Dynamics of synaptic extracellular field potentials in the nucleus laminaris of the barn owl

Abstract

Synaptic currents are frequently assumed to make a major contribution to the extracellular field potential (EFP). However, in any neuronal population, the explicit separation of synaptic sources from other contributions such as postsynaptic spikes remains a challenge. Here we take advantage of the simple organization of the barn owl nucleus laminaris (NL) in the auditory brain stem to isolate synaptic currents through the iontophoretic application of the α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)-receptor antagonist 1,2,3,4-tetrahydro-6-nitro-2,3-dioxo-benzo[f]quinoxaline-7-sulfonamide (NBQX). Responses to auditory stimulation show that the temporal dynamics of the evoked synaptic contributions to the EFP are consistent with synaptic short-term depression (STD). The estimated time constants of an STD model fitted to the data are similar to the fast time constants reported from in vitro experiments in the chick. Overall, the putative synaptic EFPs in the barn owl NL are significant but small (<1% change of the variance by NBQX). This result supports the hypothesis that the EFP in NL is generated mainly by axonal spikes, in contrast to most other neuronal systems.

NEW & NOTEWORTHY Synaptic currents are assumed to make a major contribution to the extracellular field potential in the brain, but it is hard to directly isolate these synaptic components. Here we take advantage of the simple organization of the barn owl nucleus laminaris in the auditory brain stem to isolate synaptic currents through the iontophoretic application of a synaptic blocker. We show that the responses are consistent with a simple model of short-term synaptic depression.

INTRODUCTION

Synaptic currents are commonly assumed to be the major cause of extracellular field potentials (EFPs) in the brain (Buzsáki et al. 2012). This assumption is based on the general understanding of biophysical processes leading to the generation of extracellular potentials and the abundance of synapses in most regions being recorded from (Buzsáki et al. 2012; Nunez and Srinivasan 2006). However, directly segregating EFPs due only to synaptic currents is a challenge (Ray 2015) and is rarely done, with either pharmacological (Kent and Grill 2013) or statistical (Makarov et al. 2010; Makarova et al. 2011) methods. Isolating the synaptic component of the EFP is especially difficult in brain regions with a complex architecture (Makarova et al. 2011) because any experimental intervention to manipulate synaptic currents will likewise modify recurrent and outgoing neuronal activity, in possibly nonintuitive ways (Gonzalez-Sulser et al. 2012; Grosser et al. 2014).

The barn owl has a highly specialized auditory system with several features that make it suitable to isolation of synaptic contributions to the EFP. First, the earliest binaural nucleus in the auditory processing pathway, called nucleus laminaris (NL), has a well-studied anatomy with a single type of postsynaptic neuron: Afferent axons from the nucleus magnocellularis (NM) form excitatory synapses onto NL neurons, and NL neurons and NM axons are organized to form a tonotopic map (Carr et al. 2013; Carr and Konishi 1990; Rubel and Parks 1975). Second, the responses of the NM and NL neurons to acoustic stimuli are well understood: For tonal stimulation, neurons in both nuclei phase lock to the stimulus; NL neurons also modulate their firing rate in response to changes in the interaural time difference (ITD). Third, the recurrent inhibitory inputs to NL are much slower (Burger et al. 2005; Lu and Trussell 2000) and are neither frequency specific (Yang et al. 1999) nor ITD specific (Burger et al. 2005). We show here that these properties make it feasible to separate synaptic currents from those due to other sources such as postsynaptic (NL neurons) or presynaptic (NM axons) spiking activity.

The EFP in NL has been the subject of several previous studies. Interestingly, it appears that the EFP is mostly attributable to the incoming axons from NM (Kuokkanen et al. 2010, 2013, 2018; McColgan et al. 2017). We hypothesized that the synaptic contribution to the EFP was small. Experimentally confirming the presence of a small, but significant, contribution from synapses to the EFP would thus support the theory of a predominantly axonal EFP in NL.

Synaptic currents in the avian auditory system have been studied extensively in vitro in chickens (Cook et al. 2003; Fukui and Ohmori 2004; Funabiki et al. 1998; Kuba et al. 2002; MacLeod and Carr 2012; Oline et al. 2016; Oline and Burger 2014; Rathouz and Trussell 1998). In chick brain slice preparations, the efficacy of synapses formed by auditory nerve fibers in NM is subject to strong short-term depression (STD) (Brenowitz and Trussell 2001; Zhang and Trussell 1994). The properties of STD in NM follow a tonotopic gradient (Oline et al. 2016). STD is also present in the intensity-processing pathway of the auditory brain stem in avians, in particular in the cochlear nucleus angularis (MacLeod et al. 2007, 2010; MacLeod and Carr 2012; MacLeod and Horiuchi 2011) and in the calyx of Held in gerbils (Hermann et al. 2007). In NL, evidence for the presence of STD was found in vitro by Kuba et al. (2002), who suggested that STD can enhance the direction sensitivity of the postsynaptic neurons. In the avian NL, STD has not yet been studied in vivo.

STD may play a role in several functional tasks, for example, gain control (Abbott et al. 1997), as a temporal filter (Fortune and Rose 2001), and for detection of transients (Abbott et al. 1997; for reviews see Abbott and Regehr 2004; Klug et al. 2012; Regehr 2012). These roles could all be relevant in the context of the barn owl auditory system. The tonotopic organization of STD points toward a functional role in signal processing (Oline et al. 2016). STD could also form a building block for more sophisticated adaptive behavior found in higher brain areas such as “stimulus-specific adaptation” (Chung et al. 2002; Gutfreund 2012). Studies of STD in vivo are, however, rare (Izaki et al. 2002; Mulder et al. 1997; Wang et al. 2013). The relevance of data on STD collected in vitro has been questioned because chronic and transient activation patterns (Hermann et al. 2009) and calcium concentrations (von Gersdorff and Borst 2002) can be quite different from those found in vivo (for review, see Borst 2010). Here we quantify, for the first time, STD in vivo in the avian NL and show values of STD are similar to those observed in vitro.

MATERIALS AND METHODS

Experimental procedures.

Experiments were conducted at the Department of Biology of the University of Maryland. Data were collected from six barn owls (Tyto furcata pratincola) in eight recording sessions, with one owl providing data from two recording sessions at the same stereotactic coordinates but 2 h apart. A second owl provided data for one vehicle control and a 1,2,3,4-tetrahydro-6-nitro-2,3-dioxo-benzo[f]quinoxaline-7-sulfonamide (NBQX) experiment at different stereotaxic locations. Procedures conformed to National Institutes of Health guidelines for animal research and were reviewed and approved by the Animal Care and Use Committee of the University of Maryland. Anesthesia was induced before each experiment by intramuscular injection of a total of 8–10 ml/kg of 20% urethane divided into three or four injections over the course of 3 h. Body temperature was maintained at 39°C by a feedback-controlled heating blanket.

We used iontophoresis to deliver drugs to NL, with methods and concentrations similar to those in previous experiments in the barn owl, chick, and rat inferior colliculus (Feldman and Knudsen 1994; Sanchez et al. 2007; Zhang and Trussell 1994). All data reported here were obtained with glass pipette barrels of Carbostar-3 or -4 LT microiontophoresis electrodes (Kation Scientific, Minneapolis, MN). Microelectrode barrels were filled with the α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)/kainate-receptor antagonist NBQX (5 mM, pH 9.0; Sigma, St. Louis, MO). NBQX is a highly selective competitive antagonist of both AMPA and kainate receptors, with no significant effect on NMDA receptor-mediated currents (Randle et al. 1992). Note that although we have demonstrated the presence of AMPA receptor subunits in barn owl NL (Levin et al. 1997) and NMDA receptor subunits in chicken (Tang and Carr 2007), we cannot exclude the possibility that kainate receptors contribute to some NBQX-sensitive responses. The remaining iontophoresis barrels were filled with 0.15 M NaCl, pH 3.5, for current balancing. Retention and ejection currents were applied to the drug barrels via a dual microiontophoresis current generator (WPI, Sarasota, FL). A carbon fiber served as the recording electrode (impedance ≈ 0.5 MΩ). In preliminary experiments not reported here, we determined that owls anesthetized with xylazine and ketamine showed effects of NBQX, but we switched to urethane anesthesia for the experiments reported here because of potential interactions between ketamine and NMDA receptors (Lodge and Johnson 1990) and because urethane provided a more stable plane of anesthesia. On the day of the experiment, 5 mM NBQX was dissolved in 0.15 M NaCl vehicle and filled one barrel of the electrode. Each barrel of the pipette was connected via a chlorided silver wire to a separate channel of the microiontophoresis current generator. NBQX was retained with positive currents (+10 nA) and ejected with negative currents (−30 to −60 nA).

Recordings were made in a sound-attenuating chamber (IAC Acoustics, New York, NY). In all recordings, a AgCl ground electrode (WPI) was placed on the dura near the midsagittal sinus. Electrode signals were amplified, and the line noise was removed with a HumBug line noise eliminator (Quest Scientific, North Vancouver, BC, Canada), which only affects the signals at 60 Hz and its higher harmonics. Amplified electrode signals were passed to an analog-to-digital converter [DD1, Tucker-Davis Technologies (TDT), Gainesville, FL] connected to a personal computer via an optical interface (TDT). Acoustic stimuli were digitally generated by custom-made software (“Xdphys” written in Dr. M. Konishi’s laboratory at Caltech) driving a signal-processing board (DSP2, TDT). Acoustic signals were fed to miniature earphones via digital-to-analog converters (DD1, TDT), antialiasing filters (FT6–2, TDT), and attenuators (PA4, TDT). Custom-made sound systems containing the earphones and miniature microphones were placed into the owl’s left and right ear canals. The sound systems were calibrated individually for both amplitude and phase before the recordings. Voltage responses were recorded with a sampling frequency of 48,077 Hz and saved for off-line analysis.

ITD responses were determined by playing stimuli with different ITDs. First, the ITD with maximum response was roughly determined in a preliminary measurement. Then the full tuning curve was measured by playing stimuli at 11 different ITDs, spaced by 30 μs and centered at the ITD with maximal response. A preliminary attenuation tuning was recorded to select an appropriate sound level. We presented stimuli from 10 to 60 dB sound pressure level (SPL) in intervals of 10 dB SPL and chose one or two attenuations that evoked intermediate responses.

Control experiments.

Because the effect of NBQX on the EFP in NL was small, we used single-unit recordings in NM as a positive control. Before recording in NL, each iontophoresis electrode was first tested in the 4–6 kHz region of NM, where NM neurons typically have few or no dendrites (Carr and Boudreau 1993a). We aimed for an average spike reduction of ~63% following iontophoresis using −30 to −60 nA current, consistent with the NBQX blockade of responses in the inferior colliculus (Sanchez et al. 2007). Such a recording session lasted ~40 min, and we typically carried out an entire iontophoresis cycle, with ejection washout, for one or two NM units, in order to determine appropriate current settings for the application of NBQX. Driven and spontaneous rates were determined for each NM unit before, during, and after iontophoresis of NBQX. We observed a mean reduction in firing rate after 6 min of iontophoresis of 56 ± 12% (n = 7) for a 10-nA holding current and a −60-nA ejection current.

In addition to the positive control recordings in NM, we also performed vehicle control experiments in the NL of two owls in which both barrels were filled with 0.15 M NaCl. We recorded responses in NL after iontophoresis of saline, as above, retained with positive current (+10 nA), and then ejected saline with negative current (−30 to −60 nA). There were several rounds of ejecting and retaining currents in each experiment. The vehicle control showed no effect on the EFP except a small drift in signal strength during the duration of the recording (~2 h).

We also performed a control recording to estimate the noise levels due to the recording setup by performing an identical stimulation protocol with the recording electrode in saline. We compared the responses from these control recordings to those from recordings from the main experiments and found that the instrument noise level accounted for <0.1% of the variance.

Data analysis.

Data was analyzed with a custom library (pyXdPhys, https://github.com/phreeza/pyXdPhys) for XdPhys data files. Individual response traces were tagged according to the experimental condition in which they were recorded, NBQX or control, as well as ITD, frequency, and attenuation used for stimulus presentation. For the EFPs shown in Fig. 1, we selected the ITD and frequency that evoked the maximal response, as judged by the average standard deviation of the traces. If several attenuations were recorded, we chose the loudest one. From this subset, all responses from each condition were aggregated and averaged using the arithmetic mean.

Fig. 1.

1,2,3,4-Tetrahydro-6-nitro-2,3-dioxo-benzo[f]quinoxaline-7-sulfonamide (NBQX) alters extracellular field potential responses in nucleus laminaris. A: tone-burst stimulus (duration 200 ms, frequency 6.8 kHz; black bar) and wideband (1 Hz to 10 kHz) responses averaged over all trials in the control condition (blue) and during NBQX application (orange; overlap in brown). B: high-pass (>1 kHz) filtered responses from A (same color code). Inset: a 1-ms excerpt for detail. C: low-pass (<1 kHz) filtered responses from A (same color code). Inset: a 10-ms excerpt for detail. Significance level from Bonferroni-corrected 2-sided t-test of difference between the curves indicated beside insets in B and C. n.s., Not significant. *P < 10⁻³. D: difference between the low-pass filtered responses in NBQX and control conditions shown in C. E: band-pass (1–500 Hz) filtered differences between NBQX and control conditions from 5 recording locations in 4 owls. Note that the displayed amplitudes of voltages traces are identical but the voltage scales (vertical black bars indicate 30 μV) are different.

Filtering was performed with Butterworth filters of order 5 with the cutoff frequencies stated. To avoid delays introduced by the filters, we applied each filter twice, once in the causal and once in the acausal direction.

To test the statistical significance of the difference between the conditions in Fig. 1, we applied the nonparametric cluster-based permutation test described by Maris and Oostenveld (2007). This technique solved the multiple-comparisons problem and took into account the temporal correlations inherent in the data. Briefly, the technique consists of randomly assigning conditions to trials and then calculating the uncorrected significance levels for the differences between these permuted conditions at each time step. Adjacent time steps with significant differences were then grouped into clusters, and an empirical distribution of cluster sizes was tabulated. The cluster sizes were then calculated for the actual NBQX and control conditions, and the significance of the difference was calculated based on the empirical distribution of cluster sizes.

To test the replicability of the findings across several repetitions of “NBQX-injection and control” cycles, we tested for the difference in the changes between condition blocks (i.e., NBQX injection or washout) in the following way: For the responses r(t) we calculated the time-dependent “in-block variance” ${\text{σ}}_j^2\left(t_i\right)$ across trials k ∈ [1, N] for each time point t_i ∈ [1, T] within a single iontophoretic condition block j. From these in-block variances, we calculated the variance for the transition from block j = A to block j = B as σ²(t_i)_B,A = σ²(t_i)_A + σ²(t_i)_B. The average response amplitudes were $〈r\left(t_i\right)〉=1/N\cdot {\displaystyle \sum }_{k=1}^N{r}_k\left(t_i\right)$. The amplitude of the transitions ${\text{τ}}_{A,B}\left(t_i\right)={〈r\left(t_i\right)〉}_B-{〈r\left(t_i\right)〉}_A$ (i.e., the difference of the trial-averaged responses of blocks A and B as seen in Fig. 3C, insets) were calculated as to have consistent polarity, i.e., an NBQX block was always subtracted from a washout block, regardless of the temporal order of the conditions. Because the washout was not always complete, we normalized the amplitudes of the transitions to have a maximum of 1: ${\widehat{\text{τ}}}_{A,B}\left(t_i\right)={\text{τ}}_{A,B}\left(t_i\right)/{\text{max}}_i\left[{\text{τ}}_{A,B}\left(t_i\right)\right]$. The transition variances were also normalized, by dividing them by the square of the nonnormalized transition amplitude: ${\widehat{\text{σ}}}^2{(t_i)}_{B,A}={\text{σ}}^2{(t_i)}_{B,A}/{\left\{{\max }_i\left[{\text{τ}}_{A,B}\left(t_i\right)\right]\right\}}^2$. We then performed a pairwise t-test for the significance of the difference of all ${\widehat{\text{σ}}}^2{(t_i)}_{B,A}$ (across all time points, between all transitions recorded at the same location in 1 owl).

Fig. 3.

Diffusion of 1,2,3,4-tetrahydro-6-nitro-2,3-dioxo-benzo[f]quinoxaline-7-sulfonamide (NBQX) explains time course of amplitudes of synaptic contributions to the extracellular field potential. A: simulated NBQX concentrations for different distances (indicated in key) from an iontophoretic point source. Switching between ejection (NBQX on) and holding (NBQX off) currents indicated by dotted and dashed lines. B: simulated synaptic current amplitudes (signal strengths) for a synapse at given distances (colors as in A) from the iontophoretic point source. Signal strengths were obtained by applying the dose-response curve (inset) to the concentrations shown in A. Black line shows the predicted signal assuming a homogeneous distribution of synapses in nucleus laminaris. C: response amplitudes (signal strengths in mV) in the frequency band associated with synaptic currents (<1 kHz) during application of NBQX. Brown dots show individual trials in an experiment, and blue line is the average over time (sliding window width 500 s), along with the 95% confidence interval (from the standard deviation in the sliding window) in light blue. Iontophoresis switching times indicated by dotted and dashed lines as in A and B. Insets: differences between average stimulus responses for 2 consecutive blocks, equivalent to Fig. 1D. Red line shows the modeled signal (black line in B) scaled to a maximum amplitude of 0.145 mV.

We also tested the diffusive nature of the NBQX effect by examining the time course of responses in Fig. 3. For the analysis of NBQX diffusion in Fig. 3C, we filtered the individual trial response traces with the same cutoff frequencies (<1 kHz) as in Fig. 1, C and D, and calculated the standard deviation of the filtered trace.

Model of short-term plasticity of synaptic currents.

To model the synaptic currents under STD, we used the phenomenological Tsodyks-Markram model with only depression (Tsodyks et al. 1998). In this model, the time-dependent synaptic efficacy x(t) (with dimensionless values between 0 and 1) returns to its resting state with value 1 with time constant τ_D. Upon an action potential reaching the synapse, a fixed fraction 0 < U < 1 of the available neurotransmitter is released, causing an increase of the synaptic current I(t). An individual postsynaptic current is modeled as an exponentially decaying function with time constant τ_s and amplitude A; this function is scaled by the synaptic efficacy x.

Following a simplified approach by Tsodyks et al. (1998), we considered a mean-field approximation of the spike-based model. Spikes were replaced by an average firing rate R(t) that depended on the time t. The model is then governed by the following equations:

$$\begin{array}{c}\frac{\text{d}}{\text{d}t}x\left(t\right)=\frac{1-x\left(t\right)}{{\text{τ}}_{\text{D}}}-Ux\left(t\right)R\left(t\right)\\ I\left(t\right)={\text{τ}}_{\text{s}}AUx\left(t\right)R\left(t\right)\mathrm{.}\end{array}$$ (1)

In preliminary attempts to fit this model to the data, we obtained time constants τ_D in the range of seconds, similar to the value 1.1 s for the slow recovery reported by Cook et al. (2003). However, we could not estimate τ_D reliably from our data because of an approximate degeneracy with the parameters τ_s and A that describe single postsynaptic events; in other words, the fitted values of τ_D, τ_s, and A were quite variable, but this variability was highly interdependent. Because of the nature of our data, i.e., EFPs that reflected the summed activity of many synapses, we could not isolate single events, which would be necessary to estimate τ_s and A.

To overcome these limitations of the STD model, we exploited the fact that firing rates R are expected to be high (>200 spikes/s) and assumed a large τ_D such that the condition 1/τ_D ≪ UR is fulfilled. This assumption allowed us to omit in Eq. 1 the term x/τ_D, which was considered to be small compared with the term xUR. Introducing the new dynamic variable y = τ_Dx and defining $\overline{I}=\frac{{\text{τ}}_s}{{\text{τ}}_{\text{D}}}A$, we then could simplify the model as

$$\begin{array}{c}\frac{1}{UR}\frac{\text{d}}{\text{d}t}y=\frac{1}{UR}-y\\ I=\overline{I}URy\mathrm{.}\end{array}$$ (2)

The new dynamic variable y is a scaled (by τ_D) synaptic efficacy. It reaches the steady-state value $1/(UR)$ with time constant $1/(UR)$. Both the steady-state value and the time constant depend on the firing rate R. We emphasize that we have assumed that the new time constant $1/(UR)$ is much smaller than τ_D, which was confirmed by our fits (see results). We further note that the steady-state value of the current I is equal to Ī, which is independent of both U and R. The time constant $1/(UR)$ for the decay of I, however, does depend on U and R.

Let us discuss a generic example to illustrate the time course of I resulting from the solution of the differential Eq. 2. We consider a population of synapses that have been driven with a constant rate R₀ for a long time. The constant average steady-state current is then I = Ī. Changing the firing rate from R₀ to R₁ in a steplike manner at t = t₀ results in a time-dependent current

$$I\left(t\right)=\{\begin{array}{ll}\overline{I}& \mathrm{f}\mathrm{o}\mathrm{r}t<t_0\\ \overline{I}+\overline{I}\frac{\left(R_1-R_0\right)}{R_0}{e}^{-U{R}_1\left(t-t_0\right)}& \mathrm{f}\mathrm{o}\mathrm{r}t\ge t_0\mathrm{.}\end{array}\begin{array}{l}\end{array}$$ (3)

This means that at time t₀ the current changes by the amount Ī(R₁ − R₀)/R₀, which is proportional to the relative change in the firing rate. Then the current I exponentially decays back to the steady state Ī with the time constant $1/(U{R}_1)$, as mentioned above, meaning that the decay depends only on U and the new firing rate R₁ but not on the firing rate R₀ before the step.

In the simplified STD model in Eq. 2, we could combine in Ī the three variables τ_s, τ_D, and A because they do not occur independently in the model. This property means that they are fully degenerate, i.e., they cannot be determined independently, which is related to their approximate degeneracy in the more complex STD model in Eq. 1.

Because extracellular potentials in the brain are proportional to a weighted sum of the membrane currents, here we modeled the extracellular potential as a linearly scaled version of the membrane current I. This changed the unit of the variable Ī from a current to a potential. From I we also subtracted the steady-state value Ī because we could not measure DC offsets in the EFP.

To fit this simplified model of STD in Eq. 2 to the experimentally observed EFP traces, we determined the values for U and Ī as well as the time course of R(t) by minimizing the mean square difference between model response and the traces. To fit the firing rate profile R(t), we modeled it as a piecewise linear function with a resting firing rate R₀, a driven firing rate R₁, and a fixed (for each recording location) onset delay t₀ = 8 ± 6 ms with respect to the acoustic stimulus, which accounted for neural and cochlear conduction delays (Köppl 1997a; McColgan et al. 2014). Note that this range is relatively broad compared with measurements of click latencies (McColgan et al. 2014; Wagner et al. 2009). Since we intended to fit only the low-frequency (<1 kHz) responses in the EFP, we did not take into account phase locking and the oscillation of R(t) with the stimulus frequency, which was always in the kilohertz range. After a delay t₀ following stimulus onset, the firing rate ramped up to R₁ with a ramp duration of 5 ms, as in the acoustic stimulus. After the duration of the stimulus (200 ms) and including again the delay t₀, the rate ramped back down to R₀ with the same slope. We did not take into account the overshoot of the firing rate at the onset, as observed in MacLeod et al. (2010) because this additional feature did not increase the quality of the fit.

To disambiguate between parameter combinations that have similar mean square error values, we performed the following regularizations based on prior knowledge from the literature (Köppl 1997a; Peña et al. 1996). We added a penalty of (R₀ − 200 Hz)² for values of R₀ > 200 Hz, and (R₁ − 400 Hz)² for values of R₁ < 400 Hz. Both regularization terms were scaled and converted to appropriate units by a factor of $\lambda =0.1{\left(\text{mV}/\text{kHz}\right)}^2$.

Model of spatial responses.

We simulated the spatial structure of the EFP by implementing in the NEURON simulator a simplified version of the two-compartment model of an NL neuron by Ashida et al. (2007). Our model neuron consisted of a cylindrical somatic compartment with diameter 30 μm and length 25.465 μm (total surface area 2,400 μm² as in Ashida et al. 2007, equivalent to a sphere with radius 13.8 μm). This soma was connected to a cylindrical, myelinated axon hillock of length 50 μm and diameter 15 μm, which was connected to a node of Ranvier that was 2 μm long and had a diameter of 8 μm (Carr and Boudreau 1993b). This node was connected to a last compartment, which was a myelinated axon segment of length 50 μm and diameter 2 μm (not included in the Ashida et al. 2007 model). All segments formed a straight line, which was aligned with the vertical axis in Fig. 5B. As in the model by Ashida et al. (2007), further nodes and axonal segments were omitted. Further segments are expected to have a minor effect on the EFP, in particular because the axon turns in a right angle after the first node. In contrast to the model by Ashida et al. (2007), in which spikes could be initiated in an active node, here we used a passive node with a bulk membrane conductance of 0.19 S/cm² that included both the leak conductance and the active conductances. The soma had a bulk membrane conductance of 1 mS/cm². For the axon hillock and the myelinated axon segment, the axial resistivity was R_a = 100 Ω·cm and the membrane conductance was 0. The capacitance of the myelinated hillock was 0.02 μF/cm². The soma and the node had a capacitance of 1 μF/cm².

Fig. 5.

Polarity of extracellular field potentials (EFPs) evoked by synaptic currents can be explained by a spatially extended model of a nucleus laminaris (NL) neuron. A: experimental EFP responses obtained at 2 different recording locations can show opposite polarities (same examples as in Fig. 1E but low-pass filtered < 100 Hz). Stimulus (black) in gray box at top. B: simulated time courses of the EFP (blue traces) generated by an NL neuron in response to a synaptic input (excitatory postsynaptic current, black trace in gray box) in the soma. Simulated NL neuron (soma and axon) shown in gray, with the first node of Ranvier highlighted in red. Recording locations (vertical position with respect to the NL neuron) indicated by the start of the respective blue traces (horizontal distances not to scale). Spatial (vertical) and voltage scales indicated by vertical bar. C: simulated EFP responses at different recording locations (same as in B) for synaptic currents governed by short-term depression dynamics (as shown in Fig. 2) and the input firing rate profile sketched in gray box for 1 neuron (see also materials and methods). Spatial and voltage scales indicated by vertical bar.

To simulate a synaptic input from an NM axon terminal onto the NL soma, we induced a time-dependent conductance in the somatic compartment. The reversal potential of this postsynaptic current was 0 mV. The resulting excitatory postsynaptic current (EPSC) that we induced in the soma had the shape of an alpha function with a time constant of 0.1 ms and a maximum amplitude of 3.6 nS. This simulated EPSC was used in the LFPy package (Lindén et al. 2014) to calculate the extracellular potential at various locations. We chose the recording locations at intervals of 100 μm and in parallel with the axonal trunk, radially offset at a distance of 25 μm.

To simulate the spatial profile of STD-related currents for 200-ms tonal acoustic stimulation, we simulated the resulting synaptic current as described in Eq. 2. We normalized these responses by dividing by the total charge transfer (area under the EPSC). Convolving the resulting normalized curves with the spatial responses for a single EPSC resulted in the desired spatial response to the entire stimulation. Scaling these responses up by the number of synapses per neuron N = 300 (Ashida et al. 2013) gave the estimated synaptic response of a single NL neuron.

Linear response decomposition.

To separate the NBQX- and ITD-related effects in the response, we devised a linear model to fit the data (Draper and Smith 2014). We began by considering each sample of each single-trial trace (not averaged or filtered) as y_ij, where i enumerated the number of the sample within the trace and j the number of the trace. Each trace consisted of 19,230 samples (sampling rate 48,077 Hz, 400-ms time interval). The example shown in Fig. 4 consisted of 1,375 traces. We then introduced two regressors: the first regressor for the NBQX condition c_j = −1 if NBQX was being applied during trial j and c_j = 1 otherwise. As seen in Fig. 3, the effect of NBQX is gradual, and not binary. We are thus estimating the average effect of NBQX over the entire duration of application. The second regressor was the presented ITD τ_j in trial j. Because of the sinusoidal stimulation, as a first approximation, the ITD-tuned responses at time t_i of the ith sample are linear in sin[2πf(t_i + τ_j)] and cos[2πf(t_i + τ_j)], where f is the stimulation frequency. The linear regression model including interaction terms was thus

$$\begin{array}{l}{\widehat{y}}_{ij}=A_i{c}_j\\ \hspace{1em}\hspace{1em}\hspace{0.17em}+B_i^{\sin }\sin \left[2\text{π}f\left(t_i+{\text{τ}}_j\right)\right]+B_i^{\cos }\cos \left[2\text{π}f\left(t_i+{\text{τ}}_j\right)\right]\\ \hspace{1em}\hspace{1em}\hspace{0.17em}+C_i^{\sin }{c}_j\sin \left[2\text{π}f\left(t_i+{\text{τ}}_j\right)\right]+C_i^{\cos }{c}_j\cos \left[2\text{π}f\left(t_i+{\text{τ}}_j\right)\right]\\ \hspace{1em}\hspace{1em}\hspace{0.17em}+D_i\end{array}$$ (4)

with coefficients A_i, $B_i^{\text{sin}}$, $B_i^{\text{cos}}$, $C_i^{\text{sin}}$, $C_i^{\text{cos}}$, and D_i to be fitted. The amplitudes of the ITD-modulated components were then calculated as $B_i=\sqrt{{\left(B_i^{\text{sin}}\right)}^2+{\left(B_i^{\text{cos}}\right)}^2}$, and analogously for C_i, which represent the amplitudes of the interaction between the ITD-related and the NBQX-related components. The coefficients A_i, B_i, and C_i were then plotted in Fig. 4, A, B, and C, respectively. The coefficients D_i were not plotted because they are not attributable to a single putative source of the EFP (see examples below).

Fig. 4.

Decomposition of extracellular field potential responses into nucleus laminaris neuron-dependent [interaural time difference (ITD) related] and synapse-dependent [1,2,3,4-tetrahydro-6-nitro-2,3-dioxo-benzo[f]quinoxaline-7-sulfonamide (NBQX) related] parts. A: voltages of the purely NBQX-related component of the linear response model; see materials and methods for details. The colors of the horizontal bar indicate the parts with significant responses, with P < 0.05 (dark gray) and P < 10⁻³ (red) determined with a cluster-based permutation test. Stimulus presentation interval (200 ms) indicated by black bar at top. B: amplitude of the ITD modulation in the linear response model. Significance of the coefficients indicated as in A. C: amplitude of the interaction between the NBQX- and ITD-related parts in the linear response model. Interaction-related components were not found to be significant at any time point. n.s., Not significant.

The significance of the coefficients was determined by means of a two-sided t-test based on the standard deviation of the coefficients, to which a Bonferroni correction was applied for the number of coefficients that were fit. In the case of B_i and C_i, the maximum of the two P values on the cosine and sine terms was used. We chose this conservative measure to avoid false positives from correlations between the coefficients.

This kind of model is able to separate components with different response profiles to ITD and NBQX. This can be understood by examining the best fit results to three idealized cases.

First, if a response y is not at all affected by NBQX, which we assume for the contributions from NM axons, then we expect that A_i and C_i will all be zero. As shown by Kuokkanen et al. (2013), the axonal part of the average EFP at a fixed location, when only the delay of the contralateral ear is modified to produce an ITD, can be written as y_ij = a_Isin[2πf(t_i + Δt_I)] +a_Csin[2πf(t_i + Δt_C + τ_j)] with free parameters a_I, a_C, Δt_I, and Δt_C. This can be rewritten as

$$\begin{array}{c}{y}_{ij}=a_{\text{I}}\text{sin}\left[2\text{π}f\left(t_i+\text{Δ}{t}_{\text{I}}\right)\right]+a_{\text{C}}\text{cos}[2\text{π}f\text{Δ}{t}_{\text{C}}]\text{sin}\left[2\text{π}f\left(t_i+{\text{τ}}_j\right)\right]\\ +a_{\text{C}}\text{sin}[2\text{π}f\text{Δ}{t}_{\text{C}}]\text{cos}\left[2\text{π}f\left(t_i+{\text{τ}}_j\right)\right]\mathrm{.}\end{array}$$ (5)

By comparison of the coefficients in Eqs. 4 and 5, we can see that A_i = 0, $B_i^{\text{sin}}=a_{\text{C}}\text{cos}\left(2\text{π}f\Delta t_{\text{C}}\right)$, $B_i^{\text{cos}}=a_{\text{C}}\text{sin}\left(2\text{π}f\text{Δ}{t}_{\text{C}}\right)$, $C_i^{\text{sin}}=C_i^{\text{cos}}=0$, and D_i = a_Isin[2πf(t_i + Δt_I)]. This means that B_i = a_C, which was exactly the part of the EFP modified by ITD.

Second, we consider the case of a purely NBQX-dependent response that is not modulated by ITD, and we expect that only the A_i and D_i will be nonzero. This would be the case for the average synaptic contributions at all frequencies different from the frequency of a sustained tonal stimulus (Kuokkanen et al. 2010). For example, we can model the synaptic component as y_ij = a_syn(1 + c_j)/2, meaning that it has the amplitude 0 when NBQX is being applied and a_syn otherwise. This can be rewritten as y_ij = a_syn/2 + a_sync_j/2. By comparison of the coefficients with Eq. 4, we can see that this corresponds to A_i = D_i = a_syn/2 and B_i = C_i = 0.

Third, a response that is dependent on ITD and whose amplitude is modified by NBQX is the only case that would result in nonzero C_i. For example, we expect that the contribution of NL neurons’ spiking to the EFP is both NBQX and ITD dependent.

Because of the linearity of the model in Eq. 4, components of the EFP that have the idealized properties of ITD and NBQX dependence described in the previous three paragraphs can be combined and also decomposed again in the fit (Draper and Smith 2014). However, since all components can contribute to D_i, we cannot disentangle these contributions. We can thus draw conclusions about different contributions with the properties discussed above from the fit of the coefficients A_i, B_i, and C_i.

Diffusion simulation.

We based our simulations of diffusion from an iontophoretic injection on the calculations by Nicholson and Phillips (1981) and Crank (1979). They showed that for an iontophoretic point source activated at time t = 0 with a flow rate q and a diffusion coefficient D in a homogeneous, infinite medium, the concentration C at a distance r from the point source is $C\left(r,t\right)=\frac{q}{4\text{π}Dr}\text{erfc}\left(\frac{r}{2\sqrt{Dt}}\right)$ where erfc is the complementary error function. Switching off the iontophoretic source was then simulated by adding a source with opposite flow rate −q at the time of switching off. Note that D and q are taken to be effective values, and they might differ from their free-space equivalents because of porosity and tortuosity of the tissue. The value for the flow rate is given by q = nI_p/F, where I_p = 60 nA is the current flowing through the pipette, F is the Faraday constant, and n = 6.5 × 10⁻⁴ is the transport number, which determines the fraction of the current that is carried by the NBQX ions. We determined the value for n empirically, which is possible because it linearly scales the response. We chose the effective diffusion coefficient $D=2\times {10}^{-6}\frac{{\text{cm}}^2}{\text{s}}$ as determined by Pararas et al. (2011) for the closely related AMPA-receptor antagonist 6,7-dinitroquinoxaline-2,3(1H,4H)-dione (DNQX).

To calculate the effective remaining synaptic currents at a given concentration, we used the results from Zhou and Parks (1991), where the efficacy of NBQX was determined in the chick NL. We approximated their results with an IC₅₀ curve, with the percentage of current remaining given by the expression 50% − 50%·erf{k·[log₁₀(C) − log₁₀(IC₅₀)]} with the slope factor k = 3 and the half-activation value IC₅₀ = 1.4 μM.

The effective contribution of a population of synapses was calculated by approximating NL as a sphere of radius 1 mm in which synapses were homogeneously distributed. This simplified NL was embedded into an infinite homogeneous medium into which the NBQX could diffuse. Analogous to the calculation made by Kuokkanen et al. (2010), we assumed that the amplitudes of the synaptic responses scale as 1/r². Because the number of synapses in a thin spherical shell with radius r is proportional to r², the overall contribution to the response of each concentric shell is then independent of r. This feature resulted in the population response being an arithmetic average over the single-synapse responses at all radii from 0 to 1 mm.

RESULTS

Using pharmacological methods in vivo in anesthetized barn owls, we identified a distinct component of the EFP in the NL that can be attributed to synaptic activity. The time course of this component is consistent with synaptic STD, and it is blocked by NBQX.

Application of NBQX reveals a small synaptic contribution to the EFP

To understand the contributions of synaptic currents to the EFP in NL, we used pure-tone burst stimuli (200-ms duration). Stimulation evoked the well-known EFP or neurophonic response in NL (Fig. 1, A–C). The wideband responses (Fig. 1A) showed transients that were consistent with findings from previous studies of the neurophonic (Carr and Konishi 1990; Kuokkanen et al. 2010). To isolate the characteristic frequency-following part of the neurophonic, which is prominent for tonal stimuli ≲9 kHz in the barn owl (Köppl 1997b), we applied a high-pass filter with a cutoff of 1 kHz to the responses (Fig. 1B). The resulting responses consisted mainly of the phase-locked, frequency-following component associated with the EFP and are mainly attributable to presynaptic spikes from NM afferents (Kuokkanen et al. 2010, 2013, 2018; McColgan et al. 2017).

Although the high-frequency component of the response is mostly due to axonal contributions, the low-frequency component was expected to contain some contributions from synapses (Kuokkanen et al. 2010). Synapses should contribute more to the low-frequency component because they can be described by alpha functions, which are low-pass filters (Funabiki et al. 2011). Therefore, in what follows, we focus more on the low-frequency component of the EFP to identify a synaptic contribution. To do so, we applied a low-pass filter, again using a cutoff of 1 kHz (Fig. 1C). This component showed no phase locking but had transients at stimulus onset and offset, with a slower decay back to the baseline after both.

To separate the contribution of synapses to the EFP from other sources, we iontophoresed the AMPA-receptor antagonist NBQX inside NL in urethane-anesthetized birds, typically for several minutes (see materials and methods for details). In particular, we alternated the application of NBQX with periods of similar durations in which the flow of NBQX was stopped, resulting in washout of NBQX. We called the blocks of drug application the “NBQX condition” and the block before and after NBQX application the “control condition” (Fig. 1, A–C). Comparing the averaged wideband responses for these two conditions (Fig. 1A), we found that the gross structures of the EFP were quite similar, which indicated that synaptic contributions blocked by NBQX were small. Each experiment contained either two or three control and NBQX blocks each.

To further isolate and quantify differences between the control and NBQX conditions, we first examined the high-pass filtered component (Fig. 1B). The mean responses were similar between control and NBQX conditions, and we found no statistically significant difference between them when applying a cluster-based permutation test (see materials and methods and Maris and Oostenveld 2007). In contrast, for the low-pass filtered responses control and NBQX conditions did differ (Fig. 1C). This difference was confirmed with the cluster-based permutation test, which found the means to be different with P < 10⁻³.

In the low-pass filtered responses, the difference between the NBQX and the control conditions revealed synaptic and NL spiking contributions to the EFP (Fig. 1D). We focus on the low-frequency component, even though synapses should also contribute (but to a lesser relative extent) to higher frequencies. In the following sections, we show why NBQX-related differences are likely to be almost entirely synaptic and not due to NL spiking. The putative synaptic contribution in Fig. 1D had a characteristic shape, with a fast rise (<5 ms) at the beginning of the stimulus presentation followed by a slower decay back to the baseline. At the end of stimulus presentation, there was another fast transient with the opposite direction from the one at stimulus onset, once again followed by a slower decay.

These transient responses, as observed in the difference between NBQX and control conditions (“NBQX effect”), had opposite polarities at the onset and offset of the tone burst and were robust and repeatable, with similar shapes found in five recording locations in four owls (Fig. 1E). When we obtained several washout and injection cycles in a single owl, we performed a statistical test to confirm that the (normalized) NBQX effects did have the same characteristics across cycles (see Data analysis). We found no significant differences across cycles in any of the cases we studied. To make the comparison across owls easier, we normalized the plotted response amplitudes and applied a slightly tighter band-pass filter (1–500 Hz). All responses shared the same double-transient shape.

The putative synaptic contribution to the EFP was very small, explaining only 0.6% of the variance observed across all repetitions and samples. In contrast, the average response over all trials for each sample (regardless of NBQX state) explained 34.1% of the observed variance. Most of the remaining variance was explained by the changes in the presented ITD (see Linear response decomposition) and the stochastic nature of NM firing.

NBQX can have a seemingly paradoxical effect on the magnitude and the sign of the slow transients of the EFP: in the displayed example (Fig. 1, A and C) the response magnitude in the NBQX condition was larger than in the control condition. This paradox is resolved by taking into account the fact that the EFP contains large components other than those generated by synaptic currents. For example, incoming axonal currents can result in a EFP component that has a different polarity than the synaptic component (McColgan et al. 2017). This opposite polarity of axonal and synaptic contributions can result in either a net increase or a net decrease of the summed response amplitude when the synaptic contribution is removed by NBQX. We also note that the low-pass filtered transients in Fig. 1E (compare the first to the other four examples) can have opposite polarities; we return to this feature at the end of results.

A simple model of short-term plasticity explains the time course of synaptic contributions to the EFP.

Inspired by previous in vitro experiments and modeling in the chick (Cook et al. 2003; Kuba et al. 2002), we hypothesized that synaptic currents in NL may be subject to STD and that the time course of the low-pass filtered synaptic contributions to the EFP identified in Fig. 1, D and E could be explained by a model of STD (Abbott et al. 1997; Tsodyks et al. 1998; Tsodyks and Markram 1997). To test this hypothesis, we implemented a mean-field model of the currents flowing at such a synapse, based on a single reservoir of neurotransmitter that gets partially released on every incoming action potential and gradually replenishes over time (see materials and methods for details). The free model parameters were the fraction U of available transmitter released at each event, the firing rate R [here the resting (R₀) and driven (R₁) firing rates of NM], and the scaling factor Ī of the response. Interestingly, the exact value of the putative slow time constant τ_D for the recovery of the synaptic reservoir [estimated by Cook et al. (2003) to be 1.1 s] was not necessary to explain the time course of synaptic contributions to the EFP. Instead, steady states were reached exponentially in the model with time constant $\frac{1}{(UR)}\approx 14-21\text{ ms}$ (see materials and methods for details).

This model of STD fit the observed time course of the putative synaptic potentials well (Fig. 2A). The residuals of the model fit (Fig. 2B) were small (50.1% explained variance in the example shown, 40 ± 14% across all examples) and contained a low-frequency (<100 Hz) component of unknown origin (see discussion) and a high-frequency (>200 Hz) noise that can be attributed to the stochastic nature of NM firing activity. Instrument noise accounted for a very small amount (<0.1%) of the variance.

Fig. 2.

Model of short-term depression (STD) fits synaptic contributions to the extracellular field potential. A: auditory stimulus (top; same as in Fig. 1) and extracellular correlate of the putative synaptic currents (bottom, blue; same as in Fig. 1D) compared with a model of synaptic STD (orange; see also materials and methods). B: residuals of the fit in A. C: firing rate profile implied by the fit in A. D: normalized synaptic efficacy (value 1 corresponds to steady-state efficacy for spontaneous input rate) in response to the stimulus as implied by the fit in A.

In the example shown in Fig. 2, the inferred firing rate profile of the input from NM had a resting firing rate of 240 spikes/s and a driven rate of 380 spikes/s (Fig. 2C). Across all examples, the firing rates were 220 ± 16 spikes/s at rest and 386 ± 9 spikes/s during stimulation. This profile is in the same range as suggested by the literature [from 119.3 to 291.7, mean 219.4 spikes/s at rest (Köppl 1997a) and 423 ± 113 spikes/s during stimulation (Peña et al. 1996)].

We found that including spike rate adaptation of NM units at the onset of the firing rate profile (Fig. 2C) did not improve the fit. We hypothesized that this lack of improvement was due to the short time constant (<10 ms) of spike rate adaptation in our experimental conditions. Such short time constants are consistent with the findings of MacLeod et al. (2010), who reported a value of 8 ms.

The utilization factor of the STD process was fit as U = 0.19 in the example shown in Fig. 2 and was U = 0.10 ± 0.06 across all examples. The value for the scaling factor Ī was 0.43 mV in the example shown and 0.18 ± 0.15 mV across all examples.

Since the model synapses receive an input with a high spiking rate even during rest, they probably never reach a state in which their vesicle pool is full. Because we could not estimate the synaptic efficacy in the fully recovered state from the data, we normalized the synaptic efficacy to its steady-state value at resting firing rate (value 1 in Fig. 2D) and showed the dynamics of change with respect to this baseline.

In the example shown in Fig. 2, during stimulation the synaptic efficacy approached the fraction 0.63 of its resting state, which equals the ratio of the firing rates R₀ = 240 spikes/s and R₁ = 380 spikes/s (see materials and methods for details). Steady states were reached with time constants $1/(UR)$ (see materials and methods for details). After the onset of the acoustic stimulus, the steady state was reached with the time constant $1/(U{R}_1)$ = 14 ms, and after the offset of the stimulus the synaptic efficacy decayed back to its resting value with the slightly longer time constant $1/(U{R}_0)$ = 21 ms. These time constants match the time constant of fast recovery (15 ms) reported by Cook et al. (2003). Beyond the predicted two different fast recovery time constants at onset and offset, the different magnitudes of the transients in Fig. 2A were also reproduced by the model: the amplitude (including the sign) of the transient of the EFP was predicted to be proportional to the relative difference of the firing rates (see materials and methods for details): at the onset we have (R₁ − R₀)/R₀ = 0.58, and at the offset we find (R₀ − R₁)/R₁ = −0.37, which is smaller in amplitude and opposite in sign.

We thus concluded that the nature of the observed component can be explained by STD, and that the system operates in a highly depleted regime.

Diffusion of NBQX in NL is consistent with the slow time course of the synaptic contribution to the EFP.

To further test whether the observed changes in the putative synaptic contributions to the EFP were consistent with the effects of NBQX iontophoresis, we considered the diffusion of NBQX in the tissue surrounding the pipette. We calculated the time course of the expected concentration of NBQX in our experimental setting where iontophoresis of NBQX was switched on and off repeatedly. The concentration of NBQX at a given distance from the tip of the pipette can be modeled by solving the diffusion equation (see materials and methods). Because the distances of the synapses from the tip of the pipette are unknown, we first calculated NBQX concentrations for various distances, for example, from 200 to 500 μm (Fig. 3A), which confirmed that NBQX could reach large fractions of NL within the duration (<1,000 s) of NBQX application. Using values for the effectiveness of NBQX on synaptic currents in the chick NL (Zhou and Parks 1991) (Fig. 3B, inset), we were then able to predict the amount of remaining synaptic currents at a given concentration of NBQX. Transforming the time course of the concentrations in Fig. 3A with this dose-effect function yielded a predicted (normalized) synaptic current for a synapse at a given distance from the electrode (Fig. 3B). Assuming a homogeneous distribution of synapses in a sphere with a radius of 1 mm around the recording electrode and a 1/r² scaling of the contribution of a given synapse at distance r from the pipette and the recording electrode, we calculated the population signal by averaging the signal strengths for distances up to 1 mm (Fig. 3B; see materials and methods for details).

We then compared the predicted progression of synaptic current amplitude during NBQX application with the experimental data. By taking the average amplitude of the EFP signal in the frequency band (<1 kHz) identified in Fig. 1 to be related to the NBQX effect, we were able to estimate the magnitude of the signal strength for every stimulus presentation (a 200-ms tone burst) individually. Figure 3C shows how the signal strength evolved over time. The time course of the experimentally measured signal strength has a shape similar to the predicted population signal if its voltage scales are matched (Fig. 3C). In both the experiment and the model, we observed a rapid fall of the signal amplitude when the NBQX injection was switched on, followed by a saturation within 10 min and a slower recovery after switching off the NBQX injection. The model could not account for a slow drift of the signal strength.

To test whether the effect observed in Fig. 1 is reliable, we calculated the difference in response between consecutive control and NBQX conditions. The resulting curves, calculated in the same way as Fig. 1D, showed the same shape as those seen in Fig. 1, with the differences from a NBQX to a control block having the opposite sign, as expected. This led us to conclude that the effect was indeed reproducible and washed out during each control block.

The observed time course of synaptic contributions to the EFP is thus consistent with a diffusive spread of a synaptic antagonist, as expected for an iontophoretic application of NBQX. This consistency serves as a further control that the observed effect is indeed due to a blockage of synaptic currents by NBQX and not an experimental artifact.

NL spikes do not contribute significantly to the observed responses.

NBQX is an AMPA-receptor antagonist, and neurons in NL receive their excitatory input mainly through AMPA synapses (Kuba et al. 2002; Raman et al. 1994; Zhou and Parks 1991), although small contributions from kainate and NMDA receptor activation are also possible (Zhou and Parks 1991). We expect that the application of NBQX reduces the postsynaptic firing activity of NL cells. This decreased firing of NL neurons could contribute to changes in the EFP between NBQX and control conditions, which we have analyzed in the previous sections. This NL firing component hampers the interpretation of NBQX-related effects in terms of synaptic currents. However, from previous analyses (Kuokkanen et al. 2010, 2013, 2018) we know that the number of independent sources needed to generate the observed EFP greatly exceeds the number of NL neurons that are close enough to the recording electrode, and thus we expect their contribution to the EFP to be small. To confirm that there was no significant contribution of NL spikes to the EFP, we performed additional data analyses.

To extract the contribution of postsynaptic firing of NL neurons from the EFP, we took advantage of the binaural nature of the NL system. NL neurons are tuned to specific ITDs, which enabled us to manipulate their firing rate during stimulation by varying the ITD of the binaural stimulus. Because there is a map of ITD (Carr et al. 2013), the NL neurons close to the electrode may contribute to an ITD-tuned component of the EFP beyond the ITD-tuned component due to linear summation of the two monaural input-related components (Kuokkanen et al. 2013). Such an interaction between NBQX and ITD would indicate a postsynaptic NL firing component.

To measure ITD-related modulation of the difference between NBQX and control conditions, we recorded responses at varying ITDs (see materials and methods) and fit a linear model to the unfiltered responses like that shown in Fig. 1A (see materials and methods for details). The ITD component of the model was fit to the typical sinusoidal ITD response pattern (Carr and Konishi 1990; Kuokkanen et al. 2013), and we here report the amplitude of this sinusoidal modulation. This linear model had four groups of coefficients: the purely NBQX-modulated component, the purely ITD-modulated component, the interaction between ITD and NBQX modulation, and the unmodulated component, which was affected neither by ITD nor by NBQX. A significant interaction-related component would indicate a contribution to the EFP of postsynaptic NL firing activity, which depends on ITD.

The resulting model coefficients are shown in Fig. 4. For each coefficient, we calculated the Bonferroni-corrected probability of the null hypothesis that the coefficients are equal to zero, based on the empirical variance estimate returned for the coefficient by the fitting procedure. Figure 4A shows the coefficients for the effect of NBQX. As expected, it resembles the difference between NBQX and control conditions shown in Fig. 1D. The coefficients are found to be significantly different from zero mostly for the times following stimulus onset and offset, as predicted by the STD model fitted in Fig. 2.

Figure 4B shows the coefficients for the purely ITD-related component. Also as expected, all coefficients during stimulus presentation were highly significant because the EFP depends on ITD. The coefficients also showed the sharp transient at stimulus onset associated with the input firing behavior (Kuokkanen et al. 2010; MacLeod et al. 2010).

When we examined the interaction-related coefficients in Fig. 4C, we found no coefficient to be significantly different from zero. There appears to be a small change in the variance during stimulus presentation, which can be explained by the higher overall noise levels during stimulation. The interaction-related component is not related to the average currents from synapses and incoming axons because ITD does not affect the mean firing rates at which incoming axons and the resulting synaptic currents are driven; the ITD merely determines their relative timing on a submillisecond timescale. Because of the summation of contralateral and ipsilateral components in the axonal/synaptic parts of the EFP, this submillisecond timing only affects the axonal/synaptic EFP in a narrow frequency range around the stimulus frequency and does not affect the axonal/synaptic EFP at other frequencies (Kuokkanen et al. 2010).

The full fit explained 48% of the variance of all observed samples. The component that did not change across ITD or NBQX conditions explained 39% of the variance. The putative synaptic contributions that were modified only by NBQX explained <1% of the variance (Fig. 4A), the putative axonal contributions that were modified only by ITD explained 7% (Fig. 4B), and the putative NL spiking contributions explained <0.01% of the variance (Fig. 4C).

We repeated this fit for all n = 5 examples and found no significant NBQX-ITD interactions in any of the owls. We also repeated the fit for the low-pass filtered responses, as shown in Fig. 1, C and D. Here, the putative synaptic component played a more important role, explaining 1.8% of the variance, and ITD- and interaction-related components explained <0.2% of the variance. The constant component played a very large role, explaining 90% of the variance. These ratios further show that restricting our analysis to the low-pass filtered signal and subtracting out the constant part, as done in Fig. 1, D and E, and Fig. 2, is the best way to isolate the synaptic component.

Together, these results lead us to conclude that the difference between NBQX and control conditions examined in the previous sections does not contain significant contributions from postsynaptic NL firing activity. We cannot exclude the presence of a small contribution, but the majority must come from a different source, making the interpretation as a synaptic process subject to STD more likely.

A spatial model of EFP structure explains the polarity of the transient responses.

As outlined in previous sections, NL synapses generated transient responses in the EFP with polarities that varied across recording locations (Fig. 5A; see also Fig. 1E). Taking into account NL anatomy, the varying polarity may be explained by the location of the recording electrodes relative to the somata and axons of NL neurons: NL neurons are known to be almost spherical, with small, stubby dendrites and only an axon protruding from the soma (Carr and Boudreau 1993b; Kuokkanen et al. 2010). This configuration leads to a ball-and-stick-like structure of an NL neuron with a spherical soma and a myelinated axon (see materials and methods for details), which we expected to transform excitatory synaptic input currents into EFP responses with different polarities across locations.

To test the hypothesis that the recording location affects the polarity of transients, we simulated the extracellular field produced by this model NL neuron in response to a single synaptic event at the soma (Fig. 5B). The polarity of the resulting extracellular voltage was negative at locations opposite to the outgoing axon of an NL neuron and positive otherwise. The polarity reversal occurred between the soma and the first node of Ranvier along the axon.

To predict the extracellular signature of the synaptic currents in response to the stimulations that we presented in our experiments, we applied the fitted STD process in Fig. 2 to this spatial model. The resulting predicted extracellular responses to full stimulation are shown in Fig. 5C. Not surprisingly, they also show a polarity reversal, meaning that both polarities observed in experiments can be reproduced in the spatial model. Simulated synapses on a single NL neuron generated an EFP response (recorded at 25-μm radial distance from the soma-axon axis) with an amplitude (up to ~5 μV in Fig. 5C) of the same order of magnitude as the experimentally observed traces in Fig. 1E and Fig. 5A. The match in voltage scales suggests that the synaptic portion of the EFP may be dominated by an NL neuron that is close to the electrode. Furthermore, this implies that the polarity of the response can be dominated by the closest NL neuron.

The modeling results presented in Fig. 5, B and C, were simulations of a single-neuron response. The experimentally observed response is expected to be a summation of such synaptic potentials originating from many NL neurons. Responses with similar polarity may add particularly well if axons of nearby NL neurons are aligned in parallel and if NL neurons in a narrow enough spatial region (along the primary soma-axon axis) are activated by our stimuli. Both assumptions are justified: NL neurons are tonotopically arranged, and our tonal stimulation activates NL neurons in a narrow (≲600 μm) frequency lamina (Kuokkanen et al. 2010); NL axons are roughly parallel to each other and travel orthogonal to the NM axons and parallel to the ventral border of NL (Carr and Boudreau 1993b). We therefore expect a similar overall response of a population of NL neurons as shown in Fig. 5C.

This special anatomy of NL allowed us, in further experiments, to test the hypothesis that the location of the electrode determines the polarity of the response. Unfortunately, it is not possible to advance an electrode parallel to an NL axon within NL (along the lateral-medial axis) because this axis is inaccessible to electrophysiology (the owl’s ear is in the way). Alternatively, with a fixed electrode location, we tried to change the location at which NL neurons are activated by altering the stimulus frequency. Because of the tonotopic layout of NL (Carr and Konishi 1990; Takahashi and Konishi 1988), different stimulus frequencies should lead to the activation of different subpopulations of NL neurons at different locations relative to the recording electrode. We attempted this in three experiments but were unable to elicit a polarity change; the amplitude of the NBQX effect diminished with shifting stimulus frequencies but did not reappear with opposite polarity. This observation is consistent with our hypothesis that synaptic contributions to the EFP are dominated by the NL neuron closest to the electrode.

To conclude, the spatial relationship between the activated synapses and the recording location can explain the presence of different polarities in the EFP responses. This result further supports our hypothesis that the observed EFP component is of synaptic origin.

DISCUSSION

We have identified a small but consistent effect of the AMPA-receptor blocker NBQX on the EFP recorded in the barn owl auditory brain stem. We used the known properties of the NL to show that the most likely source of the NBQX-modulated EFP component is the synaptic current flowing in NL neurons. These putative synaptic currents are subject to STD, consistent with studies in vitro (Cook et al. 2003; Kuba et al. 2002). Our model of short-term plasticity suggests that in vivo the system operates in a highly depleted regime.

Composition of the neurophonic potential in NL.

The discovery of a small (<1% of the overall variance) synaptic component in the EFP reinforces the theory of a predominantly axonal origin of the EFP in NL (Kuokkanen et al. 2010, 2013, 2018; McColgan et al. 2017). Note that this putative synaptic component is not small per se but rather dwarfed by the large axonal component of the EFP. The measured NBQX-sensitive responses were between 0.03 and 0.3 mV, consistent with recordings of visually evoked potentials in cortex, for example, by Montey and Quinlan (2011).

Our estimate of the magnitude of the synaptic component was derived from experiments with local application of NBQX, and the results in Fig. 3A show that the concentration of NBQX is higher than the saturating concentration only at distances < 300 μm. Synaptic contributions from larger distances would not be fully blocked by NBQX. We therefore underestimate the magnitude of synaptic contributions to the EFP. This error should nevertheless be small (much less than an order of magnitude) because the spatial extent of NL is in the range of only 1 mm and tonal stimulation activates NL neurons only in a narrow (≲600 μm) frequency lamina (Kuokkanen et al. 2010). The size of the activated frequency layer is in the same range as the radius 300 μm around an electrode at which we reached saturating concentrations of NBQX. Moreover, we hypothesize that synaptic contributions to the EFP are dominated by single NL neurons close (<50 μm) to the electrode (Fig. 5).

This closest-neuron dominance of synaptic contributions to the EFP is supported by the anatomy of NL. The average distance between neurons is ∼100 μm (Kuokkanen et al. 2010). The decay of the synaptic signal amplitude with distance, especially within the first 20–30 μm from the electrode, can be flatter than in the “far-field” condition (Kuokkanen et al. 2018; Pettersen and Einevoll 2008). We had previously estimated that the response amplitude from a single neuron decayed to about 1/10th within the first 50-μm distance from the soma (Kuokkanen et al. 2018).

The contribution of NL spikes to the EFP is even smaller than the putative synaptic contribution and is estimated to be about <0.1% of the variance (Fig. 4). In Kuokkanen et al. (2018), such a small component of the nontransient EFP was associated with NL spiking activity; the amplitude of this component strongly depends on the distance between the recording electrode and the nearest NL neuron and can be neglected for distances > 200 μm.

Overlap of the dendrites of adjacent NL neurons is less of a concern for the interpretation of our data because of the unique anatomy of NL. We restricted our recordings to the high-frequency region of NL (best frequencies >3 kHz), where dendrites are short (<5 ± 2 μm; Carr and Boudreau 1993a) and neuronal cell bodies are spaced ∼100 μm apart (see discussion in Kuokkanen et al. 2010). This unusual anatomy allows for no overlap of the dendrites of neighboring neurons (they are too far apart) and allows for the technically difficult isolation of putative synaptic potentials in vivo.

The residuals of our fit to a model of STD in Fig. 2B reveal further unexplained contributions to the neurophonic. The residuals have a high-frequency (≳200 Hz) component that is most likely due to the stochastic nature of the activity of NM axons, which we could not capture with our model that is based on average firing rates. There is, however, also a slower (≲100 Hz) component visible in the residuals, which could be of a different origin. A possible candidate is the ITD-independent and frequency-nonspecific recurrent inhibition from the superior olivary nucleus (Burger et al. 2005; Yang et al. 1999), which has timescales of ≈100 ms (Burger et al. 2005; Lu and Trussell 2000; Tang and Lu 2012). A second possibility could be slow potassium currents on the somata of NL neurons, which serve to compensate for DC offsets in the synaptic current (Ashida et al. 2007; Grau-Serrat et al. 2003; Kuba et al. 2005).

Relevance to the study of synaptic processes.

In our phenomenological model for STD of synaptic currents in Fig. 2, we assumed that the time constant τ_D of the slow recovery process was in the range of seconds, similar to the value of 1.1 s reported by Cook et al. (2003) for the chick. Such a long time constant may seem surprising in a system that must deal with high firing rates R in the range of >100 spikes/s, i.e., average interspike intervals < 10 ms. The synapse is thus always beyond its “limiting frequency” (Tsodyks et al. 1998; Tsodyks and Markram 1997), and the synaptic efficacy is small compared with the fully recovered state (Fig. 2D). This scenario is plausible, and it is consistent with the results from in vitro work in gerbils on the calyx of Held (Hermann et al. 2007) and on excitatory synaptic inputs to medial superior olivary neurons (Couchman et al. 2010). A long time constant τ_D, together with the high firing rate R of the input (even in the resting state), means that the synapse is always in a state in which the vesicle pool is depleted. As a result, the mean steady-state current generated by such a synapse is independent of the input rate. Since the mean input rate encodes sound pressure, this property of a depressing synapse can contribute to the relative insensitivity of NL neurons to sound pressure level (Cook et al. 2003; Kuba et al. 2002; Peña et al. 1996). This insensitivity emerges for a wide range of utilization factors U of the STD model. The value for the utilization factor U ≈ 0.7 determined by Cook et al. (2003) was, however, different from the value of U ≈ 0.2 found here. This might be due to differences in maturity, firing rates, temperatures (39°C here, 33–35°C used by Cook et al. 2003), or extracellular calcium concentrations between the in vivo and in vitro cases (Klug et al. 2012). For a review of some causes of low release probability in vivo, see Borst (2010).

In analyzing possible causes of the STD, we observed that it did not appear to interact with spike rate adaptation in the firing patterns of NM. Including a simple exponential spike rate adaptation (time constant and amplitude were the additional free-fit parameters in the model) did not improve the fit to the data in Fig. 2. We hypothesized that spike rate adaptation in NM is rapid, i.e., takes place on shorter timescales than STD. Short (<10 ms) NM spike rate adaptation timescales are consistent with the envelope shape of the high-frequency component in Fig. 1B and Fig. 4B. Short timescales (8 ms) in NM spike rate adaptation were also reported by MacLeod et al. (2010). These time constants are possibly intensity dependent, with shorter time constants for higher intensities, as observed in the auditory nerve (Westerman and Smith 1984; Zilany et al. 2009). We used relatively high sound pressure levels (40–60 dB SPL), which further support our assumption that spike rate adaptation is faster than STD. Future studies could investigate the interaction of the two adaptive processes (STD and NM spike rate adaptation) by recording at a range of sound pressures and simultaneously recording NM activation statistics. When recording at low sound pressure levels, NM adaptation might become slower and interfere with STD, making it hard to disentangle the two effects without paired recordings, which is why we did not perform recordings at lower levels in this study. To conclude, even though STD and spike rate adaptation could contribute to the observed adaptation of synaptic currents, both effects would support our hypothesis that the NBQX-modulated low-frequency (<1 kHz) component of the EFP is caused by synapses from NM axons onto NL neurons.

Cellular properties may also affect synaptic depression. In the medial superior olive, the control of coincidence detection by regulating/adapting excitability via intrinsic conductances on a millisecond timescale may act synergistically with synaptic depression (acting on an estimated timescale of >10 ms) (Franken et al. 2015). Such synergistic effects also cannot be excluded in NL neurons, even if they may not be observable in the field potential (Kuokkanen et al. 2018).

Conclusions.

We have shown a signature of putative synaptic currents in the EFP in the NL of the barn owl in vivo. We were able to explain the dynamics of synaptic currents by a simple model of STD, as suggested by previous work in vitro in the chick (Cook et al. 2003; Kuba et al. 2002). Putative synaptic currents and membrane currents related to the spiking activity of NL neurons were quite small, which further supports the hypothesis that currents from afferent axons dominate the EFP (Kuokkanen et al. 2010; McColgan et al. 2017). Finally, the ability to quantify STD in vivo should enable further study of its functional role. The application of a variety of different stimuli, i.e., beyond the pure tones used in our experiments, could provide further insights into the dynamics of STD in the auditory system of barn owls and other animals.

GRANTS

This work was supported by the German Federal Ministry for Education [Research Grants 01GQ1001A and 01GQ0972, National Institutes of Health (NIH) DCD 000436 and US-American Collaboration in Computational Neuroscience “Field Potentials in the Auditory System” as part of the National Science Foundation/NIH/French National Research Agency/German Ministry of Education and Research/United States-Israel Binational Science Foundation Collaborative Research in Computational Neuroscience Program, Research Grant 01GQ1505A] and the Deutsche Forschungsgemeinschaft Research Grant SFB1315.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

T.M., C.E.C., and R.K. conceived and designed research; T.M., P.T.K., and C.E.C. performed experiments; T.M. analyzed data; T.M., P.T.K., C.E.C., and R.K. interpreted results of experiments; T.M. prepared figures; T.M. drafted manuscript; T.M., P.T.K., C.E.C., and R.K. edited and revised manuscript; T.M., P.T.K., C.E.C., and R.K. approved final version of manuscript.