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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
J Neurosci. Author manuscript; available in PMC 2010 August 10.
Published in final edited form as:
PMCID: PMC2827923
NIHMSID: NIHMS176989

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

Abstract

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 (V1/2 = −30 mV), they exhibited an unusually negative range of steady-state inactivation (V1/2 = − 77 mV), leaving ~92% of VGSCs inactivated at the resting potential (~ −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 vs. unilateral excitatory synaptic inputs. Taken together, these findings suggest that the pattern of sodium channel expression in MSO neurons contributes to these neurons’ selectivity for coincident binaural inputs.

Keywords: Medial superior olive, auditory brainstem, sodium channels, synaptic integration, EPSP amplification, binaural cues

Introduction

The medial superior olive (MSO) is a brainstem nucleus that processes binaural cues used for sound localization. Principal neurons of the MSO compute differences in the time required for sounds to propagate to each ear. To extract these submillisecond interaural time delays (ITDs), principal neurons of the MSO detect convergence in the timing of binaural excitatory inputs segregated onto each limb of the neurons’ bipolar dendritic trees (Lindsey, 1975; Stotler, 1953). The integration of these excitatory inputs, which are phase locked to frequencies up to 2 kHz, is further influenced by phase-locked inhibition restricted to the soma (Brand et al., 2002; Kapfer et al., 2002). MSO neurons integrate these inputs, modulating their firing rate in response to changes in ITD (Brand 2002; Goldberg 1969; Spitzer 1995; Yin 1990).

Voltage-gated sodium channels (VGSCs) expressed in the soma and dendrites of neurons propagate action potentials, mediate local electrogenic events and shape synaptic integration. These voltage-gated channels, comprised of an alpha subunit with four homologous domains, typically associate with one or more auxiliary beta subunits (reviewed in Catterall 2000). Several alpha subunits, Nav1.1, Nav1.2 and Nav1.6, are broadly expressed in mammalian central neurons, while others, Nav1.3 and Nav1.7, are expressed less commonly. Somatic VGSCs typically propagate axonally-generated action potentials into the soma yielding action potentials that overshoot 0 mV. In the dendrites there is considerable heterogeneity in the density of VGSCs and the efficacy of action potential backpropagation across neurons (Stuart et al., 1997). VGSCs in the dendrites of some neurons are even able to mediate local, fast sodium spikes, facilitating the contribution of distal excitatory inputs to somatic depolarization (reviewed in Häusser et al., 2000; Larkum and Nevian, 2008). In addition, these channels are able to shape synaptic integration by enhancing subthreshold EPSPs in either the soma or dendrites, particularly when evoked at depolarized potentials (Andreasen and Lambert, 1999; González-Burgos and Barrionuevo, 2001; Stuart and Sakmann, 1995; Urban et al., 1998).

In MSO neurons, axonally-initiated action potentials appear unusually small at the soma and undergo strong attenuation as they backpropagate into the dendrites (Scott et al., 2005; Scott et al., 2007). In addition MSO dendrites do not exhibit the strong electrogenesis found in many cell types (Scott et al., 2005). While low voltage-activated potassium channels contribute to the small size of action potentials measured at the soma, somatic action potentials do not overshoot 0 mV even after potassium channels are blocked. These findings suggest MSO neurons express a low density of VGSCs in their somas and dendrites.

In the present study, we used voltage- and current-clamp experiments to explore sodium channel function in MSO principal neurons. Our results reveal that VGSCs are restricted to the soma and proximal dendrites, and exhibit an unusually hyperpolarized steady-state inactivation range. While VGSC inactivation results in small action potential amplitudes at the soma, the density of channels is nevertheless sufficient to amplify subthreshold synaptic potentials, providing compensation for the sublinear summation of EPSPs mediated by low voltage-activatedpotassium channels.

Methods

Slice preparation

Mongolian gerbils (Meriones unguiculatus) were obtained from Charles River Laboratories (Wilmington, MA) or bred at the University of Texas at Austin Animal Resource Center. Procedures were approved by the UT-Austin IACUC. Current-clamp recordings were made in brain slices from gerbils between P16–19, within the first week after hearing onset (~P12). Voltage-clamp recordings were made in brain slices from animals between P15–18.

Gerbils were anesthetized via the inhalation of halothane. Animals were decapitated and the brain was removed while submerged in artificial cerebrospinal fluid (ACSF, in mM: 125 NaCl, 2.5 KCl, 2 CaCl2, 1 MgSO4, 25 NaHCO3, 1.25 NaH2PO4, 25 glucose; pH 7.45 with NaOH) saturated with 95% O2/5% CO2. Horizontal sections (200 μm) were cut at 32°C using an oscillating tissue slicer (Leica VT-1000S, Solms, Germany) and then transferred to an incubating chamber containing oxygenated ACSF at 35°C. After 30 minutes, slices were held at room temperature until recording. Individual slices were transferred to a recording stage and bathed with oxygenated ACSF. MSO neurons were visualized using infrared differential interference contrast microscopy (Zeiss Axioskop 2FS Plus, Oberkochen, Germany) in combination with a Newvicon™ tube camera (Dage-MTI, Michigan City, IN).

Whole-cell current-clamp recordings

Whole-cell patch recordings were made using heat-polished borosilicate patch pipettes (1.65 mm OD, World Precision Instruments, Sarasota, FL) with open tip resistances of 2–4 MΩ (somatic electrodes) and 6–10 MΩ (dendritic electrodes). The internal solution in whole-cell patch pipettes contained (in mM): 115 potassium gluconate, 20 KCl, 10 sodium phosphocreatine, 0.5 EGTA, 4 MgATP, 0.3 NaGTP, 10 HEPES, pH 7.3 with KOH. Biocytin (0.1%) was also included in the internal solution for subsequent morphological analyses of the recorded cells. During recordings the bath solution was maintained at 35°C. Tetrodotoxin (TTX; 1 μM) was bath applied to block VGSCs. Somatic and dendritic recordings were made with Dagan BVC-700A amplifiers (Minneapolis, MN) in current-clamp mode using bridge balance and capacitance compensation. In a few experiments, inhibitory synaptic conductances (IPSGs) were implemented in dynamic clamp using commercial software (SM-2; Cambridge Conductance, Cambridge, UK) controlling a DSP board at 50 kHz (Toro-8, Innovative Integration, Simi Valley, CA). The identification of recorded cells was made on the basis of their location in the slice, cell body shape, and responses to depolarizing current steps. Additionally, most cells were successfully labeled with biocytin and their morphology was examined after recordings (see below). Individual experiments were included if the series resistance was <15 MΩ at the soma and <40 MΩ for dendritic recordings. Data was low-pass filtered at 5 kHz (soma) and acquired at 50–100 kHz using custom macros in IgorPro (WaveMetrics, Inc., Lake Oswego, OR). Simulated excitatory and inhibitory postsynaptic currents (sEPSCs and sIPSCs, respectively) consisted of a dual exponential waveform (sEPSCs: 0.2 ms rise and 0.2 ms decay; sIPSCs: 0.45 ms rise and 2 ms decay). Synaptically evoked EPSPs were elicited with a 100 μs constant current pulse delivered through a glass pipette with a tip diameter of ~10 μm.

Nucleated patch recordings

Nucleated patches were pulled from the soma of morphologically identified MSO neurons using protocols described previously (Sather et al., 1992). Briefly, the cell was first patched in a whole-cell configuration. Then, light suction (0.3–0.5 psi) was applied to the recording pipette (3–4 MΩ tip resistance) and a slow, vertical movement was used to draw the nucleus up with the pipette. Upon resealing of the membrane behind the nucleus, a patch was deemed stable if the input resistance exceeded 1 GΩ (measured using a 3 mV step from a holding potential of −60 mV). The diameter of the patch was between 7–9 μm, corresponding to a surface membrane area of ~154–254 μm2. The internal solution used for nucleated patches contained (in mM): 135 CsCl, 5 EGTA, 10 sodium phosphocreatine, 4 MgATP, 0.3 NaGTP, 10 HEPES, pH 7.3 with CsOH. To isolate Na+ currents, normal ACSF additionally included ZD7288 (50 μM), TEA (10 mM), CoCl2 (200μM) and NiCl (50 μM), blockers of hyperpolarization-activated channels, potasssium channels, and voltage-gated calcium channels, respectively. CNQX (10μM) and D-AP5 (50μM) were added to the bath to block AMPA and NMDA receptors. Recordings were made using an Axopatch 200B voltage-clamp amplifier (Axon Instruments) at room temperature (25°C). Pipettes were wrapped with Parafilm to reduce stray capacitance. Remaining pipette capacitance, whole-cell capacitance and series resistance (≥ 80%) was compensated online. Data was low pass filtered at 10 kHz and acquired at 100 kHz using custom macros programmed in IgorPro.

Cell-attached recordings

Somatic and dendritic cell-attached patch recordings were made using normal ACSF. The pipette solution contained (in mM): 150 NaCl, 3 KCl, 10 HEPES, 2 CaCl2 and 1 MgCl. In addition, 10 mM TEA and 100 μM 4-AP were included in the pipette to reduce voltage-dependentpotassium conductances. In a few recordings a small hyperpolarization-activated cation current (Ih) was observed, but these currents were too slow to affect peak Na+ currents. Ih channel blockers were not used because they significantly changed the resting membrane potential in a time-dependent manner. Recordings were made at room temperature (25°C). To record the relative density of VGSCs along the soma and dendrites, recording pipettes were restricted to those with open-tip resistances of 6–7 MΩ to limit patch-to-patch variation in membrane area. Pipette capacitance neutralization and data acquisition were performed in the same manner as in nucleated-patch recordings.

Analysis

All electrophysiological analyses were completed in IgorPro. Somatic action potential amplitude was measured from the inflection point, defined as the local minimum of the 2nd derivative of voltage within the rising phase of the action potential. EPSP amplitudes were measured relative to rest. The amount of subthreshold EPSP amplification was measured as the difference between EPSP amplitudes in control and TTX conditions at a voltage just below action potential threshold. Means are presented ± SEM and compared using two-tailed paired Student’s t-test.

Anatomy

Slices with biocytin-labeled cells were fixed in 4% paraformaldehyde and subsequently processed using an ABC kit (nickel-enhanced DAB reaction, Vectorlabs, Burlingame, CA). MSO principal neurons were verified by their location in the slice, and by cell morphology. Cells were traced at 40X using an Axioskop FS2 with a camera lucida.

Computational Modeling

A three-dimensional reconstruction of a biocytin-filled MSO neuron was made using Neurolucida (MBF Bioscience, Williston, VT) in semi-automated mode. Simulations using this morphological reconstruction were carried out in the NEURON simulation environment (version 6.0; Hines and Carnevale, 1997). The time step used was 5 μs. Passive parameters were uniform in all compartments and were: Ra = 150 Ωcm, and Cm = 1 μF/cm2. The resting membrane properties of the model were tuned by adjusting two active conductances; a low voltage-activated potassium conductance and a hyperpolarization-activated cation conductance (gK-LVA and gH) and a leak conductance (gLEAK). The respective densities of gK-LVA and gH were balanced to maintain a resting potential near −60 mV, a membrane time constant within the range found experimentally in P16–P19 gerbils (300–1000 μs; Scott et al., 2005), and the voltage-dependent EPSP sharpening found in MSO neurons. In the model, gK-LVA was expressed at greatest density in the soma (0.06 S/cm2), and at a lower, linearly declining density from proximal to distal dendrites (0.003–0.00015 S/cm2), approximating the experimentally determined gradient of gK-LVA found in MSO neurons (Mathews et al., Soc Neurosci. Abstr. 2008:664.17). In addition, gLEAK was added to the dendrites at a uniform density (0.00005 S/cm2, reversal potential at −60). Because the dendritic density of gH is not known, a uniform density of gH was added to the soma and dendrites (0.001 S/cm2), but extra gLEAK (0.0004 S/cm2, reversal potential at −60) was required at the soma to achieve the characteristic sharpening of EPSPs as a function of voltage. The initial segment was defined as the first 25 μm of the axon, based on Scott et al., 2007, and included gK-LVA, gH and gLEAK at densities of 0.025, 0.0005 and 0.00005 S/cm2, respectively. Only gK-LVA and gH were included in the main axon (0.001 and 0.0005 S/cm2, respectively).

The gating of gH was modeled based on direct fits to voltage-clamp data, and exhibited both fast and slow activation components (Khurana and Golding, unpublished results). The time constants for these components were based on fits to activating currents between −110 and −50 mV. The model description of gNa and gK-LVA were based on the present data set and data from Mathews et al. (Soc Neurosci. Abstr. 2008:664.17). For each conductance, current families from 4–6 experiments were simultaneously fit for both the amplitude and kinetics of recorded currents using Neurofit software (Willms, 2002). The individual fits were then averaged to obtain the parameters for the simulated conductances. The mean time constants for gK-LVA and gNa gating were obtained from fits of currents between −70 and 40 mV and −60 and 20 mV, respectively, with equations that matched the data in that range. During simulations, membrane voltages stayed between −70 to −10 mV, within the voltage range well described by the electrophysiological data for these two conductances. The full set of equations governing channel gating and kinetics are provided in the Appendix and are shown in Supplemental Fig. 2. To match experimental data, all simulations were carried out at 35°C, and when necessary channel kinetics were adjusted using a temperature coefficient (Q10) of 3. Further analysis and display of simulation results were done in IgorPro (WaveMetrics, Inc., Lake Oswego, OR). The waveform of the synaptic conductance introduced at the soma or dendrites was described by an alpha function (g = gmax * (t/τsyn) * exp(1 − t/τsyn)), with τsyn = 0.2 ms and Vrev= 0 mV. All simulations included a one second settling period prior to the onset of the synaptic conductance(s).

Results

To determine the expression level and properties of VGSCs in MSO neurons, pharmacologically isolated sodium currents were recorded in nucleated patches pulled from the soma (Fig. 1A). Surprisingly, MSO neurons exhibited substantial TTX-sensitive sodium current in nucleated patches (average density: 22 ± 4.2 pS/μm2), only 26% less than estimates of sodium current density made in hippocampal neurons using similar techniques (30 pS/μm2 average density in nucleated patches; Martina and Jonas, 1997). Channel activation was measured by stepping to voltages between −70 and +20 mV from a −120 mV pre-pulse (Fig. 1B). Sodium currents activated rapidly (τact < 100 μs) and inactivated rapidly as well (τinact < 2 ms). These currents were maximal at −10 mV, and both the voltage of half-activation and slope of Boltzmann fits were comparable to those found in other neurons (−30.9 ± 1.3 mV and 7.5 ± 0.3, respectively; Fig. 1C, D). The reversal potential measured by linear extrapolation was +62.1 ± 2.0 mV, close to the theoretical equilibrium potential for Na+ ions of +69 mV predicted under these recording conditions (see Methods; data not shown). These results are consistent with the movement of ions through a VGSC channel.

Figure 1
Kinetic properties of VGSCs in nucleated patches from MSO neurons.

The substantial amplitude of somatic sodium currents was unexpected considering the small amplitude of somatic action potentials in MSO neurons observed in previous studies (Scott et al., 2005, 2007). To assess how steady-state inactivation impacts somatic VGSC availability during action potential propagation, we stepped nucleated patches to −10 mV from holding voltages between −120 and −20 mV. The voltage of half steady-state inactivation (V1/2), −77.4 ± 1.4 mV, is more hyperpolarized than that for typical neuronal VGSCs (Hu et al., 2009; Kuba and Ohmori 2009; Martina and Jonas 1997; Ming and Wang 2003; Fig. 2A,B). A similar voltage-dependence was measured in cell-attached patch recordings, indicating the relatively negative voltage range of steady-state inactivation was not a dialysis-related phenomenon. This left-shifted curve indicates that ~90% of VGSCs are inactivated at the resting potential for MSO neurons, approximately −60 mV (92% and 89% inactivation in nucleated and cell-attached patches, respectively). To further characterize inactivation properties, sodium channel recovery from inactivation was measured in nucleated patches by varying the time interval between two depolarizing step pulses (steps to −10 mV, 10 and 30 ms duration; Fig. 2C). Sodium channels recovered rapidly from inactivation when held at negative voltages between pulses (Fig. 2D). With a holding voltage of −120 mV, 50% of the current was recovered in ~ 0.7 ms. Recovery from inactivation was considerably slower at a holding voltage of −70 mV, as currents reached 50% peak amplitude in ~4.5 ms.

Figure 2
VGSC steady-state inactivation and recovery from inactivation.

Our previous finding that action potentials propagate poorly into MSO dendrites raises the question as to the density of sodium currents in this compartment. To determine current density along the soma and dendrites, pharmacologically isolated voltage-gated sodium currents were recorded in cell-attached patches at room temperature with a step pulse from −120 to −10 mV (Fig. 3). The resting membrane potential was measured after each recording to ensure the potential was close to that of the estimated value (−50 mV with ion channel blockers in the bath). Recording pipette size was kept as uniform as possible to minimize membrane area differences between patches. Somatic patches averaged 6.42 ± 1.82 pA of sodium current, whereas current density decreased rapidly in the dendrites as a function of distance from the soma.

Figure 3
Density of Na+ currents decreases along the dendrites of MSO neurons

In addition to generating action potentials, VGSCs also amplify EPSPs in the subthreshold range in many neuron types. To test whether VGSCs influence subthreshold excitation in the MSO, dual somatic and dendritic current-clamp recordings of MSO principal neurons were made in response to a series of simulated EPSC waveforms (sEPSCs) injected at either recording site. The amount of VGSC-dependent amplification was assessed by comparing the just-subthreshold EPSP amplitude during control conditions and bath application of 1 μM TTX. In these experiments 20.9 ± 3.3% VGSC-dependent amplification of the subthreshold EPSP was observed at the soma, whereas in the dendrites amplification was nearly absent (3.4 ± 2.0%; n = 5; Fig. 4A-C). EPSP amplification at the soma did not require the presence of an intact axon. Even when an action potential could not be evoked with a large depolarization and recovered morphology indicated the axon was severed near the soma during slicing, EPSP amplification still occurred at the soma but not in the dendrites (n = 3; data not shown). Interestingly, the EPSC-EPSP relationship was sub-linear during TTX application, indicating sodium channels contribute to the construction of a linear input-output function in the subthreshold voltage range. While the contribution of VGSCs to near-threshold EPSP amplitude was not large (2.36 ± 0.44 mV), blocking VGSCs imposed a requirement for substantially more current to reach threshold (716 ± 258 pA; Fig. 4B,C). To determine whether such a linear input-output relationship occurs under more physiological conditions, synaptic stimulation was used to evoke responses from independent populations of synapses (Fig. 4D). Input independence was ascertained using a 5-pulse synaptic depression paradigm to show that prior depression of one synaptic input population (4 pulses at 500 Hz) did not significantly affect the EPSP evoked from the second synaptic input population (data not shown). The summation of independent synaptic responses was near the arithmetic sum, showing that a linear input-output relationship is maintained with physiological stimuli.

Figure 4
VGSC-dependent amplification of subthreshold EPSPs occurs at the soma but not in the dendrites. A, Dual somatic and dendritic (40 μm, lateral) recordings from a single neuron (P17; Vrest = −60 mV). Responses to a series of EPSCs injected ...

As shown above, VGSCs in the perisomatic regions of MSO neurons are mostly inactivated at rest but show rapid recovery from inactivation at negative potentials. These findings raise the possibility that inhibitory synaptic activity could increase VGSC availability through recovery from inactivation, potentially enhancing amplification of subthreshold excitation. To test this hypothesis, IPSC- and EPSC-like waveforms were injected at the soma of MSO neurons during current-clamp recordings. A family of EPSCs was delivered 2.5 ms after the start of an IPSC, just after maximum hyperpolarization. The IPSC amplitude was set to evoke 7–10 mV IPSPs. EPSP amplitudes measured in control and TTX conditions revealed a similar magnitude of just-subthreshold EPSP amplification with and without leading inhibition (Fig. 5A-C). However, the voltage threshold for action potential initiation decreased ~1.4 mV with leading inhibition (p < 0.002; n = 7). As such, VGSC recovery during the IPSP maintained a constant magnitude of near-threshold EPSP amplification despite also reducing the action potential voltage threshold and hence the voltage at which subthreshold amplification must have taken place. Independent of VGSCs, leading IPSPs increased the current required to reach threshold by ~340 pA (p < 0.05, n = 7; Fig. 5D), thus decreasing subthreshold membrane sensitivity, or gain. To determine whether shunting provided by inhibitory conductances (IPSGs) altered somatic EPSP amplification more than IPSC-evoked IPSPs, three experiments were performed by injecting both IPSCs as well as IPSGs implemented in dynamic clamp at 50 kHz (see Methods). The percent amplification of somatic EPSPs with preceding inhibition differed by 1% or less between IPSP conditions. Also, the voltage threshold for action potential initiation differed by less than 0.5 mV between conditions. As expected, leading 7–10 mV IPSG-evoked IPSPs raised the current threshold for action potential initiation 200–400 pA more than the same sized IPSC-evoked IPSPs. Together these findings show that when brief inhibition precedes excitation, linearity in the subthreshold input-output range is preserved (Fig. 5B).

Figure 5
Leading inhibition alters subthreshold gain and lowers the threshold for action potential initiation, but the magnitude of just-subthreshold EPSP amplification by VGSCs remains relatively constant. A, Somatic recordings from a single neuron (P16; Vrest ...

Since we observed that relatively little recovery from inactivation occurred during a single IPSP, we hypothesized that longer membrane hyperpolarizations, as might occur during trains of IPSPs, would increase subthreshold EPSP amplification. To test this hypothesis, EPSPs were delivered either alone or in the presence of a long, 7–10 mV hyperpolarization (80 ms step; Fig. 6A, insets). Prolonged membrane hyperpolarization lowered the voltage threshold for action potential initiation by ~2.5 mV (n = 9, p < 5 × 10−5) but nevertheless increased the current required to reach threshold by ~580 pA (Fig. 6A-D; n=9, p < 0.05). Despite the long hyperpolarization, VGSCs provided the same magnitude of just-subthreshold EPSP amplification as in resting conditions (n=9; p > 0.1). Thus, as for the single IPSC, when a long hyperpolarization precedes excitation near spike threshold, enhanced VGSC amplification is precluded by a concomitant reduction in voltage threshold for spike initiation. Under the conditions of these experiments, the primary influence of preceding inhibition is to increase the excitability of the axon and action potential initiation. At the same time, the linearity of subthreshold gain is preserved over a reduced subthreshold voltage range.

Figure 6
Prolonged membrane hyperpolarization lowers the voltage threshold for action potential initiation and shifts resting conductances, but VGSCs provide the same magnitude of just-subthreshold EPSP amplification as in resting conditions. A, Somatic recordings ...

The finding that EPSP amplification still occurred at the soma when the axon is severed proximally suggests VGSCs at the soma may be specifically required for this amplification. To test this idea further, sodium currents were added into different compartments of a computational model. A Neurolucida reconstruction of an MSO neuron was used to generate a model in NEURON. The gK-LVA and gH properties were fit to currents isolated from MSO neurons (P. Mathews and S. Khurana) and adjusted to match the input resistance, time constant, and dendrosomatic EPSP propagation characteristics recorded in MSO neurons (Fig. 7A). Subthreshold responses were evoked by an EPSG-like waveform inserted at the soma. Like MSO neurons in the presence of TTX, with no gNa added to the model there was a sublinear relationship in the input-output function (black trace; Fig. 7B, left panel). Incremental addition of gNa at the soma led to larger somatic EPSP amplitudes without distorting the shape of the EPSP. This amplification was even more prominent when the recording site was shifted to the axon initial segment (Fig. 7B, right panel). As there were no axonal VGSCs in this condition, the increased amplification was likely the result of the far lower capacitive load in the initial segment. When VGSCs were restricted to the initial segment, EPSPs were strongly amplified locally (Fig. 7C, right panel), but had little effect on the soma other than a slight broadening of EPSPs (Fig. 7C, left panel). The findings shown in Fig. 7 were not altered by the use of EPSCs instead of EPSGs (data not shown). Moreover, axonal sodium channels did not amplify somatic EPSPs even when the density of gK-LVA and gH in the axon initial segment or in both the initial segment and soma was reduced by an order of magnitude (Supplementary Fig. 1). Thus, our computational model predicts that somatic, and not axonal sodium currents are essential for the amplification of EPSPs at the soma and contribute to the linearity of the subthreshold gain.

Figure 7
Subthreshold amplification of EPSPs by somatic VGSCs in a computational model of an MSO neuron. A, Membrane properties of a model neuron with gK-LVA, gleak, and gH, but no gNa. Step pulses (5 ms, −0.2 to 0.2 nA in 0.05 nA steps) were injected ...

In some neurons, subthreshold amplification of EPSPs relies upon persistent sodium current. The perisomatic sodium currents in MSO neurons have a small persistent component (<2%). To explore whether this persistent component is necessary for somatic EPSP amplification, we eliminated this component of the VGSC in our computational model. Sodium conductance with and without a persistent component was added incrementally to the soma, and EPSGs were injected at the soma. For VGSCs with and without a persistent component the threshold synaptic conductance and percent amplification of just subthreshold somatic EPSPs both differed by less than 1.5% at all levels of total sodium conductance. As this implies, somatically located gNa with and without a small persistent component amplifies somatic EPSPs to the same extent.

The low density of sodium current and lack of EPSP amplification in the dendrites raises the question as to whether restricting amplification of EPSPs to the soma has a computational advantage in MSO neurons. To explore this question, dendritic synapses were attached to a model cell with either somatically restricted gNa or gNa distributed throughout the soma and dendrites (gNa reported as total conductance added to the model cell). Synapses were placed unilaterally or bilaterally on the dendrites either 50 or 100 μm from the soma (Fig. 8A–C show findings for unilateral synapses at 50 μm). For select simulations EPSCs were substituted for synaptic EPSGs to ensure the following results were replicated in current-clamp. The action potential voltage threshold was set at a 12 mV above rest in the soma, the average threshold for action potential generation in MSO neurons. As expected, EPSPs at the site of the synapses were highly sensitive to the presence of local VGSCs and were amplified much less when VGSCs were restricted to the soma (Fig. 8B). Consistent with electrophysiological recordings of MSO neurons, when sodium channels were restricted to the soma large dendritic depolarizations did not elicit dendritic electrogenesis (data not shown). For unilateral synapses placed 50 μm from the soma, the amplification of somatic EPSPs appeared to be insensitive to the distribution of VGSCs (Fig. 8C). However, the inclusion of all synaptic conditions (unilateral and bilateral synapses placed at 50 or 100 μm from the soma) revealed a different conclusion. The percent somatic EPSP amplification varied little when sodium channels were restricted to the soma but varied more widely when sodium channels were distributed throughout the soma and dendrites. Similar to what was seen in electrophysiological recordings of MSO neurons, somatic EPSPs were amplified by 19.9–20.8% when 45 S total gNa was confined to the soma (Fig. 8D). When 45 S of gNa was instead distributed throughout the soma and dendrites, somatic EPSP amplification became far more sensitive to the spatial arrangement of synaptic inputs, varying between 16.5–31.9% across the tested configurations (Fig. 8D). These findings indicate that restricting VGSCs to the soma improves the uniformity of EPSP amplitude and gain in the face of variable spatial patterns of synaptic excitation.

Figure 8
Restriction of VGSCs to the perisomatic region reduces variability of EPSP amplitude with changes in synapse location. A, Stimulus configuration and VGSC distribution of the computational model used in B and C. EPSG-like waveforms were injected 50 μm ...

MSO neurons display far more sensitivity to binaural vs. monaural inputs in vivo. Previous computational modeling by Agmon-Snir et al. (1998) has shown that the separation of excitatory inputs from each ear across different dendrites reduces sublinear summation of unilateral inputs within each dendrite. To explore how the distribution of VGSCs influences this sensitivity of MSO neurons to bilateral versus unilateral synapses, threshold conductances measured in the simulations outlined above were compared across VGSC distribution and synaptic input conditions. Consistent with Agmon-Snir et al. (1998), simulations run with gNa at the soma showed a lower threshold conductance for two bilateral synapses than for each synapse individually. With 45 S of gNa, bilateral thresholds were 5–11% lower at synapses 50 μm from the soma and 21–24% lower for synapses 100 μm from the soma. In contrast, thresholds for bilateral synapses were only 2–7% or 10–11% lower than thresholds for individual synapses when VGSCs were distributed over the soma and dendrites. To ascertain whether sodium channel distribution influenced this bilateral threshold advantage when the unilateral and bilateral conditions had the same number of synapses, simulations were run either with two unilateral or with two bilateral synapses placed at 50 and 100 microns from the soma (Fig. 9A). When 45 S of sodium conductance was inserted at the soma the threshold conductance was 5–11% (1–2.4 nS) less in the bilateral than the unilateral conditions (Fig. 9B). In contrast, when gNa was distributed throughout the soma and dendrites, the thresholds for the unilateral and bilateral conditions overlapped (Fig. 9B). Thus, restricting VGSCs to the soma enhances MSO neurons’ selectivity for bilateral over unilateral coincident inputs.

Figure 9
Restricting VGSCs to the soma enhances MSO neurons’ sensitivity to bilateral vs. unilateral coincident inputs. A, Stimulus configurations used in the computational model. Unilateral simulations (left schematics) were run with two synapses on either ...

Discussion

The present findings indicate that in principal neurons of the MSO, voltage-gated sodium channels are restricted mainly to the perisomatic and axonal compartments. Somatic VGSCs in MSO neurons activate and inactivate quickly, allowing brief, sharply timed amplification of depolarizing synaptic inputs. The sharp decline in sodium current density along the dendrites limits the amplification of local dendritic EPSPs and accounts for our previous findings that action potential backpropagation and electrogenesis are severely limited in the dendrites of MSO neurons (Scott et al., 2005). The significant magnitude of somatic sodium current demonstrated in this report is paradoxical with our previous finding that action potentials are small at the soma. However, this discrepancy is explained by an unusually hyperpolarized voltage-dependence for steady-state inactivation that limits somatic sodium current during action potential backpropagation. Instead, a major contribution of VGSCs in the somatic compartment is to amplify integrated synaptic inputs, compensating for the attenuating influence of voltage-gated potassium channels. In this way, somatic VGSCs are able to regulate the gain of integrated synaptic inputs in principal MSO neurons.

Steady-state inactivation

In cerebellar Purkinje neurons and both hippocampal pyramidal and fast-spiking neurons, where somatic sodium channel steady-state inactivation is more depolarized (V1/2 = −55 to −65 mV) and a substantial portion of VGSCs are available at rest, somatic VGSCs backpropagate large somatic action potentials that overshoot 0 mV (Fricker et al., 1999; Martina and Jonas, 1997; Raman and Bean, 1997). Though unusual for excitable mammalian cells, the left-shifted steady-state inactivation curve for somatic VGSCs in MSO neurons is not without precedent. Similar to MSO neurons, some neurons in the inferior colliculus (IC) have VGSCs with half steady-state inactivation at −75 mV (Liu and Li, 2004). Interestingly, IC neuron action potentials do not always overshoot. More extreme relationships between VGSC steady-state inactivation and resting potential also exist. In vestibular and immature auditory hair cells as well as in small dorsal root ganglion neurons, the voltage of half steady-state inactivation for transient VGSCs approaches −90 mV, substantially lower than the cells’ resting potentials of −70 mV. Vestibular and immature auditory hair cells rarely elicit spikes with depolarizations from rest (Chabbert et al., 2003; Marcotti et al., 2003; Oliver et al., 1997; Wooltorton et al., 2007).

While unusual, the MSO VGSCs are unlikely to comprise novel VGSC subunits. The rapid gating kinetics and recovery from inactivation reported here are similar to those of Nav1.6-containing VGSCs expressed pre- and postsynaptically in the MNTB (Leão et al., 2005). In expression systems Nav1.6 channels exhibit a more negative steady-state inactivation range than Nav1.1 and 1.2 channels (Nav1.6: V1/2 ~ −53 mV, (Burbidge et al., 2002;Isom et al., 1992;Smith and Goldin, 1998)), although not nearly as negative as that exhibited by MSO VGSCs. However, the small fraction of persistent current exhibited by MSO VGSCs (<2%) is more similar to homomeric Nav1.2 than Nav1.6 channels (Burbidge et al., 2002;Isom et al., 1992;Smith and Goldin, 1998). Since MSO VGSCs are not identical to any VGSCs recorded in heterologous expression systems, modulatory proteins likely play a role in shaping their properties. The Navβ1 accessory subunit, widely expressed in brain, negatively shifts the steady-state inactivation of heterologously expressed Nav currents closer to that of MSO VGSCs (Burbidge et al., 2002; Isom et al., 1992; Smith and Goldin, 1998). Other important structural and modulatory mechanisms include alternative splicing, glycosylation, calmodulin binding, phosphorylation, and the concentration of intracellular bicarbonate ions (Bruehl and Witte, 2003). With such diverse mechanisms shaping the functional properties of VGSCs, one Nav α-subunit isoform can give rise to currents with highly variable properties depending upon cell type and conditions (Carr et al., 2003; Cummins et al., 2001; Pan and Beam, 1999).

Recent studies of VGSC trafficking in neurons suggest that VGSCs are inserted into the plasma membrane throughout the cell. Endocytosis limits VGSC expression in the soma and dendrites but not in the axon initial segment, where a higher density of VGSCs is maintained via their association with ankyrin G (reviewed in Cusdin et al., 2008). In MSO neurons, the hyperpolarized range of VGSC inactivation may serve to limit somatodendritic excitability beyond what is achieved through a reduction in channel density via endocytosis. Since large-amplitude action potentials typically generate strong, afterhyperpolarizations, the sharp reduction in the size of the action potential in the soma and dendrites may be advantageous for preventing spiking from distorting future cycles of ITD computations.

Role of VGSCs in dendritic integration

The present experiments indicate somatic VGSCs actively construct linear summation during synaptic integration in MSO neurons by counterbalancing the suppression of EPSP amplitudes by low voltage-activated potassium channels. The activation of both channel types during excitation results in a linear or slightly supra-linear input-output relationship in the subthreshold range. Our computational modeling revealed that somatic VGSCs are essential for reproducing the EPSP amplification recorded experimentally. While these results do not preclude a significant contribution of axonal VGSCs to EPSP amplification, our models predict that these contributions would be restricted to the axon and not easily detected by somatic recordings. Subthreshold EPSPs also undergo amplification by somatic VGSCs in other neuron types, including prefrontal and somatosensory cortical neurons and hippocampal pyramidal neurons (Golding et al., 1999; González-Burgos and Barrionuevo, 2001; Lipowsky et al., 1996; Schwarz and Puil, 1997; Stuart and Sakmann, 1995; Urban et al., 1998). Several groups have postulated that this subthreshold EPSP amplification is generated by persistent VGSCs (Andreasen and Lambert, 1999; Schwindt and Crill, 1995). However, the persistent component of MSO VGSCs was not necessary for synaptic amplification in our computational model. MSO principal neurons also strongly differed from other cell types in the way that synaptic amplification by VGSCs affected synaptic timing. VGSC amplification typically increases the duration of excitation, causing a loss of temporal precision. However, in MSO neurons the timing of amplified EPSPs was maintained. Strong co-activation of low voltage-activated potassium channels expressed in high density in MSO principal neurons rapidly repolarizes both subthreshold EPSPs and action potentials (Scott et al., 2005, 2007; Svirskis et al., 2004). Thus, in MSO neurons, synaptic amplification by fast-inactivating VGSCs is well suited for improving membrane sensitivity without compromising temporal fidelity.

Our results provide direct experimental support for the idea that VGSCs can counterbalance inhibitory synaptic potentials, as first proposed by Zhou and Colburn (Zhou et al., 2005). However, our experiments reveal a complex interaction between somatic inhibition and VGSC populations in the soma and axon. During inhibitory events, linear membrane sensitivity in the subthreshold voltage range is preserved at the soma through VGSC amplification. Simultaneously, the voltage threshold for spike generation is decreased, presumably through the de-inactivation of sodium channels in the axon initial segment, the site of action potential initiation in binaural coincidence detector neurons (Scott et al., 2005, 2007; Kuba et al., 2006). While VGSCs in the soma undergo increased recovery from inactivation to maintain the same magnitude of EPSP amplification, the lowered spike threshold in the axon appears as the most consequential manifestation of inhibitory voltage changes on synaptic integration. These effects are consistent with the previous finding that action potentials in MSO neurons occur preferentially when excitation is preceded with brief hyperpolarizations during the course of mixed excitatory and inhibitory stimuli (Svirskis et al., 2004).

Although VGSCs are able to maintain EPSP amplification, leading inhibition still increases the amount of current needed to generate an action potential. Dodla et al. (2006) found that leading inhibition facilitated spiking, but such post-inhibitory facilitation required a short inhibitory time constant (< 1 ms). Our experiments used IPSC and IPSG durations similar to those reported by Magnusson et al. (2005), which are much longer than one millisecond. In keeping with the predictions made by Dodla and colleagues (2006), longer, more physiological IPSPs increased the overall current required to reach threshold in MSO neurons. Taken together, our results indicate that the interplay between inhibition and the dynamics of VGSC gating causes inhibitory inputs to adjust the gain of transformation between EPSPs and action potential output while maintaining the linearity of synaptic integration at the soma.

Our computational modeling experiments indicate that EPSP amplification by perisomatic VGSCs in MSO neurons is relatively insensitive to dendritic synapse location. Although models with dendritic VGSCs also boosted subthreshold EPSPs, the more distributed nature of the underlying sodium currents rendered amplification for action potential initiation more dependent on differences in input location. Our simulations also revealed lower conductance thresholds for bilateral inputs than unilateral inputs when VGSCs were excluded from the dendrites. Interestingly, a modeling study by Agmon-Snir et al. (1998) showed a larger driving force when excitation was distributed bilaterally vs. unilaterally, resulting in more effective action potential initiation. Our current findings indicate that somatically-located VGSCs preserve this bilateral advantage. Somatic VGSC amplification thus acts in concert with the bipolar dendritic morphology to further enhance MSO neuron sensitivity to temporally correlated patterns of bilateral excitation.

Supplementary Material

Supp1

Supplementary Figure 1.

Reducing the density of gKLVA and gH in the axon initial segment did not alter the impact of axonal gNa on somatic EPSPs. A, Passive properties measured with gKLVA, gleak, and gH, but no gNa. Step pulses (5 ms, −0.2 to 0.2 pA in 0.05 pA steps) were injected at the initial segment. The slope of the maximal voltage response plotted vs. current amplitude indicated the input resistance for the high axonal conductance condition (the same condition as shown in Figure 7) was 59 MΩ (Vrest = −61 mV). Lowering gK-LVA gleak, and gH an order of magnitude in the initial segment increased input resistance to 60.0 MΩ (Vrest = −61 mV). The additional increase of somatic input resistance (to 24.0 MΩ) through the reduction of all somatic and initial segment conductances by an order of magnitude increased the input resistance in the initial segment to 70.0 MΩ (Vrest = −57 mV). B, For the same model cell as in A (data also shown in Figure 7), two simulation configurations are indicated using a 2-dimensional morphological representation of the cell. An EPSG-like waveform at the soma evoked responses recorded at the soma (left panels) or at the distal initial segment (right panels). Sodium conductance was inserted in the initial segment (red). The amount of sodium conductance is indicated by line or trace color (S/cm2). Sample traces show responses to EPSGs in 5 nS steps to threshold, set at a 12 mV EPSP at the soma. A plot of EPSP amplitude vs. EPSG amplitude (0 to 50 nS, 5 nS steps) is shown below. Asterisks indicate when action potentials were generated below a 12 mV depolarization at the soma. Sodium conductance in the initial segment greatly amplified EPSPs in the initial segment, but only prolonged the peak of the somatic EPSPs. C, Lowering the density of gKLVA, gleak, and gH in the initial segment increased the amount of gNa-dependent EPSP amplification in the initial segment, but axonally-located gNa still did not amplify the peak of somatic EPSPs. C, Lowering the density of gKLVA, gleak, and gH in both the initial segment and soma greatly enhanced EPSP amplification in the axon initial segement. Moderate boosting of the somatic EPSPs occurred in extreme cases, in which near-electrogenic activity was displayed in both compartments. However, the somatic EPSP was highly distorted, which was never recorded in MSO neurons.

Supplementary Figure 2.

Properties of the voltage-dependent conductances used in the computational model. A, Voltage dependence of the activation gate for Ih (left panel). The fast (middle panel) and slow (right panel) time constants for the activation gate over the voltage range covered during computational simulations. B, Voltage dependence of the activation (black) and inactivation (red) gate for IKlva (left panel). Time constants for the activation gate (middle panel) and inactivation gate (right panel) over the voltage range of the computational simulations. C, Voltage dependence of the activation (black) and inactivation (red) gate for INa (left panel). Time constants for the activation gate (middle panel) and inactivation gate (right panel) over the voltage range of the computational simulations.

Acknowledgments

We thank Dr. Dan Johnston for the use of his Neurolucida system, and Drs. Sukant Khurana and Michael Roberts for critically reading the manuscript. This work was supported by a grant from the NIH (RO1 DC006788 to NLG). LLS and PJM were supported by individual Ruth Kirschstein NRSAs (DC007245 and DC008030 respectively).

Appendix

For ionic currents, the unit for voltage is mV, current density is μA/cm2, gating variable time constants are in ms, and temperature is 35°C.

Ih

g=gmaxrih=gh(veh)eh=39mV
r(v)=1/{1+exp[(v+64.2)/7.32]}r=τratio(v){[r(v)r]/τ1(v)}+[1τratio(v)]{[r(v)r]/τ2(v)}τ1=2000+(1990exp{[loge(v/128)/3.05]2});maximallimitat200τ2=8590+(8630exp{[loge(v/187)/3.66]2});maximallimitat1000τratio:0.741+(0.433/{1+exp[(68.4v)/9.00]})

INa

g=gmaxm4[(0.993h)+0.007]iNa=gNa(veNa)eNa=69mV
m(v)=1/{1+exp[(v+46)/11]}h(v)=1/{1+exp[(v+62.5)/7.77]}
m=[m(v)m]/τm(v)τm=[0.141+(0.0826/{1+exp[(20.5v)/10.8]})]/3h=[h(v)h]/τh(v)τh=[4.00+(3.74/{1+exp[(40.6v)/5.05]})]/3

IK-LVA

g=gmaxw4[(0.82z)+0.18]iK=gK(veK)eK=90mV
w(v)=1/{1+exp[(v+57.3)/11.7]}z(v)=1/{1+exp[(v+57.0)/5.44]}
w=[w(v)w]/τw(v)τw=0.0382+1.29exp[(v+70)/8.82]+0.876exp[(v+70)/61.9];maximallimitat10z=[z(v)z]/τz(v)τz=41.932.2/{1+exp[(55.4+v)/9.85]}

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