Octopus cells of the mammalian ventral cochlear nucleus sense the rate of depolarization

Imaging Voltage Globally and in Isofrequency Lamina in Slices of Mouse Ventral Cochlear Nucleus

The cochlear nuclei (CNs) receive sensory information from the ear and perform fundamental computations before relaying this information to higher processing centers. These computations are performed by distinct types of neurons interconnected in circuits dedicated to the specialized roles of the auditory system. In the present study, we explored the use of voltage imaging to investigate CN circuitry. We tested two approaches based on fundamentally different voltage sensing technologies. Using a voltage-sensitive dye we recorded glutamate receptor-independent signals arising predominantly from axons. The mean conduction velocity of these fibers of 0.27 m/s was rapid but in range with other unmyelinated axons. We then used a genetically-encoded hybrid voltage sensor (hVOS) to image voltage from a specific population of neurons. Probe expression was controlled using Cre recombinase linked to c-fos activation. This activity-induced gene enabled targeting of neurons that are activated when a mouse hears a pure 15-kHz tone. In CN slices from these animals auditory nerve fiber stimulation elicited a glutamate receptor-dependent depolarization in hVOS probe-labeled neurons. These cells resided within a band corresponding to an isofrequency lamina, and responded with a high degree of synchrony. In contrast to the axonal origin of voltage-sensitive dye signals, hVOS signals represent predominantly postsynaptic responses. The introduction of voltage imaging to the CN creates the opportunity to investigate auditory processing circuitry in populations of neurons targeted on the basis of their genetic identity and their roles in sensory processing.

What Is the Benefit of Ramped Pulse Shapes for Activating Auditory Cortex Neurons? An Electrophysiological Study in an Animal Model of Cochlear Implant

In all commercial cochlear implant (CI) devices, the activation of auditory nerve fibers is performed with rectangular pulses that have two phases of opposite polarity. Recently, several papers proposed that ramped pulse shapes could be an alternative shape for efficiently activating auditory nerve fibers. Here, we investigate whether ramped pulse shapes can activate auditory cortex (ACx) neurons in a more efficient way than the classical rectangular pulses. Guinea pigs were implanted with CI devices and responses of ACx neurons were tested with rectangular pulses and with four ramped pulse shapes, with a first-phase being either cathodic or anodic. The thresholds, i.e., the charge level necessary for obtaining significant cortical responses, were almost systematically lower with ramped pulses than with rectangular pulses. The maximal firing rate (FR) elicited by the ramped pulses was higher than with rectangular pulses. As the maximal FR occurred with lower charge levels, the dynamic range (between threshold and the maximal FR) was not modified. These effects were obtained with cathodic and anodic ramped pulses. By reducing the charge levels required to activate ACx neurons, the ramped pulse shapes should reduce charge consumption and should contribute to more battery-efficient CI devices in the future.

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.

Distinct neuronal types contribute to hybrid temporal encoding strategies in primate auditory cortex

Studies of the encoding of sensory stimuli by the brain often consider recorded neurons as a pool of identical units. Here, we report divergence in stimulus-encoding properties between subpopulations of cortical neurons that are classified based on spike timing and waveform features. Neurons in auditory cortex of the awake marmoset (Callithrix jacchus) encode temporal information with either stimulus-synchronized or nonsynchronized responses. When we classified single-unit recordings using either a criteria-based or an unsupervised classification method into regular-spiking, fast-spiking, and bursting units, a subset of intrinsically bursting neurons formed the most highly synchronized group, with strong phase-locking to sinusoidal amplitude modulation (SAM) that extended well above 20 Hz. In contrast with other unit types, these bursting neurons fired primarily on the rising phase of SAM or the onset of unmodulated stimuli, and preferred rapid stimulus onset rates. Such differentiating behavior has been previously reported in bursting neuron models and may reflect specializations for detection of acoustic edges. These units responded to natural stimuli (vocalizations) with brief and precise spiking at particular time points that could be decoded with high temporal stringency. Regular-spiking units better reflected the shape of slow modulations and responded more selectively to vocalizations with overall firing rate increases. Population decoding using time-binned neural activity found that decoding behavior differed substantially between regular-spiking and bursting units. A relatively small pool of bursting units was sufficient to identify the stimulus with high accuracy in a manner that relied on the temporal pattern of responses. These unit type differences may contribute to parallel and complementary neural codes.

Neurons in auditory cortex show highly diverse responses to sounds. This study suggests that neuronal type inferred from baseline firing properties accounts for much of this diversity, with a subpopulation of bursting units being specialized for precise temporal encoding.

The Perception of Ramped Pulse Shapes in Cochlear Implant Users

The electric stimulation provided by current cochlear implants (CI) is not power efficient. One underlying problem is the poor efficiency by which information from electric pulses is transformed into auditory nerve responses. A novel stimulation paradigm using ramped pulse shapes has recently been proposed to remedy this inefficiency. The primary motivation is a better biophysical fit to spiral ganglion neurons with ramped pulses compared to the rectangular pulses used in most contemporary CIs. Here, we tested the hypotheses that ramped pulses provide more efficient stimulation compared to rectangular pulses and that a rising ramp is more efficient than a declining ramp. Rectangular, rising ramped and declining ramped pulse shapes were compared in terms of charge efficiency and discriminability, and threshold variability in seven CI listeners. The tasks included single-channel threshold detection, loudness-balancing, discrimination of pulse shapes, and threshold measurement across the electrode array. Results showed that reduced charge, but increased peak current amplitudes, was required at threshold and most comfortable levels with ramped pulses relative to rectangular pulses. Furthermore, only one subject could reliably discriminate between equally-loud ramped and rectangular pulses, suggesting variations in neural activation patterns between pulse shapes in that participant. No significant difference was found between rising and declining ramped pulses across all tests. In summary, the present findings show some benefits of charge efficiency with ramped pulses relative to rectangular pulses, that the direction of a ramped slope is of less importance, and that most participants could not perceive a difference between pulse shapes.

Similarities in the Biophysical Properties of Spiral-Ganglion and Vestibular-Ganglion Neurons in Neonatal Rats

The membranes of auditory and vestibular afferent neurons each contain diverse groups of ion channels that lead to heterogeneity in their intrinsic biophysical properties. Pioneering work in both auditory- and vestibular-ganglion physiology have individually examined this remarkable diversity, but there are few direct comparisons between the two ganglia. Here the firing patterns recorded by whole-cell patch-clamping in neonatal vestibular- and spiral ganglion neurons are compared. Indicative of an overall heterogeneity in ion channel composition, both ganglia exhibit qualitatively similar firing patterns ranging from sustained-spiking to transient-spiking in response to current injection. The range of resting potentials, voltage thresholds, current thresholds, input-resistances, and first-spike latencies are similarly broad in both ganglion groups. The covariance between several biophysical properties (e.g., resting potential to voltage threshold and their dependence on postnatal age) was similar between the two ganglia. Cell sizes were on average larger and more variable in VGN than in SGN. One sub-group of VGN stood out as having extra-large somata with transient-firing patterns, very low-input resistance, fast first-spike latencies, and required large current amplitudes to induce spiking. Despite these differences, the input resistance per unit area of the large-bodied transient neurons was like that of smaller-bodied transient-firing neurons in both VGN and SGN, thus appearing to be size-scaled versions of other transient-firing neurons. Our analysis reveals that although auditory and vestibular afferents serve very different functions in distinct sensory modalities, their biophysical properties are more closely related by firing pattern and cell size than by sensory modality.

A phenomenological spiking model for octopus cells in the posterior-ventral cochlear nucleus

Octopus cells in the posteroventral cochlear nucleus exhibit characteristic onset responses to broad band transients but are little investigated in response to more complex sound stimuli. In this paper, we propose a phenomenological, but biophysically motivated, modeling approach that allows to simulate responses of large populations of octopus cells to arbitrary sound pressure waves. The model depends on only few parameters and reproduces basic physiological characteristics like onset firing and phase locking to amplitude modulations. Simulated responses to speech stimuli suggest that octopus cells are particularly sensitive to high-frequency transients in natural sounds and their sustained firing to phonemes provides a population code for sound level.

Different sensitivity of action potential generation to the rate of depolarization in vagal afferent A-fiber versus C-fiber neurons

This study demonstrates that the action potential discharge in vagal afferent A-fiber neurons is about 20 times more sensitive to the rate of membrane depolarization compared to C-fiber neurons. The sensitivity of action potential generation to the depolarization rate in vagal sensory neurons is independent of the intensity of current stimuli but nearly abrogated by inhibiting the D-type potassium channel. These findings help better understand the mechanisms that control the activation of vagal afferent nerves.

Ramped pulse shapes are more efficient for cochlear implant stimulation in an animal model

In all commercial cochlear implant (CI) devices, the electric stimulation is performed with a rectangular pulse that generally has two phases of opposite polarity. To date, developing new stimulation strategies has relied on the efficacy of this shape. Here, we investigate the potential of a novel stimulation paradigm that uses biophysically-inspired electrical ramped pulses. Using electrically-evoked auditory brainstem response (eABR) recordings in mice, we found that less charge, but higher current level amplitude, is needed to evoke responses with ramped shapes that are similar in amplitude to responses obtained with rectangular shapes. The most charge-efficient pulse shape had a rising ramp over both phases, supporting findings from previous in vitro studies. This was also true for longer phase durations. Our study presents the first physiological data on CI-stimulation with ramped pulse shapes. By reducing charge consumption ramped pulses have the potential to produce more battery-efficient CIs and may open new perspectives for designing other efficient neural implants in the future.

Spike threshold adaptation diversifies neuronal operating modes in the auditory brain stem

Single neurons function along a spectrum of neuronal operating modes whose properties determine how the output firing activity is generated from synaptic input. The auditory brain stem contains a diversity of neurons, from pure coincidence detectors to pure integrators and those with intermediate properties. We investigated how intrinsic spike initiation mechanisms regulate neuronal operating mode in the avian cochlear nucleus. Although the neurons in one division of the avian cochlear nucleus, nucleus magnocellularis, have been studied in depth, the spike threshold dynamics of the tonically firing neurons of a second division of cochlear nucleus, nucleus angularis (NA), remained unexplained. The input-output functions of tonically firing NA neurons were interrogated with directly injected in vivo-like current stimuli during whole cell patch-clamp recordings in vitro. Increasing the amplitude of the noise fluctuations in the current stimulus enhanced the firing rates in one subset of tonically firing neurons ("differentiators") but not another ("integrators"). We found that spike thresholds showed significantly greater adaptation and variability in the differentiator neurons. A leaky integrate-and-fire neuronal model with an adaptive spike initiation process derived from sodium channel dynamics was fit to the firing responses and could recapitulate >80% of the precise temporal firing across a range of fluctuation and mean current levels. Greater threshold adaptation explained the frequency-current curve changes due to a hyperpolarized shift in the effective adaptation voltage range and longer-lasting threshold adaptation in differentiators. The fine-tuning of the intrinsic properties of different NA neurons suggests they may have specialized roles in spectrotemporal processing.NEW & NOTEWORTHY Avian cochlear nucleus angularis (NA) neurons are responsible for encoding sound intensity for sound localization and spectrotemporal processing. An adaptive spike threshold mechanism fine-tunes a subset of repetitive-spiking neurons in NA to confer coincidence detector-like properties. A model based on sodium channel inactivation properties reproduced the activity via a hyperpolarized shift in adaptation conferring fluctuation sensitivity.

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.

The ion channels and synapses responsible for the physiological diversity of mammalian lower brainstem auditory neurons

The auditory part of the brainstem is composed of several nuclei specialized in the computation of the different spectral and temporal features of the sound before it reaches the higher auditory regions. There are a high diversity of neuronal types in these nuclei, many with remarkable electrophysiological and synaptic properties unique to these structures. This diversity reflects specializations necessary to process the different auditory signals in order to extract precisely the acoustic information necessary for the auditory perception by the animal. Low threshold Kv1 channels and HCN channels are expressed in neurons that use timing clues for auditory processing, like bushy and octopus cells, in order to restrict action potential firing and reduce input resistance and membrane time constant. Kv3 channels allow principal neurons of the MNTB and pyramidal DCN neurons to fire fast trains of action potentials. Calcium channels on cartwheel DCN neurons produce complex spikes characteristic of these neurons. Calyceal synapses compensate the low input resistance of bushy and principal neurons of the MNTB by releasing hundreds of glutamate vesicles resulting in large EPSCs acting in fast ionotropic glutamate receptors, in order to reduce temporal summation of synaptic potentials, allowing more precise correspondence of pre- and post-synaptic potentials, and phase-locking. Pre-synaptic calyceal sodium channels have fast recovery from inactivation allowing extremely fast trains of action potential firing, and persistent sodium channels produce spontaneous activity of fusiform neurons at rest, which expands the dynamic range of these neurons. The unique combinations of different ion channels, ionotropic receptors and synaptic structures create a unique functional diversity of neurons extremely adapted to their complex functions in the auditory processing.

Compensation for Traveling Wave Delay Through Selection of Dendritic Delays Using Spike-Timing-Dependent Plasticity in a Model of the Auditory Brainstem

Asynchrony among synaptic inputs may prevent a neuron from responding to behaviorally relevant sensory stimuli. For example, “octopus cells” are monaural neurons in the auditory brainstem of mammals that receive input from auditory nerve fibers (ANFs) representing a broad band of sound frequencies. Octopus cells are known to respond with finely timed action potentials at the onset of sounds despite the fact that due to the traveling wave delay in the cochlea, synaptic input from the auditory nerve is temporally diffuse. This paper provides a proof of principle that the octopus cells' dendritic delay may provide compensation for this input asynchrony, and that synaptic weights may be adjusted by a spike-timing dependent plasticity (STDP) learning rule. This paper used a leaky integrate and fire model of an octopus cell modified to include a “rate threshold,” a property that is known to create the appropriate onset response in octopus cells. Repeated audio click stimuli were passed to a realistic auditory nerve model which provided the synaptic input to the octopus cell model. A genetic algorithm was used to find the parameters of the STDP learning rule that reproduced the microscopically observed synaptic connectivity. With these selected parameter values it was shown that the STDP learning rule was capable of adjusting the values of a large number of input synaptic weights, creating a configuration that compensated the traveling wave delay of the cochlea.

Dual Coding of Frequency Modulation in the Ventral Cochlear Nucleus

Frequency modulation (FM) is a common acoustic feature of natural sounds and is known to play a role in robust sound source recognition. Auditory neurons show precise stimulus-synchronized discharge patterns that may be used for the representation of low-rate FM. However, it remains unclear whether this representation is based on synchronization to slow temporal envelope (ENV) cues resulting from cochlear filtering or phase locking to faster temporal fine structure (TFS) cues. To investigate the plausibility of those encoding schemes, single units of the ventral cochlear nucleus of guinea pigs of either sex were recorded in response to sine FM tones centered at the unit's best frequency (BF). The results show that, in contrast to high-BF units, for modulation depths within the receptive field, low-BF units (<4 kHz) demonstrate good phase locking to TFS. For modulation depths extending beyond the receptive field, the discharge patterns follow the ENV and fluctuate at the modulation rate. The receptive field proved to be a good predictor of the ENV responses for most primary-like and chopper units. The current in vivo data also reveal a high level of diversity in responses across unit types. TFS cues are mainly conveyed by low-frequency and primary-like units and ENV cues by chopper and onset units. The diversity of responses exhibited by cochlear nucleus neurons provides a neural basis for a dual-coding scheme of FM in the brainstem based on both ENV and TFS cues.SIGNIFICANCE STATEMENT Natural sounds, including speech, convey informative temporal modulations in frequency. Understanding how the auditory system represents those frequency modulations (FM) has important implications as robust sound source recognition depends crucially on the reception of low-rate FM cues. Here, we recorded 115 single-unit responses from the ventral cochlear nucleus in response to FM and provide the first physiological evidence of a dual-coding mechanism of FM via synchronization to temporal envelope cues and phase locking to temporal fine structure cues. We also demonstrate a diversity of neural responses with different coding specializations. These results support the dual-coding scheme proposed by psychophysicists to account for FM sensitivity in humans and provide new insights on how this might be implemented in the early stages of the auditory pathway.

Cellular Computations Underlying Detection of Gaps in Sounds and Lateralizing Sound Sources

In mammals, acoustic information arises in the cochlea and is transmitted to the ventral cochlear nuclei (VCN). Three groups of VCN neurons extract different features from the firing of auditory nerve fibers and convey that information along separate pathways through the brainstem. Two of these pathways process temporal information: octopus cells detect coincident firing among auditory nerve fibers and transmit signals along monaural pathways, and bushy cells sharpen the encoding of fine structure and feed binaural pathways. The ability of these cells to signal with temporal precision depends on a low-voltage-activated K⁺ conductance (g_KL) and a hyperpolarization-activated conductance (g_h). This 'tale of two conductances' traces gap detection and sound lateralization to their cellular and biophysical origins.

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.

Phasic Firing and Coincidence Detection by Subthreshold Negative Feedback: Divisive or Subtractive or, Better, Both

Phasic neurons typically fire only for a fast-rising input, say at the onset of a step current, but not for steady or slow inputs, a property associated with type III excitability. Phasic neurons can show extraordinary temporal precision for phase locking and coincidence detection. Exemplars are found in the auditory brain stem where precise timing is used in sound localization. Phasicness at the cellular level arises from a dynamic, voltage-gated, negative feedback that can be recruited subthreshold, preventing the neuron from reaching spike threshold if the voltage does not rise fast enough. We consider two mechanisms for phasicness: a low threshold potassium current (subtractive mechanism) and a sodium current with subthreshold inactivation (divisive mechanism). We develop and analyze three reduced models with either divisive or subtractive mechanisms or both to gain insight into the dynamical mechanisms for the potentially high temporal precision of type III-excitable neurons. We compare their firing properties and performance for a range of stimuli. The models have characteristic non-monotonic input-output relations, firing rate vs. input intensity, for either stochastic current injection or Poisson-timed excitatory synaptic conductance trains. We assess performance according to precision of phase-locking and coincidence detection by the models' responses to repetitive packets of unitary excitatory synaptic inputs with more or less temporal coherence. We find that each mechanism contributes features but best performance is attained if both are present. The subtractive mechanism confers extraordinary precision for phase locking and coincidence detection but only within a restricted parameter range when the divisive mechanism of sodium inactivation is inoperative. The divisive mechanism guarantees robustness of phasic properties, without compromising excitability, although with somewhat less precision. Finally, we demonstrate that brief transient inhibition if properly timed can enhance the reliability of firing.

Genetic perturbations suggest a role of the resting potential in regulating the expression of the ion channels of the KCNA and HCN families in octopus cells of the ventral cochlear nucleus

Low-voltage-activated K⁺ (g_KL) and hyperpolarization-activated mixed cation conductances (g_h) mediate currents, I_KL and I_h, through channels of the Kv1 (KCNA) and HCN families respectively and give auditory neurons the temporal precision required for signaling information about the onset, fine structure, and time of arrival of sounds. Being partially activated at rest, g_KL and g_h contribute to the resting potential and shape responses to even small subthreshold synaptic currents. Resting g_KL and g_h also affect the coupling of somatic depolarization with the generation of action potentials. To learn how these important conductances are regulated we have investigated how genetic perturbations affect their expression in octopus cells of the ventral cochlear nucleus (VCN). We report five new findings: First, the magnitude of g_h and g_KL varied over more than two-fold between wild type strains of mice. Second, average resting potentials are not different in different strains of mice even in the face of large differences in average g_KL and g_h. Third, I_KL has two components, one being α-dendrotoxin (α-DTX)-sensitive and partially inactivating and the other being α-DTX-insensitive, tetraethylammonium (TEA)-sensitive, and non-inactivating. Fourth, the loss of Kv1.1 results in diminution of the α-DTX-sensitive I_KL, and compensatory increased expression of an α-DTX-insensitive, tetraethylammonium (TEA)-sensitive I_KL. Fifth, I_h and I_KL are balanced at the resting potential in all wild type and mutant octopus cells even when resting potentials vary in individual cells over nearly 10 mV, indicating that the resting potential influences the expression of g_h and g_KL. The independence of resting potentials on g_KL and g_h shows that g_KL and g_h do not, over days or weeks, determine the resting potential but rather that the resting potential plays a role in regulating the magnitude of either or both g_KL and g_h.

A biophysical model examining the role of low-voltage-activated potassium currents in shaping the responses of vestibular ganglion neurons

The vestibular nerve is characterized by two broad groups of neurons that differ in the timing of their interspike intervals; some fire at highly regular intervals, whereas others fire at highly irregular intervals. Heterogeneity in ion channel properties has been proposed as shaping these firing patterns (Highstein SM, Politoff AL. Brain Res 150: 182-187, 1978; Smith CE, Goldberg JM. Biol Cybern 54: 41-51, 1986). Kalluri et al. (J Neurophysiol 104: 2034-2051, 2010) proposed that regularity is controlled by the density of low-voltage-activated potassium currents (IKL). To examine the impact of IKL on spike timing regularity, we implemented a single-compartment model with three conductances known to be present in the vestibular ganglion: transient sodium (gNa), low-voltage-activated potassium (gKL), and high-voltage-activated potassium (gKH). Consistent with in vitro observations, removing gKL depolarized resting potential, increased input resistance and membrane time constant, and converted current step-evoked firing patterns from transient (1 spike at current onset) to sustained (many spikes). Modeled neurons were driven with a time-varying synaptic conductance that captured the random arrival times and amplitudes of glutamate-driven synaptic events. In the presence of gKL, spiking occurred only in response to large events with fast onsets. Models without gKL exhibited greater integration by responding to the superposition of rapidly arriving events. Three synaptic conductance were modeled, each with different kinetics to represent a variety of different synaptic processes. In response to all three types of synaptic conductance, models containing gKL produced spike trains with irregular interspike intervals. Only models lacking gKL when driven by rapidly arriving small excitatory postsynaptic currents were capable of generating regular spiking.

Enhanced Sensitivity to Rapid Input Fluctuations by Nonlinear Threshold Dynamics in Neocortical Pyramidal Neurons

The way in which single neurons transform input into output spike trains has fundamental consequences for network coding. Theories and modeling studies based on standard Integrate-and-Fire models implicitly assume that, in response to increasingly strong inputs, neurons modify their coding strategy by progressively reducing their selective sensitivity to rapid input fluctuations. Combining mathematical modeling with in vitro experiments, we demonstrate that, in L5 pyramidal neurons, the firing threshold dynamics adaptively adjust the effective timescale of somatic integration in order to preserve sensitivity to rapid signals over a broad range of input statistics. For that, a new Generalized Integrate-and-Fire model featuring nonlinear firing threshold dynamics and conductance-based adaptation is introduced that outperforms state-of-the-art neuron models in predicting the spiking activity of neurons responding to a variety of in vivo-like fluctuating currents. Our model allows for efficient parameter extraction and can be analytically mapped to a Generalized Linear Model in which both the input filter—describing somatic integration—and the spike-history filter—accounting for spike-frequency adaptation—dynamically adapt to the input statistics, as experimentally observed. Overall, our results provide new insights on the computational role of different biophysical processes known to underlie adaptive coding in single neurons and support previous theoretical findings indicating that the nonlinear dynamics of the firing threshold due to Na⁺-channel inactivation regulate the sensitivity to rapid input fluctuations.

Over the last decades, a variety of simplified spiking models have been shown to achieve a surprisingly high performance in predicting the neuronal responses to in vitro somatic current injections. Because of the complex adaptive behavior featured by cortical neurons, this success is however restricted to limited stimulus ranges: model parameters optimized for a specific input regime are often inappropriate to describe the response to input currents with different statistical properties. In the present study, a new spiking neuron model is introduced that captures single-neuron computation over a wide range of input statistics and explains different aspects of the neuronal dynamics within a single framework. Our results indicate that complex forms of single neuron adaptation are mediated by the nonlinear dynamics of the firing threshold and that the input-output transformation performed by cortical pyramidal neurons can be intuitively understood in terms of an enhanced Generalized Linear Model in which both the input filter and the spike-history filter adapt to the input statistics.

Reducing Current Spread by Use of a Novel Pulse Shape for Electrical Stimulation of the Auditory Nerve

Improving the electrode-neuron interface to reduce current spread between individual electrodes has been identified as one of the main objectives in the search for future improvements in cochlear-implant performance. Here, we address this problem by presenting a novel stimulation strategy that takes account of the biophysical properties of the auditory neurons (spiral ganglion neurons, SGNs) stimulated in electrical hearing. This new strategy employs a ramped pulse shape, where the maximum amplitude is achieved through a linear slope in the injected current. We present the theoretical framework that supports this new strategy and that suggests it will improve the modulation of SGNs’ activity by exploiting their sensitivity to the rising slope of current pulses. The theoretical consequence of this sensitivity to the slope is a reduction in the spread of excitation within the cochlea and, consequently, an increase in the neural dynamic range. To explore the impact of the novel stimulation method on neural activity, we performed in vitro recordings of SGNs in culture. We show that the stimulus efficacy required to evoke action potentials in SGNs falls as the stimulus slope decreases. This work lays the foundation for a novel, and more biomimetic, stimulation strategy with considerable potential for implementation in cochlear-implant technology.

Spike timing precision changes with spike rate adaptation in the owl's auditory space map

Spike rate adaptation (SRA) is a continuing change of responsiveness to ongoing stimuli, which is ubiquitous across species and levels of sensory systems. Under SRA, auditory responses to constant stimuli change over time, relaxing toward a long-term rate often over multiple timescales. With more variable stimuli, SRA causes the dependence of spike rate on sound pressure level to shift toward the mean level of recent stimulus history. A model based on subtractive adaptation (Benda J, Hennig RM. J Comput Neurosci 24: 113-136, 2008) shows that changes in spike rate and level dependence are mechanistically linked. Space-specific neurons in the barn owl's midbrain, when recorded under ketamine-diazepam anesthesia, showed these classical characteristics of SRA, while at the same time exhibiting changes in spike timing precision. Abrupt level increases of sinusoidally amplitude-modulated (SAM) noise initially led to spiking at higher rates with lower temporal precision. Spike rate and precision relaxed toward their long-term values with a time course similar to SRA, results that were also replicated by the subtractive model. Stimuli whose amplitude modulations (AMs) were not synchronous across carrier frequency evoked spikes in response to stimulus envelopes of a particular shape, characterized by the spectrotemporal receptive field (STRF). Again, abrupt stimulus level changes initially disrupted the temporal precision of spiking, which then relaxed along with SRA. We suggest that shifts in latency associated with stimulus level changes may differ between carrier frequency bands and underlie decreased spike precision. Thus SRA is manifest not simply as a change in spike rate but also as a change in the temporal precision of spiking.

Biophysical Insights into How Spike Threshold Depends on the Rate of Membrane Potential Depolarization in Type I and Type II Neurons

Dynamic spike threshold plays a critical role in neuronal input-output relations. In many neurons, the threshold potential depends on the rate of membrane potential depolarization (dV/dt) preceding a spike. There are two basic classes of neural excitability, i.e., Type I and Type II, according to input-output properties. Although the dynamical and biophysical basis of their spike initiation has been established, the spike threshold dynamic for each cell type has not been well described. Here, we use a biophysical model to investigate how spike threshold depends on dV/dt in two types of neuron. It is observed that Type II spike threshold is more depolarized and more sensitive to dV/dt than Type I. With phase plane analysis, we show that each threshold dynamic arises from the different separatrix and K+ current kinetics. By analyzing subthreshold properties of membrane currents, we find the activation of hyperpolarizing current prior to spike initiation is a major factor that regulates the threshold dynamics. The outward K+ current in Type I neuron does not activate at the perithresholds, which makes its spike threshold insensitive to dV/dt. The Type II K+ current activates prior to spike initiation and there is a large net hyperpolarizing current at the perithresholds, which results in a depolarized threshold as well as a pronounced threshold dynamic. These predictions are further attested in several other functionally equivalent cases of neural excitability. Our study provides a fundamental description about how intrinsic biophysical properties contribute to the threshold dynamics in Type I and Type II neurons, which could decipher their significant functions in neural coding.

Input-output relation and energy efficiency in the neuron with different spike threshold dynamics

Neuron encodes and transmits information through generating sequences of output spikes, which is a high energy-consuming process. The spike is initiated when membrane depolarization reaches a threshold voltage. In many neurons, threshold is dynamic and depends on the rate of membrane depolarization (dV/dt) preceding a spike. Identifying the metabolic energy involved in neural coding and their relationship to threshold dynamic is critical to understanding neuronal function and evolution. Here, we use a modified Morris-Lecar model to investigate neuronal input-output property and energy efficiency associated with different spike threshold dynamics. We find that the neurons with dynamic threshold sensitive to dV/dt generate discontinuous frequency-current curve and type II phase response curve (PRC) through Hopf bifurcation, and weak noise could prohibit spiking when bifurcation just occurs. The threshold that is insensitive to dV/dt, instead, results in a continuous frequency-current curve, a type I PRC and a saddle-node on invariant circle bifurcation, and simultaneously weak noise cannot inhibit spiking. It is also shown that the bifurcation, frequency-current curve and PRC type associated with different threshold dynamics arise from the distinct subthreshold interactions of membrane currents. Further, we observe that the energy consumption of the neuron is related to its firing characteristics. The depolarization of spike threshold improves neuronal energy efficiency by reducing the overlap of Na(+) and K(+) currents during an action potential. The high energy efficiency is achieved at more depolarized spike threshold and high stimulus current. These results provide a fundamental biophysical connection that links spike threshold dynamics, input-output relation, energetics and spike initiation, which could contribute to uncover neural encoding mechanism.

Broadband onset inhibition can suppress spectral splatter in the auditory brainstem

In vivo intracellular responses to auditory stimuli revealed that, in a particular population of cells of the ventral nucleus of the lateral lemniscus (VNLL) of rats, fast inhibition occurred before the first action potential. These experimental data were used to constrain a leaky integrate-and-fire (LIF) model of the neurons in this circuit. The post-synaptic potentials of the VNLL cell population were characterized using a method of triggered averaging. Analysis suggested that these inhibited VNLL cells produce action potentials in response to a particular magnitude of the rate of change of their membrane potential. The LIF model was modified to incorporate the VNLL cells’ distinctive action potential production mechanism. The model was used to explore the response of the population of VNLL cells to simple speech-like sounds. These sounds consisted of a simple tone modulated by a saw tooth with exponential decays, similar to glottal pulses that are the repeated impulses seen in vocalizations. It was found that the harmonic component of the sound was enhanced in the VNLL cell population when compared to a population of auditory nerve fibers. This was because the broadband onset noise, also termed spectral splatter, was suppressed by the fast onset inhibition. This mechanism has the potential to greatly improve the clarity of the representation of the harmonic content of certain kinds of natural sounds.

Action potential generation in an anatomically constrained model of medial superior olive axons

Neurons in the medial superior olive (MSO) encode interaural time differences (ITDs) with sustained firing rates of >100 Hz. They are able to generate such high firing rates for several hundred milliseconds despite their extremely low-input resistances of only few megaohms and high synaptic conductances in vivo. The biophysical mechanisms by which these leaky neurons maintain their excitability are not understood. Since action potentials (APs) are usually assumed to be generated in the axon initial segment (AIS), we analyzed anatomical data of proximal MSO axons in Mongolian gerbils and found that the axon diameter is <1 μm and the internode length is ∼100 μm. Using a morphologically constrained computational model of the MSO axon, we show that these thin axons facilitate the excitability of the AIS. However, for ongoing high rates of synaptic inputs the model generates a substantial fraction of APs in its nodes of Ranvier. These distally initiated APs are mediated by a spatial gradient of sodium channel inactivation and a strong somatic current sink. The model also predicts that distal AP initiation increases the dynamic range of the rate code for ITDs.

Spike-threshold adaptation predicted by membrane potential dynamics in vivo

Neurons encode information in sequences of spikes, which are triggered when their membrane potential crosses a threshold. In vivo, the spiking threshold displays large variability suggesting that threshold dynamics have a profound influence on how the combined input of a neuron is encoded in the spiking. Threshold variability could be explained by adaptation to the membrane potential. However, it could also be the case that most threshold variability reflects noise and processes other than threshold adaptation. Here, we investigated threshold variation in auditory neurons responses recorded in vivo in barn owls. We found that spike threshold is quantitatively predicted by a model in which the threshold adapts, tracking the membrane potential at a short timescale. As a result, in these neurons, slow voltage fluctuations do not contribute to spiking because they are filtered by threshold adaptation. More importantly, these neurons can only respond to input spikes arriving together on a millisecond timescale. These results demonstrate that fast adaptation to the membrane potential captures spike threshold variability in vivo.

Neurons spike when their membrane potential exceeds a threshold value, but this value has been shown to be variable in the same neuron recorded in vivo. This variability could reflect noise, or deterministic processes that make the threshold vary with the membrane potential. The second alternative would have important functional consequences. Here, we show that threshold variability is a genuine feature of neurons, which reflects adaptation to the membrane potential at a short timescale, with little contribution from noise. This demonstrates that a deterministic model can predict spikes based only on the membrane potential.

Biophysical mechanism of spike threshold dependence on the rate of rise of the membrane potential by sodium channel inactivation or subthreshold axonal potassium current

Spike threshold filters incoming inputs and thus gates activity flow through neuronal networks. Threshold is variable, and in many types of neurons there is a relationship between the threshold voltage and the rate of rise of the membrane potential (dVm/dt) leading to the spike. In primary sensory cortex this relationship enhances the sensitivity of neurons to a particular stimulus feature. While Na⁺ channel inactivation may contribute to this relationship, recent evidence indicates that K⁺ currents located in the spike initiation zone are crucial. Here we used a simple Hodgkin-Huxley biophysical model to systematically investigate the role of K⁺ and Na⁺ current parameters (activation voltages and kinetics) in regulating spike threshold as a function of dVm/dt. Threshold was determined empirically and not estimated from the shape of the Vm prior to a spike. This allowed us to investigate intrinsic currents and values of gating variables at the precise voltage threshold. We found that Na⁺ nactivation is sufficient to produce the relationship provided it occurs at hyperpolarized voltages combined with slow kinetics. Alternatively, hyperpolarization of the K⁺ current activation voltage, even in the absence of Na⁺ inactivation, is also sufficient to produce the relationship. This hyperpolarized shift of K⁺ activation allows an outward current prior to spike initiation to antagonize the Na⁺ inward current such that it becomes self-sustaining at a more depolarized voltage. Our simulations demonstrate parameter constraints on Na⁺ inactivation and the biophysical mechanism by which an outward current regulates spike threshold as a function of dVm/dt.

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.

Generating synchrony from the asynchronous: compensation for cochlear traveling wave delays by the dendrites of individual brainstem neurons

Broadband transient sounds, such as clicks and consonants, activate a traveling wave in the cochlea. This wave evokes firing in auditory nerve fibers that are tuned to high frequencies several milliseconds earlier than in fibers tuned to low frequencies. Despite this substantial traveling wave delay, octopus cells in the brainstem receive broadband input and respond to clicks with submillisecond temporal precision. The dendrites of octopus cells lie perpendicular to the tonotopically organized array of auditory nerve fibers, placing the earliest arriving inputs most distally and the latest arriving closest to the soma. Here, we test the hypothesis that the topographic arrangement of synaptic inputs on dendrites of octopus cells allows octopus cells to compensate the traveling wave delay. We show that in mice the full cochlear traveling wave delay is 1.6 ms. Because the dendrites of each octopus cell spread across approximately one-third of the tonotopic axis, a click evokes a soma-directed sweep of synaptic input lasting 0.5 ms in individual octopus cells. Morphologically and biophysically realistic, computational models of octopus cells show that soma-directed sweeps with durations matching in vivo measurements result in the largest and sharpest somatic EPSPs. A low input resistance and activation of a low-voltage-activated potassium conductance that are characteristic of octopus cells are important determinants of sweep sensitivity. We conclude that octopus cells have dendritic morphologies and biophysics tailored to accomplish the precise encoding of broadband transient sounds.

An in vivo investigation of inferior colliculus single neuron responses to cochlear nucleus pulse train stimulation

The auditory brain stem implant (ABI) is being used clinically to restore hearing to patients unable to benefit from a cochlear implant (CI). Speech perception outcomes for ABI users are typically poor compared with most CI users. The ABI is implanted either on the surface of or penetrating through the cochlear nucleus in the auditory brain stem and uses stimulation strategies developed for auditory nerve stimulation with a CI. Although the stimulus rate may affect speech perception outcomes with current stimulation strategies, no studies have systematically investigated the effect of stimulus rate electrophysiologically or clinically. We therefore investigated rate response properties and temporal response properties of single inferior colliculus (IC) neurons from penetrating ABI stimulation using stimulus rates ranging from 100 to 1,600 pulses/s in the rat. We found that the stimulus rate affected the proportion of response types, thresholds, and dynamic ranges of IC activation. The stimulus rate was also found to affect the temporal properties of IC responses, with higher rates providing more temporally similar responses to acoustic stimulation. Suppression of neural firing and inhibition in IC neurons was also found, with response properties varying with the stimulus rate. This study demonstrated that changes in the ABI stimulus rate results in significant differences in IC neuron response properties. Due to electrophysiological differences, the stimulus rate may also change perceptual properties. We suggest that clinical evaluation of the ABI stimulus rate should be performed.

Synaptic integration in dendrites: exceptional need for speed

Some neurons in the mammalian auditory system are able to detect and report the coincident firing of inputs with remarkable temporal precision. A strong, low-voltage-activated potassium conductance (g(KL)) at the cell body and dendrites gives these neurons sensitivity to the rate of depolarization by EPSPs, allowing neurons to assess the coincidence of the rising slopes of unitary EPSPs. Two groups of neurons in the brain stem, octopus cells in the posteroventral cochlear nucleus and principal cells of the medial superior olive (MSO), extract acoustic information by assessing coincident firing of their inputs over a submillisecond timescale and convey that information at rates of up to 1000 spikes s(-1). Octopus cells detect the coincident activation of groups of auditory nerve fibres by broadband transient sounds, compensating for the travelling wave delay by dendritic filtering, while MSO neurons detect coincident activation of similarly tuned neurons from each of the two ears through separate dendritic tufts. Each makes use of filtering that is introduced by the spatial distribution of inputs on dendrites.

Intrinsic firing properties in the avian auditory brain stem allow both integration and encoding of temporally modulated noisy inputs in vitro

The intrinsic properties of tonically firing neurons in the cochlear nucleus contribute to representing average sound intensity by favoring synaptic integration across auditory nerve inputs, reducing phase locking to fine temporal acoustic structure and enhancing envelope locking. To determine whether tonically firing neurons of the avian cochlear nucleus angularis (NA) resemble ideal integrators, we investigated their firing responses to noisy current injections during whole cell patch-clamp recordings in brain slices. One subclass of neurons (36% of tonically firing neurons, mainly subtype tonic III) showed no significant changes in firing rate with noise fluctuations, acting like pure integrators. In contrast, many tonically firing neurons (>60%, mainly subtype tonic I or II) showed a robust sensitivity to noisy current fluctuations, increasing their firing rates with increased fluctuation amplitudes. For noise-sensitive tonic neurons, the firing rate vs. average current curves with noise had larger maximal firing rates, lower gains, and wider dynamic ranges compared with FI curves for current steps without noise. All NA neurons showed fluctuation-driven patterning of spikes with a high degree of temporal reliability and millisecond spike time precision. Single-spiking neurons in NA also responded to noisy currents with higher firing rates and reliable spike trains, although less precisely than nucleus magnocellularis neurons. Thus some NA neurons function as integrators by encoding average input levels over wide dynamic ranges regardless of current fluctuations, others detect the degree of coherence in the inputs, and most encode the temporal patterns contained in their inputs with a high degree of precision.

The physiology of the axon initial segment

The action potential generally begins in the axon initial segment (AIS), a principle confirmed by 60 years of research; however, the most recent advances have shown that a very rich biology underlies this simple observation. The AIS has a remarkably complex molecular composition, with a wide variety of ion channels and attendant mechanisms for channel localization, and may feature membrane domains each with distinct roles in excitation. Its function may be regulated in the short term through the action of neurotransmitters, in the long term through activity- and Ca(2+)-dependent processes. Thus, the AIS is not merely the beginning of the axon, but rather a key site in the control of neuronal excitability.

Elemental spiking neuron model for reproducing diverse firing patterns and predicting precise firing times

In simulating realistic neuronal circuitry composed of diverse types of neurons, we need an elemental spiking neuron model that is capable of not only quantitatively reproducing spike times of biological neurons given in vivo-like fluctuating inputs, but also qualitatively representing a variety of firing responses to transient current inputs. Simplistic models based on leaky integrate-and-fire mechanisms have demonstrated the ability to adapt to biological neurons. In particular, the multi-timescale adaptive threshold (MAT) model reproduces and predicts precise spike times of regular-spiking, intrinsic-bursting, and fast-spiking neurons, under any fluctuating current; however, this model is incapable of reproducing such specific firing responses as inhibitory rebound spiking and resonate spiking. In this paper, we augment the MAT model by adding a voltage dependency term to the adaptive threshold so that the model can exhibit the full variety of firing responses to various transient current pulses while maintaining the high adaptability inherent in the original MAT model. Furthermore, with this addition, our model is actually able to better predict spike times. Despite the augmentation, the model has only four free parameters and is implementable in an efficient algorithm for large-scale simulation due to its linearity, serving as an element neuron model in the simulation of realistic neuronal circuitry.

Difference in response reliability predicted by spectrotemporal tuning in the cochlear nuclei of barn owls

The brainstem auditory pathway is obligatory for all aural information. Brainstem auditory neurons must encode the level and timing of sounds, as well as their time-dependent spectral properties, the fine structure, and envelope, which are essential for sound discrimination. This study focused on envelope coding in the two cochlear nuclei of the barn owl, nucleus angularis (NA) and nucleus magnocellularis (NM). NA and NM receive input from bifurcating auditory nerve fibers and initiate processing pathways specialized in encoding interaural time (ITD) and level (ILD) differences, respectively. We found that NA neurons, although unable to accurately encode stimulus phase, lock more strongly to the stimulus envelope than NM units. The spectrotemporal receptive fields (STRFs) of NA neurons exhibit a pre-excitatory suppressive field. Using multilinear regression analysis and computational modeling, we show that this feature of STRFs can account for enhanced across-trial response reliability, by locking spikes to the stimulus envelope. Our findings indicate a dichotomy in envelope coding between the time and intensity processing pathways as early as at the level of the cochlear nuclei. This allows the ILD processing pathway to encode envelope information with greater fidelity than the ITD processing pathway. Furthermore, we demonstrate that the properties of the STRFs of the neurons can be quantitatively related to spike timing reliability.

The magnitudes of hyperpolarization-activated and low-voltage-activated potassium currents co-vary in neurons of the ventral cochlear nucleus

In the ventral cochlear nucleus (VCN), neurons have hyperpolarization-activated conductances, which in some cells are enormous, that contribute to the ability of neurons to convey acoustic information in the timing of their firing by decreasing the input resistance and speeding-up voltage changes. Comparisons of the electrophysiological properties of neurons in the VCN of mutant mice that lack the hyperpolarization-activated cyclic nucleotide-gated channel α subunit 1 (HCN1(-/-)) (Nolan et al. 2003) with wild-type controls (HCN1(+/+)) and with outbred ICR mice reveal that octopus, T stellate, and bushy cells maintain their electrophysiological distinctions in all strains. Hyperpolarization-activated (I(h)) currents were smaller and slower, input resistances were higher, and membrane time constants were longer in HCN1(-/-) than in HCN1(+/+) in octopus, bushy, and T stellate cells. There were significant differences in the average magnitudes of I(h), input resistances, and time constants between HCN1(+/+) and ICR mice, but the resting potentials did not differ between strains. I(h) is opposed by a low-voltage-activated potassium (I(KL)) current in bushy and octopus cells, whose magnitudes varied widely between neuronal types and between strains. The magnitudes of I(h) and I(KL) were correlated across neuronal types and across mouse strains. Furthermore, these currents balanced one another at the resting potential in individual cells. The magnitude of I(h) and I(KL) is linked in bushy and octopus cells and varies not only between HCN1(-/-) and HCN1(+/+) but also between "wild-type" strains of mice, raising the question to what extent the wild-type strains reflect normal mice.

Impact of fast sodium channel inactivation on spike threshold dynamics and synaptic integration

Neurons spike when their membrane potential exceeds a threshold value. In central neurons, the spike threshold is not constant but depends on the stimulation. Thus, input-output properties of neurons depend both on the effect of presynaptic spikes on the membrane potential and on the dynamics of the spike threshold. Among the possible mechanisms that may modulate the threshold, one strong candidate is Na channel inactivation, because it specifically impacts spike initiation without affecting the membrane potential. We collected voltage-clamp data from the literature and we found, based on a theoretical criterion, that the properties of Na inactivation could indeed cause substantial threshold variability by itself. By analyzing simple neuron models with fast Na inactivation (one channel subtype), we found that the spike threshold is correlated with the mean membrane potential and negatively correlated with the preceding depolarization slope, consistent with experiments. We then analyzed the impact of threshold dynamics on synaptic integration. The difference between the postsynaptic potential (PSP) and the dynamic threshold in response to a presynaptic spike defines an effective PSP. When the neuron is sufficiently depolarized, this effective PSP is briefer than the PSP. This mechanism regulates the temporal window of synaptic integration in an adaptive way. Finally, we discuss the role of other potential mechanisms. Distal spike initiation, channel noise and Na activation dynamics cannot account for the observed negative slope-threshold relationship, while adaptive conductances (e.g. K+) and Na inactivation can. We conclude that Na inactivation is a metabolically efficient mechanism to control the temporal resolution of synaptic integration.

Neurons spike when their combined inputs exceed a threshold value, but recent experimental findings have shown that this value also depends on the inputs. Thus, to understand how neurons respond to input spikes, it is important to know how inputs modify the spike threshold. Spikes are generated by sodium channels, which inactivate when the neuron is depolarized, raising the threshold for spike initiation. We found that inactivation properties of sodium channels could indeed cause substantial threshold variability in central neurons. We then analyzed in models the implications of this form of threshold modulation on neuronal function. We found that this mechanism makes neurons more sensitive to coincident spikes and provides them with an energetically efficient form of gain control.

The multiple functions of T stellate/multipolar/chopper cells in the ventral cochlear nucleus

Acoustic information is brought to the brain by auditory nerve fibers, all of which terminate in the cochlear nuclei, and is passed up the auditory pathway through the principal cells of the cochlear nuclei. A population of neurons variously known as T stellate, type I multipolar, planar multipolar, or chopper cells forms one of the major ascending auditory pathways through the brainstem. T Stellate cells are sharply tuned; as a population they encode the spectrum of sounds. In these neurons, phasic excitation from the auditory nerve is made more tonic by feedforward excitation, coactivation of inhibitory with excitatory inputs, relatively large excitatory currents through NMDA receptors, and relatively little synaptic depression. The mechanisms that make firing tonic also obscure the fine structure of sounds that is represented in the excitatory inputs from the auditory nerve and account for the characteristic chopping response patterns with which T stellate cells respond to tones. In contrast with other principal cells of the ventral cochlear nucleus (VCN), T stellate cells lack a low-voltage-activated potassium conductance and are therefore sensitive to small, steady, neuromodulating currents. The presence of cholinergic, serotonergic and noradrenergic receptors allows the excitability of these cells to be modulated by medial olivocochlear efferent neurons and by neuronal circuits associated with arousal. T Stellate cells deliver acoustic information to the ipsilateral dorsal cochlear nucleus (DCN), ventral nucleus of the trapezoid body (VNTB), periolivary regions around the lateral superior olivary nucleus (LSO), and to the contralateral ventral lemniscal nuclei (VNLL) and inferior colliculus (IC). It is likely that T stellate cells participate in feedback loops through both medial and lateral olivocochlear efferent neurons and they may be a source of ipsilateral excitation of the LSO.

Auditory nerve fibers excite targets through synapses that vary in convergence, strength, and short-term plasticity

Auditory nerve fibers are the major source of excitation to the three groups of principal cells of the ventral cochlear nucleus (VCN), bushy, T stellate, and octopus cells. Shock-evoked excitatory postsynaptic currents (eEPSCs) in slices from mice showed systematic differences between groups of principal cells, indicating that target cells contribute to determining pre- and postsynaptic properties of synapses from spiral ganglion cells. Bushy cells likely to be small spherical bushy cells receive no more than three, most often two, excitatory inputs; those likely to be globular bushy cells receive at least four, most likely five, inputs. T stellate cells receive 6.5 inputs. Octopus cells receive >60 inputs. The N-methyl-d-aspartate (NMDA) components of eEPSCs were largest in T stellate, smaller in bushy, and smallest in octopus cells, and they were larger in neurons from younger than older mice. The average AMPA conductance of a unitary input is 22 ± 15 nS in both groups of bushy cells, <1.5 nS in octopus cells, and 4.6 ± 3 nS in T stellate cells. Sensitivity to philanthotoxin (PhTX) and rectification in the intracellular presence of spermine indicate that AMPA receptors that mediate eEPSCs in T stellate cells contain more GluR2 subunits than those in bushy and octopus cells. The AMPA components of eEPSCs were briefer in bushy (0.5 ms half-width) than in T stellate and octopus cells (0.8-0.9 ms half-width). Widening of eEPSCs in the presence of cyclothiazide (CTZ) indicates that desensitization shortens eEPSCs. CTZ-insensitive synaptic depression of the AMPA components was greater in bushy and octopus than in T stellate cells.

A threshold equation for action potential initiation

In central neurons, the threshold for spike initiation can depend on the stimulus and varies between cells and between recording sites in a given cell, but it is unclear what mechanisms underlie this variability. Properties of ionic channels are likely to play a role in threshold modulation. We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels and synaptic conductances on spike threshold. We propose a threshold equation which quantifies the contribution of all these mechanisms. It provides an instantaneous time-varying value of the threshold, which applies to neurons with fluctuating inputs. We deduce a differential equation for the threshold, similar to the equations of gating variables in the Hodgkin-Huxley formalism, which describes how the spike threshold varies with the membrane potential, depending on channel properties. We find that spike threshold depends logarithmically on Na channel density, and that Na channel inactivation and K channels can dynamically modulate it in an adaptive way: the threshold increases with membrane potential and after every action potential. Our equation was validated with simulations of a previously published multicompartemental model of spike initiation. Finally, we observed that threshold variability in models depends crucially on the shape of the Na activation function near spike initiation (about −55 mV), while its parameters are adjusted near half-activation voltage (about −30 mV), which might explain why many models exhibit little threshold variability, contrary to experimental observations. We conclude that ionic channels can account for large variations in spike threshold.

Neurons communicate primarily with stereotypical electrical impulses, action potentials, which are fired when a threshold level of excitation is reached. This threshold varies between cells and over time as a function of previous stimulations, which has major functional implications on the integrative properties of neurons. Ionic channels are thought to play a central role in this modulation but the precise relationship between their properties and the threshold is unclear. We examined this relationship in biophysical models and derived a formula which quantifies the contribution of various mechanisms. The originality of our approach is that it provides an instantaneous time-varying value for the threshold, which applies to the highly fluctuating regimes characterizing neurons in vivo. In particular, two known ionic mechanisms were found to make the threshold adapt to the membrane potential, thus providing the cell with a form of gain control.

Asymmetric excitatory synaptic dynamics underlie interaural time difference processing in the auditory system

Low-frequency sound localization depends on the neural computation of interaural time differences (ITD) and relies on neurons in the auditory brain stem that integrate synaptic inputs delivered by the ipsi- and contralateral auditory pathways that start at the two ears. The first auditory neurons that respond selectively to ITD are found in the medial superior olivary nucleus (MSO). We identified a new mechanism for ITD coding using a brain slice preparation that preserves the binaural inputs to the MSO. There was an internal latency difference for the two excitatory pathways that would, if left uncompensated, position the ITD response function too far outside the physiological range to be useful for estimating ITD. We demonstrate, and support using a biophysically based computational model, that a bilateral asymmetry in excitatory post-synaptic potential (EPSP) slopes provides a robust compensatory delay mechanism due to differential activation of low threshold potassium conductance on these inputs and permits MSO neurons to encode physiological ITDs. We suggest, more generally, that the dependence of spike probability on rate of depolarization, as in these auditory neurons, provides a mechanism for temporal order discrimination between EPSPs.

Control of submillisecond synaptic timing in binaural coincidence detectors by K(v)1 channels

Neurons in the medial superior olive process sound-localization cues via binaural coincidence detection, in which excitatory synaptic inputs from each ear are segregated onto different branches of a bipolar dendritic structure and summed at the soma and axon with submillisecond time resolution. Although synaptic timing and dynamics critically shape this computation, synaptic interactions with intrinsic ion channels have received less attention. Using paired somatic and dendritic patch-clamp recordings in gerbil brainstem slices together with compartmental modeling, we found that activation of K(v)1 channels by dendritic excitatory postsynaptic potentials (EPSPs) accelerated membrane repolarization in a voltage-dependent manner and actively improved the time resolution of synaptic integration. We found that a somatically biased gradient of K(v)1 channels underlies the degree of compensation for passive cable filtering during propagation of EPSPs in dendrites. Thus, both the spatial distribution and properties of K(v)1 channels are important for preserving binaural synaptic timing.

Mode-locked spike trains in responses of ventral cochlear nucleus chopper and onset neurons to periodic stimuli

We report evidence of mode-locking to the envelope of a periodic stimulus in chopper units of the ventral cochlear nucleus (VCN). Mode-locking is a generalized description of how responses in periodically forced nonlinear systems can be closely linked to the input envelope, while showing temporal patterns of higher order than seen during pure phase-locking. Re-analyzing a previously unpublished dataset in response to amplitude modulated tones, we find that of 55% of cells (6/11) demonstrated stochastic mode-locking in response to sinusoidally amplitude modulated (SAM) pure tones at 50% modulation depth. At 100% modulation depth SAM, most units (3/4) showed mode-locking. We use interspike interval (ISI) scattergrams to unravel the temporal structure present in chopper mode-locked responses. These responses compared well to a leaky integrate-and-fire model (LIF) model of chopper units. Thus the timing of spikes in chopper unit responses to periodic stimuli can be understood in terms of the complex dynamics of periodically forced nonlinear systems. A larger set of onset (33) and chopper units (24) of the VCN also shows mode-locked responses to steady-state vowels and cosine-phase harmonic complexes. However, while 80% of chopper responses to complex stimuli meet our criterion for the presence of mode-locking, only 40% of onset cells show similar complex-modes of spike patterns. We found a correlation between a unit's regularity and its tendency to display mode-locked spike trains as well as a correlation in the number of spikes per cycle and the presence of complex-modes of spike patterns. These spiking patterns are sensitive to the envelope as well as the fundamental frequency of complex sounds, suggesting that complex cell dynamics may play a role in encoding periodic stimuli and envelopes in the VCN.