Introduction

Spatial information in the auditory system is critical for humans and other mammals to assemble a 3-dimensional view of the world as well as to understand speech and communication signals, especially in environments with many sounds overlapping in time and in frequency. The auditory system is distinct from vision or touch in that there is no explicit peripheral representation of space, in this case in the cochlea, only a representation of frequency. Accordingly, the central auditory system must compute horizontal sound location indirectly by combining a series of monaural and binaural cues ^1,2. Spatial coding in the central auditory system is a prime example of a centrally synthesized or computational map.

Interaural time difference cues are used by birds and mammals to compute horizontal sound location at low frequencies ³. In mammals this computation takes place in the medial superior olive (MSO), whose neurons are the first to receive converging excitatory and inhibitory inputs driven from the two ears. Intriguingly, in individual neurons, binaural inputs are integrated within a bipolar dendritic architecture, with ipsilateral and contralateral excitatory inputs segregated onto lateral and medial dendritic branches respectively ^4,5. Ipsilateral and contralateral inhibition converges onto the soma and proximal dendrites ^4–8. MSO neurons detect the optimal combination of these inputs, converting temporal coincidence into a rate code ^6,9,10.

The concept of internal delay is central to coincidence detection in the MSO, where acoustic delays to the two ears are countered in time by a mechanism of delay inside the brain. This internal temporal asymmetry was postulated in early models to arise from axonal delay lines formed by ladder-like combinations of bilateral excitatory inputs (the “Jeffress model”) ¹¹. While the Jeffress model enjoys strong support in birds ^12–14, comparable studies in mammals have failed to reveal systematic axonal input delay lines nor any mapping of delay along the nucleus ^6,15,16. More recently, there is evidence that fast inhibition mediates internal delay by shifting the peaks of EPSPs ^17–19. However, this mechanism is subject to vigorous debate ^20–22, and it is not clear that this mechanism alone can explain the range of receptive field locations in the MSO or their insensitivity to sound level. Other mechanisms have been proposed to mediate internal binaural asymmetry, including asymmetrical axon position, medio-lateral differences in the rising slopes of EPSPs ²³, and differences in tuning of binaural inputs (“stereausis”) ^24,25.

All models of coincidence detection must address the issue of the temporal distortions imposed by the dendrites themselves. However, to date models of MSO neurons have been represented either as point neurons or as simplified, symmetrical “ball-and-stick” models ^17,26–30. Previous measurements of dendritic propagation have revealed that EPSPs encounter delays in their propagation to the soma up to ∼150 µs, despite some degree of temporal compensation by activation of low voltage-activated K channels in the soma and proximal dendrites ²⁷. However, these measurements have largely been restricted to the proximal half of the dendritic arbor and have relied on averaging highly variable populations of neurons. Given that the dendrites of MSO neurons alter their branching pattern and diameters during early hearing and following disruptions of normal hearing ^31–33, they might serve as a potential mechanism for adjusting the timing requirements for sounds from the two ears to arrive coincidently at the soma and axon.

Here we demonstrate that the dendritic arbors of MSO neurons are highly heterogeneous and show a striking continuum of asymmetry across the medial and lateral branches that receive segregated inputs driven respectively from the two ears. We show with dual 2-photon fluorescence-guided patch recordings that inputs to smaller and/or more distal dendrites show more substantial propagation delays than previously recognized, and computational modeling of a large population of intact neuronal morphologies shows that these dendritic asymmetries translate into stable internal delays that, as a population, could account for the full range of naturally occurring horizontal locations. Finally, we show that inhibition preserves the effects of dendritic asymmetry on interaural time differences (ITDs) and helps bring the region of maximum slope of firing changes within the ecologically relevant range. Thus dendrite-based delay lines likely work synergistically with other integrative mechanisms purported to shape the perception of horizontal position in mammals.

Results

To understand how MSO neurons process interaural time differences in the dendrites, we made fluorescence-guided dendritic and somatic patch-clamp recordings visualized under 2-photon microscopy. Using this approach, we were able to target the distal third of the dendritic arbor, including secondary and tertiary branches, regions that have largely escaped investigation in these neurons. We then injected simulated EPSCs (τ_rise and τ_decay, 0.2 ms) into the dendritic pipette and recorded potentials simultaneously at both dendrites and soma. We observed strong variability in both the percent amplitude attenuation at the soma as well as the propagation delay of the EPSP, measured as the difference in EPSP peak time at the soma relative to the dendrite (Fig. 1). Notably, the delays measured in these recordings ranged between 100 and 300 µs, exceeding the physiological range of ITDs measured in gerbils. In these recordings, there was little correlation between local morphological features of recorded dendrites and propagation delay of the EPSP, measured as the difference in the peak timing of dendritic and somatic EPSPs (Fig. 2a-c). However, there was a stronger correlation between the local dendritic membrane time constant and EPSP propagation delay (Fig. 2d). In addition, there was a weak trend of increasing dendritic membrane time constant with recording distance (Fig. 2e), possibly because of proximity to the dendritic terminations. These results may reflect that an understanding of the integrative properties of the dendrites requires an analysis of the larger morphological and electrotonic structure of the neuron.

Fig. 1:

Fig. 2:

To understand how overall dendritic structure impacts binaural coincidence detection, we analyzed a database of biocytin-filled MSO neurons that exhibited complete dendritic structures (40 of 270 neurons from Bondy et al., 2021 ³⁴ ; Fig. 3). We quantified dendritic length, surface area and branching, with special emphasis on comparisons of medial and lateral dendritic arbors. Higher-order (2° and higher) dendritic branches were prominent in these neurons, comprising 70% of the membrane surface area (Fig. S1).

Fig. 3:

A striking feature of most neurons in this data set was an overall asymmetry between the lateral and medial dendritic arbors, reflecting differences in length, branching, and/or diameter of the dendrites (Fig. 3a-c). We quantified this asymmetry according to two parameters, the average path length (average length from each dendritic end to the soma) and membrane surface area, with the latter parameter reflecting the collective influence of dendritic length, diameter and branching pattern. We then defined the degree of bilateral asymmetry as fold differences between the larger vs. smaller dendritic measure for each parameter. We observed no obvious correlation between dendritic asymmetry and tonotopic location (Fig. 3a, left and 3b, top). However, we found that dendritic asymmetry formed a finely graded continuum, with a slight bias toward lateral dendrites (Fig. 3b, bottom). Interestingly, there were no significant differences in population averages of the medio-lateral path length and surface area (1.080 ± 0.057 and 1.112 ± 0.133 fold differences; p=0.562), though there was a slight lateral bias. These results indicate that the averaging of dendritic morphological parameters across neurons obscures what is likely a key structural and computational feature.

To understand how morphological asymmetry impacts synaptic integration, we constructed compartmental models using the same 40 reconstructions analyzed in Fig. 3. We introduced an excitatory synaptic conductance (alpha function: τ = 290 µs) into each dendritic compartment and then measured the voltage attenuation and propagation delay from the dendritic input location to the soma (Figs. 4-5). At comparable distances from the soma, EPSP amplitude at the site of synaptic input and following propagation to the soma varied considerably, like the physiological data from paired recordings in Figure 1 (Fig. 4a). Plots of local dendritic and propagated somatic EPSP amplitudes across all synapse locations further revealed striking asymmetries in propagation efficacy of EPSPs to the soma (Fig. 4b, “Active cell”). In MSO neurons, the timing and attenuation of EPSPs along dendrites are influenced both by passive cable filtering as well as interactions with low voltage-activated K channels, which are active in the subthreshold voltage range in these neurons ²⁷. To determine the degree to which asymmetries in low voltage-activated K channels impact EPSP attenuation at the soma we converted all voltage-activated conductances to leak channels (Fig. 4b, “Passive cell”; see Methods). While EPSPs propagated slightly more effectively to the soma from all dendritic locations in the passive model, it did not fundamentally disrupt mediolateral asymmetry, indicating that these differences arose primarily from the passive electrotonic architecture of the cell. The branching structure had a significant effect on dendritic propagation asymmetry. This could be better visualized in inward morphoelectrotonic transforms of cells, which exhibits dendritic compartments according to their electrotonic, versus physical lengths. In the example neuron in Fig. 4c, large primary dendrites are deemphasized, while thinner secondary and tertiary branches appear as electrotonically elongated. Differences between the medial and lateral dendritic arbors in this neuron and many others gave rise to asymmetries in the magnitude of the average EPSP arriving at the soma.

Fig. 4:

Fig. 5:

Further, we observed that our population of cells formed a continuum in the degree of somatic depolarization asymmetry, in line with the asymmetry in dendritic structure (Fig. 4d). Dendritic asymmetry also translated into differences in average EPSP timing across the medial and lateral dendrites. Figure 5a shows for two example neurons the spatial profile of delays of EPSPs propagating from each dendritic compartment to the soma. The asymmetry in dendritic timing can be more quantitatively visualized in plots of peak EPSP delay (t_dend – t_soma) as a function of dendritic distance from the soma (Fig. 5b). Dendritic branch points often introduced substantial jumps in propagation delays, and this is reflected in these plots as increases in slope. To quantify the influence of dendritic asymmetry on the optimal summation of bilateral EPSPs at the soma, we measured the electrotonic delay at the soma for every 2 µm compartment of lateral and medial dendritic subtrees. In our population of 40 neuron models, there were differences in the average relative time of arrival of EPSPs to the soma from compartments in the medial and lateral dendrites. Further, these differences formed a smoothly graded continuum of delays (Fig. 5c).

MSO neurons exhibit a range of intrinsic electrical properties, and so we examined a subset of neuron morphologies to understand the functional implications of this physiological diversity. Using a neuron with an asymmetric dendritic arbor, we systematically slowed the membrane time constant by reducing the density of both low voltage-activated K channels and HCN channels (Fig. S2). In both cases, the timing of EPSPs reaching the soma was linearly related to the value of the membrane time constant. Thus, the effects of dendritic asymmetry on EPSP timing and amplitude at the soma are expected to be substantially higher in MSO neurons with slower intrinsic membrane properties. To understand how the differential timing of EPSPs propagating from medial and lateral dendrites is translated into ITDs, we simulated binaural excitatory input using a spiking model of MSO neurons (see Methods). This model featured one axonal input per terminal branch segment as well as a centripetal (dendrite-to-soma) pattern of dendritic innervation, running from the terminal compartments to the soma, in accordance with results from anatomical studies (Fig. 6a) ^15,16,28. The conduction velocity of these inputs was set to 1 ms^-1, approximating values of unmyelinated terminal axonal arborizations of similar caliber ^13,35. The timing of ipsilateral and contralateral inputs was varied systematically, triggering spiking only when the two inputs were in close coincidence (Fig. 6b). The location of these excitatory ITD functions were dependent on medio-lateral asymmetry. Functions shifted toward the side of the electrically longer dendrite, reflecting the need for earlier activation of that side to compensate for a longer dendritic propagation delay (Fig. 6c). Our population of 40 neurons showed peak firing at delays that traversed a continuum of values (-0.11 to 0.08 ms, median -0.02; Fig. 6d; Fig. S3). The precise range of values depended in part on the assumptions on the velocity of excitatory axons. The largest range of ITDs was achieved when there was closer matching between the velocity of axonal input velocity and postsynaptic EPSPs propagating from the dendrites to the soma, which maximized temporal coincidence at the soma of spatially disparate inputs in the dendrites (Fig. 6e). Finally, ITDs shifted less than 3% in the face of input amplitude changes that resulted in firing probabilities between 0.2 and 0.8, indicating that dendritic asymmetry is highly stable across changing stimulus conditions.

Fig. 6:

Inhibition is a critical component of ITD encoding, although its precise role is subject to vigorous debate. To understand how dendritic asymmetry impacts the effects of inhibition, we added bilateral inhibitory conductances to the somatic compartment of the bilateral excitatory model in Fig. 6, consistent with the known somatically biased innervation of MSO neurons from the lateral and medial nuclei of the trapezoid body (LNTB and MNTB; ^8,36). We set the timing of inhibitory conductances to be 500 µs in advance of excitatory inputs from the same side, in accordance with a previously published estimate ²¹. We then adjusted the amplitude of inhibitory conductances to produce summed IPSPs of between ∼1-3 mV, which reduced firing probability by 20, 40, 60 and 100% (Fig. 7a). With increasing amplitude of IPSPs, resultant ITD functions decreased in halfwidth by 57%, but the location of functions with increasing levels of inhibition were not significantly different from the model with only excitatory inputs (0.070-0.078 ms; centroid, p=0.984; group data). However, the region of maximum slope consistently shifted towards zero, in accordance with a sinking iceberg receptive field scenario (Fig. 7d; -0.27 to 0.07 ms). We then tested how the relative timing of excitatory and inhibitory inputs altered ITD functions. Varying the timing of IPSPs relative to EPSPs from –0.5 ms to 0.25 ms altered the location of ITD functions by 0.04 ms, from 0.07 to 0.11 ms. Over the population of MSO neuron morphologies, the presence of inhibition reduced firing probability without fundamentally shifting the location of ITD functions. However, the region of the function where there is maximal change in firing rate is necessarily impacted by the decrease in ITD width (Fig. S4), suggesting that dendritic asymmetry and inhibition provide separate contributions to MSO neurons’ receptive field locations.

Fig. 7:

Discussion

The passive cable properties of neuronal dendrites are known to impart both attenuation and delay on EPSPs as they propagate to the soma, commensurate with the distance traversed and the anatomical features of the dendrite itself. However, the functional significance of dendritic geometry and its impact on action potential firing is often difficult to assess. Here we have newly identified a critical function for dendritic structure in the processing of sound localization cues in MSO neurons of the auditory brainstem. We have shown that the bipolar dendritic arbor of MSO neurons is typically asymmetrical, imposing a corresponding asymmetry in the relative timing required for excitatory inputs to drive optimal patterns of action potential output. Our compartmental models show that variation in dendritic morphology across cells exerts a continuum of temporal influences sufficient to shift spatial receptive fields across the full biological range of ITDs available to the gerbil. These shifts are insensitive to differences in intensity and likely work together with other sources of internal delay to enable MSO neurons to stably encode spatial locations along the horizontal plane.

Role of dendritic-based delays in the detection of input sequences

The idea that dendritic structure could dictate detection of temporal sequences of input was first explored in the pioneering computer models of Wilfred Rall. These studies showed that attenuation and propagation delays of EPSPs traveling from the dendrites to the soma could impart greater sensitivity to somatically vs distally directed activation sequences of excitatory inputs, where the longer propagation time of more distal EPSPs is compensated by their earlier activation ³⁷. Preferential firing to centripetal (distal to proximal) temporal sequences of uncaged glutamate at spines has been demonstrated in cortical neurons in slices, but it is not clear what natural conditions would generate such sequences ³⁸. By contrast, single excitatory axonal inputs to MSO dendrites mediate a natural centripetal sequence of synaptic activity ^15,28,39, and both current and previous modeling results highlight the importance of matching of input sequence conduction velocity with that of MSO dendrites, which conduct EPSPs at an average of ∼0.3 ms^-1. In the present study, with the aid of 2-photon fluorescence-guided recordings we have been able to sample smaller diameter secondary and tertiary dendrites at longer distances from the soma. Our results reveal that the attenuation and delays of EPSPs propagating from these processes to the soma are more severe than previously estimated ⁴⁰. In our sample of modeled MSO neurons, these slower-conducting non-primary dendrites make up 70% of the surface area of the dendritic arbor in our sample of MSO neurons and thus play an outsized role in exerting temporal shifts in ITD curves in neurons with asymmetrical dendritic trees. These results emphasize that both branching and dendritic diameter are critical determinants of dendritic delay, as seen reflected in the morphoelectrotonic transforms (Fig. 5).

In the visual system, asymmetrical length and branching of the dendrites drives temporal disparities in the pattern of inhibition of ganglion cells, providing directional tuning to object movement ^41–43. The computation in the auditory system differs from vision in several fundamental ways. In the retina, spatial information is directly represented at the level of the photoreceptors, and tuning to spatial movement relies on the relative arrival times of excitatory and inhibitory inputs to the dendrites and soma. By contrast, in the cochlea space is not explicitly represented on the basilar membrane, which decomposes complex sounds spatially into different frequency channels. Accordingly, horizontal spatial receptive fields must be constructed de novo in the MSO through the detection of synaptic binaural coincidence. In this way, ITDs serve as a proxy for horizontal position.

Other sources of asymmetry in binaural coincidence detection

Although our data reveal that the dendrites may contribute significant interaural delays in the binaural circuitry in the MSO, they likely work together with other mechanisms that have been proposed to influence binaural coincidence detection. In ∼25% of MSO neurons in gerbils, the axon emerges from either the lateral or medial dendrites ^44,45, and these results appear to extend to other mammalian species, including guinea pigs and cats ^46,47. Results from computer models suggest these offset axons, like asymmetrical dendrites, introduce strong asymmetries in synaptic integration and ITD tuning ⁴⁸.

Inhibition has received considerable attention as a mechanism for ITD tuning based on shifts of tuning curves measured in single-unit recordings in vivo upon iontophoretic block of glycinergic synapses ^18,19. However, these results are controversial, as strong inhibition has not been observed in both juxtacellular and intracellular patch recordings in vivo ^20,21,49, and there have been concerns about iontophoretic strychnine having off-target effects that that alter both firing probability and input resistance ²⁰. We found that inhibition did not shift the overall location of ITD curves across the functional range of IPSP magnitudes (Fig. 7), consistent with pressure-applied strychnine data in vivo ²⁰. Inhibition shifted the location of maximal change in firing rate, consistent with a conventional “iceberg” model of inhibitory action on neuronal receptive fields. In mammals, the maximum rate of change, or slope of ITDs may be more important for population encoding of ITDs. Given that the maximal rising slope of firing invariably shifts toward 0 µs ITD when inhibition narrows ITD curves, both inhibition and dendritic asymmetry would both play key roles in setting the location of individual MSO neurons’ receptive fields.

Comparison with avian binaural coincidence detectors

Binaural coincidence detection has been extensively studied in birds, and thus the comparison to mammals is noteworthy. Unlike mammals, dendritic morphology in bird MSO (nucleus laminaris) shows striking dependence on tonotopic location, exhibiting longer, more highly branched dendrites in neurons from low frequency regions ^33,50. While these tonotopic differences in dendritic length have garnered considerable attention, a close examination of dendritic parameters shows that nucleus laminaris neurons, like those in mammalian MSO, exhibit a continuum of dendritic asymmetry in the length of dendrites receiving ipsilateral and contralateral inputs (Smith and Rubel 1979, their Fig. 15 ³³). In these low frequency regions, inputs are restricted to distal, higher order branches ⁵¹. Based on both our electrophysiological and modeling data, these higher order branches incur the largest delays as compared to the large-caliber primary dendrites and thus would be the primary determinants of dendritic propagation delay on each side. In the more highly specialized barn owls, the dendrites of laminaris neurons are more limited, and thus internal delay compensation must lie squarely on those provided by unmyelinated afferents ¹³.

Dendritic morphology and the scaling problem across species

The biological range of ITDs varies with head size ^52,53, and thus any mechanism of internal delay must be scalable across species, accounting for ITDs differing by hundreds of microseconds (e.g., gerbil: ±130 µs ⁵⁴, human: ± 600-700 µs ⁵⁵). A dendrite-based source of internal delay would be easily scalable, as the length of MSO dendrites increases with the size of different species. Although quantitative data are not available, previous morphological studies in guinea pig, ferret, cat and humans show that the dendritic arbors show considerable asymmetries ^46,47,56,57.

Methods

All procedures were conducted in agreement with the Institutional Animal Care and Use Committee at The University of Texas at Austin (UT-Austin), which followed the guidelines of the National Institutes of Health. Mongolian gerbils (Meriones unguiculatus) were housed and raised in a colony at the UT-Austin Animal Resource Center. Animals experienced a 50/50 day/night cycle and had continuous access to food and water.

Brain slice preparation

both male and female gerbils (17-40 days old) were anesthetized with isoflurane and decapitated upon loss of the choroid reflex. The brain was removed from the cranium under warm (34-35°C) artificial cerebrospinal fluid (ACSF), the cerebellum was removed and the isolated hindbrain was glued to the stage of an oscillating tissue slicer (Leica VT-1200S). Horizontal sections were prepared at 200 µm thickness and stored at 35°C in a holding chamber for 45-60 min., and then gradually cooled to room temperature (24°C). All solutions were continuously bubbled with 95% O₂ / 5% CO₂. ACSF contained (in mM): 125 mM NaCl, 25 mM D-glucose, 2.5 mM KCl, 25 mM NaHCO₃, 1.25 mM NaH₂PO₄, 1.5mM MgSO₄, 1.5 mM CaCl₂, pH adjusted to 7.45 with NaOH, and final osmolarity at 315 mOsm.

Imaging and electrophysiological acquisition and analyses

neurons in the MSO were visualized under gradient contrast optics on a Leica TCS SP5 System equipped with a Coherent Chameleon Ultra II Ti:sapphire laser and an 8 kHz resonant scanner under control of Leica LAS AF Imaging Software. We found that gradient contrast images acquired via the photomultiplier tubes were of poor contrast in the heavily myelinated regions of the auditory brainstem, and so cell selection and seal formation was carried out under gradient contrast imaging through the epifluorescence port of the microscope and detected on a high-resolution monochrome digital camera (Zeiss Axiocam 503) running Zen software. The soma was recorded in whole-cell current clamp mode with a pipette (4 to 8 MΩ resistance) containing a potassium gluconate-based solution with 40-80 µM Alexa 594 added for visualizing cell morphology. After waiting ∼10 min. for the dye to fill the dendritic arbor, a dendritic recording was made under 2-photon fluorescence with a second pipette (8 to 15 MΩ resistance) containing the same K Gluconate solution with 40-80 µM Alexa 488. Pipette solutions had a composition of 115 mM K-gluconate, 4.42 mM KCl, 0.5 mM EGTA, 10 mM HEPES, 10 mM, Na₂Phosphocreatine, 4 mM MgATP, and 0.3 mM NaGTP. Osmolality was adjusted to 300 mOsm/L with sucrose, and pH was adjusted to 7.30 with KOH. Seal resistances exceeded 1 GΩ, and recordings were discontinued if series resistances exceeded 20 or 50 MΩ for somatic and dendritic recordings, respectively.

Electrophysiological recordings were under the control of custom routines written in IGOR-Pro (Wavemetrics). Pipettes were prepared on a Sutter P-1000 puller using borosilicate glass (1.5 mm O.D.). Data was acquired using a pair of Dagan BVC-700, amplifiers in conjunction with an ITC-18 computer interface (Heka Instruments). Data was low-pass filtered at 5 kHz, sampled at 50 kHz, and stored on a Macintosh computer for further analyses using custom-written routines in IGOR-Pro.

Compartment model construction

A subpopulation of 40 fully intact reconstructed MSO neurons was selected from those gathered in Bondy et al. (2021) ³⁴. The reconstructed morphologies were imported into the NEURON simulation environment, using its Neurolucida importing tool. Computational compartments were created every 2 μm (Fig. S5a). Somatic and dendritic compartments were applied channel kinetics differentially, consisting of low and high-voltage-activated K channels ^27,58, HCN channels⁵⁹, and leak channels, with sodium channels⁶⁰ exclusively in the somatic compartments. In simulations modeling a passive cell, high and low-voltage potassium and HCN channels were replaced with passive leak channels with conductances set to the average resting conductance of the preexisting active channels. In simulations with an axon, a model axon, with morphology as in Lehnert (2014) ⁶¹, was attached at the center of the model soma. The axon channel kinetics implemented consisted of sodium channels, low-threshold potassium channels and leak channels in the nodes and initial segments, with solely leak channels in the internodes. Measurements from the axon were all recorded from the fifth node. Simulated synapses were conductance-based and shaped by an alpha function (τ = 290 µs).

Table 1:

Simulation variations

When measuring EPSP propagation, synapses were placed every 2 µm, with a unitary conductance that would maximally depolarize the soma 1 mV (unless noted otherwise). Each synapse was then stimulated and recorded separately. In ITD coincident detection procedures, dendrites were innervated with synapses (release probability=0.45) placed every 2 μm, totaling ∼125 synapses for each side ⁶². To mimic axonal activation, an artificial axonal input delay (Δt_axon) was calculated for each synapse as a function of conduction velocity (ν_input) and axonal travel distance. The travel distance was considered zero at each side’s furthest point from the soma. Otherwise, the axonal travel distance consists of two components: the mediolateral distance from the furthest point (Δt_axon=0) to the synapse’s closest terminal segment; the path length from that terminal segment to the synapse (Fig. S5b). Artificial ITDs could then be added onto the calculated axonal delay. Each artificial ITD value (-0.5 to 0.5 ms, incremented by 0.01), was tested with 400 trials, and each trial consisted of a single stimulation of all synapses. To provide a more binary output, a model axon was attached to the cell’s soma, and a spike was reported if a 25 mV depolarization from rest was recorded at the fifth and final axonal node. The synapses could then be adjusted with a unitary conductance to achieve an acceptable maximum firing probability. When implementing IPSP inputs to the ITD procedure, two inhibitory synapses were added at the soma, one corresponding to each mediolateral side. Each synapse generated an IPSP shaped by an alpha function with a time constant of 1.5 ms ⁶². The timing of the synapses was adjusted relative to the artificial excitatory ITD signals. The amplitude of the IPSPs was adjusted by modifying the inhibitory synapses’ conductances to achieve a combined IPSP hyperpolarization of approximately 1, 2, and 3 mV.

Data analyses

Measures of dendritic distance, both in slice experiments and in compartment models, were taken as the length along the dendritic arbor to the center of the somatic compartment. To address the variable size of the MSO within the slice plane, a normalized tonotopic location was calculated as the cell’s distance from the most dorsal point of the MSO, relative to the entire MSO dorsoventral length. To provide a quantitative value of asymmetry between each cell’s morphological measures, a unit of fold difference was used, with a value of 1 and 2 representing equal and double values, respectively. Average path length measurements were taken from the distances along the dendrite to the soma from each terminal section of the corresponding mediolateral arbor. Measurements for propagation attenuation and timing were taken at both the synaptic and somatic compartments of the model cell. For attenuation, the somatic depolarization for mediolateral sides was calculated by averaging each synaptic compartments propagated EPSP amplitude at the soma. Morpho-electrotonic transforms were created by scaling each sections length according to the natural logarithm of its attenuation . EPSP delay values were calculated by measuring the time between peak depolarization in the synaptic and somatic compartments. The corresponding delay transforms are scaled according to the delay contribution of each section. Mediolateral comparisons of delay were calculated by subtracting each sides average EPSP delay for all compartments. To minimize noise and data filtering for the ITD response, the centroid of the curve was measured, where half of the total area under the curve exists on either side. Comparisons were made using the absolute ITD centroid values to highlight the population of neurons’ collective change. The ITD firing probabilities were smoothed with a Savitzky–Golay filter for the purpose of reasonably identifying the region of max slope for the curves.

Data availability

Data consist of both original physiological recordings as well as computational modeling. Modeling code can be accessed at the following repository: (https://github.com/golding-lab/golding_mso Powered

Additional files

Supplementary figures

Additional information

Funding

National Institute on Deafness and Other Communication Disorders (NIDCD) (NIH RO1 DC00788)

• Nace L Golding

National Institute on Deafness and Other Communication Disorders (NIDCD) (NIH F32 DC019534)

• Rebecca I Voglewede

National Institute on Deafness and Other Communication Disorders (NIDCD) (NIH F32 DC014890)

• Bradley Winters