Weak action potential backpropagation is associated with high-frequency axonal firing capability in principal neurons of the gerbil medial superior olive

Developmental fine-tuning of medial superior olive neurons mitigates their predisposition to contralateral sound sources

Having two ears enables us to localize sound sources by exploiting interaural time differences (ITDs) in sound arrival. Principal neurons of the medial superior olive (MSO) are sensitive to ITD, and each MSO neuron responds optimally to a best ITD (bITD). In many cells, especially those tuned to low sound frequencies, these bITDs correspond to ITDs for which the contralateral ear leads, and are often larger than the ecologically relevant range, defined by the ratio of the interaural distance and the speed of sound. Using in vivo recordings in gerbils, we found that shortly after hearing onset the bITDs were even more contralaterally leading than found in adult gerbils, and travel latencies for contralateral sound-evoked activity clearly exceeded those for ipsilateral sounds. During the following weeks, both these latencies and their interaural difference decreased. A computational model indicated that spike timing-dependent plasticity can underlie this fine-tuning. Our results suggest that MSO neurons start out with a strong predisposition toward contralateral sounds due to their longer neural travel latencies, but that, especially in high-frequency neurons, this predisposition is subsequently mitigated by differential developmental fine-tuning of the travel latencies.

Somatic Integration of Incoherent Dendritic Inputs in the Gerbil Medial Superior Olive

The medial superior olive (MSO) is a binaural nucleus that is specialized in detecting the relative arrival times of sounds at both ears. Excitatory inputs to its neurons originating from either ear are segregated to different dendrites. To study the integration of synaptic inputs both within and between dendrites, we made juxtacellular and whole-cell recordings from the MSO in anesthetized female gerbils, while presenting a "double zwuis" stimulus, in which each ear received its own set of tones, which were chosen in a way that all second-order distortion products (DP2s) could be uniquely identified. MSO neurons phase-locked to multiple tones within the multitone stimulus, and vector strength, a measure for spike phase-locking, generally depended linearly on the size of the average subthreshold response to a tone. Subthreshold responses to tones in one ear depended little on the presence of sound in the other ear, suggesting that inputs from different ears sum linearly without a substantial role for somatic inhibition. The "double zwuis" stimulus also evoked response components in the MSO neuron that were phase-locked to DP2s. Bidendritic subthreshold DP2s were quite rare compared with bidendritic suprathreshold DP2s. We observed that in a small subset of cells, the ability to trigger spikes differed substantially between both ears, which might be explained by a dendritic axonal origin. Some neurons that were driven monaurally by only one of the two ears nevertheless showed decent binaural tuning. We conclude that MSO neurons are remarkably good in finding binaural coincidences even among uncorrelated inputs.SIGNIFICANCE STATEMENT Neurons in the medial superior olive are essential for precisely localizing low-frequency sounds in the horizontal plane. From their soma, only two dendrites emerge, which are innervated by inputs originating from different ears. Using a new sound stimulus, we studied the integration of inputs both within and between these dendrites in unprecedented detail. We found evidence that inputs from different dendrites add linearly at the soma, but that small increases in somatic potentials could lead to large increases in the probability of generating a spike. This basic scheme allowed the MSO neurons to detect the relative arrival time of inputs at both dendrites remarkably efficient, although the relative size of these inputs could differ considerably.

Structure and dynamics that specialize neurons for high-frequency coincidence detection in the barn owl nucleus laminaris

A principal cue for sound source localization is the difference in arrival times of sounds at an animal's two ears (interaural time difference, ITD). Neurons that process ITDs are specialized to compare the timing of inputs with submillisecond precision. In the barn owl, ITD processing begins in the nucleus laminaris (NL) region of the auditory brain stem. Remarkably, NL neurons are sensitive to ITDs in high-frequency sounds (kilohertz-range). This contrasts with ITD-based sound localization in analogous regions in mammals where ITD sensitivity is typically restricted to lower-frequency sounds. Guided by previous experiments and modeling studies of tone-evoked responses of NL neurons, we propose NL neurons achieve high-frequency ITD sensitivity if they respond selectively to the small-amplitude, high-frequency oscillations in their inputs, and remain relatively non-responsive to mean input level. We use a biophysically based model to study the effects of soma-axon coupling on dynamics and function in NL neurons. First, we show that electrical separation of the soma from the axon region in the neuron enhances high-frequency ITD sensitivity. This soma-axon coupling configuration promotes linear subthreshold dynamics and rapid spike initiation, making the model more responsive to input oscillations, rather than mean input level. Second, we provide new evidence for the essential role of phasic dynamics for high-frequency neural coincidence detection. Transforming our model to the phasic firing mode further tunes the model to respond selectively to the oscillating inputs that carry ITD information. Similar structural and dynamical mechanisms specialize mammalian auditory brain stem neurons for ITD sensitivity, and thus, our work identifies common principles of ITD processing and neural coincidence detection across species and for sounds at widely different frequencies.

Voltage Clamp Errors During Estimation of Concurrent Excitatory and Inhibitory Synaptic Input to Neurons with Dendrites

The whole-cell voltage clamp technique is commonly used to estimate synaptic conductances. While previous work has shown how these estimates are affected by series resistance and space clamp errors during isolated synaptic events, how voltage clamp errors impact on synaptic conductance estimates during concurrent excitation and inhibition is less clear. This issue is particularly relevant given that many studies now use the whole-cell voltage clamp technique to estimate synaptic conductances in vivo, where both excitation and inhibition are intact. Using both simplistic and morphologically realistic models, we investigate how imperfect voltage clamp conditions distort estimates of excitatory and inhibitory synaptic conductance estimated using the Borg-Graham method during concurrent synaptic input onto dendrites. These simulations demonstrate that dendritically located conductances are underestimated even when dynamic clamp reinjection faithfully reproduces the voltage response at the soma to the actual conductances. Inhibitory conductances are underestimated more than excitatory conductances, leading to errors in the excitatory to inhibitory conductance ratio and negative inhibitory conductance estimates during distal inhibition. Interactions between unclamped dendritic excitatory and inhibitory conductances also introduce correlations when the actual conductances are uncorrelated, as well as distortions in the time course of estimated excitatory and inhibitory conductances. Finally, we show that space clamp errors are exacerbated by the inclusion of dendritic voltage-activated conductances. In summary, we highlight issues with the interpretation of synaptic conductance estimates obtained using somatic whole-cell voltage clamp during concurrent excitatory and inhibitory input to neurons with dendrites.

Physiological Diversity Influences Detection of Stimulus Envelope and Fine Structure in Neurons of the Medial Superior Olive

The neurons of the medial superior olive (MSO) of mammals extract azimuthal information from the delays between sounds reaching the two ears [interaural time differences (ITDs)]. Traditionally, all models of sound localization have assumed that MSO neurons represent a single population of cells with specialized and homogeneous intrinsic and synaptic properties that enable the detection of synaptic coincidence on a timescale of tens to hundreds of microseconds. Here, using patch-clamp recordings from large populations of anatomically labeled neurons in brainstem slices from male and female Mongolian gerbils (Meriones unguiculatus), we show that MSO neurons are far more physiologically diverse than previously appreciated, with properties that depend regionally on cell position along the topographic map of frequency. Despite exhibiting a similar morphology, neurons in the MSO exhibit subthreshold oscillations of differing magnitudes that drive action potentials at rates between 100 and 800 Hz. These oscillations are driven primarily by voltage-gated sodium channels and are distinct from resonant properties derived from other active membrane properties. We show that graded differences in these and other physiological properties across the MSO neuron population enable the MSO to duplex the encoding of ITD information in both fast, submillisecond time-varying signals as well as in slower envelopes.SIGNIFICANCE STATEMENT Neurons in the medial superior olive (MSO) encode sound localization cues by detecting microsecond differences in the arrival times of inputs from the left and right ears, and it has been assumed that this computation is made possible by highly stereotyped structural and physiological specializations. Here we report using a large (>400) sample size in which MSO neurons show a strikingly large continuum of functional properties despite exhibiting similar morphologies. We demonstrate that subthreshold oscillations mediated by voltage-gated Na+ channels play a key role in conferring graded differences in firing properties. This functional diversity likely confers capabilities of processing both fast, submillisecond-scale synaptic activity (acoustic "fine structure"), and slow-rising envelope information that is found in amplitude-modulated sounds and speech patterns.

Electrical match between initial segment and somatodendritic compartment for action potential backpropagation in retinal ganglion cells

The action potential of most vertebrate neurons initiates in the axon initial segment (AIS) and is then transmitted to the soma where it is regenerated by somatodendritic sodium channels. For successful transmission, the AIS must produce a strong axial current, so as to depolarize the soma to the threshold for somatic regeneration. Theoretically, this axial current depends on AIS geometry and Na⁺ conductance density. We measured the axial current of mouse retinal ganglion cells using whole cell recordings with post hoc AIS labeling. We found that this current is large, implying high Na⁺ conductance density, and carries a charge that covaries with capacitance so as to depolarize the soma by ∼30 mV. Additionally, we observed that the axial current attenuates strongly with depolarization, consistent with sodium channel inactivation, but temporally broadens so as to preserve the transmitted charge. Thus, the AIS appears to be organized so as to reliably backpropagate the axonal action potential.NEW & NOTEWORTHY We measured the axial current produced at spike initiation by the axon initial segment of mouse retinal ganglion cells. We found that it is a large current, requiring high sodium channel conductance density, which covaries with cell capacitance so as to ensure a ∼30 mV depolarization. During sustained depolarization the current attenuated, but it broadened to preserve somatic depolarization. Thus, properties of the initial segment are adjusted to ensure backpropagation of the axonal action potential.

Electrophysiology using coaxial atom probe array: live imaging reveals hidden circuits of a hippocampal neural network

Since the 1960s, it is held that when a neuron fires, a nerve spike passes only through the selective branches, the calculated choice is a key to learning by rewiring. It is argued by chemically estimating the membrane's ion channel density that different axonal branches get active to pass the spike-branches blink at firing at different time domains. Here, using a new time-lapse dielectric imaging, we visualize the classic branch selection process; thenceforth, hidden circuits operating at different time domains become visible. The fractal grid of coaxial probes captures wireless snapshots of material's vibration at various depths below the membrane by setting a suitable frequency. Thus far, branch selection observed emitted energy or particle but never the emitters, what they do. As each dielectric material transmits and reflects signals of different frequencies, we image live how filaments search for many branch-made circuits, choose a unique pathway 10³ times faster than a single nerve spike. It reveals that neural branches and circuit visible in a microscope are not absolute, there coexist many circuits each operating in different dime domains, operating at a time.NEW & NOTEWORTHY Using dielectric resonance scanner, we show electromagnetic field connections between physically separated neurons. Electromagnetic field creates field lines that pass through gap junctions, connect Axon initial segment with the dendrites through Soma, and connect axonal or dendritic branches even if there is no synaptic junction. Consequently, many distinct loops connecting various branches form coexisting circuits. Our discovery suggests that physically appearing neural circuit is a fractional view of many simultaneously operating circuits in different time domains in a neural network.

Auditory Brainstem Models: Adapting Cochlear Nuclei Improve Spatial Encoding by the Medial Superior Olive in Reverberation

Listeners typically perceive a sound as originating from the direction of its source, even as direct sound is followed milliseconds later by reflected sound from multiple different directions. Early-arriving sound is emphasised in the ascending auditory pathway, including the medial superior olive (MSO) where binaural neurons encode the interaural-time-difference (ITD) cue for spatial location. Perceptually, weighting of ITD conveyed during rising sound energy is stronger at 600 Hz than at 200 Hz, consistent with the minimum stimulus rate for binaural adaptation, and with the longer reverberation times at 600 Hz, compared with 200 Hz, in many natural outdoor environments. Here, we computationally explore the combined efficacy of adaptation prior to the binaural encoding of ITD cues, and excitatory binaural coincidence detection within MSO neurons, in emphasising ITDs conveyed in early-arriving sound. With excitatory inputs from adapting, nonlinear model spherical bushy cells (SBCs) of the bilateral cochlear nuclei, a nonlinear model MSO neuron with low-threshold potassium channels reproduces the rate-dependent emphasis of rising vs. peak sound energy in ITD encoding; adaptation is equally effective in the model MSO. Maintaining adaptation in model SBCs, and adjusting membrane speed in model MSO neurons, 'left' and 'right' populations of computationally efficient, linear model SBCs and MSO neurons reproduce this stronger weighting of ITD conveyed during rising sound energy at 600 Hz compared to 200 Hz. This hemispheric population model demonstrates a link between strong weighting of spatial information during rising sound energy, and correct unambiguous lateralisation of a speech source in reverberation.

Diversity of Axonal and Dendritic Contributions to Neuronal Output

Our general understanding of neuronal function is that dendrites receive information that is transmitted to the axon, where action potentials (APs) are initiated and propagated to eventually trigger neurotransmitter release at synaptic terminals. Even though this canonical division of labor is true for a number of neuronal types in the mammalian brain (including neocortical and hippocampal pyramidal neurons or cerebellar Purkinje neurons), many neuronal types do not comply with this classical polarity scheme. In fact, dendrites can be the site of AP initiation and propagation, and even neurotransmitter release. In several interneuron types, all functions are carried out by dendrites as these neurons are devoid of a canonical axon. In this article, we present a few examples of "misbehaving" neurons (with a non-canonical polarity scheme) to highlight the diversity of solutions that are used by mammalian neurons to transmit information. Moreover, we discuss how the contribution of dendrites and axons to neuronal excitability may impose constraints on the morphology of these compartments in specific functional contexts.

Early Binaural Hearing: The Comparison of Temporal Differences at the Two Ears

Many mammals, including humans, are exquisitely sensitive to tiny time differences between sounds at the two ears. These interaural time differences are an important source of information for sound detection, for sound localization in space, and for environmental awareness. Two brainstem circuits are involved in the initial temporal comparisons between the ears, centered on the medial and lateral superior olive. Cells in these nuclei, as well as their afferents, display a large number of striking physiological and anatomical specializations to enable submillisecond sensitivity. As such, they provide an important model system to study temporal processing in the central nervous system. We review the progress that has been made in characterizing these primary binaural circuits as well as the variety of mechanisms that have been proposed to underlie their function.

Soma-axon coupling configurations that enhance neuronal coincidence detection

Coincidence detector neurons transmit timing information by responding preferentially to concurrent synaptic inputs. Principal cells of the medial superior olive (MSO) in the mammalian auditory brainstem are superb coincidence detectors. They encode sound source location with high temporal precision, distinguishing submillisecond timing differences among inputs. We investigate computationally how dynamic coupling between the input region (soma and dendrite) and the spike-generating output region (axon and axon initial segment) can enhance coincidence detection in MSO neurons. To do this, we formulate a two-compartment neuron model and characterize extensively coincidence detection sensitivity throughout a parameter space of coupling configurations. We focus on the interaction between coupling configuration and two currents that provide dynamic, voltage-gated, negative feedback in subthreshold voltage range: sodium current with rapid inactivation and low-threshold potassium current, I_KLT. These currents reduce synaptic summation and can prevent spike generation unless inputs arrive with near simultaneity. We show that strong soma-to-axon coupling promotes the negative feedback effects of sodium inactivation and is, therefore, advantageous for coincidence detection. Furthermore, the feedforward combination of strong soma-to-axon coupling and weak axon-to-soma coupling enables spikes to be generated efficiently (few sodium channels needed) and with rapid recovery that enhances high-frequency coincidence detection. These observations detail the functional benefit of the strongly feedforward configuration that has been observed in physiological studies of MSO neurons. We find that I_KLT further enhances coincidence detection sensitivity, but with effects that depend on coupling configuration. For instance, in models with weak soma-to-axon and weak axon-to-soma coupling, I_KLT in the axon enhances coincidence detection more effectively than I_KLT in the soma. By using a minimal model of soma-to-axon coupling, we connect structure, dynamics, and computation. Although we consider the particular case of MSO coincidence detectors, our method for creating and exploring a parameter space of two-compartment models can be applied to other neurons.

Brain cells (neurons) are spatially extended structures. The locations at which neurons receive inputs and generate outputs are often distinct. We formulate and study a minimal mathematical model that describes the dynamical coupling between the input and output regions of a neuron. We construct our model to reflect known properties of neurons in the auditory brainstem that play an important role in our ability to locate sound sources. These neurons are known as coincidence detectors because they are most likely to respond when they receive simultaneous inputs. We use simulations to explore coincidence detection sensitivity throughout the parameter space of input-output coupling and to identify the coupling configurations that are best for neural coincidence detection. We find that strong forward coupling (from input region to output region), enhances coincidence detection sensitivity in our model and that low-threshold potassium current further improves coincidence detection. Our study is significant in that we detail how cell structure affects neuronal dynamics and, consequently, the ability of neurons to perform as temporally-precise coincidence detectors.

Distinct Distribution Patterns of Potassium Channel Sub-Units in Somato-Dendritic Compartments of Neurons of the Medial Superior Olive

Coincidence detector neurons of the medial superior olive (MSO) are sensitive to interaural time differences in the range of a few tens of microseconds. The biophysical basis for this remarkable acuity is a short integration time constant of the membrane, which is achieved by large low voltage-activated potassium and hyperpolarization-activated inward cation conductances. Additional temporal precision is thought to be achieved through a sub-cellular distribution of low voltage-activated potassium channel expression biased to the soma. To evaluate the contribution of potassium channels, we investigated the presence and sub-cellular distribution profile of seven potassium channel sub-units in adult MSO neurons of gerbils. We find that low- and high voltage-activated potassium channels are present with distinct sub-cellular distributions. Overall, low voltage-activated potassium channels appear to be biased to the soma while high voltage-activated potassium channels are more evenly distributed and show a clear expression at distal dendrites. Additionally, low voltage-activated potassium channel sub-units co-localize with glycinergic inputs while HCN1 channels co-localize more with high voltage-activated potassium channels. Functionally, high voltage-activated potassium currents are already active at low voltages near the resting potential. We describe a possible role of high voltage-activated potassium channels in modulating EPSPs in a computational model and contributing to setting the integration time window of coincidental inputs. Our data shows that MSO neurons express a large set of different potassium channels with distinct functional relevance.

Function and energy consumption constrain neuronal biophysics in a canonical computation: Coincidence detection

Neural morphology and membrane properties vary greatly between cell types in the nervous system. The computations and local circuit connectivity that neurons support are thought to be the key factors constraining the cells' biophysical properties. Nevertheless, additional constraints can be expected to further shape neuronal design. Here, we focus on a particularly energy-intense system (as indicated by metabolic markers): principal neurons in the medial superior olive (MSO) nucleus of the auditory brainstem. Based on a modeling approach, we show that a trade-off between the level of performance of a functionally relevant computation and energy consumption predicts optimal ranges for cell morphology and membrane properties. The biophysical parameters appear most strongly constrained by functional needs, while energy use is minimized as long as function can be maintained. The key factors that determine model performance and energy consumption are 1) the saturation of the synaptic conductance input and 2) the temporal resolution of the postsynaptic signals as they reach the soma, which is largely determined by active membrane properties. MSO cells seem to operate close to pareto optimality, i.e., the trade-off boundary between performance and energy consumption that is formed by the set of optimal models. Good performance for drastically lower costs could in theory be achieved by small neurons without dendrites, as seen in the avian auditory system, pointing to additional constraints for mammalian MSO cells, including their circuit connectivity.

Glycinergic Inhibitory Plasticity in Binaural Neurons Is Cumulative and Gated by Developmental Changes in Action Potential Backpropagation

Utilization of timing-based sound localization cues by neurons in the medial superior olive (MSO) depends critically on glycinergic inhibitory inputs. After hearing onset, the strength and subcellular location of these inhibitory inputs are dramatically altered, but the cellular processes underlying this experience-dependent refinement are unknown. Here we reveal a form of inhibitory long-term potentiation (iLTP) in MSO neurons that is dependent on spiking and synaptic activation but is not affected by their fine-scale relative timing at higher frequencies prevalent in auditory circuits. We find that iLTP reinforces inhibitory inputs coactive with binaural excitation in a cumulative manner, likely well suited for networks featuring persistent high-frequency activity. We also show that a steep drop in action potential size and backpropagation limits induction of iLTP to the first 2 weeks of hearing. These intrinsic changes would deprive more distal inhibitory synapses of reinforcement, conceivably establishing the mature, soma-biased pattern of inhibition.

Enhanced Transmission at the Calyx of Held Synapse in a Mouse Model for Angelman Syndrome

The neurodevelopmental disorder Angelman syndrome (AS) is characterized by intellectual disability, motor dysfunction, distinct behavioral aspects, and epilepsy. AS is caused by a loss of the maternally expressed UBE3A gene, and many of the symptoms are recapitulated in a Ube3a mouse model of this syndrome. At the cellular level, changes in the axon initial segment (AIS) have been reported, and changes in vesicle cycling have indicated the presence of presynaptic deficits. Here we studied the role of UBE3A in the auditory system by recording synaptic transmission at the calyx of Held synapse in the medial nucleus of the trapezoid body (MNTB) through in vivo whole cell and juxtacellular recordings. We show that MNTB principal neurons in Ube3a mice exhibit a hyperpolarized resting membrane potential, an increased action potential (AP) amplitude and a decreased AP half width. Moreover, both the pre- and postsynaptic AP in the calyx of Held synapse of Ube3a mice showed significantly faster recovery from spike depression. An increase in AIS length was observed in the principal MNTB neurons of Ube3a mice, providing a possible substrate for these gain-of-function changes. Apart from the effect on APs, we also observed that EPSPs showed decreased short-term synaptic depression (STD) during long sound stimulations in AS mice, and faster recovery from STD following these tones, which is suggestive of a presynaptic gain-of-function. Our findings thus provide in vivo evidence that UBE3A plays a critical role in controlling synaptic transmission and excitability at excitatory synapses.

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.

Physiological models of the lateral superior olive

In computational biology, modeling is a fundamental tool for formulating, analyzing and predicting complex phenomena. Most neuron models, however, are designed to reproduce certain small sets of empirical data. Hence their outcome is usually not compatible or comparable with other models or datasets, making it unclear how widely applicable such models are. In this study, we investigate these aspects of modeling, namely credibility and generalizability, with a specific focus on auditory neurons involved in the localization of sound sources. The primary cues for binaural sound localization are comprised of interaural time and level differences (ITD/ILD), which are the timing and intensity differences of the sound waves arriving at the two ears. The lateral superior olive (LSO) in the auditory brainstem is one of the locations where such acoustic information is first computed. An LSO neuron receives temporally structured excitatory and inhibitory synaptic inputs that are driven by ipsi- and contralateral sound stimuli, respectively, and changes its spike rate according to binaural acoustic differences. Here we examine seven contemporary models of LSO neurons with different levels of biophysical complexity, from predominantly functional ones (‘shot-noise’ models) to those with more detailed physiological components (variations of integrate-and-fire and Hodgkin-Huxley-type). These models, calibrated to reproduce known monaural and binaural characteristics of LSO, generate largely similar results to each other in simulating ITD and ILD coding. Our comparisons of physiological detail, computational efficiency, predictive performances, and further expandability of the models demonstrate (1) that the simplistic, functional LSO models are suitable for applications where low computational costs and mathematical transparency are needed, (2) that more complex models with detailed membrane potential dynamics are necessary for simulation studies where sub-neuronal nonlinear processes play important roles, and (3) that, for general purposes, intermediate models might be a reasonable compromise between simplicity and biological plausibility.

Computational models help our understanding of complex biological systems, by identifying their key elements and revealing their operational principles. Close comparisons between model predictions and empirical observations ensure our confidence in a model as a building block for further applications. Most current neuronal models, however, are constructed to replicate only a small specific set of experimental data. Thus, it is usually unclear how these models can be generalized to different datasets and how they compare with each other. In this paper, seven neuronal models are examined that are designed to reproduce known physiological characteristics of auditory neurons involved in the detection of sound source location. Despite their different levels of complexity, the models generate largely similar results when their parameters are tuned with common criteria. Comparisons show that simple models are computationally more efficient and theoretically transparent, and therefore suitable for rigorous mathematical analyses and engineering applications including real-time simulations. In contrast, complex models are necessary for investigating the relationship between underlying biophysical processes and sub- and suprathreshold spiking properties, although they have a large number of unconstrained, unverified parameters. Having identified their advantages and drawbacks, these auditory neuron models may readily be used for future studies and applications.

Signatures of Somatic Inhibition and Dendritic Excitation in Auditory Brainstem Field Potentials

Extracellular voltage recordings (V_e ; field potentials) provide an accessible view of in vivo neural activity, but proper interpretation of field potentials is a long-standing challenge. Computational modeling can aid in identifying neural generators of field potentials. In the auditory brainstem of cats, spatial patterns of sound-evoked V_e can resemble, strikingly, V_e generated by current dipoles. Previously, we developed a biophysically-based model of a binaural brainstem nucleus, the medial superior olive (MSO), that accounts qualitatively for observed dipole-like V_e patterns in sustained responses to monaural tones with frequencies >∼1000 Hz (Goldwyn et al., 2014). We have observed, however, that V_e patterns in cats of both sexes appear more monopole-like for lower-frequency tones. Here, we enhance our theory to accurately reproduce dipole and non-dipole features of V_e responses to monaural tones with frequencies ranging from 600 to 1800 Hz. By applying our model to data, we estimate time courses of paired input currents to MSO neurons. We interpret these inputs as dendrite-targeting excitation and soma-targeting inhibition (the latter contributes non-dipole-like features to V_e responses). Aspects of inferred inputs are consistent with synaptic inputs to MSO neurons including the tendencies of inhibitory inputs to attenuate in response to high-frequency tones and to precede excitatory inputs. Importantly, our updated theory can be tested experimentally by blocking synaptic inputs. MSO neurons perform a critical role in sound localization and binaural hearing. By solving an inverse problem to uncover synaptic inputs from V_e patterns we provide a new perspective on MSO physiology.SIGNIFICANCE STATEMENT Extracellular voltages (field potentials) are a common measure of brain activity. Ideally, one could infer from these data the activity of neurons and synapses that generate field potentials, but this "inverse problem" is not easily solved. We study brainstem field potentials in the region of the medial superior olive (MSO); a critical center in the auditory pathway. These field potentials exhibit distinctive spatial and temporal patterns in response to pure tone sounds. We use mathematical modeling in combination with physiological and anatomical knowledge of MSO neurons to plausibly explain how dendrite-targeting excitation and soma-targeting inhibition generate these field potentials. Inferring putative synaptic currents from field potentials advances our ability to study neural processing of sound in the MSO.

Enhancement of phase-locking in rodents. I. An axonal recording study in gerbil

The trapezoid body (TB) contains axons of neurons in the anteroventral cochlear nucleus projecting to monaural and binaural nuclei in the superior olivary complex (SOC). Characterization of these monaural inputs is important for the interpretation of response properties of SOC neurons. In particular, understanding of the sensitivity to interaural time differences (ITDs) in neurons of the medial and lateral superior olive requires knowledge of the temporal firing properties of the monaural excitatory and inhibitory inputs to these neurons. In recent years, studies of ITD sensitivity of SOC neurons have made increasing use of small animal models with good low-frequency hearing, particularly the gerbil. We presented stimuli as used in binaural studies to monaural neurons in the TB and studied their temporal coding. We found that general trends as have been described in the cat are present in gerbil, but with some important differences. Phase-locking to pure tones tends to be higher in TB axons and in neurons of the medial nucleus of the TB (MNTB) than in the auditory nerve for neurons with characteristic frequencies (CFs) below 1 kHz, but this enhancement is quantitatively more modest than in cat. Stronger enhancement is common when TB neurons are stimulated at low frequencies below CF. It is rare for TB neurons in gerbil to entrain to low-frequency stimuli, i.e., to discharge a well-timed spike on every stimulus cycle. Also, complex phase-locking behavior, with multiple modes of increased firing probability per stimulus cycle, is common in response to low frequencies below CF.NEW & NOTEWORTHY Phase-locking is an important property of neurons in the early auditory pathway: it is critical for the sensitivity to time differences between the two ears enabling spatial hearing. Studies in cat have shown an improvement in phase-locking from the peripheral to the central auditory nervous system. We recorded from axons in an output tract of the cochlear nucleus and show that a similar but more limited form of temporal enhancement is present in gerbil.

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.

Physiology and anatomy of neurons in the medial superior olive of the mouse

In mammals with good low-frequency hearing, the medial superior olive (MSO) computes sound location by comparing differences in the arrival time of a sound at each ear, called interaural time disparities (ITDs). Low-frequency sounds are not reflected by the head, and therefore level differences and spectral cues are minimal or absent, leaving ITDs as the only cue for sound localization. Although mammals with high-frequency hearing and small heads (e.g., bats, mice) barely experience ITDs, the MSO is still present in these animals. Yet, aside from studies in specialized bats, in which the MSO appears to serve functions other than ITD processing, it has not been studied in small mammals that do not hear low frequencies. Here we describe neurons in the mouse brain stem that share prominent anatomical, morphological, and physiological properties with the MSO in species known to use ITDs for sound localization. However, these neurons also deviate in some important aspects from the typical MSO, including a less refined arrangement of cell bodies, dendrites, and synaptic inputs. In vitro, the vast majority of neurons exhibited a single, onset action potential in response to suprathreshold depolarization. This spiking pattern is typical of MSO neurons in other species and is generated from a complement of K_v1, K_v3, and I_H currents. In vivo, mouse MSO neurons show bilateral excitatory and inhibitory tuning as well as an improvement in temporal acuity of spiking during bilateral acoustic stimulation. The combination of classical MSO features like those observed in gerbils with more unique features similar to those observed in bats and opossums make the mouse MSO an interesting model for exploiting genetic tools to test hypotheses about the molecular mechanisms and evolution of ITD processing.

Neuronal coupling by endogenous electric fields: cable theory and applications to coincidence detector neurons in the auditory brain stem

The ongoing activity of neurons generates a spatially and time-varying field of extracellular voltage (Ve). This Ve field reflects population-level neural activity, but does it modulate neural dynamics and the function of neural circuits? We provide a cable theory framework to study how a bundle of model neurons generates Ve and how this Ve feeds back and influences membrane potential (Vm). We find that these "ephaptic interactions" are small but not negligible. The model neural population can generate Ve with millivolt-scale amplitude, and this Ve perturbs the Vm of "nearby" cables and effectively increases their electrotonic length. After using passive cable theory to systematically study ephaptic coupling, we explore a test case: the medial superior olive (MSO) in the auditory brain stem. The MSO is a possible locus of ephaptic interactions: sounds evoke large (millivolt scale)Vein vivo in this nucleus. The Ve response is thought to be generated by MSO neurons that perform a known neuronal computation with submillisecond temporal precision (coincidence detection to encode sound source location). Using a biophysically based model of MSO neurons, we find millivolt-scale ephaptic interactions consistent with the passive cable theory results. These subtle membrane potential perturbations induce changes in spike initiation threshold, spike time synchrony, and time difference sensitivity. These results suggest that ephaptic coupling may influence MSO function.

Predicting binaural responses from monaural responses in the gerbil medial superior olive

Accurate sound source localization of low-frequency sounds in the horizontal plane depends critically on the comparison of arrival times at both ears. A specialized brainstem circuit containing the principal neurons of the medial superior olive (MSO) is dedicated to this comparison. MSO neurons are innervated by segregated inputs from both ears. The coincident arrival of excitatory inputs from both ears is thought to trigger action potentials, with differences in internal delays creating a unique sensitivity to interaural time differences (ITDs) for each cell. How the inputs from both ears are integrated by the MSO neurons is still debated. Using juxtacellular recordings, we tested to what extent MSO neurons from anesthetized Mongolian gerbils function as simple cross-correlators of their bilateral inputs. From the measured subthreshold responses to monaural wideband stimuli we predicted the rate-ITD functions obtained from the same MSO neuron, which have a damped oscillatory shape. The rate of the oscillations and the position of the peaks and troughs were accurately predicted. The amplitude ratio between dominant and secondary peaks of the rate-ITD function, captured in the width of its envelope, was not always exactly reproduced. This minor imperfection pointed to the methodological limitation of using a linear representation of the monaural inputs, which disregards any temporal sharpening occurring in the cochlear nucleus. The successful prediction of the major aspects of rate-ITD curves supports a simple scheme in which the ITD sensitivity of MSO neurons is realized by the coincidence detection of excitatory monaural inputs.

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.

A model of the medial superior olive explains spatiotemporal features of local field potentials

Local field potentials are important indicators of in vivo neural activity. Sustained, phase-locked, sound-evoked extracellular fields in the mammalian auditory brainstem, known as the auditory neurophonic, reflect the activity of neurons in the medial superior olive (MSO). We develop a biophysically based model of the neurophonic that accounts for features of in vivo extracellular recordings in the cat auditory brainstem. By making plausible idealizations regarding the spatial symmetry of MSO neurons and the temporal synchrony of their afferent inputs, we reduce the challenging problem of computing extracellular potentials in a 3D volume conductor to a one-dimensional problem. We find that postsynaptic currents in bipolar MSO neuron models generate extracellular voltage responses that strikingly resemble in vivo recordings. Simulations reproduce distinctive spatiotemporal features of the in vivo neurophonic response to monaural pure tones: large oscillations (hundreds of microvolts to millivolts), broad spatial reach (millimeter scale), and a dipole-like spatial profile. We also explain how somatic inhibition and the relative timing of bilateral excitation may shape the spatial profile of the neurophonic. We observe in simulations, and find supporting evidence in in vivo data, that coincident excitatory inputs on both dendrites lead to a drastically reduced spatial reach of the neurophonic. This outcome surprises because coincident inputs are thought to evoke maximal firing rates in MSO neurons, and it reconciles previously puzzling evoked potential results in humans and animals. The success of our model, which has no axon or spike-generating sodium currents, suggests that MSO spikes do not contribute appreciably to the neurophonic.

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.

On the localization of complex sounds: temporal encoding based on input-slope coincidence detection of envelopes

Behavioral and neural findings demonstrate that animals can locate low-frequency sounds along the azimuth by detecting microsecond interaural time differences (ITDs). Information about ITDs is also available in the amplitude modulations (i.e., envelope) of high-frequency sounds. Since medial superior olivary (MSO) neurons encode low-frequency ITDs, we asked whether they employ a similar mechanism to process envelope ITDs with high-frequency carriers, and the effectiveness of this mechanism compared with the process of low-frequency sound. We developed a novel hybrid in vitro dynamic-clamp approach, which enabled us to mimic synaptic input to brain-slice neurons in response to virtual sound and to create conditions that cannot be achieved naturally but are useful for testing our hypotheses. For each simulated ear, a virtual sound, computer generated, was used as input to a computational auditory-nerve model. Model spike times were converted into synaptic input for MSO neurons, and ITD tuning curves were derived for several virtual-sound conditions: low-frequency pure tones, high-frequency tones modulated with two types of envelope, and speech sequences. Computational models were used to verify the physiological findings and explain the biophysical mechanism underlying the observed ITD coding. Both recordings and simulations indicate that MSO neurons are sensitive to ITDs carried by spectrotemporally complex virtual sounds, including speech tokens. Our findings strongly suggest that MSO neurons can encode ITDs across a broad-frequency spectrum using an input-slope-based coincidence-detection mechanism. Our data also provide an explanation at the cellular level for human localization performance involving high-frequency sound described by previous investigators.

Coincidence detection in the medial superior olive: mechanistic implications of an analysis of input spiking patterns

Coincidence detection by binaural neurons in the medial superior olive underlies sensitivity to interaural time difference (ITD) and interaural correlation (ρ). It is unclear whether this process is akin to a counting of individual coinciding spikes, or rather to a correlation of membrane potential waveforms resulting from converging inputs from each side. We analyzed spike trains of axons of the cat trapezoid body (TB) and auditory nerve (AN) in a binaural coincidence scheme. ITD was studied by delaying "ipsi-" vs. "contralateral" inputs; ρ was studied by using responses to different noises. We varied the number of inputs; the monaural and binaural threshold and the coincidence window duration. We examined physiological plausibility of output "spike trains" by comparing their rate and tuning to ITD and ρ to those of binaural cells. We found that multiple inputs are required to obtain a plausible output spike rate. In contrast to previous suggestions, monaural threshold almost invariably needed to exceed binaural threshold. Elevation of the binaural threshold to values larger than 2 spikes caused a drastic decrease in rate for a short coincidence window. Longer coincidence windows allowed a lower number of inputs and higher binaural thresholds, but decreased the depth of modulation. Compared to AN fibers, TB fibers allowed higher output spike rates for a low number of inputs, but also generated more monaural coincidences. We conclude that, within the parameter space explored, the temporal patterns of monaural fibers require convergence of multiple inputs to achieve physiological binaural spike rates; that monaural coincidences have to be suppressed relative to binaural ones; and that the neuron has to be sensitive to single binaural coincidences of spikes, for a number of excitatory inputs per side of 10 or less. These findings suggest that the fundamental operation in the mammalian binaural circuit is coincidence counting of single binaural input spikes.

Directional hearing by linear summation of binaural inputs at the medial superior olive

Neurons in the medial superior olive (MSO) enable sound localization by their remarkable sensitivity to submillisecond interaural time differences (ITDs). Each MSO neuron has its own "best ITD" to which it responds optimally. A difference in physical path length of the excitatory inputs from both ears cannot fully account for the ITD tuning of MSO neurons. As a result, it is still debated how these inputs interact and whether the segregation of inputs to opposite dendrites, well-timed synaptic inhibition, or asymmetries in synaptic potentials or cellular morphology further optimize coincidence detection or ITD tuning. Using in vivo whole-cell and juxtacellular recordings, we show here that ITD tuning of MSO neurons is determined by the timing of their excitatory inputs. The inputs from both ears sum linearly, whereas spike probability depends nonlinearly on the size of synaptic inputs. This simple coincidence detection scheme thus makes accurate sound localization possible.

Time-dependent gene expression analysis of the developing superior olivary complex

The superior olivary complex (SOC) is an essential auditory brainstem relay involved in sound localization. To identify the genetic program underlying its maturation, we profiled the rat SOC transcriptome at postnatal days 0, 4, 16, and 25 (P0, P4, P16, and P25, respectively), using genome-wide microarrays (41,012 oligonucleotides (oligos)). Differences in gene expression between two consecutive stages were highest between P4 and P16 (3.6%) and dropped to 0.06% between P16 and P25. To identify SOC-related genetic programs, we also profiled the entire brain at P4 and P25. The number of differentially expressed oligonucleotides between SOC and brain almost doubled from P4 to P25 (4.4% versus 7.6%). These data demonstrate considerable molecular specification around hearing onset, which is rapidly finalized. Prior to hearing onset, several transcription factors associated with the peripheral auditory system were up-regulated, probably coordinating the development of the auditory system. Additionally, crystallin-γ subunits and serotonin-related genes were highly expressed. The molecular repertoire of mature neurons was sculpted by SOC-related up- and down-regulation of voltage-gated channels and G-proteins. Comparison with the brain revealed a significant enrichment of hearing impairment-related oligos in the SOC (26 in the SOC, only 11 in the brain). Furthermore, 29 of 453 SOC-related oligos mapped within 19 genetic intervals associated with hearing impairment. Together, we identified sequential genetic programs in the SOC, thereby pinpointing candidates that may guide its development and ensure proper function. The enrichment of hearing impairment-related genes in the SOC may have implications for restoring hearing because central auditory structures might be more severely affected than previously appreciated.

Human interaural time difference thresholds for sine tones: the high-frequency limit

The smallest detectable interaural time difference (ITD) for sine tones was measured for four human listeners to determine the dependence on tone frequency. At low frequencies, 250-700 Hz, threshold ITDs were approximately inversely proportional to tone frequency. At mid-frequencies, 700-1000 Hz, threshold ITDs were smallest. At high frequencies, above 1000 Hz, thresholds increased faster than exponentially with increasing frequency becoming unmeasurably high just above 1400 Hz. A model for ITD detection began with a biophysically based computational model for a medial superior olive (MSO) neuron that produced robust ITD responses up to 1000 Hz, and demonstrated a dramatic reduction in ITD-dependence from 1000 to 1500 Hz. Rate-ITD functions from the MSO model became inputs to binaural display models-both place based and rate-difference based. A place-based, centroid model with a rigid internal threshold reproduced almost all features of the human data. A signal-detection version of this model reproduced the high-frequency divergence but badly underestimated low-frequency thresholds. A rate-difference model incorporating fast contralateral inhibition reproduced the major features of the human threshold data except for the divergence. A combined, hybrid model could reproduce all the threshold data.

Development of on-off spiking in superior paraolivary nucleus neurons of the mouse

The superior paraolivary nucleus (SPON) is a prominent cell group in the auditory brain stem that has been increasingly implicated in representing temporal sound structure. Although SPON neurons selectively respond to acoustic signals important for sound periodicity, the underlying physiological specializations enabling these responses are poorly understood. We used in vitro and in vivo recordings to investigate how SPON neurons develop intrinsic cellular properties that make them well suited for encoding temporal sound features. In addition to their hallmark rebound spiking at the stimulus offset, SPON neurons were characterized by spiking patterns termed onset, adapting, and burst in response to depolarizing stimuli in vitro. Cells with burst spiking had some morphological differences compared with other SPON neurons and were localized to the dorsolateral region of the nucleus. Both membrane and spiking properties underwent strong developmental regulation, becoming more temporally precise with age for both onset and offset spiking. Single-unit recordings obtained in young mice demonstrated that SPON neurons respond with temporally precise onset spiking upon tone stimulation in vivo, in addition to the typical offset spiking. Taken together, the results of the present study demonstrate that SPON neurons develop sharp on-off spiking, which may confer sensitivity to sound amplitude modulations or abrupt sound transients. These findings are consistent with the proposed involvement of the SPON in the processing of temporal sound structure, relevant for encoding communication cues.

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.

The mechanisms of repetitive spike generation in an axonless retinal interneuron

Several types of retinal interneurons exhibit spikes but lack axons. One such neuron is the AII amacrine cell, in which spikes recorded at the soma exhibit small amplitudes (<10 mV) and broad time courses (>5 ms). Here, we used electrophysiological recordings and computational analysis to examine the mechanisms underlying this atypical spiking. We found that somatic spikes likely represent large, brief action potential-like events initiated in a single, electrotonically distal dendritic compartment. In this same compartment, spiking undergoes slow modulation, likely by an M-type K conductance. The structural correlate of this compartment is a thin neurite that extends from the primary dendritic tree: local application of TTX to this neurite, or excision of it, eliminates spiking. Thus, the physiology of the axonless AII is much more complex than would be anticipated from morphological descriptions and somatic recordings; in particular, the AII possesses a single dendritic structure that controls its firing pattern.

Computation of interaural time difference in the owl's coincidence detector neurons

Both the mammalian and avian auditory systems localize sound sources by computing the interaural time difference (ITD) with submillisecond accuracy. The neural circuits for this computation in birds consist of axonal delay lines and coincidence detector neurons. Here, we report the first in vivo intracellular recordings from coincidence detectors in the nucleus laminaris of barn owls. Binaural tonal stimuli induced sustained depolarizations (DC) and oscillating potentials whose waveforms reflected the stimulus. The amplitude of this sound analog potential (SAP) varied with ITD, whereas DC potentials did not. The amplitude of the SAP was correlated with firing rate in a linear fashion. Spike shape, synaptic noise, the amplitude of SAP, and responsiveness to current pulses differed between cells at different frequencies, suggesting an optimization strategy for sensing sound signals in neurons tuned to different frequencies.

Frequency-dependent interaural delays in the medial superior olive: implications for interaural cochlear delays

Neurons in the medial superior olive (MSO) are tuned to the interaural time difference (ITD) of sound arriving at the two ears. MSO neurons evoke a strongest response at their best delay (BD), at which the internal delay between bilateral inputs to MSO matches the external ITD. We performed extracellular recordings in the superior olivary complex of the anesthetized gerbil and found a majority of single units localized to the MSO to exhibit BDs that shifted with tone frequency. The relation of best interaural phase difference to tone frequency revealed nonlinearities in some MSO units and others with linear relations with characteristic phase between 0.4 and 0.6 cycles. The latter is usually associated with the interaction of ipsilateral excitation and contralateral inhibition, as in the lateral superior olive, yet all MSO units exhibited evidence of bilateral excitation. Interaural cochlear delays and phase-locked contralateral inhibition are two mechanisms of internal delay that have been suggested to create frequency-dependent delays. Best interaural phase-frequency relations were compared with a cross-correlation model of MSO that incorporated interaural cochlear delays and an additional frequency-independent delay component. The model with interaural cochlear delay fit phase-frequency relations exhibiting frequency-dependent delays with precision. Another model of MSO incorporating inhibition based on realistic biophysical parameters could not reproduce observed frequency-dependent delays.

Beyond faithful conduction: short-term dynamics, neuromodulation, and long-term regulation of spike propagation in the axon

Most spiking neurons are divided into functional compartments: a dendritic input region, a soma, a site of action potential initiation, an axon trunk and its collaterals for propagation of action potentials, and distal arborizations and terminals carrying the output synapses. The axon trunk and lower order branches are probably the most neglected and are often assumed to do nothing more than faithfully conducting action potentials. Nevertheless, there are numerous reports of complex membrane properties in non-synaptic axonal regions, owing to the presence of a multitude of different ion channels. Many different types of sodium and potassium channels have been described in axons, as well as calcium transients and hyperpolarization-activated inward currents. The complex time- and voltage-dependence resulting from the properties of ion channels can lead to activity-dependent changes in spike shape and resting potential, affecting the temporal fidelity of spike conduction. Neural coding can be altered by activity-dependent changes in conduction velocity, spike failures, and ectopic spike initiation. This is true under normal physiological conditions, and relevant for a number of neuropathies that lead to abnormal excitability. In addition, a growing number of studies show that the axon trunk can express receptors to glutamate, GABA, acetylcholine or biogenic amines, changing the relative contribution of some channels to axonal excitability and therefore rendering the contribution of this compartment to neural coding conditional on the presence of neuromodulators. Long-term regulatory processes, both during development and in the context of activity-dependent plasticity may also affect axonal properties to an underappreciated extent.

Dynamic interaction of Ih and IK-LVA during trains of synaptic potentials in principal neurons of the medial superior olive

In neurons of the medial superior olive (MSO), voltage-gated ion channels control the submillisecond time resolution of binaural coincidence detection, but little is known about their interplay during trains of synaptic activity that would be experienced during auditory stimuli. Here, using modeling and patch-clamp recordings from MSO principal neurons in gerbil brainstem slices, we examined interactions between two major currents controlling subthreshold synaptic integration: a low-voltage-activated potassium current (I(K-LVA)) and a hyperpolarization-activated cation current (I(h)). Both I(h) and I(K-LVA) contributed strongly to the resting membrane conductance and, during trains of simulated EPSPs, exhibited cumulative deactivation and inactivation, respectively. In current-clamp recordings, regular and irregular trains of simulated EPSCs increased input resistance up to 60%, effects that accumulated and decayed (after train) over hundreds of milliseconds. Surprisingly, the mean voltage and peaks of EPSPs increased by only a few millivolts during trains. Using a model of an MSO cell, we demonstrated that the nearly uniform response during modest depolarizing stimuli relied on changes in I(h) and I(K-LVA), such that their sum remained nearly constant over time. Experiments and modeling showed that, for simplified binaural stimuli (EPSC pairs in a noisy background), spike probability gradually increased in parallel with the increasing input resistance. Nevertheless, the interplay between I(h) and I(K-LVA) helps to maintain a nearly uniform shape of individual synaptic responses, and we show that the time resolution of synaptic coincidence detection can be maintained during trains if EPSC size gradually decreases (as in synaptic depression), counteracting slow increases in excitability.

Sound localization: Jeffress and beyond

Many animals use the interaural time differences (ITDs) to locate the source of low frequency sounds. The place coding theory proposed by Jeffress has long been a dominant model to account for the neural mechanisms of ITD detection. Recent research, however, suggests a wider range of strategies for ITD coding in the binaural auditory brainstem. We discuss how ITD is coded in avian, mammalian, and reptilian nervous systems, and review underlying synaptic and cellular properties that enable precise temporal computation. The latest advances in recording and analysis techniques provide powerful tools for both overcoming and utilizing the large field potentials in these nuclei.

Axon Physiology

Axons are generally considered as reliable transmission cables in which stable propagation occurs once an action potential is generated. Axon dysfunction occupies a central position in many inherited and acquired neurological disorders that affect both peripheral and central neurons. Recent findings suggest that the functional and computational repertoire of the axon is much richer than traditionally thought. Beyond classical axonal propagation, intrinsic voltage-gated ionic currents together with the geometrical properties of the axon determine several complex operations that not only control signal processing in brain circuits but also neuronal timing and synaptic efficacy. Recent evidence for the implication of these forms of axonal computation in the short-term dynamics of neuronal communication is discussed. Finally, we review how neuronal activity regulates both axon morphology and axonal function on a long-term time scale during development and adulthood.

Presynaptic action potential waveform determines cortical synaptic latency

Synaptic latency at cortical synapses is determined by the presynaptic release probability (Pr). Short- and long-term presynaptic plasticity is associated with modulation of synaptic delay. We show here that the duration and amplitude of the presynaptic action potential also determine synaptic latency at neocortical and hippocampal excitatory synapses. Blockade of voltage-gated potassium (Kv) channels with 4-aminopyridine or dendrotoxin-I, but not tetraethylammonium, induced a 1–2 ms shift in latency at excitatory synaptic connections formed by pairs of neocortical pyramidal neurons. 4-Aminopyridine or dendrotoxin-I, but not tetraethylammonium, increased the duration of the action potential recorded in the axon, suggesting that presynaptic spike duration is controlled by axonal Kv1 potassium channels. Spike width-dependent changes in latency have been identified at the mossy fibre–CA3 cell synapses and contribute to stabilization of synaptic timing during repetitive stimulation. The effects of presynaptic spike amplitude on synaptic latency were also examined. Decreasing the amplitude of the presynaptic action potential with 15–30 nm TTX reduced synaptic latency by ∼0.5 ms. The regulation of synaptic timing by potassium and sodium channel blockers could not be attributed to modulation of axonal conduction. Rather, these effects are compatible with modifications of the kinetics of the presynaptic calcium current. We conclude that synaptic latency at cortical neurons is not constant but dynamically regulated by presynaptic action potential waveform.

Oscillatory dipoles as a source of phase shifts in field potentials in the mammalian auditory brainstem

A popular model of binaural processing, proposed by Jeffress (1948), states that external interaural time delays (ITDs) are compensated by internal axonal delays allowing ITD to be spatially represented by a population of coincidence detectors in the medial superior olive (MSO). Isolating single-neuron responses in MSO is difficult because of the presence of a strong extracellular field potential known as the neurophonic, so that few studies have tested Jeffress's key prediction. Phase delays in the nucleus laminaris neurophonic in owls have been observed and are consistent with a Jeffress-like model. Here, we recorded neurophonic responses in cat MSO to monaural tones at locations along its dendritic axis. Fourier analysis of the neurophonic was used to extract amplitude and phase at the stimulus frequency. Amplitude, as a function of depth, showed two peaks separated by a dip. A half-cycle phase shift was observed at depths close to the dip, over a wide frequency range. Current source density analysis for contralateral (ipsilateral) stimulation shows a current source close to the neurophonic amplitude peak and a sink a few hundred micrometers ventromedially (dorsolaterally). These results are consistent with a dipole configuration: contralateral (ipsilateral) excitation causes a current sink at the ventromedial (dorsolateral) dendrites and a source at the soma and dorsolateral (ventromedial) dendrites. Incorporating these results in a dipole model explains the phase and amplitude patterns observed. We conclude that the half-cycle phase shift is consistent with a current dipole, making it difficult to derive measurements of axonal delays from the neurophonic.

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.

Tonotopic tuning in a sound localization circuit

Nucleus laminaris (NL) neurons encode interaural time difference (ITD), the cue used to localize low-frequency sounds. A physiologically based model of NL input suggests that ITD information is contained in narrow frequency bands around harmonics of the sound frequency. This suggested a theory, which predicts that, for each tone frequency, there is an optimal time course for synaptic inputs to NL that will elicit the largest modulation of NL firing rate as a function of ITD. The theory also suggested that neurons in different tonotopic regions of NL require specialized tuning to take advantage of the input gradient. Tonotopic tuning in NL was investigated in brain slices by separating the nucleus into three regions based on its anatomical tonotopic map. Patch-clamp recordings in each region were used to measure both the synaptic and the intrinsic electrical properties. The data revealed a tonotopic gradient of synaptic time course that closely matched the theoretical predictions. We also found postsynaptic band-pass filtering. Analysis of the combined synaptic and postsynaptic filters revealed a frequency-dependent gradient of gain for the transformation of tone amplitude to NL firing rate modulation. Models constructed from the experimental data for each tonotopic region demonstrate that the tonotopic tuning measured in NL can improve ITD encoding across sound frequencies.

Perisomatic voltage-gated sodium channels actively maintain linear synaptic integration in principal neurons of the medial superior olive

Principal neurons of the medial superior olive (MSO) compute azimuthal sound location by integrating phase-locked inputs from each ear. While previous experimental and modeling studies have proposed that voltage-gated sodium channels (VGSCs) play an important role in synaptic integration in the MSO, these studies appear at odds with the unusually weak active backpropagation of action potentials into the soma and dendrites. To understand the spatial localization and biophysical properties of VGSCs, we isolated sodium currents in MSO principal neurons in gerbil brainstem slices. Nucleated and cell-attached patches revealed that VGSC density at the soma is comparable to that of many other neuron types, but channel expression is largely absent from the dendrites. Further, while somatic VGSCs activated with conventional voltage dependence (V(1/2) = -30 mV), they exhibited an unusually negative range of steady-state inactivation (V(1/2) = -77 mV), leaving approximately 92% of VGSCs inactivated at the resting potential (approximately -58 mV). In current-clamp experiments, non-inactivated VGSCs were sufficient to amplify subthreshold EPSPs near action potential threshold, counterbalancing the suppression of EPSP peaks by low voltage-activated potassium channels. EPSP amplification was restricted to the perisomatic region of the neuron, and relatively insensitive to preceding inhibition. Finally, computational modeling showed that the exclusion of VGSCs from the dendrites equalizes somatic EPSP amplification across synaptic locations and lowered the threshold for bilateral versus unilateral excitatory synaptic inputs. Together, these findings suggest that the pattern of sodium channel expression in MSO neurons contributes to these neurons' selectivity for coincident binaural inputs.

Influence of inhibitory synaptic kinetics on the interaural time difference sensitivity in a linear model of binaural coincidence detection

Temporal correlations between the sound waves arriving at the two ears are used to extract the azimuthal position of sound sources. Nerve cells in the mammalian medial superior olive (MSO) that extract these binaural correlations are sensitive to interaural time differences (ITDs) in the range of about 10 micros. These neurons receive inputs from the two ears via four pathways, two excitatory and two inhibitory ones. In this paper, a simple linear model is fitted to the frequency dependence of ITD sensitivity of MSO neurons, which is quantified by the two parameters, characteristic phase and characteristic delay. The fit parameters are the relative delays and the relative strengths of the two inhibitory pathways and thus specify the underlying ITD-detecting circuit assuming a non-Jeffress-like situation, i.e., no excitatory delay lines but phase-locked inhibition. The fitting procedure finds the parameters of these inhibitory pathways such that they account for a desired frequency dependence of ITD sensitivity. It is found that positive characteristic delays require a finite amount of ipsilateral inhibition that arrives at roughly the same time as ipsilateral excitation as well as contralateral inhibition that lags contralateral excitation so much that it effectively leads excitation of the next cycle.