1) RC multipolar cells and (2) commissural multipolar cells that are small- and medium-sized neurons that project exclusively (in this context) to the contralateral CN. These results identify separate structural groups of multipolar cells that may correspond to physiological unit types described in the literature. They also provide protocols for isolating and studying different populations of multipolar cells to determine the neural mechanisms that govern their responses to sound.

Response properties of an integrate-and-fire model that receives subthreshold inputs

A computational technique is described for calculation of the interspike interval and poststimulus time histograms for the responses of an integrate-and-fire model to arbitrary inputs. The effects of the model parameters on the response statistics were studied systematically. Specifically, the probability distribution of the membrane potential was calculated as a function of time, and the mean interspike interval and PST histogram were calculated for arbitrary inputs. For stationary inputs, the regularity of the output was studied in detail for various model parameters. For nonstationary inputs, the effects of the model parameters on the output synchronization index were explored. The results show that enhanced synchronization in response to low-frequency stimuli required a large number (n > 25) of weak inputs. Irregular responses and a linear input-output rate relationship required strong (but subthreshold) inputs with a small time constant. A model cell with mixed-amplitude synaptic inputs can respond to stationary inputs irregularly and have enhanced synchronization to nonstationary inputs that are phase-locked to low-frequency inputs. Both of these response properties have been reported for some cells in the ventral cochlear nucleus in the auditory brainstem.

A functional point-neuron model simulating cochlear nucleus ideal onset responses

Cochlear nucleus neurons revealing ideal onset (OI)-type peri-stimulus time histograms (PSTH) encode temporal features of acoustic stimuli with very high precision. These neurons are therefore assumed to be involved in the recognition of natural sounds with temporally varying envelopes such as speech. A functional point-neuron model is presented here for the simulation of OI-unit responses found in cochlear nucleus octopus cells. The model assumes a biphasic response of the membrane potential to a current impulse, the membrane impulse response, and a dynamic spike-blocking mechanism. The predicted responses to pure tones at low and high frequencies, injected current steps, and amplitude modulated tones are compared to recordings from the literature. The model accounts for the main response properties in the data using the same small set of parameters for all experimental conditions. The assumed biphasic shape of the membrane impulse response, reflecting a higher sensitivity to stimulus transients and fast changes relative to sustained stimulus portions, allows for a description of OI-unit responses that cannot be accounted for by a coincidence detector model with an integrate-to-threshold dynamic. The presented functional model may be useful as a processing module in more complex models of auditory signal processing and perception.

Mathematical models of cochlear nucleus onset neurons: II. model with dynamic spike-blocking state

Onset (On) neurons in the cochlear nucleus (CN), characterized by their prominent response to the onset followed by little or no response to the steady-state of sustained stimuli, have a remarkable ability to entrain (firing 1 spike per cycle of a periodic stimulus) to low-frequency tones up to 1000 Hz. In this article, we present a point-neuron model with independent, excitatory auditory-nerve (AN) inputs that accounts for the ability of On neurons to both produce onset responses for high-frequency tone bursts and entrain to a wide range of low-frequency tones. With a fixed-duration spike-blocking state after a spike (an absolute refractory period), the model produces entrainment to a broad range of low-frequency tones and an On response with short interspike intervals (chopping) for high-frequency tone bursts. To produce On response patterns with no chopping, we introduce a novel, more complex, active membrane model in which the spike-blocking state is maintained until the instantaneous membrane voltage falls below a transition voltage. During the sustained depolarization for a high-frequency tone burst, the new model does not chop because it enters a spike-blocking state after the first spike and fails to leave this state until the membrane voltage returns toward rest at the end of the stimulus. The model entrains to low-frequency tones because the membrane voltage falls below the transition voltage on every cycle when the AN inputs are phase-locked. With the complex membrane model, On response patterns having moderate steady-state activity for high-frequency tone bursts (On-L) are distinguished from those having no steady-state activity (On-I) by requiring fewer AN inputs. Voltage-gated ion channels found in On-responding neurons of the CN may underlie the hypothesized dynamic spike-blocking state. These results provide a mechanistic rationale for distinguishing between the different physiological classes of CN On neurons.